{VERSION 6 0 "IBM INTEL NT" "6.0" }
{USTYLETAB {CSTYLE "Maple Input" -1 0 "Courier" 1 12 255 0 0 1 2 1 2 
2 1 2 0 0 0 1 }{CSTYLE "2D Output" -1 20 "Times" 1 12 0 0 255 1 2 2 2 
2 2 2 0 0 0 1 }{PSTYLE "Normal" -1 0 1 {CSTYLE "" -1 -1 "Times" 1 12 
0 0 0 1 2 2 2 2 2 2 1 1 1 1 }1 1 0 0 0 0 2 0 2 0 2 2 0 1 }{PSTYLE "Map
le Output" -1 11 1 {CSTYLE "" -1 -1 "Times" 1 12 0 0 0 1 2 2 2 2 2 2 
1 1 1 1 }3 1 0 0 0 0 2 0 2 0 2 2 0 1 }}
{SECT 0 {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 8 "restart;" }}}{EXCHG 
{PARA 0 "> " 0 "" {MPLTEXT 1 0 36 "with(LinearAlgebra):\nwith(combinat
):" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 365 "v[1]:=Vector([4,-1,-
1,-1,-1]):\nv[2]:=Vector([-1,4,1,1,1]):\nv[3]:=Vector([-1,-1,4,-1,-1])
:\nv[4]:=Vector([-1,-1,-1,4,-1]):\nv[5]:=Vector([-2,2,-2,-2,-2]):\nv[1
],v[2],v[3],v[4],v[5];\nprint(\"|v[1]|^2\"=Norm(v[1],2)^2);\n#checking
 for decreasing order;\nfor i from 1 by 1 to 4 do \n   if (Norm(v[i],2
)^2 > Norm(v[i+1],2)^2) then print(\"not satisfied\",(i,i+1)) end if; \+
\nend do;" }}{PARA 11 "" 1 "" {XPPMATH 20 "6'-%'RTABLEG6%\"*S!pA@-%'MA
TRIXG6#7'7#\"\"%7#!\"\"F-F-F-&%'VectorG6#%'columnG-F$6%\"*/\"pA@-F(6#7
'F-F+7#\"\"\"F9F9F/-F$6%\"*o\"pA@-F(6#7'F-F-F+F-F-F/-F$6%\"*K#pA@-F(6#
7'F-F-F-F+F-F/-F$6%\"*'HpA@-F(6#7'7#!\"#7#\"\"#FMFMFMF/" }}{PARA 11 "
" 1 "" {XPPMATH 20 "6#/Q)|grv[1]|gr^26\"\"#?" }}}{EXCHG {PARA 0 "> " 
0 "" {MPLTEXT 1 0 6469 "#checking for 2|v[j].v[i]|=<|v[i]|^2;\nL2:=cho
ose(5, 2):\nfor i from 1 by 1 to numbcomb(5, 2) do\n   if (2*abs(v[L2[
i][2]].v[L2[i][1]]) > Norm(v[L2[i][1]],2)^2) then \n      print(\"not \+
satisfied\",\"v_i,v_j\",L2[i][1],L2[i][2]) \n   end if;\nend do;\n#che
cking for 2|v[k].(v[i]+v[j])|=<|v[i]+v[j]|^2;\nL3:=choose(5, 3):\nfor \+
s from 0 by 1 to 1 do\n   for i from 1 by 1 to numbcomb(5, 3) do\n    \+
  if (2*abs(v[L3[i][3]].(v[L3[i][1]]+(-1)^s*v[L3[i][2]])) > Norm(v[L3[
i][1]]+(-1)^s*v[L3[i][2]],2)^2) then \n         print(\"not satisfied
\",\"v_i,v_j,v_k\",L3[i][1],(-1)^s*L3[i][2],L3[i][3]); \n      end if;
\n   end do;\nend do;\n#checking for 2|v[l].(v[i]+v[j]+v[k])|=<|v[i]+v
[j]+v[k]|^2;\nL4:=choose(5, 4):\nfor s from 0 by 1 to 1 do\n   for i f
rom 1 by 1 to numbcomb(5, 4) do\n      if (2*abs(v[L4[i][4]].(v[L4[i][
1]]+(-1)^s*v[L4[i][2]]+(-1)^0*v[L4[i][3]])) >\n         Norm(v[L4[i][1
]]+(-1)^s*v[L4[i][2]]+(-1)^0*v[L4[i][3]],2)^2) then \n         print(
\"not satisfied\",\"v_i,v_j,v_k,v_l\",L4[i][1],(-1)^s*L4[i][2],(-1)^0*
L4[i][3],L4[i][4]); \n      end if;\n   end do;\nend do;\nfor s from 2
 by 1 to 3 do\n   t:=convert(s,base,2):\n   for i from 1 by 1 to numbc
omb(5, 4) do\n      if (2*abs(v[L4[i][4]].(v[L4[i][1]]+(-1)^(t[1])*v[L
4[i][2]]+(-1)^(t[2])*v[L4[i][3]])) >\n         Norm(v[L4[i][1]]+(-1)^(
t[1])*v[L4[i][2]]+(-1)^(t[2])*v[L4[i][3]],2)^2) then \n         print(
\"not satisfied\",\"v_i,v_j,v_k,v_l\",L4[i][1],(-1)^(t[1])*L4[i][2],(-
1)^(t[2])*L4[i][3],L4[i][4]); \n      end if;\n   end do;\nend do:\n#c
hecking for 2|v[m].(v[i]+v[j]+v[k]+v[l])|=<|v[i]+v[j]+v[k]+v[l]|^2;\nf
or s from 0 by 1 to 1 do\n   if (2*abs(v[5].(v[1]+(-1)^s*v[2]+(-1)^0*v
[3]+(-1)^0*v[4])) > \n       Norm(v[1]+(-1)^s*v[2]+(-1)^0*v[3]+(-1)^0*
v[4],2)^2) then \n      print(\"not satisfied\",\"v_i,v_j,v_k,v_l,v_m
\",1,(-1)^s*2,3,4,5); \n   end if;\nend do;\nfor s from 2 by 1 to 3 do
\n   t:=convert(s,base,2):\n   if (2*abs(v[5].(v[1]+(-1)^(t[1])*v[2]+(
-1)^(t[2])*v[3]+(-1)^0*v[4])) > \n       Norm(v[1]+(-1)^(t[1])*v[2]+(-
1)^(t[2])*v[3]+(-1)^0*v[4],2)^2) then \n      print(\"not satisfied\",
\"v_i,v_j,v_k,v_l,v_m\",1,+(-1)^(t[1])*2,(-1)^(t[2])*3,(-1)^0*4,5); \n
   end if;\nend do:\nfor s from 4 by 1 to 7 do\n   t:=convert(s,base,2
):\n   if (2*abs(v[5].(v[1]+(-1)^(t[1])*v[2]+(-1)^(t[2])*v[3]+(-1)^(t[
3])*v[4])) > \n       Norm(v[1]+(-1)^(t[1])*v[2]+(-1)^(t[2])*v[3]+(-1)
^(t[3])*v[4],2)^2) then \n      print(\"not satisfied\",\"v_i,v_j,v_k,
v_l,v_m\",1,(-1)^(t[1])*2,+(-1)^(t[2])*3,(-1)^(t[3])*4,5); \n   end if
;\nend do:\n#checking for |v[i]+v[1]+v[2]+v[3]+v[4]+v[5]|^2>=|v[i]|^2;
\nfor s from 0 by 1 to 1 do\n   if (Norm(2*v[1]+(-1)^s*v[2]+v[3]+v[4]+
v[5],2)^2 < Norm(v[1],2)^2) then \n      print(\"not satisfied\",\"2*v
_1\") \n   end if;\nend do;\nfor s from 2 by 1 to 3 do\n   t:=convert(
s,base,2):\n   if (Norm(2*v[1]+(-1)^(t[1])*v[2]+(-1)^(t[2])*v[3]+v[4]+
v[5],2)^2 < Norm(v[1],2)^2) then \n      print(\"not satisfied\",\"2*v
_1\") \n   end if; \nend do:\nfor s from 4 by 1 to 7 do\n   t:=convert
(s,base,2):\n   if (Norm(2*v[1]+(-1)^(t[1])*v[2]+(-1)^(t[2])*v[3]+(-1)
^(t[3])*v[4]+v[5],2)^2 < Norm(v[1],2)^2) then \n      print(\"not sati
sfied\",\"2*v_1\") \n   end if; \nend do:\nfor s from 8 by 1 to 15 do
\n   t:=convert(s,base,2):\n   if (Norm(2*v[1]+(-1)^(t[1])*v[2]+(-1)^(
t[2])*v[3]+(-1)^(t[3])*v[4]+(-1)^(t[4])*v[5],2)^2 < Norm(v[1],2)^2) th
en \n      print(\"not satisfied\",\"2*v_1\") \n   end if; \nend do:\n
for s from 0 by 1 to 1 do\n   if (Norm(v[1]+(-1)^s*2*v[2]+v[3]+v[4]+v[
5],2)^2 < Norm(v[2],2)^2) then \n      print(\"not satisfied\",\"2*v_2
\") \n   end if;\nend do;\nfor s from 2 by 1 to 3 do\n   t:=convert(s,
base,2):\n   if (Norm(v[1]+(-1)^(t[1])*2*v[2]+(-1)^(t[2])*v[3]+v[4]+v[
5],2)^2 < Norm(v[2],2)^2) then \n      print(\"not satisfied\",\"2*v_2
\") \n   end if; \nend do:\nfor s from 4 by 1 to 7 do\n   t:=convert(s
,base,2):\n   if (Norm(v[1]+(-1)^(t[1])*2*v[2]+(-1)^(t[2])*v[3]+(-1)^(
t[3])*v[4]+v[5],2)^2 < Norm(v[2],2)^2) then \n      print(\"not satisf
ied\",\"2*v_2\") \n   end if; \nend do:\nfor s from 8 by 1 to 15 do\n \+
  t:=convert(s,base,2):\n   if (Norm(v[1]+(-1)^(t[1])*2*v[2]+(-1)^(t[2
])*v[3]+(-1)^(t[3])*v[4]+(-1)^(t[4])*v[5],2)^2 < Norm(v[2],2)^2) then \+
\n      print(\"not satisfied\",\"2*v_2\") \n   end if; \nend do:\nfor
 s from 0 by 1 to 1 do\n   if (Norm(v[1]+(-1)^s*v[2]+2*v[3]+v[4]+v[5],
2)^2 < Norm(v[3],2)^2) then \n      print(\"not satisfied\",\"2*v_3\")
 \n   end if;\nend do;\nfor s from 2 by 1 to 3 do\n   t:=convert(s,bas
e,2):\n   if (Norm(v[1]+(-1)^(t[1])*v[2]+(-1)^(t[2])*2*v[3]+v[4]+v[5],
2)^2 < Norm(v[3],2)^2) then \n      print(\"not satisfied\",\"2*v_3\")
 \n   end if; \nend do:\nfor s from 4 by 1 to 7 do\n   t:=convert(s,ba
se,2):\n   if (Norm(v[1]+(-1)^(t[1])*v[2]+(-1)^(t[2])*2*v[3]+(-1)^(t[3
])*v[4]+v[5],2)^2 < Norm(v[3],2)^2) then \n      print(\"not satisfied
\",\"2*v_3\") \n   end if; \nend do:\nfor s from 8 by 1 to 15 do\n   t
:=convert(s,base,2):\n   if (Norm(v[1]+(-1)^(t[1])*v[2]+(-1)^(t[2])*2*
v[3]+(-1)^(t[3])*v[4]+(-1)^(t[4])*v[5],2)^2 < Norm(v[3],2)^2) then \n \+
     print(\"not satisfied\",\"2*v_3\") \n   end if; \nend do:\nfor s \+
from 0 by 1 to 1 do\n   if (Norm(v[1]+(-1)^s*v[2]+v[3]+2*v[4]+v[5],2)^
2 < Norm(v[4],2)^2) then \n      print(\"not satisfied\",\"2*v_4\") \n
   end if;\nend do;\nfor s from 2 by 1 to 3 do\n   t:=convert(s,base,2
):\n   if (Norm(v[1]+(-1)^(t[1])*v[2]+(-1)^(t[2])*v[3]+2*v[4]+v[5],2)^
2 < Norm(v[4],2)^2) then \n      print(\"not satisfied\",\"2*v_4\") \n
   end if; \nend do:\nfor s from 4 by 1 to 7 do\n   t:=convert(s,base,
2):\n   if (Norm(v[1]+(-1)^(t[1])*v[2]+(-1)^(t[2])*v[3]+(-1)^(t[3])*2*
v[4]+v[5],2)^2 < Norm(v[4],2)^2) then \n      print(\"not satisfied\",
\"2*v_4\") \n   end if; \nend do:\nfor s from 8 by 1 to 15 do\n   t:=c
onvert(s,base,2):\n   if (Norm(v[1]+(-1)^(t[1])*v[2]+(-1)^(t[2])*v[3]+
(-1)^(t[3])*2*v[4]+(-1)^(t[4])*v[5],2)^2 < Norm(v[4],2)^2) then \n    \+
  print(\"not satisfied\",\"2*v_4\") \n   end if; \nend do:\nfor s fro
m 0 by 1 to 1 do\n   if (Norm(v[1]+(-1)^s*v[2]+v[3]+v[4]+2*v[5],2)^2 <
 Norm(v[5],2)^2) then \n      print(\"not satisfied\",\"2*v_5\") \n   \+
end if;\nend do;\nfor s from 2 by 1 to 3 do\n   t:=convert(s,base,2):
\n   if (Norm(v[1]+(-1)^(t[1])*v[2]+(-1)^(t[2])*v[3]+v[4]+2*v[5],2)^2 \+
< Norm(v[5],2)^2) then \n      print(\"not satisfied\",\"2*v_5\") \n  \+
 end if; \nend do:\nfor s from 4 by 1 to 7 do\n   t:=convert(s,base,2)
:\n   if (Norm(v[1]+(-1)^(t[1])*v[2]+(-1)^(t[2])*v[3]+(-1)^(t[3])*v[4]
+2*v[5],2)^2 < Norm(v[5],2)^2) then \n      print(\"not satisfied\",\"
2*v_5\") \n   end if; \nend do:\nfor s from 8 by 1 to 15 do\n   t:=con
vert(s,base,2):\n   if (Norm(v[1]+(-1)^(t[1])*v[2]+(-1)^(t[2])*v[3]+(-
1)^(t[3])*v[4]+(-1)^(t[4])*2*v[5],2)^2 < Norm(v[5],2)^2) then \n      \+
print(\"not satisfied\",\"2*v_5\") \n   end if; \nend do:" }}{PARA 11 
"" 1 "" {XPPMATH 20 "6&Q.not~satisfied6\"Q(v_i,v_jF$\"\"\"\"\"#" }}}
{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "> " 0 "
" {MPLTEXT 1 0 365 "v[1]:=Vector([4,-1,-1,-1,-1]):\nv[2]:=Vector([-1,4
,-1,-1,-1]):\nv[3]:=Vector([-1,1,4,1,1]):\nv[4]:=Vector([-1,-1,-1,4,-1
]):\nv[5]:=Vector([-2,-2,2,-2,-2]):\nv[1],v[2],v[3],v[4],v[5];\nprint(
\"|v[1]|^2\"=Norm(v[1],2)^2);\n#checking for decreasing order;\nfor i \+
from 1 by 1 to 4 do \n   if (Norm(v[i],2)^2 > Norm(v[i+1],2)^2) then p
rint(\"not satisfied\",(i,i+1)) end if; \nend do;" }}{PARA 11 "" 1 "" 
{XPPMATH 20 "6'-%'RTABLEG6%\"*Giz#=-%'MATRIXG6#7'7#\"\"%7#!\"\"F-F-F-&
%'VectorG6#%'columnG-F$6%\"*#H'z#=-F(6#7'F-F+F-F-F-F/-F$6%\"*cjz#=-F(6
#7'F-7#\"\"\"F+F?F?F/-F$6%\"*?kz#=-F(6#7'F-F-F-F+F-F/-F$6%\"*%['z#=-F(
6#7'7#!\"#FM7#\"\"#FMFMF/" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#/Q)|grv[1
]|gr^26\"\"#?" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 6469 "#checkin
g for 2|v[j].v[i]|=<|v[i]|^2;\nL2:=choose(5, 2):\nfor i from 1 by 1 to
 numbcomb(5, 2) do\n   if (2*abs(v[L2[i][2]].v[L2[i][1]]) > Norm(v[L2[
i][1]],2)^2) then \n      print(\"not satisfied\",\"v_i,v_j\",L2[i][1]
,L2[i][2]) \n   end if;\nend do;\n#checking for 2|v[k].(v[i]+v[j])|=<|
v[i]+v[j]|^2;\nL3:=choose(5, 3):\nfor s from 0 by 1 to 1 do\n   for i \+
from 1 by 1 to numbcomb(5, 3) do\n      if (2*abs(v[L3[i][3]].(v[L3[i]
[1]]+(-1)^s*v[L3[i][2]])) > Norm(v[L3[i][1]]+(-1)^s*v[L3[i][2]],2)^2) \+
then \n         print(\"not satisfied\",\"v_i,v_j,v_k\",L3[i][1],(-1)^
s*L3[i][2],L3[i][3]); \n      end if;\n   end do;\nend do;\n#checking \+
for 2|v[l].(v[i]+v[j]+v[k])|=<|v[i]+v[j]+v[k]|^2;\nL4:=choose(5, 4):\n
for s from 0 by 1 to 1 do\n   for i from 1 by 1 to numbcomb(5, 4) do\n
      if (2*abs(v[L4[i][4]].(v[L4[i][1]]+(-1)^s*v[L4[i][2]]+(-1)^0*v[L
4[i][3]])) >\n         Norm(v[L4[i][1]]+(-1)^s*v[L4[i][2]]+(-1)^0*v[L4
[i][3]],2)^2) then \n         print(\"not satisfied\",\"v_i,v_j,v_k,v_
l\",L4[i][1],(-1)^s*L4[i][2],(-1)^0*L4[i][3],L4[i][4]); \n      end if
;\n   end do;\nend do;\nfor s from 2 by 1 to 3 do\n   t:=convert(s,bas
e,2):\n   for i from 1 by 1 to numbcomb(5, 4) do\n      if (2*abs(v[L4
[i][4]].(v[L4[i][1]]+(-1)^(t[1])*v[L4[i][2]]+(-1)^(t[2])*v[L4[i][3]]))
 >\n         Norm(v[L4[i][1]]+(-1)^(t[1])*v[L4[i][2]]+(-1)^(t[2])*v[L4
[i][3]],2)^2) then \n         print(\"not satisfied\",\"v_i,v_j,v_k,v_
l\",L4[i][1],(-1)^(t[1])*L4[i][2],(-1)^(t[2])*L4[i][3],L4[i][4]); \n  \+
    end if;\n   end do;\nend do:\n#checking for 2|v[m].(v[i]+v[j]+v[k]
+v[l])|=<|v[i]+v[j]+v[k]+v[l]|^2;\nfor s from 0 by 1 to 1 do\n   if (2
*abs(v[5].(v[1]+(-1)^s*v[2]+(-1)^0*v[3]+(-1)^0*v[4])) > \n       Norm(
v[1]+(-1)^s*v[2]+(-1)^0*v[3]+(-1)^0*v[4],2)^2) then \n      print(\"no
t satisfied\",\"v_i,v_j,v_k,v_l,v_m\",1,(-1)^s*2,3,4,5); \n   end if;
\nend do;\nfor s from 2 by 1 to 3 do\n   t:=convert(s,base,2):\n   if \+
(2*abs(v[5].(v[1]+(-1)^(t[1])*v[2]+(-1)^(t[2])*v[3]+(-1)^0*v[4])) > \n
       Norm(v[1]+(-1)^(t[1])*v[2]+(-1)^(t[2])*v[3]+(-1)^0*v[4],2)^2) t
hen \n      print(\"not satisfied\",\"v_i,v_j,v_k,v_l,v_m\",1,+(-1)^(t
[1])*2,(-1)^(t[2])*3,(-1)^0*4,5); \n   end if;\nend do:\nfor s from 4 \+
by 1 to 7 do\n   t:=convert(s,base,2):\n   if (2*abs(v[5].(v[1]+(-1)^(
t[1])*v[2]+(-1)^(t[2])*v[3]+(-1)^(t[3])*v[4])) > \n       Norm(v[1]+(-
1)^(t[1])*v[2]+(-1)^(t[2])*v[3]+(-1)^(t[3])*v[4],2)^2) then \n      pr
int(\"not satisfied\",\"v_i,v_j,v_k,v_l,v_m\",1,(-1)^(t[1])*2,+(-1)^(t
[2])*3,(-1)^(t[3])*4,5); \n   end if;\nend do:\n#checking for |v[i]+v[
1]+v[2]+v[3]+v[4]+v[5]|^2>=|v[i]|^2;\nfor s from 0 by 1 to 1 do\n   if
 (Norm(2*v[1]+(-1)^s*v[2]+v[3]+v[4]+v[5],2)^2 < Norm(v[1],2)^2) then \+
\n      print(\"not satisfied\",\"2*v_1\") \n   end if;\nend do;\nfor \+
s from 2 by 1 to 3 do\n   t:=convert(s,base,2):\n   if (Norm(2*v[1]+(-
1)^(t[1])*v[2]+(-1)^(t[2])*v[3]+v[4]+v[5],2)^2 < Norm(v[1],2)^2) then \+
\n      print(\"not satisfied\",\"2*v_1\") \n   end if; \nend do:\nfor
 s from 4 by 1 to 7 do\n   t:=convert(s,base,2):\n   if (Norm(2*v[1]+(
-1)^(t[1])*v[2]+(-1)^(t[2])*v[3]+(-1)^(t[3])*v[4]+v[5],2)^2 < Norm(v[1
],2)^2) then \n      print(\"not satisfied\",\"2*v_1\") \n   end if; \+
\nend do:\nfor s from 8 by 1 to 15 do\n   t:=convert(s,base,2):\n   if
 (Norm(2*v[1]+(-1)^(t[1])*v[2]+(-1)^(t[2])*v[3]+(-1)^(t[3])*v[4]+(-1)^
(t[4])*v[5],2)^2 < Norm(v[1],2)^2) then \n      print(\"not satisfied
\",\"2*v_1\") \n   end if; \nend do:\nfor s from 0 by 1 to 1 do\n   if
 (Norm(v[1]+(-1)^s*2*v[2]+v[3]+v[4]+v[5],2)^2 < Norm(v[2],2)^2) then \+
\n      print(\"not satisfied\",\"2*v_2\") \n   end if;\nend do;\nfor \+
s from 2 by 1 to 3 do\n   t:=convert(s,base,2):\n   if (Norm(v[1]+(-1)
^(t[1])*2*v[2]+(-1)^(t[2])*v[3]+v[4]+v[5],2)^2 < Norm(v[2],2)^2) then \+
\n      print(\"not satisfied\",\"2*v_2\") \n   end if; \nend do:\nfor
 s from 4 by 1 to 7 do\n   t:=convert(s,base,2):\n   if (Norm(v[1]+(-1
)^(t[1])*2*v[2]+(-1)^(t[2])*v[3]+(-1)^(t[3])*v[4]+v[5],2)^2 < Norm(v[2
],2)^2) then \n      print(\"not satisfied\",\"2*v_2\") \n   end if; \+
\nend do:\nfor s from 8 by 1 to 15 do\n   t:=convert(s,base,2):\n   if
 (Norm(v[1]+(-1)^(t[1])*2*v[2]+(-1)^(t[2])*v[3]+(-1)^(t[3])*v[4]+(-1)^
(t[4])*v[5],2)^2 < Norm(v[2],2)^2) then \n      print(\"not satisfied
\",\"2*v_2\") \n   end if; \nend do:\nfor s from 0 by 1 to 1 do\n   if
 (Norm(v[1]+(-1)^s*v[2]+2*v[3]+v[4]+v[5],2)^2 < Norm(v[3],2)^2) then \+
\n      print(\"not satisfied\",\"2*v_3\") \n   end if;\nend do;\nfor \+
s from 2 by 1 to 3 do\n   t:=convert(s,base,2):\n   if (Norm(v[1]+(-1)
^(t[1])*v[2]+(-1)^(t[2])*2*v[3]+v[4]+v[5],2)^2 < Norm(v[3],2)^2) then \+
\n      print(\"not satisfied\",\"2*v_3\") \n   end if; \nend do:\nfor
 s from 4 by 1 to 7 do\n   t:=convert(s,base,2):\n   if (Norm(v[1]+(-1
)^(t[1])*v[2]+(-1)^(t[2])*2*v[3]+(-1)^(t[3])*v[4]+v[5],2)^2 < Norm(v[3
],2)^2) then \n      print(\"not satisfied\",\"2*v_3\") \n   end if; \+
\nend do:\nfor s from 8 by 1 to 15 do\n   t:=convert(s,base,2):\n   if
 (Norm(v[1]+(-1)^(t[1])*v[2]+(-1)^(t[2])*2*v[3]+(-1)^(t[3])*v[4]+(-1)^
(t[4])*v[5],2)^2 < Norm(v[3],2)^2) then \n      print(\"not satisfied
\",\"2*v_3\") \n   end if; \nend do:\nfor s from 0 by 1 to 1 do\n   if
 (Norm(v[1]+(-1)^s*v[2]+v[3]+2*v[4]+v[5],2)^2 < Norm(v[4],2)^2) then \+
\n      print(\"not satisfied\",\"2*v_4\") \n   end if;\nend do;\nfor \+
s from 2 by 1 to 3 do\n   t:=convert(s,base,2):\n   if (Norm(v[1]+(-1)
^(t[1])*v[2]+(-1)^(t[2])*v[3]+2*v[4]+v[5],2)^2 < Norm(v[4],2)^2) then \+
\n      print(\"not satisfied\",\"2*v_4\") \n   end if; \nend do:\nfor
 s from 4 by 1 to 7 do\n   t:=convert(s,base,2):\n   if (Norm(v[1]+(-1
)^(t[1])*v[2]+(-1)^(t[2])*v[3]+(-1)^(t[3])*2*v[4]+v[5],2)^2 < Norm(v[4
],2)^2) then \n      print(\"not satisfied\",\"2*v_4\") \n   end if; \+
\nend do:\nfor s from 8 by 1 to 15 do\n   t:=convert(s,base,2):\n   if
 (Norm(v[1]+(-1)^(t[1])*v[2]+(-1)^(t[2])*v[3]+(-1)^(t[3])*2*v[4]+(-1)^
(t[4])*v[5],2)^2 < Norm(v[4],2)^2) then \n      print(\"not satisfied
\",\"2*v_4\") \n   end if; \nend do:\nfor s from 0 by 1 to 1 do\n   if
 (Norm(v[1]+(-1)^s*v[2]+v[3]+v[4]+2*v[5],2)^2 < Norm(v[5],2)^2) then \+
\n      print(\"not satisfied\",\"2*v_5\") \n   end if;\nend do;\nfor \+
s from 2 by 1 to 3 do\n   t:=convert(s,base,2):\n   if (Norm(v[1]+(-1)
^(t[1])*v[2]+(-1)^(t[2])*v[3]+v[4]+2*v[5],2)^2 < Norm(v[5],2)^2) then \+
\n      print(\"not satisfied\",\"2*v_5\") \n   end if; \nend do:\nfor
 s from 4 by 1 to 7 do\n   t:=convert(s,base,2):\n   if (Norm(v[1]+(-1
)^(t[1])*v[2]+(-1)^(t[2])*v[3]+(-1)^(t[3])*v[4]+2*v[5],2)^2 < Norm(v[5
],2)^2) then \n      print(\"not satisfied\",\"2*v_5\") \n   end if; \+
\nend do:\nfor s from 8 by 1 to 15 do\n   t:=convert(s,base,2):\n   if
 (Norm(v[1]+(-1)^(t[1])*v[2]+(-1)^(t[2])*v[3]+(-1)^(t[3])*v[4]+(-1)^(t
[4])*2*v[5],2)^2 < Norm(v[5],2)^2) then \n      print(\"not satisfied
\",\"2*v_5\") \n   end if; \nend do:" }}{PARA 11 "" 1 "" {XPPMATH 20 "
6&Q.not~satisfied6\"Q(v_i,v_jF$\"\"\"\"\"$" }}}{EXCHG {PARA 0 "> " 0 "
" {MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 365 "v[1]
:=Vector([4,-1,-1,-1,-1]):\nv[2]:=Vector([-1,4,-1,-1,-1]):\nv[3]:=Vect
or([-1,-1,4,-1,-1]):\nv[4]:=Vector([-1,1,1,4,1]):\nv[5]:=Vector([-2,-2
,-2,2,-2]):\nv[1],v[2],v[3],v[4],v[5];\nprint(\"|v[1]|^2\"=Norm(v[1],2
)^2);\n#checking for decreasing order;\nfor i from 1 by 1 to 4 do \n  \+
 if (Norm(v[i],2)^2 > Norm(v[i+1],2)^2) then print(\"not satisfied\",(
i,i+1)) end if; \nend do;" }}{PARA 11 "" 1 "" {XPPMATH 20 "6'-%'RTABLE
G6%\"*_J\"RA-%'MATRIXG6#7'7#\"\"%7#!\"\"F-F-F-&%'VectorG6#%'columnG-F$
6%\"*;K\"RA-F(6#7'F-F+F-F-F-F/-F$6%\"*!G8RA-F(6#7'F-F-F+F-F-F/-F$6%\"*
WL\"RA-F(6#7'F-7#\"\"\"FEF+FEF/-F$6%\"*3M\"RA-F(6#7'7#!\"#FMFM7#\"\"#F
MF/" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#/Q)|grv[1]|gr^26\"\"#?" }}}
{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 6470 "#checking for 2|v[j].v[i]|
=<|v[i]|^2;\nL2:=choose(5, 2):\nfor i from 1 by 1 to numbcomb(5, 2) do
\n   if (2*abs(v[L2[i][2]].v[L2[i][1]]) > Norm(v[L2[i][1]],2)^2) then \+
\n      print(\"not satisfied\",\"v_i,v_j\",L2[i][1],L2[i][2]) \n   en
d if;\nend do;\n#checking for 2|v[k].(v[i]+v[j])|=<|v[i]+v[j]|^2;\nL3:
=choose(5, 3):\nfor s from 0 by 1 to 1 do\n   for i from 1 by 1 to num
bcomb(5, 3) do\n      if (2*abs(v[L3[i][3]].(v[L3[i][1]]+(-1)^s*v[L3[i
][2]])) > Norm(v[L3[i][1]]+(-1)^s*v[L3[i][2]],2)^2) then \n         pr
int(\"not satisfied\",\"v_i,v_j,v_k\",L3[i][1],(-1)^s*L3[i][2],L3[i][3
]); \n      end if;\n   end do;\nend do;\n#checking for 2|v[l].(v[i]+v
[j]+v[k])|=<|v[i]+v[j]+v[k]|^2;\nL4:=choose(5, 4):\nfor s from 0 by 1 \+
to 1 do\n   for i from 1 by 1 to numbcomb(5, 4) do\n      if (2*abs(v[
L4[i][4]].(v[L4[i][1]]+(-1)^s*v[L4[i][2]]+(-1)^0*v[L4[i][3]])) >\n    \+
     Norm(v[L4[i][1]]+(-1)^s*v[L4[i][2]]+(-1)^0*v[L4[i][3]],2)^2) then
 \n         print(\"not satisfied\",\"v_i,v_j,v_k,v_l\",L4[i][1],(-1)^
s*L4[i][2],(-1)^0*L4[i][3],L4[i][4]); \n      end if;\n   end do;\nend
 do;\nfor s from 2 by 1 to 3 do\n   t:=convert(s,base,2):\n   for i fr
om 1 by 1 to numbcomb(5, 4) do\n      if (2*abs(v[L4[i][4]].(v[L4[i][1
]]+(-1)^(t[1])*v[L4[i][2]]+(-1)^(t[2])*v[L4[i][3]])) >\n         Norm(
v[L4[i][1]]+(-1)^(t[1])*v[L4[i][2]]+(-1)^(t[2])*v[L4[i][3]],2)^2) then
 \n         print(\"not satisfied\",\"v_i,v_j,v_k,v_l\",L4[i][1],(-1)^
(t[1])*L4[i][2],(-1)^(t[2])*L4[i][3],L4[i][4]); \n      end if;\n   en
d do;\nend do:\n#checking for 2|v[m].(v[i]+v[j]+v[k]+v[l])|=<|v[i]+v[j
]+v[k]+v[l]|^2;\nfor s from 0 by 1 to 1 do\n   if (2*abs(v[5].(v[1]+(-
1)^s*v[2]+(-1)^0*v[3]+(-1)^0*v[4])) > \n       Norm(v[1]+(-1)^s*v[2]+(
-1)^0*v[3]+(-1)^0*v[4],2)^2) then \n      print(\"not satisfied\",\"v_
i,v_j,v_k,v_l,v_m\",1,(-1)^s*2,3,4,5); \n   end if;\nend do;\nfor s fr
om 2 by 1 to 3 do\n   t:=convert(s,base,2):\n   if (2*abs(v[5].(v[1]+(
-1)^(t[1])*v[2]+(-1)^(t[2])*v[3]+(-1)^0*v[4])) > \n       Norm(v[1]+(-
1)^(t[1])*v[2]+(-1)^(t[2])*v[3]+(-1)^0*v[4],2)^2) then \n      print(
\"not satisfied\",\"v_i,v_j,v_k,v_l,v_m\",1,+(-1)^(t[1])*2,(-1)^(t[2])
*3,(-1)^0*4,5); \n   end if;\nend do:\nfor s from 4 by 1 to 7 do\n   t
:=convert(s,base,2):\n   if (2*abs(v[5].(v[1]+(-1)^(t[1])*v[2]+(-1)^(t
[2])*v[3]+(-1)^(t[3])*v[4])) > \n       Norm(v[1]+(-1)^(t[1])*v[2]+(-1
)^(t[2])*v[3]+(-1)^(t[3])*v[4],2)^2) then \n      print(\"not satisfie
d\",\"v_i,v_j,v_k,v_l,v_m\",1,(-1)^(t[1])*2,+(-1)^(t[2])*3,(-1)^(t[3])
*4,5); \n   end if;\nend do:\n\n#checking for |v[i]+v[1]+v[2]+v[3]+v[4
]+v[5]|^2>=|v[i]|^2;\nfor s from 0 by 1 to 1 do\n   if (Norm(2*v[1]+(-
1)^s*v[2]+v[3]+v[4]+v[5],2)^2 < Norm(v[1],2)^2) then \n      print(\"n
ot satisfied\",\"2*v_1\") \n   end if;\nend do;\nfor s from 2 by 1 to \+
3 do\n   t:=convert(s,base,2):\n   if (Norm(2*v[1]+(-1)^(t[1])*v[2]+(-
1)^(t[2])*v[3]+v[4]+v[5],2)^2 < Norm(v[1],2)^2) then \n      print(\"n
ot satisfied\",\"2*v_1\") \n   end if; \nend do:\nfor s from 4 by 1 to
 7 do\n   t:=convert(s,base,2):\n   if (Norm(2*v[1]+(-1)^(t[1])*v[2]+(
-1)^(t[2])*v[3]+(-1)^(t[3])*v[4]+v[5],2)^2 < Norm(v[1],2)^2) then \n  \+
    print(\"not satisfied\",\"2*v_1\") \n   end if; \nend do:\nfor s f
rom 8 by 1 to 15 do\n   t:=convert(s,base,2):\n   if (Norm(2*v[1]+(-1)
^(t[1])*v[2]+(-1)^(t[2])*v[3]+(-1)^(t[3])*v[4]+(-1)^(t[4])*v[5],2)^2 <
 Norm(v[1],2)^2) then \n      print(\"not satisfied\",\"2*v_1\") \n   \+
end if; \nend do:\nfor s from 0 by 1 to 1 do\n   if (Norm(v[1]+(-1)^s*
2*v[2]+v[3]+v[4]+v[5],2)^2 < Norm(v[2],2)^2) then \n      print(\"not \+
satisfied\",\"2*v_2\") \n   end if;\nend do;\nfor s from 2 by 1 to 3 d
o\n   t:=convert(s,base,2):\n   if (Norm(v[1]+(-1)^(t[1])*2*v[2]+(-1)^
(t[2])*v[3]+v[4]+v[5],2)^2 < Norm(v[2],2)^2) then \n      print(\"not \+
satisfied\",\"2*v_2\") \n   end if; \nend do:\nfor s from 4 by 1 to 7 \+
do\n   t:=convert(s,base,2):\n   if (Norm(v[1]+(-1)^(t[1])*2*v[2]+(-1)
^(t[2])*v[3]+(-1)^(t[3])*v[4]+v[5],2)^2 < Norm(v[2],2)^2) then \n     \+
 print(\"not satisfied\",\"2*v_2\") \n   end if; \nend do:\nfor s from
 8 by 1 to 15 do\n   t:=convert(s,base,2):\n   if (Norm(v[1]+(-1)^(t[1
])*2*v[2]+(-1)^(t[2])*v[3]+(-1)^(t[3])*v[4]+(-1)^(t[4])*v[5],2)^2 < No
rm(v[2],2)^2) then \n      print(\"not satisfied\",\"2*v_2\") \n   end
 if; \nend do:\nfor s from 0 by 1 to 1 do\n   if (Norm(v[1]+(-1)^s*v[2
]+2*v[3]+v[4]+v[5],2)^2 < Norm(v[3],2)^2) then \n      print(\"not sat
isfied\",\"2*v_3\") \n   end if;\nend do;\nfor s from 2 by 1 to 3 do\n
   t:=convert(s,base,2):\n   if (Norm(v[1]+(-1)^(t[1])*v[2]+(-1)^(t[2]
)*2*v[3]+v[4]+v[5],2)^2 < Norm(v[3],2)^2) then \n      print(\"not sat
isfied\",\"2*v_3\") \n   end if; \nend do:\nfor s from 4 by 1 to 7 do
\n   t:=convert(s,base,2):\n   if (Norm(v[1]+(-1)^(t[1])*v[2]+(-1)^(t[
2])*2*v[3]+(-1)^(t[3])*v[4]+v[5],2)^2 < Norm(v[3],2)^2) then \n      p
rint(\"not satisfied\",\"2*v_3\") \n   end if; \nend do:\nfor s from 8
 by 1 to 15 do\n   t:=convert(s,base,2):\n   if (Norm(v[1]+(-1)^(t[1])
*v[2]+(-1)^(t[2])*2*v[3]+(-1)^(t[3])*v[4]+(-1)^(t[4])*v[5],2)^2 < Norm
(v[3],2)^2) then \n      print(\"not satisfied\",\"2*v_3\") \n   end i
f; \nend do:\nfor s from 0 by 1 to 1 do\n   if (Norm(v[1]+(-1)^s*v[2]+
v[3]+2*v[4]+v[5],2)^2 < Norm(v[4],2)^2) then \n      print(\"not satis
fied\",\"2*v_4\") \n   end if;\nend do;\nfor s from 2 by 1 to 3 do\n  \+
 t:=convert(s,base,2):\n   if (Norm(v[1]+(-1)^(t[1])*v[2]+(-1)^(t[2])*
v[3]+2*v[4]+v[5],2)^2 < Norm(v[4],2)^2) then \n      print(\"not satis
fied\",\"2*v_4\") \n   end if; \nend do:\nfor s from 4 by 1 to 7 do\n \+
  t:=convert(s,base,2):\n   if (Norm(v[1]+(-1)^(t[1])*v[2]+(-1)^(t[2])
*v[3]+(-1)^(t[3])*2*v[4]+v[5],2)^2 < Norm(v[4],2)^2) then \n      prin
t(\"not satisfied\",\"2*v_4\") \n   end if; \nend do:\nfor s from 8 by
 1 to 15 do\n   t:=convert(s,base,2):\n   if (Norm(v[1]+(-1)^(t[1])*v[
2]+(-1)^(t[2])*v[3]+(-1)^(t[3])*2*v[4]+(-1)^(t[4])*v[5],2)^2 < Norm(v[
4],2)^2) then \n      print(\"not satisfied\",\"2*v_4\") \n   end if; \+
\nend do:\nfor s from 0 by 1 to 1 do\n   if (Norm(v[1]+(-1)^s*v[2]+v[3
]+v[4]+2*v[5],2)^2 < Norm(v[5],2)^2) then \n      print(\"not satisfie
d\",\"2*v_5\") \n   end if;\nend do;\nfor s from 2 by 1 to 3 do\n   t:
=convert(s,base,2):\n   if (Norm(v[1]+(-1)^(t[1])*v[2]+(-1)^(t[2])*v[3
]+v[4]+2*v[5],2)^2 < Norm(v[5],2)^2) then \n      print(\"not satisfie
d\",\"2*v_5\") \n   end if; \nend do:\nfor s from 4 by 1 to 7 do\n   t
:=convert(s,base,2):\n   if (Norm(v[1]+(-1)^(t[1])*v[2]+(-1)^(t[2])*v[
3]+(-1)^(t[3])*v[4]+2*v[5],2)^2 < Norm(v[5],2)^2) then \n      print(
\"not satisfied\",\"2*v_5\") \n   end if; \nend do:\nfor s from 8 by 1
 to 15 do\n   t:=convert(s,base,2):\n   if (Norm(v[1]+(-1)^(t[1])*v[2]
+(-1)^(t[2])*v[3]+(-1)^(t[3])*v[4]+(-1)^(t[4])*2*v[5],2)^2 < Norm(v[5]
,2)^2) then \n      print(\"not satisfied\",\"2*v_5\") \n   end if; \n
end do:" }}{PARA 11 "" 1 "" {XPPMATH 20 "6&Q.not~satisfied6\"Q(v_i,v_j
F$\"\"\"\"\"%" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}
{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 365 "v[1]:=Vector([4,1,1,1,1]):
\nv[2]:=Vector([-1,4,-1,-1,-1]):\nv[3]:=Vector([-1,-1,4,-1,-1]):\nv[4]
:=Vector([-1,-1,-1,4,-1]):\nv[5]:=Vector([-2,-2,-2,-2,-2]):\nv[1],v[2]
,v[3],v[4],v[5];\nprint(\"|v[1]|^2\"=Norm(v[1],2)^2);\n#checking for d
ecreasing order;\nfor i from 1 by 1 to 4 do \n   if (Norm(v[i],2)^2 > \+
Norm(v[i+1],2)^2) then print(\"not satisfied\",(i,i+1)) end if; \nend \+
do;" }}{PARA 11 "" 1 "" {XPPMATH 20 "6'-%'RTABLEG6%\"*_[)3@-%'MATRIXG6
#7'7#\"\"%7#\"\"\"F-F-F-&%'VectorG6#%'columnG-F$6%\"*;\\)3@-F(6#7'7#!
\"\"F+F9F9F9F/-F$6%\"*!)\\)3@-F(6#7'F9F9F+F9F9F/-F$6%\"*W])3@-F(6#7'F9
F9F9F+F9F/-F$6%\"*3^)3@-F(6#7'7#!\"#FMFMFMFMF/" }}{PARA 11 "" 1 "" 
{XPPMATH 20 "6#/Q)|grv[1]|gr^26\"\"#?" }}}{EXCHG {PARA 0 "> " 0 "" 
{MPLTEXT 1 0 6469 "#checking for 2|v[j].v[i]|=<|v[i]|^2;\nL2:=choose(5
, 2):\nfor i from 1 by 1 to numbcomb(5, 2) do\n   if (2*abs(v[L2[i][2]
].v[L2[i][1]]) > Norm(v[L2[i][1]],2)^2) then \n      print(\"not satis
fied\",\"v_i,v_j\",L2[i][1],L2[i][2]) \n   end if;\nend do;\n#checking
 for 2|v[k].(v[i]+v[j])|=<|v[i]+v[j]|^2;\nL3:=choose(5, 3):\nfor s fro
m 0 by 1 to 1 do\n   for i from 1 by 1 to numbcomb(5, 3) do\n      if \+
(2*abs(v[L3[i][3]].(v[L3[i][1]]+(-1)^s*v[L3[i][2]])) > Norm(v[L3[i][1]
]+(-1)^s*v[L3[i][2]],2)^2) then \n         print(\"not satisfied\",\"v
_i,v_j,v_k\",L3[i][1],(-1)^s*L3[i][2],L3[i][3]); \n      end if;\n   e
nd do;\nend do;\n#checking for 2|v[l].(v[i]+v[j]+v[k])|=<|v[i]+v[j]+v[
k]|^2;\nL4:=choose(5, 4):\nfor s from 0 by 1 to 1 do\n   for i from 1 \+
by 1 to numbcomb(5, 4) do\n      if (2*abs(v[L4[i][4]].(v[L4[i][1]]+(-
1)^s*v[L4[i][2]]+(-1)^0*v[L4[i][3]])) >\n         Norm(v[L4[i][1]]+(-1
)^s*v[L4[i][2]]+(-1)^0*v[L4[i][3]],2)^2) then \n         print(\"not s
atisfied\",\"v_i,v_j,v_k,v_l\",L4[i][1],(-1)^s*L4[i][2],(-1)^0*L4[i][3
],L4[i][4]); \n      end if;\n   end do;\nend do;\nfor s from 2 by 1 t
o 3 do\n   t:=convert(s,base,2):\n   for i from 1 by 1 to numbcomb(5, \+
4) do\n      if (2*abs(v[L4[i][4]].(v[L4[i][1]]+(-1)^(t[1])*v[L4[i][2]
]+(-1)^(t[2])*v[L4[i][3]])) >\n         Norm(v[L4[i][1]]+(-1)^(t[1])*v
[L4[i][2]]+(-1)^(t[2])*v[L4[i][3]],2)^2) then \n         print(\"not s
atisfied\",\"v_i,v_j,v_k,v_l\",L4[i][1],(-1)^(t[1])*L4[i][2],(-1)^(t[2
])*L4[i][3],L4[i][4]); \n      end if;\n   end do;\nend do:\n#checking
 for 2|v[m].(v[i]+v[j]+v[k]+v[l])|=<|v[i]+v[j]+v[k]+v[l]|^2;\nfor s fr
om 0 by 1 to 1 do\n   if (2*abs(v[5].(v[1]+(-1)^s*v[2]+(-1)^0*v[3]+(-1
)^0*v[4])) > \n       Norm(v[1]+(-1)^s*v[2]+(-1)^0*v[3]+(-1)^0*v[4],2)
^2) then \n      print(\"not satisfied\",\"v_i,v_j,v_k,v_l,v_m\",1,(-1
)^s*2,3,4,5); \n   end if;\nend do;\nfor s from 2 by 1 to 3 do\n   t:=
convert(s,base,2):\n   if (2*abs(v[5].(v[1]+(-1)^(t[1])*v[2]+(-1)^(t[2
])*v[3]+(-1)^0*v[4])) > \n       Norm(v[1]+(-1)^(t[1])*v[2]+(-1)^(t[2]
)*v[3]+(-1)^0*v[4],2)^2) then \n      print(\"not satisfied\",\"v_i,v_
j,v_k,v_l,v_m\",1,+(-1)^(t[1])*2,(-1)^(t[2])*3,(-1)^0*4,5); \n   end i
f;\nend do:\nfor s from 4 by 1 to 7 do\n   t:=convert(s,base,2):\n   i
f (2*abs(v[5].(v[1]+(-1)^(t[1])*v[2]+(-1)^(t[2])*v[3]+(-1)^(t[3])*v[4]
)) > \n       Norm(v[1]+(-1)^(t[1])*v[2]+(-1)^(t[2])*v[3]+(-1)^(t[3])*
v[4],2)^2) then \n      print(\"not satisfied\",\"v_i,v_j,v_k,v_l,v_m
\",1,(-1)^(t[1])*2,+(-1)^(t[2])*3,(-1)^(t[3])*4,5); \n   end if;\nend \+
do:\n#checking for |v[i]+v[1]+v[2]+v[3]+v[4]+v[5]|^2>=|v[i]|^2;\nfor s
 from 0 by 1 to 1 do\n   if (Norm(2*v[1]+(-1)^s*v[2]+v[3]+v[4]+v[5],2)
^2 < Norm(v[1],2)^2) then \n      print(\"not satisfied\",\"2*v_1\") \+
\n   end if;\nend do;\nfor s from 2 by 1 to 3 do\n   t:=convert(s,base
,2):\n   if (Norm(2*v[1]+(-1)^(t[1])*v[2]+(-1)^(t[2])*v[3]+v[4]+v[5],2
)^2 < Norm(v[1],2)^2) then \n      print(\"not satisfied\",\"2*v_1\") \+
\n   end if; \nend do:\nfor s from 4 by 1 to 7 do\n   t:=convert(s,bas
e,2):\n   if (Norm(2*v[1]+(-1)^(t[1])*v[2]+(-1)^(t[2])*v[3]+(-1)^(t[3]
)*v[4]+v[5],2)^2 < Norm(v[1],2)^2) then \n      print(\"not satisfied
\",\"2*v_1\") \n   end if; \nend do:\nfor s from 8 by 1 to 15 do\n   t
:=convert(s,base,2):\n   if (Norm(2*v[1]+(-1)^(t[1])*v[2]+(-1)^(t[2])*
v[3]+(-1)^(t[3])*v[4]+(-1)^(t[4])*v[5],2)^2 < Norm(v[1],2)^2) then \n \+
     print(\"not satisfied\",\"2*v_1\") \n   end if; \nend do:\nfor s \+
from 0 by 1 to 1 do\n   if (Norm(v[1]+(-1)^s*2*v[2]+v[3]+v[4]+v[5],2)^
2 < Norm(v[2],2)^2) then \n      print(\"not satisfied\",\"2*v_2\") \n
   end if;\nend do;\nfor s from 2 by 1 to 3 do\n   t:=convert(s,base,2
):\n   if (Norm(v[1]+(-1)^(t[1])*2*v[2]+(-1)^(t[2])*v[3]+v[4]+v[5],2)^
2 < Norm(v[2],2)^2) then \n      print(\"not satisfied\",\"2*v_2\") \n
   end if; \nend do:\nfor s from 4 by 1 to 7 do\n   t:=convert(s,base,
2):\n   if (Norm(v[1]+(-1)^(t[1])*2*v[2]+(-1)^(t[2])*v[3]+(-1)^(t[3])*
v[4]+v[5],2)^2 < Norm(v[2],2)^2) then \n      print(\"not satisfied\",
\"2*v_2\") \n   end if; \nend do:\nfor s from 8 by 1 to 15 do\n   t:=c
onvert(s,base,2):\n   if (Norm(v[1]+(-1)^(t[1])*2*v[2]+(-1)^(t[2])*v[3
]+(-1)^(t[3])*v[4]+(-1)^(t[4])*v[5],2)^2 < Norm(v[2],2)^2) then \n    \+
  print(\"not satisfied\",\"2*v_2\") \n   end if; \nend do:\nfor s fro
m 0 by 1 to 1 do\n   if (Norm(v[1]+(-1)^s*v[2]+2*v[3]+v[4]+v[5],2)^2 <
 Norm(v[3],2)^2) then \n      print(\"not satisfied\",\"2*v_3\") \n   \+
end if;\nend do;\nfor s from 2 by 1 to 3 do\n   t:=convert(s,base,2):
\n   if (Norm(v[1]+(-1)^(t[1])*v[2]+(-1)^(t[2])*2*v[3]+v[4]+v[5],2)^2 \+
< Norm(v[3],2)^2) then \n      print(\"not satisfied\",\"2*v_3\") \n  \+
 end if; \nend do:\nfor s from 4 by 1 to 7 do\n   t:=convert(s,base,2)
:\n   if (Norm(v[1]+(-1)^(t[1])*v[2]+(-1)^(t[2])*2*v[3]+(-1)^(t[3])*v[
4]+v[5],2)^2 < Norm(v[3],2)^2) then \n      print(\"not satisfied\",\"
2*v_3\") \n   end if; \nend do:\nfor s from 8 by 1 to 15 do\n   t:=con
vert(s,base,2):\n   if (Norm(v[1]+(-1)^(t[1])*v[2]+(-1)^(t[2])*2*v[3]+
(-1)^(t[3])*v[4]+(-1)^(t[4])*v[5],2)^2 < Norm(v[3],2)^2) then \n      \+
print(\"not satisfied\",\"2*v_3\") \n   end if; \nend do:\nfor s from \+
0 by 1 to 1 do\n   if (Norm(v[1]+(-1)^s*v[2]+v[3]+2*v[4]+v[5],2)^2 < N
orm(v[4],2)^2) then \n      print(\"not satisfied\",\"2*v_4\") \n   en
d if;\nend do;\nfor s from 2 by 1 to 3 do\n   t:=convert(s,base,2):\n \+
  if (Norm(v[1]+(-1)^(t[1])*v[2]+(-1)^(t[2])*v[3]+2*v[4]+v[5],2)^2 < N
orm(v[4],2)^2) then \n      print(\"not satisfied\",\"2*v_4\") \n   en
d if; \nend do:\nfor s from 4 by 1 to 7 do\n   t:=convert(s,base,2):\n
   if (Norm(v[1]+(-1)^(t[1])*v[2]+(-1)^(t[2])*v[3]+(-1)^(t[3])*2*v[4]+
v[5],2)^2 < Norm(v[4],2)^2) then \n      print(\"not satisfied\",\"2*v
_4\") \n   end if; \nend do:\nfor s from 8 by 1 to 15 do\n   t:=conver
t(s,base,2):\n   if (Norm(v[1]+(-1)^(t[1])*v[2]+(-1)^(t[2])*v[3]+(-1)^
(t[3])*2*v[4]+(-1)^(t[4])*v[5],2)^2 < Norm(v[4],2)^2) then \n      pri
nt(\"not satisfied\",\"2*v_4\") \n   end if; \nend do:\nfor s from 0 b
y 1 to 1 do\n   if (Norm(v[1]+(-1)^s*v[2]+v[3]+v[4]+2*v[5],2)^2 < Norm
(v[5],2)^2) then \n      print(\"not satisfied\",\"2*v_5\") \n   end i
f;\nend do;\nfor s from 2 by 1 to 3 do\n   t:=convert(s,base,2):\n   i
f (Norm(v[1]+(-1)^(t[1])*v[2]+(-1)^(t[2])*v[3]+v[4]+2*v[5],2)^2 < Norm
(v[5],2)^2) then \n      print(\"not satisfied\",\"2*v_5\") \n   end i
f; \nend do:\nfor s from 4 by 1 to 7 do\n   t:=convert(s,base,2):\n   \+
if (Norm(v[1]+(-1)^(t[1])*v[2]+(-1)^(t[2])*v[3]+(-1)^(t[3])*v[4]+2*v[5
],2)^2 < Norm(v[5],2)^2) then \n      print(\"not satisfied\",\"2*v_5
\") \n   end if; \nend do:\nfor s from 8 by 1 to 15 do\n   t:=convert(
s,base,2):\n   if (Norm(v[1]+(-1)^(t[1])*v[2]+(-1)^(t[2])*v[3]+(-1)^(t
[3])*v[4]+(-1)^(t[4])*2*v[5],2)^2 < Norm(v[5],2)^2) then \n      print
(\"not satisfied\",\"2*v_5\") \n   end if; \nend do:" }}{PARA 11 "" 1 
"" {XPPMATH 20 "6&Q.not~satisfied6\"Q(v_i,v_jF$\"\"\"\"\"&" }}}{EXCHG 
{PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "> " 0 "" 
{MPLTEXT 1 0 365 "v[1]:=Vector([4,-1,-1,-1,-1]):\nv[2]:=Vector([-1,4,-
1,-1,-1]):\nv[3]:=Vector([1,-1,4,1,1]):\nv[4]:=Vector([-1,-1,-1,4,-1])
:\nv[5]:=Vector([-2,-2,2,-2,-2]):\nv[1],v[2],v[3],v[4],v[5];\nprint(\"
|v[1]|^2\"=Norm(v[1],2)^2);\n#checking for decreasing order;\nfor i fr
om 1 by 1 to 4 do \n   if (Norm(v[i],2)^2 > Norm(v[i+1],2)^2) then pri
nt(\"not satisfied\",(i,i+1)) end if; \nend do;" }}{PARA 11 "" 1 "" 
{XPPMATH 20 "6'-%'RTABLEG6%\"*7!ew@-%'MATRIXG6#7'7#\"\"%7#!\"\"F-F-F-&
%'VectorG6#%'columnG-F$6%\"*w!ew@-F(6#7'F-F+F-F-F-F/-F$6%\"*S\"ew@-F(6
#7'7#\"\"\"F-F+F?F?F/-F$6%\"*/#ew@-F(6#7'F-F-F-F+F-F/-F$6%\"*o#ew@-F(6
#7'7#!\"#FM7#\"\"#FMFMF/" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#/Q)|grv[1]
|gr^26\"\"#?" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 6470 "#checking
 for 2|v[j].v[i]|=<|v[i]|^2;\nL2:=choose(5, 2):\nfor i from 1 by 1 to \+
numbcomb(5, 2) do\n   if (2*abs(v[L2[i][2]].v[L2[i][1]]) > Norm(v[L2[i
][1]],2)^2) then \n      print(\"not satisfied\",\"v_i,v_j\",L2[i][1],
L2[i][2]) \n   end if;\nend do;\n#checking for 2|v[k].(v[i]+v[j])|=<|v
[i]+v[j]|^2;\nL3:=choose(5, 3):\nfor s from 0 by 1 to 1 do\n   for i f
rom 1 by 1 to numbcomb(5, 3) do\n      if (2*abs(v[L3[i][3]].(v[L3[i][
1]]+(-1)^s*v[L3[i][2]])) > Norm(v[L3[i][1]]+(-1)^s*v[L3[i][2]],2)^2) t
hen \n         print(\"not satisfied\",\"v_i,v_j,v_k\",L3[i][1],(-1)^s
*L3[i][2],L3[i][3]); \n      end if;\n   end do;\nend do;\n#checking f
or 2|v[l].(v[i]+v[j]+v[k])|=<|v[i]+v[j]+v[k]|^2;\nL4:=choose(5, 4):\nf
or s from 0 by 1 to 1 do\n   for i from 1 by 1 to numbcomb(5, 4) do\n \+
     if (2*abs(v[L4[i][4]].(v[L4[i][1]]+(-1)^s*v[L4[i][2]]+(-1)^0*v[L4
[i][3]])) >\n         Norm(v[L4[i][1]]+(-1)^s*v[L4[i][2]]+(-1)^0*v[L4[
i][3]],2)^2) then \n         print(\"not satisfied\",\"v_i,v_j,v_k,v_l
\",L4[i][1],(-1)^s*L4[i][2],(-1)^0*L4[i][3],L4[i][4]); \n      end if;
\n   end do;\nend do;\nfor s from 2 by 1 to 3 do\n   t:=convert(s,base
,2):\n   for i from 1 by 1 to numbcomb(5, 4) do\n      if (2*abs(v[L4[
i][4]].(v[L4[i][1]]+(-1)^(t[1])*v[L4[i][2]]+(-1)^(t[2])*v[L4[i][3]])) \+
>\n         Norm(v[L4[i][1]]+(-1)^(t[1])*v[L4[i][2]]+(-1)^(t[2])*v[L4[
i][3]],2)^2) then \n         print(\"not satisfied\",\"v_i,v_j,v_k,v_l
\",L4[i][1],(-1)^(t[1])*L4[i][2],(-1)^(t[2])*L4[i][3],L4[i][4]); \n   \+
   end if;\n   end do;\nend do:\n#checking for 2|v[m].(v[i]+v[j]+v[k]+
v[l])|=<|v[i]+v[j]+v[k]+v[l]|^2;\nfor s from 0 by 1 to 1 do\n   if (2*
abs(v[5].(v[1]+(-1)^s*v[2]+(-1)^0*v[3]+(-1)^0*v[4])) > \n       Norm(v
[1]+(-1)^s*v[2]+(-1)^0*v[3]+(-1)^0*v[4],2)^2) then \n      print(\"not
 satisfied\",\"v_i,v_j,v_k,v_l,v_m\",1,(-1)^s*2,3,4,5); \n   end if;\n
end do;\nfor s from 2 by 1 to 3 do\n   t:=convert(s,base,2):\n   if (2
*abs(v[5].(v[1]+(-1)^(t[1])*v[2]+(-1)^(t[2])*v[3]+(-1)^0*v[4])) > \n  \+
     Norm(v[1]+(-1)^(t[1])*v[2]+(-1)^(t[2])*v[3]+(-1)^0*v[4],2)^2) the
n \n      print(\"not satisfied\",\"v_i,v_j,v_k,v_l,v_m\",1,+(-1)^(t[1
])*2,(-1)^(t[2])*3,(-1)^0*4,5); \n   end if;\nend do:\nfor s from 4 by
 1 to 7 do\n   t:=convert(s,base,2):\n   if (2*abs(v[5].(v[1]+(-1)^(t[
1])*v[2]+(-1)^(t[2])*v[3]+(-1)^(t[3])*v[4])) > \n       Norm(v[1]+(-1)
^(t[1])*v[2]+(-1)^(t[2])*v[3]+(-1)^(t[3])*v[4],2)^2) then \n      prin
t(\"not satisfied\",\"v_i,v_j,v_k,v_l,v_m\",1,(-1)^(t[1])*2,+(-1)^(t[2
])*3,(-1)^(t[3])*4,5); \n   end if;\nend do:\n\n#checking for |v[i]+v[
1]+v[2]+v[3]+v[4]+v[5]|^2>=|v[i]|^2;\nfor s from 0 by 1 to 1 do\n   if
 (Norm(2*v[1]+(-1)^s*v[2]+v[3]+v[4]+v[5],2)^2 < Norm(v[1],2)^2) then \+
\n      print(\"not satisfied\",\"2*v_1\") \n   end if;\nend do;\nfor \+
s from 2 by 1 to 3 do\n   t:=convert(s,base,2):\n   if (Norm(2*v[1]+(-
1)^(t[1])*v[2]+(-1)^(t[2])*v[3]+v[4]+v[5],2)^2 < Norm(v[1],2)^2) then \+
\n      print(\"not satisfied\",\"2*v_1\") \n   end if; \nend do:\nfor
 s from 4 by 1 to 7 do\n   t:=convert(s,base,2):\n   if (Norm(2*v[1]+(
-1)^(t[1])*v[2]+(-1)^(t[2])*v[3]+(-1)^(t[3])*v[4]+v[5],2)^2 < Norm(v[1
],2)^2) then \n      print(\"not satisfied\",\"2*v_1\") \n   end if; \+
\nend do:\nfor s from 8 by 1 to 15 do\n   t:=convert(s,base,2):\n   if
 (Norm(2*v[1]+(-1)^(t[1])*v[2]+(-1)^(t[2])*v[3]+(-1)^(t[3])*v[4]+(-1)^
(t[4])*v[5],2)^2 < Norm(v[1],2)^2) then \n      print(\"not satisfied
\",\"2*v_1\") \n   end if; \nend do:\nfor s from 0 by 1 to 1 do\n   if
 (Norm(v[1]+(-1)^s*2*v[2]+v[3]+v[4]+v[5],2)^2 < Norm(v[2],2)^2) then \+
\n      print(\"not satisfied\",\"2*v_2\") \n   end if;\nend do;\nfor \+
s from 2 by 1 to 3 do\n   t:=convert(s,base,2):\n   if (Norm(v[1]+(-1)
^(t[1])*2*v[2]+(-1)^(t[2])*v[3]+v[4]+v[5],2)^2 < Norm(v[2],2)^2) then \+
\n      print(\"not satisfied\",\"2*v_2\") \n   end if; \nend do:\nfor
 s from 4 by 1 to 7 do\n   t:=convert(s,base,2):\n   if (Norm(v[1]+(-1
)^(t[1])*2*v[2]+(-1)^(t[2])*v[3]+(-1)^(t[3])*v[4]+v[5],2)^2 < Norm(v[2
],2)^2) then \n      print(\"not satisfied\",\"2*v_2\") \n   end if; \+
\nend do:\nfor s from 8 by 1 to 15 do\n   t:=convert(s,base,2):\n   if
 (Norm(v[1]+(-1)^(t[1])*2*v[2]+(-1)^(t[2])*v[3]+(-1)^(t[3])*v[4]+(-1)^
(t[4])*v[5],2)^2 < Norm(v[2],2)^2) then \n      print(\"not satisfied
\",\"2*v_2\") \n   end if; \nend do:\nfor s from 0 by 1 to 1 do\n   if
 (Norm(v[1]+(-1)^s*v[2]+2*v[3]+v[4]+v[5],2)^2 < Norm(v[3],2)^2) then \+
\n      print(\"not satisfied\",\"2*v_3\") \n   end if;\nend do;\nfor \+
s from 2 by 1 to 3 do\n   t:=convert(s,base,2):\n   if (Norm(v[1]+(-1)
^(t[1])*v[2]+(-1)^(t[2])*2*v[3]+v[4]+v[5],2)^2 < Norm(v[3],2)^2) then \+
\n      print(\"not satisfied\",\"2*v_3\") \n   end if; \nend do:\nfor
 s from 4 by 1 to 7 do\n   t:=convert(s,base,2):\n   if (Norm(v[1]+(-1
)^(t[1])*v[2]+(-1)^(t[2])*2*v[3]+(-1)^(t[3])*v[4]+v[5],2)^2 < Norm(v[3
],2)^2) then \n      print(\"not satisfied\",\"2*v_3\") \n   end if; \+
\nend do:\nfor s from 8 by 1 to 15 do\n   t:=convert(s,base,2):\n   if
 (Norm(v[1]+(-1)^(t[1])*v[2]+(-1)^(t[2])*2*v[3]+(-1)^(t[3])*v[4]+(-1)^
(t[4])*v[5],2)^2 < Norm(v[3],2)^2) then \n      print(\"not satisfied
\",\"2*v_3\") \n   end if; \nend do:\nfor s from 0 by 1 to 1 do\n   if
 (Norm(v[1]+(-1)^s*v[2]+v[3]+2*v[4]+v[5],2)^2 < Norm(v[4],2)^2) then \+
\n      print(\"not satisfied\",\"2*v_4\") \n   end if;\nend do;\nfor \+
s from 2 by 1 to 3 do\n   t:=convert(s,base,2):\n   if (Norm(v[1]+(-1)
^(t[1])*v[2]+(-1)^(t[2])*v[3]+2*v[4]+v[5],2)^2 < Norm(v[4],2)^2) then \+
\n      print(\"not satisfied\",\"2*v_4\") \n   end if; \nend do:\nfor
 s from 4 by 1 to 7 do\n   t:=convert(s,base,2):\n   if (Norm(v[1]+(-1
)^(t[1])*v[2]+(-1)^(t[2])*v[3]+(-1)^(t[3])*2*v[4]+v[5],2)^2 < Norm(v[4
],2)^2) then \n      print(\"not satisfied\",\"2*v_4\") \n   end if; \+
\nend do:\nfor s from 8 by 1 to 15 do\n   t:=convert(s,base,2):\n   if
 (Norm(v[1]+(-1)^(t[1])*v[2]+(-1)^(t[2])*v[3]+(-1)^(t[3])*2*v[4]+(-1)^
(t[4])*v[5],2)^2 < Norm(v[4],2)^2) then \n      print(\"not satisfied
\",\"2*v_4\") \n   end if; \nend do:\nfor s from 0 by 1 to 1 do\n   if
 (Norm(v[1]+(-1)^s*v[2]+v[3]+v[4]+2*v[5],2)^2 < Norm(v[5],2)^2) then \+
\n      print(\"not satisfied\",\"2*v_5\") \n   end if;\nend do;\nfor \+
s from 2 by 1 to 3 do\n   t:=convert(s,base,2):\n   if (Norm(v[1]+(-1)
^(t[1])*v[2]+(-1)^(t[2])*v[3]+v[4]+2*v[5],2)^2 < Norm(v[5],2)^2) then \+
\n      print(\"not satisfied\",\"2*v_5\") \n   end if; \nend do:\nfor
 s from 4 by 1 to 7 do\n   t:=convert(s,base,2):\n   if (Norm(v[1]+(-1
)^(t[1])*v[2]+(-1)^(t[2])*v[3]+(-1)^(t[3])*v[4]+2*v[5],2)^2 < Norm(v[5
],2)^2) then \n      print(\"not satisfied\",\"2*v_5\") \n   end if; \+
\nend do:\nfor s from 8 by 1 to 15 do\n   t:=convert(s,base,2):\n   if
 (Norm(v[1]+(-1)^(t[1])*v[2]+(-1)^(t[2])*v[3]+(-1)^(t[3])*v[4]+(-1)^(t
[4])*2*v[5],2)^2 < Norm(v[5],2)^2) then \n      print(\"not satisfied
\",\"2*v_5\") \n   end if; \nend do:" }}{PARA 11 "" 1 "" {XPPMATH 20 "
6&Q.not~satisfied6\"Q(v_i,v_jF$\"\"#\"\"$" }}}{EXCHG {PARA 0 "> " 0 "
" {MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 365 "v[1]
:=Vector([4,-1,-1,-1,-1]):\nv[2]:=Vector([-1,4,-1,-1,-1]):\nv[3]:=Vect
or([-1,-1,4,-1,-1]):\nv[4]:=Vector([1,-1,1,4,1]):\nv[5]:=Vector([-2,-2
,-2,2,-2]):\nv[1],v[2],v[3],v[4],v[5];\nprint(\"|v[1]|^2\"=Norm(v[1],2
)^2);\n#checking for decreasing order;\nfor i from 1 by 1 to 4 do \n  \+
 if (Norm(v[i],2)^2 > Norm(v[i+1],2)^2) then print(\"not satisfied\",(
i,i+1)) end if; \nend do;" }}{PARA 11 "" 1 "" {XPPMATH 20 "6'-%'RTABLE
G6%\"*wit6#-%'MATRIXG6#7'7#\"\"%7#!\"\"F-F-F-&%'VectorG6#%'columnG-F$6
%\"*Sjt6#-F(6#7'F-F+F-F-F-F/-F$6%\"*/kt6#-F(6#7'F-F-F+F-F-F/-F$6%\"*ok
t6#-F(6#7'7#\"\"\"F-FEF+FEF/-F$6%\"*Klt6#-F(6#7'7#!\"#FMFM7#\"\"#FMF/
" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#/Q)|grv[1]|gr^26\"\"#?" }}}{EXCHG 
{PARA 0 "> " 0 "" {MPLTEXT 1 0 6469 "#checking for 2|v[j].v[i]|=<|v[i]
|^2;\nL2:=choose(5, 2):\nfor i from 1 by 1 to numbcomb(5, 2) do\n   if
 (2*abs(v[L2[i][2]].v[L2[i][1]]) > Norm(v[L2[i][1]],2)^2) then \n     \+
 print(\"not satisfied\",\"v_i,v_j\",L2[i][1],L2[i][2]) \n   end if;\n
end do;\n#checking for 2|v[k].(v[i]+v[j])|=<|v[i]+v[j]|^2;\nL3:=choose
(5, 3):\nfor s from 0 by 1 to 1 do\n   for i from 1 by 1 to numbcomb(5
, 3) do\n      if (2*abs(v[L3[i][3]].(v[L3[i][1]]+(-1)^s*v[L3[i][2]]))
 > Norm(v[L3[i][1]]+(-1)^s*v[L3[i][2]],2)^2) then \n         print(\"n
ot satisfied\",\"v_i,v_j,v_k\",L3[i][1],(-1)^s*L3[i][2],L3[i][3]); \n \+
     end if;\n   end do;\nend do;\n#checking for 2|v[l].(v[i]+v[j]+v[k
])|=<|v[i]+v[j]+v[k]|^2;\nL4:=choose(5, 4):\nfor s from 0 by 1 to 1 do
\n   for i from 1 by 1 to numbcomb(5, 4) do\n      if (2*abs(v[L4[i][4
]].(v[L4[i][1]]+(-1)^s*v[L4[i][2]]+(-1)^0*v[L4[i][3]])) >\n         No
rm(v[L4[i][1]]+(-1)^s*v[L4[i][2]]+(-1)^0*v[L4[i][3]],2)^2) then \n    \+
     print(\"not satisfied\",\"v_i,v_j,v_k,v_l\",L4[i][1],(-1)^s*L4[i]
[2],(-1)^0*L4[i][3],L4[i][4]); \n      end if;\n   end do;\nend do;\nf
or s from 2 by 1 to 3 do\n   t:=convert(s,base,2):\n   for i from 1 by
 1 to numbcomb(5, 4) do\n      if (2*abs(v[L4[i][4]].(v[L4[i][1]]+(-1)
^(t[1])*v[L4[i][2]]+(-1)^(t[2])*v[L4[i][3]])) >\n         Norm(v[L4[i]
[1]]+(-1)^(t[1])*v[L4[i][2]]+(-1)^(t[2])*v[L4[i][3]],2)^2) then \n    \+
     print(\"not satisfied\",\"v_i,v_j,v_k,v_l\",L4[i][1],(-1)^(t[1])*
L4[i][2],(-1)^(t[2])*L4[i][3],L4[i][4]); \n      end if;\n   end do;\n
end do:\n#checking for 2|v[m].(v[i]+v[j]+v[k]+v[l])|=<|v[i]+v[j]+v[k]+
v[l]|^2;\nfor s from 0 by 1 to 1 do\n   if (2*abs(v[5].(v[1]+(-1)^s*v[
2]+(-1)^0*v[3]+(-1)^0*v[4])) > \n       Norm(v[1]+(-1)^s*v[2]+(-1)^0*v
[3]+(-1)^0*v[4],2)^2) then \n      print(\"not satisfied\",\"v_i,v_j,v
_k,v_l,v_m\",1,(-1)^s*2,3,4,5); \n   end if;\nend do;\nfor s from 2 by
 1 to 3 do\n   t:=convert(s,base,2):\n   if (2*abs(v[5].(v[1]+(-1)^(t[
1])*v[2]+(-1)^(t[2])*v[3]+(-1)^0*v[4])) > \n       Norm(v[1]+(-1)^(t[1
])*v[2]+(-1)^(t[2])*v[3]+(-1)^0*v[4],2)^2) then \n      print(\"not sa
tisfied\",\"v_i,v_j,v_k,v_l,v_m\",1,+(-1)^(t[1])*2,(-1)^(t[2])*3,(-1)^
0*4,5); \n   end if;\nend do:\nfor s from 4 by 1 to 7 do\n   t:=conver
t(s,base,2):\n   if (2*abs(v[5].(v[1]+(-1)^(t[1])*v[2]+(-1)^(t[2])*v[3
]+(-1)^(t[3])*v[4])) > \n       Norm(v[1]+(-1)^(t[1])*v[2]+(-1)^(t[2])
*v[3]+(-1)^(t[3])*v[4],2)^2) then \n      print(\"not satisfied\",\"v_
i,v_j,v_k,v_l,v_m\",1,(-1)^(t[1])*2,+(-1)^(t[2])*3,(-1)^(t[3])*4,5); \+
\n   end if;\nend do:\n#checking for |v[i]+v[1]+v[2]+v[3]+v[4]+v[5]|^2
>=|v[i]|^2;\nfor s from 0 by 1 to 1 do\n   if (Norm(2*v[1]+(-1)^s*v[2]
+v[3]+v[4]+v[5],2)^2 < Norm(v[1],2)^2) then \n      print(\"not satisf
ied\",\"2*v_1\") \n   end if;\nend do;\nfor s from 2 by 1 to 3 do\n   \+
t:=convert(s,base,2):\n   if (Norm(2*v[1]+(-1)^(t[1])*v[2]+(-1)^(t[2])
*v[3]+v[4]+v[5],2)^2 < Norm(v[1],2)^2) then \n      print(\"not satisf
ied\",\"2*v_1\") \n   end if; \nend do:\nfor s from 4 by 1 to 7 do\n  \+
 t:=convert(s,base,2):\n   if (Norm(2*v[1]+(-1)^(t[1])*v[2]+(-1)^(t[2]
)*v[3]+(-1)^(t[3])*v[4]+v[5],2)^2 < Norm(v[1],2)^2) then \n      print
(\"not satisfied\",\"2*v_1\") \n   end if; \nend do:\nfor s from 8 by \+
1 to 15 do\n   t:=convert(s,base,2):\n   if (Norm(2*v[1]+(-1)^(t[1])*v
[2]+(-1)^(t[2])*v[3]+(-1)^(t[3])*v[4]+(-1)^(t[4])*v[5],2)^2 < Norm(v[1
],2)^2) then \n      print(\"not satisfied\",\"2*v_1\") \n   end if; \+
\nend do:\nfor s from 0 by 1 to 1 do\n   if (Norm(v[1]+(-1)^s*2*v[2]+v
[3]+v[4]+v[5],2)^2 < Norm(v[2],2)^2) then \n      print(\"not satisfie
d\",\"2*v_2\") \n   end if;\nend do;\nfor s from 2 by 1 to 3 do\n   t:
=convert(s,base,2):\n   if (Norm(v[1]+(-1)^(t[1])*2*v[2]+(-1)^(t[2])*v
[3]+v[4]+v[5],2)^2 < Norm(v[2],2)^2) then \n      print(\"not satisfie
d\",\"2*v_2\") \n   end if; \nend do:\nfor s from 4 by 1 to 7 do\n   t
:=convert(s,base,2):\n   if (Norm(v[1]+(-1)^(t[1])*2*v[2]+(-1)^(t[2])*
v[3]+(-1)^(t[3])*v[4]+v[5],2)^2 < Norm(v[2],2)^2) then \n      print(
\"not satisfied\",\"2*v_2\") \n   end if; \nend do:\nfor s from 8 by 1
 to 15 do\n   t:=convert(s,base,2):\n   if (Norm(v[1]+(-1)^(t[1])*2*v[
2]+(-1)^(t[2])*v[3]+(-1)^(t[3])*v[4]+(-1)^(t[4])*v[5],2)^2 < Norm(v[2]
,2)^2) then \n      print(\"not satisfied\",\"2*v_2\") \n   end if; \n
end do:\nfor s from 0 by 1 to 1 do\n   if (Norm(v[1]+(-1)^s*v[2]+2*v[3
]+v[4]+v[5],2)^2 < Norm(v[3],2)^2) then \n      print(\"not satisfied
\",\"2*v_3\") \n   end if;\nend do;\nfor s from 2 by 1 to 3 do\n   t:=
convert(s,base,2):\n   if (Norm(v[1]+(-1)^(t[1])*v[2]+(-1)^(t[2])*2*v[
3]+v[4]+v[5],2)^2 < Norm(v[3],2)^2) then \n      print(\"not satisfied
\",\"2*v_3\") \n   end if; \nend do:\nfor s from 4 by 1 to 7 do\n   t:
=convert(s,base,2):\n   if (Norm(v[1]+(-1)^(t[1])*v[2]+(-1)^(t[2])*2*v
[3]+(-1)^(t[3])*v[4]+v[5],2)^2 < Norm(v[3],2)^2) then \n      print(\"
not satisfied\",\"2*v_3\") \n   end if; \nend do:\nfor s from 8 by 1 t
o 15 do\n   t:=convert(s,base,2):\n   if (Norm(v[1]+(-1)^(t[1])*v[2]+(
-1)^(t[2])*2*v[3]+(-1)^(t[3])*v[4]+(-1)^(t[4])*v[5],2)^2 < Norm(v[3],2
)^2) then \n      print(\"not satisfied\",\"2*v_3\") \n   end if; \nen
d do:\nfor s from 0 by 1 to 1 do\n   if (Norm(v[1]+(-1)^s*v[2]+v[3]+2*
v[4]+v[5],2)^2 < Norm(v[4],2)^2) then \n      print(\"not satisfied\",
\"2*v_4\") \n   end if;\nend do;\nfor s from 2 by 1 to 3 do\n   t:=con
vert(s,base,2):\n   if (Norm(v[1]+(-1)^(t[1])*v[2]+(-1)^(t[2])*v[3]+2*
v[4]+v[5],2)^2 < Norm(v[4],2)^2) then \n      print(\"not satisfied\",
\"2*v_4\") \n   end if; \nend do:\nfor s from 4 by 1 to 7 do\n   t:=co
nvert(s,base,2):\n   if (Norm(v[1]+(-1)^(t[1])*v[2]+(-1)^(t[2])*v[3]+(
-1)^(t[3])*2*v[4]+v[5],2)^2 < Norm(v[4],2)^2) then \n      print(\"not
 satisfied\",\"2*v_4\") \n   end if; \nend do:\nfor s from 8 by 1 to 1
5 do\n   t:=convert(s,base,2):\n   if (Norm(v[1]+(-1)^(t[1])*v[2]+(-1)
^(t[2])*v[3]+(-1)^(t[3])*2*v[4]+(-1)^(t[4])*v[5],2)^2 < Norm(v[4],2)^2
) then \n      print(\"not satisfied\",\"2*v_4\") \n   end if; \nend d
o:\nfor s from 0 by 1 to 1 do\n   if (Norm(v[1]+(-1)^s*v[2]+v[3]+v[4]+
2*v[5],2)^2 < Norm(v[5],2)^2) then \n      print(\"not satisfied\",\"2
*v_5\") \n   end if;\nend do;\nfor s from 2 by 1 to 3 do\n   t:=conver
t(s,base,2):\n   if (Norm(v[1]+(-1)^(t[1])*v[2]+(-1)^(t[2])*v[3]+v[4]+
2*v[5],2)^2 < Norm(v[5],2)^2) then \n      print(\"not satisfied\",\"2
*v_5\") \n   end if; \nend do:\nfor s from 4 by 1 to 7 do\n   t:=conve
rt(s,base,2):\n   if (Norm(v[1]+(-1)^(t[1])*v[2]+(-1)^(t[2])*v[3]+(-1)
^(t[3])*v[4]+2*v[5],2)^2 < Norm(v[5],2)^2) then \n      print(\"not sa
tisfied\",\"2*v_5\") \n   end if; \nend do:\nfor s from 8 by 1 to 15 d
o\n   t:=convert(s,base,2):\n   if (Norm(v[1]+(-1)^(t[1])*v[2]+(-1)^(t
[2])*v[3]+(-1)^(t[3])*v[4]+(-1)^(t[4])*2*v[5],2)^2 < Norm(v[5],2)^2) t
hen \n      print(\"not satisfied\",\"2*v_5\") \n   end if; \nend do:
" }}{PARA 11 "" 1 "" {XPPMATH 20 "6&Q.not~satisfied6\"Q(v_i,v_jF$\"\"#
\"\"%" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 
0 "> " 0 "" {MPLTEXT 1 0 365 "v[1]:=Vector([4,-1,-1,-1,-1]):\nv[2]:=Ve
ctor([1,4,1,1,1]):\nv[3]:=Vector([-1,-1,4,-1,-1]):\nv[4]:=Vector([-1,-
1,-1,4,-1]):\nv[5]:=Vector([-2,-2,-2,-2,-2]):\nv[1],v[2],v[3],v[4],v[5
];\nprint(\"|v[1]|^2\"=Norm(v[1],2)^2);\n#checking for decreasing orde
r;\nfor i from 1 by 1 to 4 do \n   if (Norm(v[i],2)^2 > Norm(v[i+1],2)
^2) then print(\"not satisfied\",(i,i+1)) end if; \nend do;" }}{PARA 
11 "" 1 "" {XPPMATH 20 "6'-%'RTABLEG6%\"*?3QB#-%'MATRIXG6#7'7#\"\"%7#!
\"\"F-F-F-&%'VectorG6#%'columnG-F$6%\"*%)3QB#-F(6#7'7#\"\"\"F+F9F9F9F/
-F$6%\"*[4QB#-F(6#7'F-F-F+F-F-F/-F$6%\"*75QB#-F(6#7'F-F-F-F+F-F/-F$6%
\"*w5QB#-F(6#7'7#!\"#FMFMFMFMF/" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#/Q)
|grv[1]|gr^26\"\"#?" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 6469 "#c
hecking for 2|v[j].v[i]|=<|v[i]|^2;\nL2:=choose(5, 2):\nfor i from 1 b
y 1 to numbcomb(5, 2) do\n   if (2*abs(v[L2[i][2]].v[L2[i][1]]) > Norm
(v[L2[i][1]],2)^2) then \n      print(\"not satisfied\",\"v_i,v_j\",L2
[i][1],L2[i][2]) \n   end if;\nend do;\n#checking for 2|v[k].(v[i]+v[j
])|=<|v[i]+v[j]|^2;\nL3:=choose(5, 3):\nfor s from 0 by 1 to 1 do\n   \+
for i from 1 by 1 to numbcomb(5, 3) do\n      if (2*abs(v[L3[i][3]].(v
[L3[i][1]]+(-1)^s*v[L3[i][2]])) > Norm(v[L3[i][1]]+(-1)^s*v[L3[i][2]],
2)^2) then \n         print(\"not satisfied\",\"v_i,v_j,v_k\",L3[i][1]
,(-1)^s*L3[i][2],L3[i][3]); \n      end if;\n   end do;\nend do;\n#che
cking for 2|v[l].(v[i]+v[j]+v[k])|=<|v[i]+v[j]+v[k]|^2;\nL4:=choose(5,
 4):\nfor s from 0 by 1 to 1 do\n   for i from 1 by 1 to numbcomb(5, 4
) do\n      if (2*abs(v[L4[i][4]].(v[L4[i][1]]+(-1)^s*v[L4[i][2]]+(-1)
^0*v[L4[i][3]])) >\n         Norm(v[L4[i][1]]+(-1)^s*v[L4[i][2]]+(-1)^
0*v[L4[i][3]],2)^2) then \n         print(\"not satisfied\",\"v_i,v_j,
v_k,v_l\",L4[i][1],(-1)^s*L4[i][2],(-1)^0*L4[i][3],L4[i][4]); \n      \+
end if;\n   end do;\nend do;\nfor s from 2 by 1 to 3 do\n   t:=convert
(s,base,2):\n   for i from 1 by 1 to numbcomb(5, 4) do\n      if (2*ab
s(v[L4[i][4]].(v[L4[i][1]]+(-1)^(t[1])*v[L4[i][2]]+(-1)^(t[2])*v[L4[i]
[3]])) >\n         Norm(v[L4[i][1]]+(-1)^(t[1])*v[L4[i][2]]+(-1)^(t[2]
)*v[L4[i][3]],2)^2) then \n         print(\"not satisfied\",\"v_i,v_j,
v_k,v_l\",L4[i][1],(-1)^(t[1])*L4[i][2],(-1)^(t[2])*L4[i][3],L4[i][4])
; \n      end if;\n   end do;\nend do:\n#checking for 2|v[m].(v[i]+v[j
]+v[k]+v[l])|=<|v[i]+v[j]+v[k]+v[l]|^2;\nfor s from 0 by 1 to 1 do\n  \+
 if (2*abs(v[5].(v[1]+(-1)^s*v[2]+(-1)^0*v[3]+(-1)^0*v[4])) > \n      \+
 Norm(v[1]+(-1)^s*v[2]+(-1)^0*v[3]+(-1)^0*v[4],2)^2) then \n      prin
t(\"not satisfied\",\"v_i,v_j,v_k,v_l,v_m\",1,(-1)^s*2,3,4,5); \n   en
d if;\nend do;\nfor s from 2 by 1 to 3 do\n   t:=convert(s,base,2):\n \+
  if (2*abs(v[5].(v[1]+(-1)^(t[1])*v[2]+(-1)^(t[2])*v[3]+(-1)^0*v[4]))
 > \n       Norm(v[1]+(-1)^(t[1])*v[2]+(-1)^(t[2])*v[3]+(-1)^0*v[4],2)
^2) then \n      print(\"not satisfied\",\"v_i,v_j,v_k,v_l,v_m\",1,+(-
1)^(t[1])*2,(-1)^(t[2])*3,(-1)^0*4,5); \n   end if;\nend do:\nfor s fr
om 4 by 1 to 7 do\n   t:=convert(s,base,2):\n   if (2*abs(v[5].(v[1]+(
-1)^(t[1])*v[2]+(-1)^(t[2])*v[3]+(-1)^(t[3])*v[4])) > \n       Norm(v[
1]+(-1)^(t[1])*v[2]+(-1)^(t[2])*v[3]+(-1)^(t[3])*v[4],2)^2) then \n   \+
   print(\"not satisfied\",\"v_i,v_j,v_k,v_l,v_m\",1,(-1)^(t[1])*2,+(-
1)^(t[2])*3,(-1)^(t[3])*4,5); \n   end if;\nend do:\n#checking for |v[
i]+v[1]+v[2]+v[3]+v[4]+v[5]|^2>=|v[i]|^2;\nfor s from 0 by 1 to 1 do\n
   if (Norm(2*v[1]+(-1)^s*v[2]+v[3]+v[4]+v[5],2)^2 < Norm(v[1],2)^2) t
hen \n      print(\"not satisfied\",\"2*v_1\") \n   end if;\nend do;\n
for s from 2 by 1 to 3 do\n   t:=convert(s,base,2):\n   if (Norm(2*v[1
]+(-1)^(t[1])*v[2]+(-1)^(t[2])*v[3]+v[4]+v[5],2)^2 < Norm(v[1],2)^2) t
hen \n      print(\"not satisfied\",\"2*v_1\") \n   end if; \nend do:
\nfor s from 4 by 1 to 7 do\n   t:=convert(s,base,2):\n   if (Norm(2*v
[1]+(-1)^(t[1])*v[2]+(-1)^(t[2])*v[3]+(-1)^(t[3])*v[4]+v[5],2)^2 < Nor
m(v[1],2)^2) then \n      print(\"not satisfied\",\"2*v_1\") \n   end \+
if; \nend do:\nfor s from 8 by 1 to 15 do\n   t:=convert(s,base,2):\n \+
  if (Norm(2*v[1]+(-1)^(t[1])*v[2]+(-1)^(t[2])*v[3]+(-1)^(t[3])*v[4]+(
-1)^(t[4])*v[5],2)^2 < Norm(v[1],2)^2) then \n      print(\"not satisf
ied\",\"2*v_1\") \n   end if; \nend do:\nfor s from 0 by 1 to 1 do\n  \+
 if (Norm(v[1]+(-1)^s*2*v[2]+v[3]+v[4]+v[5],2)^2 < Norm(v[2],2)^2) the
n \n      print(\"not satisfied\",\"2*v_2\") \n   end if;\nend do;\nfo
r s from 2 by 1 to 3 do\n   t:=convert(s,base,2):\n   if (Norm(v[1]+(-
1)^(t[1])*2*v[2]+(-1)^(t[2])*v[3]+v[4]+v[5],2)^2 < Norm(v[2],2)^2) the
n \n      print(\"not satisfied\",\"2*v_2\") \n   end if; \nend do:\nf
or s from 4 by 1 to 7 do\n   t:=convert(s,base,2):\n   if (Norm(v[1]+(
-1)^(t[1])*2*v[2]+(-1)^(t[2])*v[3]+(-1)^(t[3])*v[4]+v[5],2)^2 < Norm(v
[2],2)^2) then \n      print(\"not satisfied\",\"2*v_2\") \n   end if;
 \nend do:\nfor s from 8 by 1 to 15 do\n   t:=convert(s,base,2):\n   i
f (Norm(v[1]+(-1)^(t[1])*2*v[2]+(-1)^(t[2])*v[3]+(-1)^(t[3])*v[4]+(-1)
^(t[4])*v[5],2)^2 < Norm(v[2],2)^2) then \n      print(\"not satisfied
\",\"2*v_2\") \n   end if; \nend do:\nfor s from 0 by 1 to 1 do\n   if
 (Norm(v[1]+(-1)^s*v[2]+2*v[3]+v[4]+v[5],2)^2 < Norm(v[3],2)^2) then \+
\n      print(\"not satisfied\",\"2*v_3\") \n   end if;\nend do;\nfor \+
s from 2 by 1 to 3 do\n   t:=convert(s,base,2):\n   if (Norm(v[1]+(-1)
^(t[1])*v[2]+(-1)^(t[2])*2*v[3]+v[4]+v[5],2)^2 < Norm(v[3],2)^2) then \+
\n      print(\"not satisfied\",\"2*v_3\") \n   end if; \nend do:\nfor
 s from 4 by 1 to 7 do\n   t:=convert(s,base,2):\n   if (Norm(v[1]+(-1
)^(t[1])*v[2]+(-1)^(t[2])*2*v[3]+(-1)^(t[3])*v[4]+v[5],2)^2 < Norm(v[3
],2)^2) then \n      print(\"not satisfied\",\"2*v_3\") \n   end if; \+
\nend do:\nfor s from 8 by 1 to 15 do\n   t:=convert(s,base,2):\n   if
 (Norm(v[1]+(-1)^(t[1])*v[2]+(-1)^(t[2])*2*v[3]+(-1)^(t[3])*v[4]+(-1)^
(t[4])*v[5],2)^2 < Norm(v[3],2)^2) then \n      print(\"not satisfied
\",\"2*v_3\") \n   end if; \nend do:\nfor s from 0 by 1 to 1 do\n   if
 (Norm(v[1]+(-1)^s*v[2]+v[3]+2*v[4]+v[5],2)^2 < Norm(v[4],2)^2) then \+
\n      print(\"not satisfied\",\"2*v_4\") \n   end if;\nend do;\nfor \+
s from 2 by 1 to 3 do\n   t:=convert(s,base,2):\n   if (Norm(v[1]+(-1)
^(t[1])*v[2]+(-1)^(t[2])*v[3]+2*v[4]+v[5],2)^2 < Norm(v[4],2)^2) then \+
\n      print(\"not satisfied\",\"2*v_4\") \n   end if; \nend do:\nfor
 s from 4 by 1 to 7 do\n   t:=convert(s,base,2):\n   if (Norm(v[1]+(-1
)^(t[1])*v[2]+(-1)^(t[2])*v[3]+(-1)^(t[3])*2*v[4]+v[5],2)^2 < Norm(v[4
],2)^2) then \n      print(\"not satisfied\",\"2*v_4\") \n   end if; \+
\nend do:\nfor s from 8 by 1 to 15 do\n   t:=convert(s,base,2):\n   if
 (Norm(v[1]+(-1)^(t[1])*v[2]+(-1)^(t[2])*v[3]+(-1)^(t[3])*2*v[4]+(-1)^
(t[4])*v[5],2)^2 < Norm(v[4],2)^2) then \n      print(\"not satisfied
\",\"2*v_4\") \n   end if; \nend do:\nfor s from 0 by 1 to 1 do\n   if
 (Norm(v[1]+(-1)^s*v[2]+v[3]+v[4]+2*v[5],2)^2 < Norm(v[5],2)^2) then \+
\n      print(\"not satisfied\",\"2*v_5\") \n   end if;\nend do;\nfor \+
s from 2 by 1 to 3 do\n   t:=convert(s,base,2):\n   if (Norm(v[1]+(-1)
^(t[1])*v[2]+(-1)^(t[2])*v[3]+v[4]+2*v[5],2)^2 < Norm(v[5],2)^2) then \+
\n      print(\"not satisfied\",\"2*v_5\") \n   end if; \nend do:\nfor
 s from 4 by 1 to 7 do\n   t:=convert(s,base,2):\n   if (Norm(v[1]+(-1
)^(t[1])*v[2]+(-1)^(t[2])*v[3]+(-1)^(t[3])*v[4]+2*v[5],2)^2 < Norm(v[5
],2)^2) then \n      print(\"not satisfied\",\"2*v_5\") \n   end if; \+
\nend do:\nfor s from 8 by 1 to 15 do\n   t:=convert(s,base,2):\n   if
 (Norm(v[1]+(-1)^(t[1])*v[2]+(-1)^(t[2])*v[3]+(-1)^(t[3])*v[4]+(-1)^(t
[4])*2*v[5],2)^2 < Norm(v[5],2)^2) then \n      print(\"not satisfied
\",\"2*v_5\") \n   end if; \nend do:" }}{PARA 11 "" 1 "" {XPPMATH 20 "
6&Q.not~satisfied6\"Q(v_i,v_jF$\"\"#\"\"&" }}}{EXCHG {PARA 0 "> " 0 "
" {MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 365 "v[1]
:=Vector([4,-1,-1,-1,-1]):\nv[2]:=Vector([-1,4,-1,-1,-1]):\nv[3]:=Vect
or([-1,-1,4,-1,-1]):\nv[4]:=Vector([1,1,-1,4,1]):\nv[5]:=Vector([-2,-2
,-2,2,-2]):\nv[1],v[2],v[3],v[4],v[5];\nprint(\"|v[1]|^2\"=Norm(v[1],2
)^2);\n#checking for decreasing order;\nfor i from 1 by 1 to 4 do \n  \+
 if (Norm(v[i],2)^2 > Norm(v[i+1],2)^2) then print(\"not satisfied\",(
i,i+1)) end if; \nend do;" }}{PARA 11 "" 1 "" {XPPMATH 20 "6'-%'RTABLE
G6%\"*;![q@-%'MATRIXG6#7'7#\"\"%7#!\"\"F-F-F-&%'VectorG6#%'columnG-F$6
%\"*!3[q@-F(6#7'F-F+F-F-F-F/-F$6%\"*W\"[q@-F(6#7'F-F-F+F-F-F/-F$6%\"*3
#[q@-F(6#7'7#\"\"\"FEF-F+FEF/-F$6%\"*s#[q@-F(6#7'7#!\"#FMFM7#\"\"#FMF/
" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#/Q)|grv[1]|gr^26\"\"#?" }}}{EXCHG 
{PARA 0 "> " 0 "" {MPLTEXT 1 0 6469 "#checking for 2|v[j].v[i]|=<|v[i]
|^2;\nL2:=choose(5, 2):\nfor i from 1 by 1 to numbcomb(5, 2) do\n   if
 (2*abs(v[L2[i][2]].v[L2[i][1]]) > Norm(v[L2[i][1]],2)^2) then \n     \+
 print(\"not satisfied\",\"v_i,v_j\",L2[i][1],L2[i][2]) \n   end if;\n
end do;\n#checking for 2|v[k].(v[i]+v[j])|=<|v[i]+v[j]|^2;\nL3:=choose
(5, 3):\nfor s from 0 by 1 to 1 do\n   for i from 1 by 1 to numbcomb(5
, 3) do\n      if (2*abs(v[L3[i][3]].(v[L3[i][1]]+(-1)^s*v[L3[i][2]]))
 > Norm(v[L3[i][1]]+(-1)^s*v[L3[i][2]],2)^2) then \n         print(\"n
ot satisfied\",\"v_i,v_j,v_k\",L3[i][1],(-1)^s*L3[i][2],L3[i][3]); \n \+
     end if;\n   end do;\nend do;\n#checking for 2|v[l].(v[i]+v[j]+v[k
])|=<|v[i]+v[j]+v[k]|^2;\nL4:=choose(5, 4):\nfor s from 0 by 1 to 1 do
\n   for i from 1 by 1 to numbcomb(5, 4) do\n      if (2*abs(v[L4[i][4
]].(v[L4[i][1]]+(-1)^s*v[L4[i][2]]+(-1)^0*v[L4[i][3]])) >\n         No
rm(v[L4[i][1]]+(-1)^s*v[L4[i][2]]+(-1)^0*v[L4[i][3]],2)^2) then \n    \+
     print(\"not satisfied\",\"v_i,v_j,v_k,v_l\",L4[i][1],(-1)^s*L4[i]
[2],(-1)^0*L4[i][3],L4[i][4]); \n      end if;\n   end do;\nend do;\nf
or s from 2 by 1 to 3 do\n   t:=convert(s,base,2):\n   for i from 1 by
 1 to numbcomb(5, 4) do\n      if (2*abs(v[L4[i][4]].(v[L4[i][1]]+(-1)
^(t[1])*v[L4[i][2]]+(-1)^(t[2])*v[L4[i][3]])) >\n         Norm(v[L4[i]
[1]]+(-1)^(t[1])*v[L4[i][2]]+(-1)^(t[2])*v[L4[i][3]],2)^2) then \n    \+
     print(\"not satisfied\",\"v_i,v_j,v_k,v_l\",L4[i][1],(-1)^(t[1])*
L4[i][2],(-1)^(t[2])*L4[i][3],L4[i][4]); \n      end if;\n   end do;\n
end do:\n#checking for 2|v[m].(v[i]+v[j]+v[k]+v[l])|=<|v[i]+v[j]+v[k]+
v[l]|^2;\nfor s from 0 by 1 to 1 do\n   if (2*abs(v[5].(v[1]+(-1)^s*v[
2]+(-1)^0*v[3]+(-1)^0*v[4])) > \n       Norm(v[1]+(-1)^s*v[2]+(-1)^0*v
[3]+(-1)^0*v[4],2)^2) then \n      print(\"not satisfied\",\"v_i,v_j,v
_k,v_l,v_m\",1,(-1)^s*2,3,4,5); \n   end if;\nend do;\nfor s from 2 by
 1 to 3 do\n   t:=convert(s,base,2):\n   if (2*abs(v[5].(v[1]+(-1)^(t[
1])*v[2]+(-1)^(t[2])*v[3]+(-1)^0*v[4])) > \n       Norm(v[1]+(-1)^(t[1
])*v[2]+(-1)^(t[2])*v[3]+(-1)^0*v[4],2)^2) then \n      print(\"not sa
tisfied\",\"v_i,v_j,v_k,v_l,v_m\",1,+(-1)^(t[1])*2,(-1)^(t[2])*3,(-1)^
0*4,5); \n   end if;\nend do:\nfor s from 4 by 1 to 7 do\n   t:=conver
t(s,base,2):\n   if (2*abs(v[5].(v[1]+(-1)^(t[1])*v[2]+(-1)^(t[2])*v[3
]+(-1)^(t[3])*v[4])) > \n       Norm(v[1]+(-1)^(t[1])*v[2]+(-1)^(t[2])
*v[3]+(-1)^(t[3])*v[4],2)^2) then \n      print(\"not satisfied\",\"v_
i,v_j,v_k,v_l,v_m\",1,(-1)^(t[1])*2,+(-1)^(t[2])*3,(-1)^(t[3])*4,5); \+
\n   end if;\nend do:\n#checking for |v[i]+v[1]+v[2]+v[3]+v[4]+v[5]|^2
>=|v[i]|^2;\nfor s from 0 by 1 to 1 do\n   if (Norm(2*v[1]+(-1)^s*v[2]
+v[3]+v[4]+v[5],2)^2 < Norm(v[1],2)^2) then \n      print(\"not satisf
ied\",\"2*v_1\") \n   end if;\nend do;\nfor s from 2 by 1 to 3 do\n   \+
t:=convert(s,base,2):\n   if (Norm(2*v[1]+(-1)^(t[1])*v[2]+(-1)^(t[2])
*v[3]+v[4]+v[5],2)^2 < Norm(v[1],2)^2) then \n      print(\"not satisf
ied\",\"2*v_1\") \n   end if; \nend do:\nfor s from 4 by 1 to 7 do\n  \+
 t:=convert(s,base,2):\n   if (Norm(2*v[1]+(-1)^(t[1])*v[2]+(-1)^(t[2]
)*v[3]+(-1)^(t[3])*v[4]+v[5],2)^2 < Norm(v[1],2)^2) then \n      print
(\"not satisfied\",\"2*v_1\") \n   end if; \nend do:\nfor s from 8 by \+
1 to 15 do\n   t:=convert(s,base,2):\n   if (Norm(2*v[1]+(-1)^(t[1])*v
[2]+(-1)^(t[2])*v[3]+(-1)^(t[3])*v[4]+(-1)^(t[4])*v[5],2)^2 < Norm(v[1
],2)^2) then \n      print(\"not satisfied\",\"2*v_1\") \n   end if; \+
\nend do:\nfor s from 0 by 1 to 1 do\n   if (Norm(v[1]+(-1)^s*2*v[2]+v
[3]+v[4]+v[5],2)^2 < Norm(v[2],2)^2) then \n      print(\"not satisfie
d\",\"2*v_2\") \n   end if;\nend do;\nfor s from 2 by 1 to 3 do\n   t:
=convert(s,base,2):\n   if (Norm(v[1]+(-1)^(t[1])*2*v[2]+(-1)^(t[2])*v
[3]+v[4]+v[5],2)^2 < Norm(v[2],2)^2) then \n      print(\"not satisfie
d\",\"2*v_2\") \n   end if; \nend do:\nfor s from 4 by 1 to 7 do\n   t
:=convert(s,base,2):\n   if (Norm(v[1]+(-1)^(t[1])*2*v[2]+(-1)^(t[2])*
v[3]+(-1)^(t[3])*v[4]+v[5],2)^2 < Norm(v[2],2)^2) then \n      print(
\"not satisfied\",\"2*v_2\") \n   end if; \nend do:\nfor s from 8 by 1
 to 15 do\n   t:=convert(s,base,2):\n   if (Norm(v[1]+(-1)^(t[1])*2*v[
2]+(-1)^(t[2])*v[3]+(-1)^(t[3])*v[4]+(-1)^(t[4])*v[5],2)^2 < Norm(v[2]
,2)^2) then \n      print(\"not satisfied\",\"2*v_2\") \n   end if; \n
end do:\nfor s from 0 by 1 to 1 do\n   if (Norm(v[1]+(-1)^s*v[2]+2*v[3
]+v[4]+v[5],2)^2 < Norm(v[3],2)^2) then \n      print(\"not satisfied
\",\"2*v_3\") \n   end if;\nend do;\nfor s from 2 by 1 to 3 do\n   t:=
convert(s,base,2):\n   if (Norm(v[1]+(-1)^(t[1])*v[2]+(-1)^(t[2])*2*v[
3]+v[4]+v[5],2)^2 < Norm(v[3],2)^2) then \n      print(\"not satisfied
\",\"2*v_3\") \n   end if; \nend do:\nfor s from 4 by 1 to 7 do\n   t:
=convert(s,base,2):\n   if (Norm(v[1]+(-1)^(t[1])*v[2]+(-1)^(t[2])*2*v
[3]+(-1)^(t[3])*v[4]+v[5],2)^2 < Norm(v[3],2)^2) then \n      print(\"
not satisfied\",\"2*v_3\") \n   end if; \nend do:\nfor s from 8 by 1 t
o 15 do\n   t:=convert(s,base,2):\n   if (Norm(v[1]+(-1)^(t[1])*v[2]+(
-1)^(t[2])*2*v[3]+(-1)^(t[3])*v[4]+(-1)^(t[4])*v[5],2)^2 < Norm(v[3],2
)^2) then \n      print(\"not satisfied\",\"2*v_3\") \n   end if; \nen
d do:\nfor s from 0 by 1 to 1 do\n   if (Norm(v[1]+(-1)^s*v[2]+v[3]+2*
v[4]+v[5],2)^2 < Norm(v[4],2)^2) then \n      print(\"not satisfied\",
\"2*v_4\") \n   end if;\nend do;\nfor s from 2 by 1 to 3 do\n   t:=con
vert(s,base,2):\n   if (Norm(v[1]+(-1)^(t[1])*v[2]+(-1)^(t[2])*v[3]+2*
v[4]+v[5],2)^2 < Norm(v[4],2)^2) then \n      print(\"not satisfied\",
\"2*v_4\") \n   end if; \nend do:\nfor s from 4 by 1 to 7 do\n   t:=co
nvert(s,base,2):\n   if (Norm(v[1]+(-1)^(t[1])*v[2]+(-1)^(t[2])*v[3]+(
-1)^(t[3])*2*v[4]+v[5],2)^2 < Norm(v[4],2)^2) then \n      print(\"not
 satisfied\",\"2*v_4\") \n   end if; \nend do:\nfor s from 8 by 1 to 1
5 do\n   t:=convert(s,base,2):\n   if (Norm(v[1]+(-1)^(t[1])*v[2]+(-1)
^(t[2])*v[3]+(-1)^(t[3])*2*v[4]+(-1)^(t[4])*v[5],2)^2 < Norm(v[4],2)^2
) then \n      print(\"not satisfied\",\"2*v_4\") \n   end if; \nend d
o:\nfor s from 0 by 1 to 1 do\n   if (Norm(v[1]+(-1)^s*v[2]+v[3]+v[4]+
2*v[5],2)^2 < Norm(v[5],2)^2) then \n      print(\"not satisfied\",\"2
*v_5\") \n   end if;\nend do;\nfor s from 2 by 1 to 3 do\n   t:=conver
t(s,base,2):\n   if (Norm(v[1]+(-1)^(t[1])*v[2]+(-1)^(t[2])*v[3]+v[4]+
2*v[5],2)^2 < Norm(v[5],2)^2) then \n      print(\"not satisfied\",\"2
*v_5\") \n   end if; \nend do:\nfor s from 4 by 1 to 7 do\n   t:=conve
rt(s,base,2):\n   if (Norm(v[1]+(-1)^(t[1])*v[2]+(-1)^(t[2])*v[3]+(-1)
^(t[3])*v[4]+2*v[5],2)^2 < Norm(v[5],2)^2) then \n      print(\"not sa
tisfied\",\"2*v_5\") \n   end if; \nend do:\nfor s from 8 by 1 to 15 d
o\n   t:=convert(s,base,2):\n   if (Norm(v[1]+(-1)^(t[1])*v[2]+(-1)^(t
[2])*v[3]+(-1)^(t[3])*v[4]+(-1)^(t[4])*2*v[5],2)^2 < Norm(v[5],2)^2) t
hen \n      print(\"not satisfied\",\"2*v_5\") \n   end if; \nend do:
" }}{PARA 11 "" 1 "" {XPPMATH 20 "6&Q.not~satisfied6\"Q(v_i,v_jF$\"\"$
\"\"%" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 
0 "> " 0 "" {MPLTEXT 1 0 365 "v[1]:=Vector([4,-1,-1,-1,-1]):\nv[2]:=Ve
ctor([-1,4,-1,-1,-1]):\nv[3]:=Vector([1,1,4,1,1]):\nv[4]:=Vector([-1,-
1,-1,4,-1]):\nv[5]:=Vector([-2,-2,-2,-2,-2]):\nv[1],v[2],v[3],v[4],v[5
];\nprint(\"|v[1]|^2\"=Norm(v[1],2)^2);\n#checking for decreasing orde
r;\nfor i from 1 by 1 to 4 do \n   if (Norm(v[i],2)^2 > Norm(v[i+1],2)
^2) then print(\"not satisfied\",(i,i+1)) end if; \nend do;" }}{PARA 
11 "" 1 "" {XPPMATH 20 "6'-%'RTABLEG6%\"*'z@R=-%'MATRIXG6#7'7#\"\"%7#!
\"\"F-F-F-&%'VectorG6#%'columnG-F$6%\"*g=#R=-F(6#7'F-F+F-F-F-F/-F$6%\"
*C>#R=-F(6#7'7#\"\"\"F?F+F?F?F/-F$6%\"*))>#R=-F(6#7'F-F-F-F+F-F/-F$6%
\"*_?#R=-F(6#7'7#!\"#FMFMFMFMF/" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#/Q)
|grv[1]|gr^26\"\"#?" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 6469 "#c
hecking for 2|v[j].v[i]|=<|v[i]|^2;\nL2:=choose(5, 2):\nfor i from 1 b
y 1 to numbcomb(5, 2) do\n   if (2*abs(v[L2[i][2]].v[L2[i][1]]) > Norm
(v[L2[i][1]],2)^2) then \n      print(\"not satisfied\",\"v_i,v_j\",L2
[i][1],L2[i][2]) \n   end if;\nend do;\n#checking for 2|v[k].(v[i]+v[j
])|=<|v[i]+v[j]|^2;\nL3:=choose(5, 3):\nfor s from 0 by 1 to 1 do\n   \+
for i from 1 by 1 to numbcomb(5, 3) do\n      if (2*abs(v[L3[i][3]].(v
[L3[i][1]]+(-1)^s*v[L3[i][2]])) > Norm(v[L3[i][1]]+(-1)^s*v[L3[i][2]],
2)^2) then \n         print(\"not satisfied\",\"v_i,v_j,v_k\",L3[i][1]
,(-1)^s*L3[i][2],L3[i][3]); \n      end if;\n   end do;\nend do;\n#che
cking for 2|v[l].(v[i]+v[j]+v[k])|=<|v[i]+v[j]+v[k]|^2;\nL4:=choose(5,
 4):\nfor s from 0 by 1 to 1 do\n   for i from 1 by 1 to numbcomb(5, 4
) do\n      if (2*abs(v[L4[i][4]].(v[L4[i][1]]+(-1)^s*v[L4[i][2]]+(-1)
^0*v[L4[i][3]])) >\n         Norm(v[L4[i][1]]+(-1)^s*v[L4[i][2]]+(-1)^
0*v[L4[i][3]],2)^2) then \n         print(\"not satisfied\",\"v_i,v_j,
v_k,v_l\",L4[i][1],(-1)^s*L4[i][2],(-1)^0*L4[i][3],L4[i][4]); \n      \+
end if;\n   end do;\nend do;\nfor s from 2 by 1 to 3 do\n   t:=convert
(s,base,2):\n   for i from 1 by 1 to numbcomb(5, 4) do\n      if (2*ab
s(v[L4[i][4]].(v[L4[i][1]]+(-1)^(t[1])*v[L4[i][2]]+(-1)^(t[2])*v[L4[i]
[3]])) >\n         Norm(v[L4[i][1]]+(-1)^(t[1])*v[L4[i][2]]+(-1)^(t[2]
)*v[L4[i][3]],2)^2) then \n         print(\"not satisfied\",\"v_i,v_j,
v_k,v_l\",L4[i][1],(-1)^(t[1])*L4[i][2],(-1)^(t[2])*L4[i][3],L4[i][4])
; \n      end if;\n   end do;\nend do:\n#checking for 2|v[m].(v[i]+v[j
]+v[k]+v[l])|=<|v[i]+v[j]+v[k]+v[l]|^2;\nfor s from 0 by 1 to 1 do\n  \+
 if (2*abs(v[5].(v[1]+(-1)^s*v[2]+(-1)^0*v[3]+(-1)^0*v[4])) > \n      \+
 Norm(v[1]+(-1)^s*v[2]+(-1)^0*v[3]+(-1)^0*v[4],2)^2) then \n      prin
t(\"not satisfied\",\"v_i,v_j,v_k,v_l,v_m\",1,(-1)^s*2,3,4,5); \n   en
d if;\nend do;\nfor s from 2 by 1 to 3 do\n   t:=convert(s,base,2):\n \+
  if (2*abs(v[5].(v[1]+(-1)^(t[1])*v[2]+(-1)^(t[2])*v[3]+(-1)^0*v[4]))
 > \n       Norm(v[1]+(-1)^(t[1])*v[2]+(-1)^(t[2])*v[3]+(-1)^0*v[4],2)
^2) then \n      print(\"not satisfied\",\"v_i,v_j,v_k,v_l,v_m\",1,+(-
1)^(t[1])*2,(-1)^(t[2])*3,(-1)^0*4,5); \n   end if;\nend do:\nfor s fr
om 4 by 1 to 7 do\n   t:=convert(s,base,2):\n   if (2*abs(v[5].(v[1]+(
-1)^(t[1])*v[2]+(-1)^(t[2])*v[3]+(-1)^(t[3])*v[4])) > \n       Norm(v[
1]+(-1)^(t[1])*v[2]+(-1)^(t[2])*v[3]+(-1)^(t[3])*v[4],2)^2) then \n   \+
   print(\"not satisfied\",\"v_i,v_j,v_k,v_l,v_m\",1,(-1)^(t[1])*2,+(-
1)^(t[2])*3,(-1)^(t[3])*4,5); \n   end if;\nend do:\n#checking for |v[
i]+v[1]+v[2]+v[3]+v[4]+v[5]|^2>=|v[i]|^2;\nfor s from 0 by 1 to 1 do\n
   if (Norm(2*v[1]+(-1)^s*v[2]+v[3]+v[4]+v[5],2)^2 < Norm(v[1],2)^2) t
hen \n      print(\"not satisfied\",\"2*v_1\") \n   end if;\nend do;\n
for s from 2 by 1 to 3 do\n   t:=convert(s,base,2):\n   if (Norm(2*v[1
]+(-1)^(t[1])*v[2]+(-1)^(t[2])*v[3]+v[4]+v[5],2)^2 < Norm(v[1],2)^2) t
hen \n      print(\"not satisfied\",\"2*v_1\") \n   end if; \nend do:
\nfor s from 4 by 1 to 7 do\n   t:=convert(s,base,2):\n   if (Norm(2*v
[1]+(-1)^(t[1])*v[2]+(-1)^(t[2])*v[3]+(-1)^(t[3])*v[4]+v[5],2)^2 < Nor
m(v[1],2)^2) then \n      print(\"not satisfied\",\"2*v_1\") \n   end \+
if; \nend do:\nfor s from 8 by 1 to 15 do\n   t:=convert(s,base,2):\n \+
  if (Norm(2*v[1]+(-1)^(t[1])*v[2]+(-1)^(t[2])*v[3]+(-1)^(t[3])*v[4]+(
-1)^(t[4])*v[5],2)^2 < Norm(v[1],2)^2) then \n      print(\"not satisf
ied\",\"2*v_1\") \n   end if; \nend do:\nfor s from 0 by 1 to 1 do\n  \+
 if (Norm(v[1]+(-1)^s*2*v[2]+v[3]+v[4]+v[5],2)^2 < Norm(v[2],2)^2) the
n \n      print(\"not satisfied\",\"2*v_2\") \n   end if;\nend do;\nfo
r s from 2 by 1 to 3 do\n   t:=convert(s,base,2):\n   if (Norm(v[1]+(-
1)^(t[1])*2*v[2]+(-1)^(t[2])*v[3]+v[4]+v[5],2)^2 < Norm(v[2],2)^2) the
n \n      print(\"not satisfied\",\"2*v_2\") \n   end if; \nend do:\nf
or s from 4 by 1 to 7 do\n   t:=convert(s,base,2):\n   if (Norm(v[1]+(
-1)^(t[1])*2*v[2]+(-1)^(t[2])*v[3]+(-1)^(t[3])*v[4]+v[5],2)^2 < Norm(v
[2],2)^2) then \n      print(\"not satisfied\",\"2*v_2\") \n   end if;
 \nend do:\nfor s from 8 by 1 to 15 do\n   t:=convert(s,base,2):\n   i
f (Norm(v[1]+(-1)^(t[1])*2*v[2]+(-1)^(t[2])*v[3]+(-1)^(t[3])*v[4]+(-1)
^(t[4])*v[5],2)^2 < Norm(v[2],2)^2) then \n      print(\"not satisfied
\",\"2*v_2\") \n   end if; \nend do:\nfor s from 0 by 1 to 1 do\n   if
 (Norm(v[1]+(-1)^s*v[2]+2*v[3]+v[4]+v[5],2)^2 < Norm(v[3],2)^2) then \+
\n      print(\"not satisfied\",\"2*v_3\") \n   end if;\nend do;\nfor \+
s from 2 by 1 to 3 do\n   t:=convert(s,base,2):\n   if (Norm(v[1]+(-1)
^(t[1])*v[2]+(-1)^(t[2])*2*v[3]+v[4]+v[5],2)^2 < Norm(v[3],2)^2) then \+
\n      print(\"not satisfied\",\"2*v_3\") \n   end if; \nend do:\nfor
 s from 4 by 1 to 7 do\n   t:=convert(s,base,2):\n   if (Norm(v[1]+(-1
)^(t[1])*v[2]+(-1)^(t[2])*2*v[3]+(-1)^(t[3])*v[4]+v[5],2)^2 < Norm(v[3
],2)^2) then \n      print(\"not satisfied\",\"2*v_3\") \n   end if; \+
\nend do:\nfor s from 8 by 1 to 15 do\n   t:=convert(s,base,2):\n   if
 (Norm(v[1]+(-1)^(t[1])*v[2]+(-1)^(t[2])*2*v[3]+(-1)^(t[3])*v[4]+(-1)^
(t[4])*v[5],2)^2 < Norm(v[3],2)^2) then \n      print(\"not satisfied
\",\"2*v_3\") \n   end if; \nend do:\nfor s from 0 by 1 to 1 do\n   if
 (Norm(v[1]+(-1)^s*v[2]+v[3]+2*v[4]+v[5],2)^2 < Norm(v[4],2)^2) then \+
\n      print(\"not satisfied\",\"2*v_4\") \n   end if;\nend do;\nfor \+
s from 2 by 1 to 3 do\n   t:=convert(s,base,2):\n   if (Norm(v[1]+(-1)
^(t[1])*v[2]+(-1)^(t[2])*v[3]+2*v[4]+v[5],2)^2 < Norm(v[4],2)^2) then \+
\n      print(\"not satisfied\",\"2*v_4\") \n   end if; \nend do:\nfor
 s from 4 by 1 to 7 do\n   t:=convert(s,base,2):\n   if (Norm(v[1]+(-1
)^(t[1])*v[2]+(-1)^(t[2])*v[3]+(-1)^(t[3])*2*v[4]+v[5],2)^2 < Norm(v[4
],2)^2) then \n      print(\"not satisfied\",\"2*v_4\") \n   end if; \+
\nend do:\nfor s from 8 by 1 to 15 do\n   t:=convert(s,base,2):\n   if
 (Norm(v[1]+(-1)^(t[1])*v[2]+(-1)^(t[2])*v[3]+(-1)^(t[3])*2*v[4]+(-1)^
(t[4])*v[5],2)^2 < Norm(v[4],2)^2) then \n      print(\"not satisfied
\",\"2*v_4\") \n   end if; \nend do:\nfor s from 0 by 1 to 1 do\n   if
 (Norm(v[1]+(-1)^s*v[2]+v[3]+v[4]+2*v[5],2)^2 < Norm(v[5],2)^2) then \+
\n      print(\"not satisfied\",\"2*v_5\") \n   end if;\nend do;\nfor \+
s from 2 by 1 to 3 do\n   t:=convert(s,base,2):\n   if (Norm(v[1]+(-1)
^(t[1])*v[2]+(-1)^(t[2])*v[3]+v[4]+2*v[5],2)^2 < Norm(v[5],2)^2) then \+
\n      print(\"not satisfied\",\"2*v_5\") \n   end if; \nend do:\nfor
 s from 4 by 1 to 7 do\n   t:=convert(s,base,2):\n   if (Norm(v[1]+(-1
)^(t[1])*v[2]+(-1)^(t[2])*v[3]+(-1)^(t[3])*v[4]+2*v[5],2)^2 < Norm(v[5
],2)^2) then \n      print(\"not satisfied\",\"2*v_5\") \n   end if; \+
\nend do:\nfor s from 8 by 1 to 15 do\n   t:=convert(s,base,2):\n   if
 (Norm(v[1]+(-1)^(t[1])*v[2]+(-1)^(t[2])*v[3]+(-1)^(t[3])*v[4]+(-1)^(t
[4])*2*v[5],2)^2 < Norm(v[5],2)^2) then \n      print(\"not satisfied
\",\"2*v_5\") \n   end if; \nend do:" }}{PARA 11 "" 1 "" {XPPMATH 20 "
6&Q.not~satisfied6\"Q(v_i,v_jF$\"\"$\"\"&" }}}{EXCHG {PARA 0 "> " 0 "
" {MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 365 "v[1]
:=Vector([4,-1,-1,-1,-1]):\nv[2]:=Vector([-1,4,-1,-1,-1]):\nv[3]:=Vect
or([-1,-1,4,-1,-1]):\nv[4]:=Vector([1,1,1,4,1]):\nv[5]:=Vector([-2,-2,
-2,-2,-2]):\nv[1],v[2],v[3],v[4],v[5];\nprint(\"|v[1]|^2\"=Norm(v[1],2
)^2);\n#checking for decreasing order;\nfor i from 1 by 1 to 4 do \n  \+
 if (Norm(v[i],2)^2 > Norm(v[i+1],2)^2) then print(\"not satisfied\",(
i,i+1)) end if; \nend do;" }}{PARA 11 "" 1 "" {XPPMATH 20 "6'-%'RTABLE
G6%\"*+m(H>-%'MATRIXG6#7'7#\"\"%7#!\"\"F-F-F-&%'VectorG6#%'columnG-F$6
%\"*km(H>-F(6#7'F-F+F-F-F-F/-F$6%\"*Gn(H>-F(6#7'F-F-F+F-F-F/-F$6%\"*#z
wH>-F(6#7'7#\"\"\"FEFEF+FEF/-F$6%\"*co(H>-F(6#7'7#!\"#FMFMFMFMF/" }}
{PARA 11 "" 1 "" {XPPMATH 20 "6#/Q)|grv[1]|gr^26\"\"#?" }}}{EXCHG 
{PARA 0 "> " 0 "" {MPLTEXT 1 0 6469 "#checking for 2|v[j].v[i]|=<|v[i]
|^2;\nL2:=choose(5, 2):\nfor i from 1 by 1 to numbcomb(5, 2) do\n   if
 (2*abs(v[L2[i][2]].v[L2[i][1]]) > Norm(v[L2[i][1]],2)^2) then \n     \+
 print(\"not satisfied\",\"v_i,v_j\",L2[i][1],L2[i][2]) \n   end if;\n
end do;\n#checking for 2|v[k].(v[i]+v[j])|=<|v[i]+v[j]|^2;\nL3:=choose
(5, 3):\nfor s from 0 by 1 to 1 do\n   for i from 1 by 1 to numbcomb(5
, 3) do\n      if (2*abs(v[L3[i][3]].(v[L3[i][1]]+(-1)^s*v[L3[i][2]]))
 > Norm(v[L3[i][1]]+(-1)^s*v[L3[i][2]],2)^2) then \n         print(\"n
ot satisfied\",\"v_i,v_j,v_k\",L3[i][1],(-1)^s*L3[i][2],L3[i][3]); \n \+
     end if;\n   end do;\nend do;\n#checking for 2|v[l].(v[i]+v[j]+v[k
])|=<|v[i]+v[j]+v[k]|^2;\nL4:=choose(5, 4):\nfor s from 0 by 1 to 1 do
\n   for i from 1 by 1 to numbcomb(5, 4) do\n      if (2*abs(v[L4[i][4
]].(v[L4[i][1]]+(-1)^s*v[L4[i][2]]+(-1)^0*v[L4[i][3]])) >\n         No
rm(v[L4[i][1]]+(-1)^s*v[L4[i][2]]+(-1)^0*v[L4[i][3]],2)^2) then \n    \+
     print(\"not satisfied\",\"v_i,v_j,v_k,v_l\",L4[i][1],(-1)^s*L4[i]
[2],(-1)^0*L4[i][3],L4[i][4]); \n      end if;\n   end do;\nend do;\nf
or s from 2 by 1 to 3 do\n   t:=convert(s,base,2):\n   for i from 1 by
 1 to numbcomb(5, 4) do\n      if (2*abs(v[L4[i][4]].(v[L4[i][1]]+(-1)
^(t[1])*v[L4[i][2]]+(-1)^(t[2])*v[L4[i][3]])) >\n         Norm(v[L4[i]
[1]]+(-1)^(t[1])*v[L4[i][2]]+(-1)^(t[2])*v[L4[i][3]],2)^2) then \n    \+
     print(\"not satisfied\",\"v_i,v_j,v_k,v_l\",L4[i][1],(-1)^(t[1])*
L4[i][2],(-1)^(t[2])*L4[i][3],L4[i][4]); \n      end if;\n   end do;\n
end do:\n#checking for 2|v[m].(v[i]+v[j]+v[k]+v[l])|=<|v[i]+v[j]+v[k]+
v[l]|^2;\nfor s from 0 by 1 to 1 do\n   if (2*abs(v[5].(v[1]+(-1)^s*v[
2]+(-1)^0*v[3]+(-1)^0*v[4])) > \n       Norm(v[1]+(-1)^s*v[2]+(-1)^0*v
[3]+(-1)^0*v[4],2)^2) then \n      print(\"not satisfied\",\"v_i,v_j,v
_k,v_l,v_m\",1,(-1)^s*2,3,4,5); \n   end if;\nend do;\nfor s from 2 by
 1 to 3 do\n   t:=convert(s,base,2):\n   if (2*abs(v[5].(v[1]+(-1)^(t[
1])*v[2]+(-1)^(t[2])*v[3]+(-1)^0*v[4])) > \n       Norm(v[1]+(-1)^(t[1
])*v[2]+(-1)^(t[2])*v[3]+(-1)^0*v[4],2)^2) then \n      print(\"not sa
tisfied\",\"v_i,v_j,v_k,v_l,v_m\",1,+(-1)^(t[1])*2,(-1)^(t[2])*3,(-1)^
0*4,5); \n   end if;\nend do:\nfor s from 4 by 1 to 7 do\n   t:=conver
t(s,base,2):\n   if (2*abs(v[5].(v[1]+(-1)^(t[1])*v[2]+(-1)^(t[2])*v[3
]+(-1)^(t[3])*v[4])) > \n       Norm(v[1]+(-1)^(t[1])*v[2]+(-1)^(t[2])
*v[3]+(-1)^(t[3])*v[4],2)^2) then \n      print(\"not satisfied\",\"v_
i,v_j,v_k,v_l,v_m\",1,(-1)^(t[1])*2,+(-1)^(t[2])*3,(-1)^(t[3])*4,5); \+
\n   end if;\nend do:\n#checking for |v[i]+v[1]+v[2]+v[3]+v[4]+v[5]|^2
>=|v[i]|^2;\nfor s from 0 by 1 to 1 do\n   if (Norm(2*v[1]+(-1)^s*v[2]
+v[3]+v[4]+v[5],2)^2 < Norm(v[1],2)^2) then \n      print(\"not satisf
ied\",\"2*v_1\") \n   end if;\nend do;\nfor s from 2 by 1 to 3 do\n   \+
t:=convert(s,base,2):\n   if (Norm(2*v[1]+(-1)^(t[1])*v[2]+(-1)^(t[2])
*v[3]+v[4]+v[5],2)^2 < Norm(v[1],2)^2) then \n      print(\"not satisf
ied\",\"2*v_1\") \n   end if; \nend do:\nfor s from 4 by 1 to 7 do\n  \+
 t:=convert(s,base,2):\n   if (Norm(2*v[1]+(-1)^(t[1])*v[2]+(-1)^(t[2]
)*v[3]+(-1)^(t[3])*v[4]+v[5],2)^2 < Norm(v[1],2)^2) then \n      print
(\"not satisfied\",\"2*v_1\") \n   end if; \nend do:\nfor s from 8 by \+
1 to 15 do\n   t:=convert(s,base,2):\n   if (Norm(2*v[1]+(-1)^(t[1])*v
[2]+(-1)^(t[2])*v[3]+(-1)^(t[3])*v[4]+(-1)^(t[4])*v[5],2)^2 < Norm(v[1
],2)^2) then \n      print(\"not satisfied\",\"2*v_1\") \n   end if; \+
\nend do:\nfor s from 0 by 1 to 1 do\n   if (Norm(v[1]+(-1)^s*2*v[2]+v
[3]+v[4]+v[5],2)^2 < Norm(v[2],2)^2) then \n      print(\"not satisfie
d\",\"2*v_2\") \n   end if;\nend do;\nfor s from 2 by 1 to 3 do\n   t:
=convert(s,base,2):\n   if (Norm(v[1]+(-1)^(t[1])*2*v[2]+(-1)^(t[2])*v
[3]+v[4]+v[5],2)^2 < Norm(v[2],2)^2) then \n      print(\"not satisfie
d\",\"2*v_2\") \n   end if; \nend do:\nfor s from 4 by 1 to 7 do\n   t
:=convert(s,base,2):\n   if (Norm(v[1]+(-1)^(t[1])*2*v[2]+(-1)^(t[2])*
v[3]+(-1)^(t[3])*v[4]+v[5],2)^2 < Norm(v[2],2)^2) then \n      print(
\"not satisfied\",\"2*v_2\") \n   end if; \nend do:\nfor s from 8 by 1
 to 15 do\n   t:=convert(s,base,2):\n   if (Norm(v[1]+(-1)^(t[1])*2*v[
2]+(-1)^(t[2])*v[3]+(-1)^(t[3])*v[4]+(-1)^(t[4])*v[5],2)^2 < Norm(v[2]
,2)^2) then \n      print(\"not satisfied\",\"2*v_2\") \n   end if; \n
end do:\nfor s from 0 by 1 to 1 do\n   if (Norm(v[1]+(-1)^s*v[2]+2*v[3
]+v[4]+v[5],2)^2 < Norm(v[3],2)^2) then \n      print(\"not satisfied
\",\"2*v_3\") \n   end if;\nend do;\nfor s from 2 by 1 to 3 do\n   t:=
convert(s,base,2):\n   if (Norm(v[1]+(-1)^(t[1])*v[2]+(-1)^(t[2])*2*v[
3]+v[4]+v[5],2)^2 < Norm(v[3],2)^2) then \n      print(\"not satisfied
\",\"2*v_3\") \n   end if; \nend do:\nfor s from 4 by 1 to 7 do\n   t:
=convert(s,base,2):\n   if (Norm(v[1]+(-1)^(t[1])*v[2]+(-1)^(t[2])*2*v
[3]+(-1)^(t[3])*v[4]+v[5],2)^2 < Norm(v[3],2)^2) then \n      print(\"
not satisfied\",\"2*v_3\") \n   end if; \nend do:\nfor s from 8 by 1 t
o 15 do\n   t:=convert(s,base,2):\n   if (Norm(v[1]+(-1)^(t[1])*v[2]+(
-1)^(t[2])*2*v[3]+(-1)^(t[3])*v[4]+(-1)^(t[4])*v[5],2)^2 < Norm(v[3],2
)^2) then \n      print(\"not satisfied\",\"2*v_3\") \n   end if; \nen
d do:\nfor s from 0 by 1 to 1 do\n   if (Norm(v[1]+(-1)^s*v[2]+v[3]+2*
v[4]+v[5],2)^2 < Norm(v[4],2)^2) then \n      print(\"not satisfied\",
\"2*v_4\") \n   end if;\nend do;\nfor s from 2 by 1 to 3 do\n   t:=con
vert(s,base,2):\n   if (Norm(v[1]+(-1)^(t[1])*v[2]+(-1)^(t[2])*v[3]+2*
v[4]+v[5],2)^2 < Norm(v[4],2)^2) then \n      print(\"not satisfied\",
\"2*v_4\") \n   end if; \nend do:\nfor s from 4 by 1 to 7 do\n   t:=co
nvert(s,base,2):\n   if (Norm(v[1]+(-1)^(t[1])*v[2]+(-1)^(t[2])*v[3]+(
-1)^(t[3])*2*v[4]+v[5],2)^2 < Norm(v[4],2)^2) then \n      print(\"not
 satisfied\",\"2*v_4\") \n   end if; \nend do:\nfor s from 8 by 1 to 1
5 do\n   t:=convert(s,base,2):\n   if (Norm(v[1]+(-1)^(t[1])*v[2]+(-1)
^(t[2])*v[3]+(-1)^(t[3])*2*v[4]+(-1)^(t[4])*v[5],2)^2 < Norm(v[4],2)^2
) then \n      print(\"not satisfied\",\"2*v_4\") \n   end if; \nend d
o:\nfor s from 0 by 1 to 1 do\n   if (Norm(v[1]+(-1)^s*v[2]+v[3]+v[4]+
2*v[5],2)^2 < Norm(v[5],2)^2) then \n      print(\"not satisfied\",\"2
*v_5\") \n   end if;\nend do;\nfor s from 2 by 1 to 3 do\n   t:=conver
t(s,base,2):\n   if (Norm(v[1]+(-1)^(t[1])*v[2]+(-1)^(t[2])*v[3]+v[4]+
2*v[5],2)^2 < Norm(v[5],2)^2) then \n      print(\"not satisfied\",\"2
*v_5\") \n   end if; \nend do:\nfor s from 4 by 1 to 7 do\n   t:=conve
rt(s,base,2):\n   if (Norm(v[1]+(-1)^(t[1])*v[2]+(-1)^(t[2])*v[3]+(-1)
^(t[3])*v[4]+2*v[5],2)^2 < Norm(v[5],2)^2) then \n      print(\"not sa
tisfied\",\"2*v_5\") \n   end if; \nend do:\nfor s from 8 by 1 to 15 d
o\n   t:=convert(s,base,2):\n   if (Norm(v[1]+(-1)^(t[1])*v[2]+(-1)^(t
[2])*v[3]+(-1)^(t[3])*v[4]+(-1)^(t[4])*2*v[5],2)^2 < Norm(v[5],2)^2) t
hen \n      print(\"not satisfied\",\"2*v_5\") \n   end if; \nend do:
" }}{PARA 11 "" 1 "" {XPPMATH 20 "6&Q.not~satisfied6\"Q(v_i,v_jF$\"\"%
\"\"&" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 
0 "> " 0 "" {MPLTEXT 1 0 365 "v[1]:=Vector([4,-1,-1,-1,-1]):\nv[2]:=Ve
ctor([-1,4,-1,1,-1]):\nv[3]:=Vector([-1,-1,4,1,1]):\nv[4]:=Vector([-1,
-1,-1,4,-1]):\nv[5]:=Vector([-2,-2,2,-2,-2]):\nv[1],v[2],v[3],v[4],v[5
];\nprint(\"|v[1]|^2\"=Norm(v[1],2)^2);\n#checking for decreasing orde
r;\nfor i from 1 by 1 to 4 do \n   if (Norm(v[i],2)^2 > Norm(v[i+1],2)
^2) then print(\"not satisfied\",(i,i+1)) end if; \nend do;" }}{PARA 
11 "" 1 "" {XPPMATH 20 "6'-%'RTABLEG6%\"*cOJx\"-%'MATRIXG6#7'7#\"\"%7#
!\"\"F-F-F-&%'VectorG6#%'columnG-F$6%\"*?PJx\"-F(6#7'F-F+F-7#\"\"\"F-F
/-F$6%\"*%y8t<-F(6#7'F-F-F+F9F9F/-F$6%\"*[QJx\"-F(6#7'F-F-F-F+F-F/-F$6
%\"*7RJx\"-F(6#7'7#!\"#FM7#\"\"#FMFMF/" }}{PARA 11 "" 1 "" {XPPMATH 
20 "6#/Q)|grv[1]|gr^26\"\"#?" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 
0 5509 "#checking for 2|v[j].v[i]|=<|v[i]|^2;\nL2:=choose(5, 2):\nfor \+
i from 1 by 1 to numbcomb(5, 2) do\n   if (2*abs(v[L2[i][2]].v[L2[i][1
]]) > Norm(v[L2[i][1]],2)^2) then \n      print(\"not satisfied\",\"v_
i,v_j\",L2[i][1],L2[i][2]) \n   end if;\nend do;\n#checking for 2|v[k]
.(v[i]+v[j])|=<|v[i]+v[j]|^2;\nL3:=choose(5, 3):\nfor s from 0 by 1 to
 1 do\n   for i from 1 by 1 to numbcomb(5, 3) do\n      if (2*abs(v[L3
[i][3]].(v[L3[i][1]]+(-1)^s*v[L3[i][2]])) > Norm(v[L3[i][1]]+(-1)^s*v[
L3[i][2]],2)^2) then \n         print(\"not satisfied\",\"v_i,v_j,v_k
\",L3[i][1],(-1)^s*L3[i][2],L3[i][3]); \n      end if;\n   end do;\nen
d do;\n#checking for 2|v[l].(v[i]+v[j]+v[k])|=<|v[i]+v[j]+v[k]|^2;\nL4
:=choose(5, 4):\nfor s from 0 by 1 to 1 do\n   for i from 1 by 1 to nu
mbcomb(5, 4) do\n      if (2*abs(v[L4[i][4]].(v[L4[i][1]]+(-1)^s*v[L4[
i][2]]+(-1)^0*v[L4[i][3]])) >\n         Norm(v[L4[i][1]]+(-1)^s*v[L4[i
][2]]+(-1)^0*v[L4[i][3]],2)^2) then \n         print(\"not satisfied\"
,\"v_i,v_j,v_k,v_l\",L4[i][1],(-1)^s*L4[i][2],(-1)^0*L4[i][3],L4[i][4]
); \n      end if;\n   end do;\nend do;\nfor s from 2 by 1 to 3 do\n  \+
 t:=convert(s,base,2):\n   for i from 1 by 1 to numbcomb(5, 4) do\n   \+
   if (2*abs(v[L4[i][4]].(v[L4[i][1]]+(-1)^(t[1])*v[L4[i][2]]+(-1)^(t[
2])*v[L4[i][3]])) >\n         Norm(v[L4[i][1]]+(-1)^(t[1])*v[L4[i][2]]
+(-1)^(t[2])*v[L4[i][3]],2)^2) then \n         print(\"not satisfied\"
,\"v_i,v_j,v_k,v_l\",L4[i][1],(-1)^(t[1])*L4[i][2],(-1)^(t[2])*L4[i][3
],L4[i][4]); \n      end if;\n   end do;\nend do:\n#checking for |v[i]
+v[1]+v[2]+v[3]+v[4]+v[5]|^2>=|v[i]|^2;\nfor s from 0 by 1 to 1 do\n  \+
 if (Norm(2*v[1]+(-1)^s*v[2]+v[3]+v[4]+v[5],2)^2 < Norm(v[1],2)^2) the
n \n      print(\"not satisfied\",\"2*v_1\") \n   end if;\nend do;\nfo
r s from 2 by 1 to 3 do\n   t:=convert(s,base,2):\n   if (Norm(2*v[1]+
(-1)^(t[1])*v[2]+(-1)^(t[2])*v[3]+v[4]+v[5],2)^2 < Norm(v[1],2)^2) the
n \n      print(\"not satisfied\",\"2*v_1\") \n   end if; \nend do:\nf
or s from 4 by 1 to 7 do\n   t:=convert(s,base,2):\n   if (Norm(2*v[1]
+(-1)^(t[1])*v[2]+(-1)^(t[2])*v[3]+(-1)^(t[3])*v[4]+v[5],2)^2 < Norm(v
[1],2)^2) then \n      print(\"not satisfied\",\"2*v_1\") \n   end if;
 \nend do:\nfor s from 8 by 1 to 15 do\n   t:=convert(s,base,2):\n   i
f (Norm(2*v[1]+(-1)^(t[1])*v[2]+(-1)^(t[2])*v[3]+(-1)^(t[3])*v[4]+(-1)
^(t[4])*v[5],2)^2 < Norm(v[1],2)^2) then \n      print(\"not satisfied
\",\"2*v_1\") \n   end if; \nend do:\nfor s from 0 by 1 to 1 do\n   if
 (Norm(v[1]+(-1)^s*2*v[2]+v[3]+v[4]+v[5],2)^2 < Norm(v[2],2)^2) then \+
\n      print(\"not satisfied\",\"2*v_2\") \n   end if;\nend do;\nfor \+
s from 2 by 1 to 3 do\n   t:=convert(s,base,2):\n   if (Norm(v[1]+(-1)
^(t[1])*2*v[2]+(-1)^(t[2])*v[3]+v[4]+v[5],2)^2 < Norm(v[2],2)^2) then \+
\n      print(\"not satisfied\",\"2*v_2\") \n   end if; \nend do:\nfor
 s from 4 by 1 to 7 do\n   t:=convert(s,base,2):\n   if (Norm(v[1]+(-1
)^(t[1])*2*v[2]+(-1)^(t[2])*v[3]+(-1)^(t[3])*v[4]+v[5],2)^2 < Norm(v[2
],2)^2) then \n      print(\"not satisfied\",\"2*v_2\") \n   end if; \+
\nend do:\nfor s from 8 by 1 to 15 do\n   t:=convert(s,base,2):\n   if
 (Norm(v[1]+(-1)^(t[1])*2*v[2]+(-1)^(t[2])*v[3]+(-1)^(t[3])*v[4]+(-1)^
(t[4])*v[5],2)^2 < Norm(v[2],2)^2) then \n      print(\"not satisfied
\",\"2*v_2\") \n   end if; \nend do:\nfor s from 0 by 1 to 1 do\n   if
 (Norm(v[1]+(-1)^s*v[2]+2*v[3]+v[4]+v[5],2)^2 < Norm(v[3],2)^2) then \+
\n      print(\"not satisfied\",\"2*v_3\") \n   end if;\nend do;\nfor \+
s from 2 by 1 to 3 do\n   t:=convert(s,base,2):\n   if (Norm(v[1]+(-1)
^(t[1])*v[2]+(-1)^(t[2])*2*v[3]+v[4]+v[5],2)^2 < Norm(v[3],2)^2) then \+
\n      print(\"not satisfied\",\"2*v_3\") \n   end if; \nend do:\nfor
 s from 4 by 1 to 7 do\n   t:=convert(s,base,2):\n   if (Norm(v[1]+(-1
)^(t[1])*v[2]+(-1)^(t[2])*2*v[3]+(-1)^(t[3])*v[4]+v[5],2)^2 < Norm(v[3
],2)^2) then \n      print(\"not satisfied\",\"2*v_3\") \n   end if; \+
\nend do:\nfor s from 8 by 1 to 15 do\n   t:=convert(s,base,2):\n   if
 (Norm(v[1]+(-1)^(t[1])*v[2]+(-1)^(t[2])*2*v[3]+(-1)^(t[3])*v[4]+(-1)^
(t[4])*v[5],2)^2 < Norm(v[3],2)^2) then \n      print(\"not satisfied
\",\"2*v_3\") \n   end if; \nend do:\nfor s from 0 by 1 to 1 do\n   if
 (Norm(v[1]+(-1)^s*v[2]+v[3]+2*v[4]+v[5],2)^2 < Norm(v[4],2)^2) then \+
\n      print(\"not satisfied\",\"2*v_4\") \n   end if;\nend do;\nfor \+
s from 2 by 1 to 3 do\n   t:=convert(s,base,2):\n   if (Norm(v[1]+(-1)
^(t[1])*v[2]+(-1)^(t[2])*v[3]+2*v[4]+v[5],2)^2 < Norm(v[4],2)^2) then \+
\n      print(\"not satisfied\",\"2*v_4\") \n   end if; \nend do:\nfor
 s from 4 by 1 to 7 do\n   t:=convert(s,base,2):\n   if (Norm(v[1]+(-1
)^(t[1])*v[2]+(-1)^(t[2])*v[3]+(-1)^(t[3])*2*v[4]+v[5],2)^2 < Norm(v[4
],2)^2) then \n      print(\"not satisfied\",\"2*v_4\") \n   end if; \+
\nend do:\nfor s from 8 by 1 to 15 do\n   t:=convert(s,base,2):\n   if
 (Norm(v[1]+(-1)^(t[1])*v[2]+(-1)^(t[2])*v[3]+(-1)^(t[3])*2*v[4]+(-1)^
(t[4])*v[5],2)^2 < Norm(v[4],2)^2) then \n      print(\"not satisfied
\",\"2*v_4\") \n   end if; \nend do:\nfor s from 0 by 1 to 1 do\n   if
 (Norm(v[1]+(-1)^s*v[2]+v[3]+v[4]+2*v[5],2)^2 < Norm(v[5],2)^2) then \+
\n      print(\"not satisfied\",\"2*v_5\") \n   end if;\nend do;\nfor \+
s from 2 by 1 to 3 do\n   t:=convert(s,base,2):\n   if (Norm(v[1]+(-1)
^(t[1])*v[2]+(-1)^(t[2])*v[3]+v[4]+2*v[5],2)^2 < Norm(v[5],2)^2) then \+
\n      print(\"not satisfied\",\"2*v_5\") \n   end if; \nend do:\nfor
 s from 4 by 1 to 7 do\n   t:=convert(s,base,2):\n   if (Norm(v[1]+(-1
)^(t[1])*v[2]+(-1)^(t[2])*v[3]+(-1)^(t[3])*v[4]+2*v[5],2)^2 < Norm(v[5
],2)^2) then \n      print(\"not satisfied\",\"2*v_5\") \n   end if; \+
\nend do:\nfor s from 8 by 1 to 15 do\n   t:=convert(s,base,2):\n   if
 (Norm(v[1]+(-1)^(t[1])*v[2]+(-1)^(t[2])*v[3]+(-1)^(t[3])*v[4]+(-1)^(t
[4])*2*v[5],2)^2 < Norm(v[5],2)^2) then \n      print(\"not satisfied
\",\"2*v_5\") \n   end if; \nend do:" }}{PARA 11 "" 1 "" {XPPMATH 20 "
6'Q.not~satisfied6\"Q,v_i,v_j,v_kF$\"\"\"\"\"#\"\"$" }}}{EXCHG {PARA 
0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 
0 365 "v[1]:=Vector([4,-1,-1,-1,-1]):\nv[2]:=Vector([-1,4,1,-1,-1]):\n
v[3]:=Vector([-1,-1,4,-1,-1]):\nv[4]:=Vector([-1,-1,1,4,1]):\nv[5]:=Ve
ctor([-2,-2,-2,2,-2]):\nv[1],v[2],v[3],v[4],v[5];\nprint(\"|v[1]|^2\"=
Norm(v[1],2)^2);\n#checking for decreasing order;\nfor i from 1 by 1 t
o 4 do \n   if (Norm(v[i],2)^2 > Norm(v[i+1],2)^2) then print(\"not sa
tisfied\",(i,i+1)) end if; \nend do;" }}{PARA 11 "" 1 "" {XPPMATH 20 "
6'-%'RTABLEG6%\"*kgyt\"-%'MATRIXG6#7'7#\"\"%7#!\"\"F-F-F-&%'VectorG6#%
'columnG-F$6%\"*Ghyt\"-F(6#7'F-F+7#\"\"\"F-F-F/-F$6%\"*#>'yt\"-F(6#7'F
-F-F+F-F-F/-F$6%\"*ciyt\"-F(6#7'F-F-F9F+F9F/-F$6%\"*?jyt\"-F(6#7'7#!\"
#FMFM7#\"\"#FMF/" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#/Q)|grv[1]|gr^26\"
\"#?" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 6469 "#checking for 2|v
[j].v[i]|=<|v[i]|^2;\nL2:=choose(5, 2):\nfor i from 1 by 1 to numbcomb
(5, 2) do\n   if (2*abs(v[L2[i][2]].v[L2[i][1]]) > Norm(v[L2[i][1]],2)
^2) then \n      print(\"not satisfied\",\"v_i,v_j\",L2[i][1],L2[i][2]
) \n   end if;\nend do;\n#checking for 2|v[k].(v[i]+v[j])|=<|v[i]+v[j]
|^2;\nL3:=choose(5, 3):\nfor s from 0 by 1 to 1 do\n   for i from 1 by
 1 to numbcomb(5, 3) do\n      if (2*abs(v[L3[i][3]].(v[L3[i][1]]+(-1)
^s*v[L3[i][2]])) > Norm(v[L3[i][1]]+(-1)^s*v[L3[i][2]],2)^2) then \n  \+
       print(\"not satisfied\",\"v_i,v_j,v_k\",L3[i][1],(-1)^s*L3[i][2
],L3[i][3]); \n      end if;\n   end do;\nend do;\n#checking for 2|v[l
].(v[i]+v[j]+v[k])|=<|v[i]+v[j]+v[k]|^2;\nL4:=choose(5, 4):\nfor s fro
m 0 by 1 to 1 do\n   for i from 1 by 1 to numbcomb(5, 4) do\n      if \+
(2*abs(v[L4[i][4]].(v[L4[i][1]]+(-1)^s*v[L4[i][2]]+(-1)^0*v[L4[i][3]])
) >\n         Norm(v[L4[i][1]]+(-1)^s*v[L4[i][2]]+(-1)^0*v[L4[i][3]],2
)^2) then \n         print(\"not satisfied\",\"v_i,v_j,v_k,v_l\",L4[i]
[1],(-1)^s*L4[i][2],(-1)^0*L4[i][3],L4[i][4]); \n      end if;\n   end
 do;\nend do;\nfor s from 2 by 1 to 3 do\n   t:=convert(s,base,2):\n  \+
 for i from 1 by 1 to numbcomb(5, 4) do\n      if (2*abs(v[L4[i][4]].(
v[L4[i][1]]+(-1)^(t[1])*v[L4[i][2]]+(-1)^(t[2])*v[L4[i][3]])) >\n     \+
    Norm(v[L4[i][1]]+(-1)^(t[1])*v[L4[i][2]]+(-1)^(t[2])*v[L4[i][3]],2
)^2) then \n         print(\"not satisfied\",\"v_i,v_j,v_k,v_l\",L4[i]
[1],(-1)^(t[1])*L4[i][2],(-1)^(t[2])*L4[i][3],L4[i][4]); \n      end i
f;\n   end do;\nend do:\n#checking for 2|v[m].(v[i]+v[j]+v[k]+v[l])|=<
|v[i]+v[j]+v[k]+v[l]|^2;\nfor s from 0 by 1 to 1 do\n   if (2*abs(v[5]
.(v[1]+(-1)^s*v[2]+(-1)^0*v[3]+(-1)^0*v[4])) > \n       Norm(v[1]+(-1)
^s*v[2]+(-1)^0*v[3]+(-1)^0*v[4],2)^2) then \n      print(\"not satisfi
ed\",\"v_i,v_j,v_k,v_l,v_m\",1,(-1)^s*2,3,4,5); \n   end if;\nend do;
\nfor s from 2 by 1 to 3 do\n   t:=convert(s,base,2):\n   if (2*abs(v[
5].(v[1]+(-1)^(t[1])*v[2]+(-1)^(t[2])*v[3]+(-1)^0*v[4])) > \n       No
rm(v[1]+(-1)^(t[1])*v[2]+(-1)^(t[2])*v[3]+(-1)^0*v[4],2)^2) then \n   \+
   print(\"not satisfied\",\"v_i,v_j,v_k,v_l,v_m\",1,+(-1)^(t[1])*2,(-
1)^(t[2])*3,(-1)^0*4,5); \n   end if;\nend do:\nfor s from 4 by 1 to 7
 do\n   t:=convert(s,base,2):\n   if (2*abs(v[5].(v[1]+(-1)^(t[1])*v[2
]+(-1)^(t[2])*v[3]+(-1)^(t[3])*v[4])) > \n       Norm(v[1]+(-1)^(t[1])
*v[2]+(-1)^(t[2])*v[3]+(-1)^(t[3])*v[4],2)^2) then \n      print(\"not
 satisfied\",\"v_i,v_j,v_k,v_l,v_m\",1,(-1)^(t[1])*2,+(-1)^(t[2])*3,(-
1)^(t[3])*4,5); \n   end if;\nend do:\n#checking for |v[i]+v[1]+v[2]+v
[3]+v[4]+v[5]|^2>=|v[i]|^2;\nfor s from 0 by 1 to 1 do\n   if (Norm(2*
v[1]+(-1)^s*v[2]+v[3]+v[4]+v[5],2)^2 < Norm(v[1],2)^2) then \n      pr
int(\"not satisfied\",\"2*v_1\") \n   end if;\nend do;\nfor s from 2 b
y 1 to 3 do\n   t:=convert(s,base,2):\n   if (Norm(2*v[1]+(-1)^(t[1])*
v[2]+(-1)^(t[2])*v[3]+v[4]+v[5],2)^2 < Norm(v[1],2)^2) then \n      pr
int(\"not satisfied\",\"2*v_1\") \n   end if; \nend do:\nfor s from 4 \+
by 1 to 7 do\n   t:=convert(s,base,2):\n   if (Norm(2*v[1]+(-1)^(t[1])
*v[2]+(-1)^(t[2])*v[3]+(-1)^(t[3])*v[4]+v[5],2)^2 < Norm(v[1],2)^2) th
en \n      print(\"not satisfied\",\"2*v_1\") \n   end if; \nend do:\n
for s from 8 by 1 to 15 do\n   t:=convert(s,base,2):\n   if (Norm(2*v[
1]+(-1)^(t[1])*v[2]+(-1)^(t[2])*v[3]+(-1)^(t[3])*v[4]+(-1)^(t[4])*v[5]
,2)^2 < Norm(v[1],2)^2) then \n      print(\"not satisfied\",\"2*v_1\"
) \n   end if; \nend do:\nfor s from 0 by 1 to 1 do\n   if (Norm(v[1]+
(-1)^s*2*v[2]+v[3]+v[4]+v[5],2)^2 < Norm(v[2],2)^2) then \n      print
(\"not satisfied\",\"2*v_2\") \n   end if;\nend do;\nfor s from 2 by 1
 to 3 do\n   t:=convert(s,base,2):\n   if (Norm(v[1]+(-1)^(t[1])*2*v[2
]+(-1)^(t[2])*v[3]+v[4]+v[5],2)^2 < Norm(v[2],2)^2) then \n      print
(\"not satisfied\",\"2*v_2\") \n   end if; \nend do:\nfor s from 4 by \+
1 to 7 do\n   t:=convert(s,base,2):\n   if (Norm(v[1]+(-1)^(t[1])*2*v[
2]+(-1)^(t[2])*v[3]+(-1)^(t[3])*v[4]+v[5],2)^2 < Norm(v[2],2)^2) then \+
\n      print(\"not satisfied\",\"2*v_2\") \n   end if; \nend do:\nfor
 s from 8 by 1 to 15 do\n   t:=convert(s,base,2):\n   if (Norm(v[1]+(-
1)^(t[1])*2*v[2]+(-1)^(t[2])*v[3]+(-1)^(t[3])*v[4]+(-1)^(t[4])*v[5],2)
^2 < Norm(v[2],2)^2) then \n      print(\"not satisfied\",\"2*v_2\") \+
\n   end if; \nend do:\nfor s from 0 by 1 to 1 do\n   if (Norm(v[1]+(-
1)^s*v[2]+2*v[3]+v[4]+v[5],2)^2 < Norm(v[3],2)^2) then \n      print(
\"not satisfied\",\"2*v_3\") \n   end if;\nend do;\nfor s from 2 by 1 \+
to 3 do\n   t:=convert(s,base,2):\n   if (Norm(v[1]+(-1)^(t[1])*v[2]+(
-1)^(t[2])*2*v[3]+v[4]+v[5],2)^2 < Norm(v[3],2)^2) then \n      print(
\"not satisfied\",\"2*v_3\") \n   end if; \nend do:\nfor s from 4 by 1
 to 7 do\n   t:=convert(s,base,2):\n   if (Norm(v[1]+(-1)^(t[1])*v[2]+
(-1)^(t[2])*2*v[3]+(-1)^(t[3])*v[4]+v[5],2)^2 < Norm(v[3],2)^2) then \+
\n      print(\"not satisfied\",\"2*v_3\") \n   end if; \nend do:\nfor
 s from 8 by 1 to 15 do\n   t:=convert(s,base,2):\n   if (Norm(v[1]+(-
1)^(t[1])*v[2]+(-1)^(t[2])*2*v[3]+(-1)^(t[3])*v[4]+(-1)^(t[4])*v[5],2)
^2 < Norm(v[3],2)^2) then \n      print(\"not satisfied\",\"2*v_3\") \+
\n   end if; \nend do:\nfor s from 0 by 1 to 1 do\n   if (Norm(v[1]+(-
1)^s*v[2]+v[3]+2*v[4]+v[5],2)^2 < Norm(v[4],2)^2) then \n      print(
\"not satisfied\",\"2*v_4\") \n   end if;\nend do;\nfor s from 2 by 1 \+
to 3 do\n   t:=convert(s,base,2):\n   if (Norm(v[1]+(-1)^(t[1])*v[2]+(
-1)^(t[2])*v[3]+2*v[4]+v[5],2)^2 < Norm(v[4],2)^2) then \n      print(
\"not satisfied\",\"2*v_4\") \n   end if; \nend do:\nfor s from 4 by 1
 to 7 do\n   t:=convert(s,base,2):\n   if (Norm(v[1]+(-1)^(t[1])*v[2]+
(-1)^(t[2])*v[3]+(-1)^(t[3])*2*v[4]+v[5],2)^2 < Norm(v[4],2)^2) then \+
\n      print(\"not satisfied\",\"2*v_4\") \n   end if; \nend do:\nfor
 s from 8 by 1 to 15 do\n   t:=convert(s,base,2):\n   if (Norm(v[1]+(-
1)^(t[1])*v[2]+(-1)^(t[2])*v[3]+(-1)^(t[3])*2*v[4]+(-1)^(t[4])*v[5],2)
^2 < Norm(v[4],2)^2) then \n      print(\"not satisfied\",\"2*v_4\") \+
\n   end if; \nend do:\nfor s from 0 by 1 to 1 do\n   if (Norm(v[1]+(-
1)^s*v[2]+v[3]+v[4]+2*v[5],2)^2 < Norm(v[5],2)^2) then \n      print(
\"not satisfied\",\"2*v_5\") \n   end if;\nend do;\nfor s from 2 by 1 \+
to 3 do\n   t:=convert(s,base,2):\n   if (Norm(v[1]+(-1)^(t[1])*v[2]+(
-1)^(t[2])*v[3]+v[4]+2*v[5],2)^2 < Norm(v[5],2)^2) then \n      print(
\"not satisfied\",\"2*v_5\") \n   end if; \nend do:\nfor s from 4 by 1
 to 7 do\n   t:=convert(s,base,2):\n   if (Norm(v[1]+(-1)^(t[1])*v[2]+
(-1)^(t[2])*v[3]+(-1)^(t[3])*v[4]+2*v[5],2)^2 < Norm(v[5],2)^2) then \+
\n      print(\"not satisfied\",\"2*v_5\") \n   end if; \nend do:\nfor
 s from 8 by 1 to 15 do\n   t:=convert(s,base,2):\n   if (Norm(v[1]+(-
1)^(t[1])*v[2]+(-1)^(t[2])*v[3]+(-1)^(t[3])*v[4]+(-1)^(t[4])*2*v[5],2)
^2 < Norm(v[5],2)^2) then \n      print(\"not satisfied\",\"2*v_5\") \+
\n   end if; \nend do:" }}{PARA 11 "" 1 "" {XPPMATH 20 "6'Q.not~satisf
ied6\"Q,v_i,v_j,v_kF$\"\"\"\"\"#\"\"%" }}}{EXCHG {PARA 0 "> " 0 "" 
{MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 365 "v[1]:=
Vector([4,-1,1,1,-1]):\nv[2]:=Vector([-1,4,1,1,-1]):\nv[3]:=Vector([-1
,-1,4,-1,-1]):\nv[4]:=Vector([-1,-1,-1,4,-1]):\nv[5]:=Vector([-2,-2,-2
,-2,-2]):\nv[1],v[2],v[3],v[4],v[5];\nprint(\"|v[1]|^2\"=Norm(v[1],2)^
2);\n#checking for decreasing order;\nfor i from 1 by 1 to 4 do \n   i
f (Norm(v[i],2)^2 > Norm(v[i+1],2)^2) then print(\"not satisfied\",(i,
i+1)) end if; \nend do;" }}{PARA 11 "" 1 "" {XPPMATH 20 "6'-%'RTABLEG6
%\"*Ss/;#-%'MATRIXG6#7'7#\"\"%7#!\"\"7#\"\"\"F/F-&%'VectorG6#%'columnG
-F$6%\"*/t/;#-F(6#7'F-F+F/F/F-F1-F$6%\"*ot/;#-F(6#7'F-F-F+F-F-F1-F$6%
\"*Ku/;#-F(6#7'F-F-F-F+F-F1-F$6%\"*'\\Zg@-F(6#7'7#!\"#FMFMFMFMF1" }}
{PARA 11 "" 1 "" {XPPMATH 20 "6#/Q)|grv[1]|gr^26\"\"#?" }}}{EXCHG 
{PARA 0 "> " 0 "" {MPLTEXT 1 0 6469 "#checking for 2|v[j].v[i]|=<|v[i]
|^2;\nL2:=choose(5, 2):\nfor i from 1 by 1 to numbcomb(5, 2) do\n   if
 (2*abs(v[L2[i][2]].v[L2[i][1]]) > Norm(v[L2[i][1]],2)^2) then \n     \+
 print(\"not satisfied\",\"v_i,v_j\",L2[i][1],L2[i][2]) \n   end if;\n
end do;\n#checking for 2|v[k].(v[i]+v[j])|=<|v[i]+v[j]|^2;\nL3:=choose
(5, 3):\nfor s from 0 by 1 to 1 do\n   for i from 1 by 1 to numbcomb(5
, 3) do\n      if (2*abs(v[L3[i][3]].(v[L3[i][1]]+(-1)^s*v[L3[i][2]]))
 > Norm(v[L3[i][1]]+(-1)^s*v[L3[i][2]],2)^2) then \n         print(\"n
ot satisfied\",\"v_i,v_j,v_k\",L3[i][1],(-1)^s*L3[i][2],L3[i][3]); \n \+
     end if;\n   end do;\nend do;\n#checking for 2|v[l].(v[i]+v[j]+v[k
])|=<|v[i]+v[j]+v[k]|^2;\nL4:=choose(5, 4):\nfor s from 0 by 1 to 1 do
\n   for i from 1 by 1 to numbcomb(5, 4) do\n      if (2*abs(v[L4[i][4
]].(v[L4[i][1]]+(-1)^s*v[L4[i][2]]+(-1)^0*v[L4[i][3]])) >\n         No
rm(v[L4[i][1]]+(-1)^s*v[L4[i][2]]+(-1)^0*v[L4[i][3]],2)^2) then \n    \+
     print(\"not satisfied\",\"v_i,v_j,v_k,v_l\",L4[i][1],(-1)^s*L4[i]
[2],(-1)^0*L4[i][3],L4[i][4]); \n      end if;\n   end do;\nend do;\nf
or s from 2 by 1 to 3 do\n   t:=convert(s,base,2):\n   for i from 1 by
 1 to numbcomb(5, 4) do\n      if (2*abs(v[L4[i][4]].(v[L4[i][1]]+(-1)
^(t[1])*v[L4[i][2]]+(-1)^(t[2])*v[L4[i][3]])) >\n         Norm(v[L4[i]
[1]]+(-1)^(t[1])*v[L4[i][2]]+(-1)^(t[2])*v[L4[i][3]],2)^2) then \n    \+
     print(\"not satisfied\",\"v_i,v_j,v_k,v_l\",L4[i][1],(-1)^(t[1])*
L4[i][2],(-1)^(t[2])*L4[i][3],L4[i][4]); \n      end if;\n   end do;\n
end do:\n#checking for 2|v[m].(v[i]+v[j]+v[k]+v[l])|=<|v[i]+v[j]+v[k]+
v[l]|^2;\nfor s from 0 by 1 to 1 do\n   if (2*abs(v[5].(v[1]+(-1)^s*v[
2]+(-1)^0*v[3]+(-1)^0*v[4])) > \n       Norm(v[1]+(-1)^s*v[2]+(-1)^0*v
[3]+(-1)^0*v[4],2)^2) then \n      print(\"not satisfied\",\"v_i,v_j,v
_k,v_l,v_m\",1,(-1)^s*2,3,4,5); \n   end if;\nend do;\nfor s from 2 by
 1 to 3 do\n   t:=convert(s,base,2):\n   if (2*abs(v[5].(v[1]+(-1)^(t[
1])*v[2]+(-1)^(t[2])*v[3]+(-1)^0*v[4])) > \n       Norm(v[1]+(-1)^(t[1
])*v[2]+(-1)^(t[2])*v[3]+(-1)^0*v[4],2)^2) then \n      print(\"not sa
tisfied\",\"v_i,v_j,v_k,v_l,v_m\",1,+(-1)^(t[1])*2,(-1)^(t[2])*3,(-1)^
0*4,5); \n   end if;\nend do:\nfor s from 4 by 1 to 7 do\n   t:=conver
t(s,base,2):\n   if (2*abs(v[5].(v[1]+(-1)^(t[1])*v[2]+(-1)^(t[2])*v[3
]+(-1)^(t[3])*v[4])) > \n       Norm(v[1]+(-1)^(t[1])*v[2]+(-1)^(t[2])
*v[3]+(-1)^(t[3])*v[4],2)^2) then \n      print(\"not satisfied\",\"v_
i,v_j,v_k,v_l,v_m\",1,(-1)^(t[1])*2,+(-1)^(t[2])*3,(-1)^(t[3])*4,5); \+
\n   end if;\nend do:\n#checking for |v[i]+v[1]+v[2]+v[3]+v[4]+v[5]|^2
>=|v[i]|^2;\nfor s from 0 by 1 to 1 do\n   if (Norm(2*v[1]+(-1)^s*v[2]
+v[3]+v[4]+v[5],2)^2 < Norm(v[1],2)^2) then \n      print(\"not satisf
ied\",\"2*v_1\") \n   end if;\nend do;\nfor s from 2 by 1 to 3 do\n   \+
t:=convert(s,base,2):\n   if (Norm(2*v[1]+(-1)^(t[1])*v[2]+(-1)^(t[2])
*v[3]+v[4]+v[5],2)^2 < Norm(v[1],2)^2) then \n      print(\"not satisf
ied\",\"2*v_1\") \n   end if; \nend do:\nfor s from 4 by 1 to 7 do\n  \+
 t:=convert(s,base,2):\n   if (Norm(2*v[1]+(-1)^(t[1])*v[2]+(-1)^(t[2]
)*v[3]+(-1)^(t[3])*v[4]+v[5],2)^2 < Norm(v[1],2)^2) then \n      print
(\"not satisfied\",\"2*v_1\") \n   end if; \nend do:\nfor s from 8 by \+
1 to 15 do\n   t:=convert(s,base,2):\n   if (Norm(2*v[1]+(-1)^(t[1])*v
[2]+(-1)^(t[2])*v[3]+(-1)^(t[3])*v[4]+(-1)^(t[4])*v[5],2)^2 < Norm(v[1
],2)^2) then \n      print(\"not satisfied\",\"2*v_1\") \n   end if; \+
\nend do:\nfor s from 0 by 1 to 1 do\n   if (Norm(v[1]+(-1)^s*2*v[2]+v
[3]+v[4]+v[5],2)^2 < Norm(v[2],2)^2) then \n      print(\"not satisfie
d\",\"2*v_2\") \n   end if;\nend do;\nfor s from 2 by 1 to 3 do\n   t:
=convert(s,base,2):\n   if (Norm(v[1]+(-1)^(t[1])*2*v[2]+(-1)^(t[2])*v
[3]+v[4]+v[5],2)^2 < Norm(v[2],2)^2) then \n      print(\"not satisfie
d\",\"2*v_2\") \n   end if; \nend do:\nfor s from 4 by 1 to 7 do\n   t
:=convert(s,base,2):\n   if (Norm(v[1]+(-1)^(t[1])*2*v[2]+(-1)^(t[2])*
v[3]+(-1)^(t[3])*v[4]+v[5],2)^2 < Norm(v[2],2)^2) then \n      print(
\"not satisfied\",\"2*v_2\") \n   end if; \nend do:\nfor s from 8 by 1
 to 15 do\n   t:=convert(s,base,2):\n   if (Norm(v[1]+(-1)^(t[1])*2*v[
2]+(-1)^(t[2])*v[3]+(-1)^(t[3])*v[4]+(-1)^(t[4])*v[5],2)^2 < Norm(v[2]
,2)^2) then \n      print(\"not satisfied\",\"2*v_2\") \n   end if; \n
end do:\nfor s from 0 by 1 to 1 do\n   if (Norm(v[1]+(-1)^s*v[2]+2*v[3
]+v[4]+v[5],2)^2 < Norm(v[3],2)^2) then \n      print(\"not satisfied
\",\"2*v_3\") \n   end if;\nend do;\nfor s from 2 by 1 to 3 do\n   t:=
convert(s,base,2):\n   if (Norm(v[1]+(-1)^(t[1])*v[2]+(-1)^(t[2])*2*v[
3]+v[4]+v[5],2)^2 < Norm(v[3],2)^2) then \n      print(\"not satisfied
\",\"2*v_3\") \n   end if; \nend do:\nfor s from 4 by 1 to 7 do\n   t:
=convert(s,base,2):\n   if (Norm(v[1]+(-1)^(t[1])*v[2]+(-1)^(t[2])*2*v
[3]+(-1)^(t[3])*v[4]+v[5],2)^2 < Norm(v[3],2)^2) then \n      print(\"
not satisfied\",\"2*v_3\") \n   end if; \nend do:\nfor s from 8 by 1 t
o 15 do\n   t:=convert(s,base,2):\n   if (Norm(v[1]+(-1)^(t[1])*v[2]+(
-1)^(t[2])*2*v[3]+(-1)^(t[3])*v[4]+(-1)^(t[4])*v[5],2)^2 < Norm(v[3],2
)^2) then \n      print(\"not satisfied\",\"2*v_3\") \n   end if; \nen
d do:\nfor s from 0 by 1 to 1 do\n   if (Norm(v[1]+(-1)^s*v[2]+v[3]+2*
v[4]+v[5],2)^2 < Norm(v[4],2)^2) then \n      print(\"not satisfied\",
\"2*v_4\") \n   end if;\nend do;\nfor s from 2 by 1 to 3 do\n   t:=con
vert(s,base,2):\n   if (Norm(v[1]+(-1)^(t[1])*v[2]+(-1)^(t[2])*v[3]+2*
v[4]+v[5],2)^2 < Norm(v[4],2)^2) then \n      print(\"not satisfied\",
\"2*v_4\") \n   end if; \nend do:\nfor s from 4 by 1 to 7 do\n   t:=co
nvert(s,base,2):\n   if (Norm(v[1]+(-1)^(t[1])*v[2]+(-1)^(t[2])*v[3]+(
-1)^(t[3])*2*v[4]+v[5],2)^2 < Norm(v[4],2)^2) then \n      print(\"not
 satisfied\",\"2*v_4\") \n   end if; \nend do:\nfor s from 8 by 1 to 1
5 do\n   t:=convert(s,base,2):\n   if (Norm(v[1]+(-1)^(t[1])*v[2]+(-1)
^(t[2])*v[3]+(-1)^(t[3])*2*v[4]+(-1)^(t[4])*v[5],2)^2 < Norm(v[4],2)^2
) then \n      print(\"not satisfied\",\"2*v_4\") \n   end if; \nend d
o:\nfor s from 0 by 1 to 1 do\n   if (Norm(v[1]+(-1)^s*v[2]+v[3]+v[4]+
2*v[5],2)^2 < Norm(v[5],2)^2) then \n      print(\"not satisfied\",\"2
*v_5\") \n   end if;\nend do;\nfor s from 2 by 1 to 3 do\n   t:=conver
t(s,base,2):\n   if (Norm(v[1]+(-1)^(t[1])*v[2]+(-1)^(t[2])*v[3]+v[4]+
2*v[5],2)^2 < Norm(v[5],2)^2) then \n      print(\"not satisfied\",\"2
*v_5\") \n   end if; \nend do:\nfor s from 4 by 1 to 7 do\n   t:=conve
rt(s,base,2):\n   if (Norm(v[1]+(-1)^(t[1])*v[2]+(-1)^(t[2])*v[3]+(-1)
^(t[3])*v[4]+2*v[5],2)^2 < Norm(v[5],2)^2) then \n      print(\"not sa
tisfied\",\"2*v_5\") \n   end if; \nend do:\nfor s from 8 by 1 to 15 d
o\n   t:=convert(s,base,2):\n   if (Norm(v[1]+(-1)^(t[1])*v[2]+(-1)^(t
[2])*v[3]+(-1)^(t[3])*v[4]+(-1)^(t[4])*2*v[5],2)^2 < Norm(v[5],2)^2) t
hen \n      print(\"not satisfied\",\"2*v_5\") \n   end if; \nend do:
" }}{PARA 11 "" 1 "" {XPPMATH 20 "6'Q.not~satisfied6\"Q,v_i,v_j,v_kF$
\"\"\"\"\"#\"\"&" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}
{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 365 "v[1]:=Vector([4,-1,-1,-1,-1
]):\nv[2]:=Vector([-1,4,-1,-1,-1]):\nv[3]:=Vector([-1,1,4,-1,-1]):\nv[
4]:=Vector([-1,1,-1,4,1]):\nv[5]:=Vector([-2,-2,-2,2,-2]):\nv[1],v[2],
v[3],v[4],v[5];\nprint(\"|v[1]|^2\"=Norm(v[1],2)^2);\n#checking for de
creasing order;\nfor i from 1 by 1 to 4 do \n   if (Norm(v[i],2)^2 > N
orm(v[i+1],2)^2) then print(\"not satisfied\",(i,i+1)) end if; \nend d
o;" }}{PARA 11 "" 1 "" {XPPMATH 20 "6'-%'RTABLEG6%\"*c\")H$>-%'MATRIXG
6#7'7#\"\"%7#!\"\"F-F-F-&%'VectorG6#%'columnG-F$6%\"*?#)H$>-F(6#7'F-F+
F-F-F-F/-F$6%\"*%G)H$>-F(6#7'F-7#\"\"\"F+F-F-F/-F$6%\"*[$)H$>-F(6#7'F-
F?F-F+F?F/-F$6%\"*7%)H$>-F(6#7'7#!\"#FMFM7#\"\"#FMF/" }}{PARA 11 "" 1 
"" {XPPMATH 20 "6#/Q)|grv[1]|gr^26\"\"#?" }}}{EXCHG {PARA 0 "> " 0 "" 
{MPLTEXT 1 0 6469 "#checking for 2|v[j].v[i]|=<|v[i]|^2;\nL2:=choose(5
, 2):\nfor i from 1 by 1 to numbcomb(5, 2) do\n   if (2*abs(v[L2[i][2]
].v[L2[i][1]]) > Norm(v[L2[i][1]],2)^2) then \n      print(\"not satis
fied\",\"v_i,v_j\",L2[i][1],L2[i][2]) \n   end if;\nend do;\n#checking
 for 2|v[k].(v[i]+v[j])|=<|v[i]+v[j]|^2;\nL3:=choose(5, 3):\nfor s fro
m 0 by 1 to 1 do\n   for i from 1 by 1 to numbcomb(5, 3) do\n      if \+
(2*abs(v[L3[i][3]].(v[L3[i][1]]+(-1)^s*v[L3[i][2]])) > Norm(v[L3[i][1]
]+(-1)^s*v[L3[i][2]],2)^2) then \n         print(\"not satisfied\",\"v
_i,v_j,v_k\",L3[i][1],(-1)^s*L3[i][2],L3[i][3]); \n      end if;\n   e
nd do;\nend do;\n#checking for 2|v[l].(v[i]+v[j]+v[k])|=<|v[i]+v[j]+v[
k]|^2;\nL4:=choose(5, 4):\nfor s from 0 by 1 to 1 do\n   for i from 1 \+
by 1 to numbcomb(5, 4) do\n      if (2*abs(v[L4[i][4]].(v[L4[i][1]]+(-
1)^s*v[L4[i][2]]+(-1)^0*v[L4[i][3]])) >\n         Norm(v[L4[i][1]]+(-1
)^s*v[L4[i][2]]+(-1)^0*v[L4[i][3]],2)^2) then \n         print(\"not s
atisfied\",\"v_i,v_j,v_k,v_l\",L4[i][1],(-1)^s*L4[i][2],(-1)^0*L4[i][3
],L4[i][4]); \n      end if;\n   end do;\nend do;\nfor s from 2 by 1 t
o 3 do\n   t:=convert(s,base,2):\n   for i from 1 by 1 to numbcomb(5, \+
4) do\n      if (2*abs(v[L4[i][4]].(v[L4[i][1]]+(-1)^(t[1])*v[L4[i][2]
]+(-1)^(t[2])*v[L4[i][3]])) >\n         Norm(v[L4[i][1]]+(-1)^(t[1])*v
[L4[i][2]]+(-1)^(t[2])*v[L4[i][3]],2)^2) then \n         print(\"not s
atisfied\",\"v_i,v_j,v_k,v_l\",L4[i][1],(-1)^(t[1])*L4[i][2],(-1)^(t[2
])*L4[i][3],L4[i][4]); \n      end if;\n   end do;\nend do:\n#checking
 for 2|v[m].(v[i]+v[j]+v[k]+v[l])|=<|v[i]+v[j]+v[k]+v[l]|^2;\nfor s fr
om 0 by 1 to 1 do\n   if (2*abs(v[5].(v[1]+(-1)^s*v[2]+(-1)^0*v[3]+(-1
)^0*v[4])) > \n       Norm(v[1]+(-1)^s*v[2]+(-1)^0*v[3]+(-1)^0*v[4],2)
^2) then \n      print(\"not satisfied\",\"v_i,v_j,v_k,v_l,v_m\",1,(-1
)^s*2,3,4,5); \n   end if;\nend do;\nfor s from 2 by 1 to 3 do\n   t:=
convert(s,base,2):\n   if (2*abs(v[5].(v[1]+(-1)^(t[1])*v[2]+(-1)^(t[2
])*v[3]+(-1)^0*v[4])) > \n       Norm(v[1]+(-1)^(t[1])*v[2]+(-1)^(t[2]
)*v[3]+(-1)^0*v[4],2)^2) then \n      print(\"not satisfied\",\"v_i,v_
j,v_k,v_l,v_m\",1,+(-1)^(t[1])*2,(-1)^(t[2])*3,(-1)^0*4,5); \n   end i
f;\nend do:\nfor s from 4 by 1 to 7 do\n   t:=convert(s,base,2):\n   i
f (2*abs(v[5].(v[1]+(-1)^(t[1])*v[2]+(-1)^(t[2])*v[3]+(-1)^(t[3])*v[4]
)) > \n       Norm(v[1]+(-1)^(t[1])*v[2]+(-1)^(t[2])*v[3]+(-1)^(t[3])*
v[4],2)^2) then \n      print(\"not satisfied\",\"v_i,v_j,v_k,v_l,v_m
\",1,(-1)^(t[1])*2,+(-1)^(t[2])*3,(-1)^(t[3])*4,5); \n   end if;\nend \+
do:\n#checking for |v[i]+v[1]+v[2]+v[3]+v[4]+v[5]|^2>=|v[i]|^2;\nfor s
 from 0 by 1 to 1 do\n   if (Norm(2*v[1]+(-1)^s*v[2]+v[3]+v[4]+v[5],2)
^2 < Norm(v[1],2)^2) then \n      print(\"not satisfied\",\"2*v_1\") \+
\n   end if;\nend do;\nfor s from 2 by 1 to 3 do\n   t:=convert(s,base
,2):\n   if (Norm(2*v[1]+(-1)^(t[1])*v[2]+(-1)^(t[2])*v[3]+v[4]+v[5],2
)^2 < Norm(v[1],2)^2) then \n      print(\"not satisfied\",\"2*v_1\") \+
\n   end if; \nend do:\nfor s from 4 by 1 to 7 do\n   t:=convert(s,bas
e,2):\n   if (Norm(2*v[1]+(-1)^(t[1])*v[2]+(-1)^(t[2])*v[3]+(-1)^(t[3]
)*v[4]+v[5],2)^2 < Norm(v[1],2)^2) then \n      print(\"not satisfied
\",\"2*v_1\") \n   end if; \nend do:\nfor s from 8 by 1 to 15 do\n   t
:=convert(s,base,2):\n   if (Norm(2*v[1]+(-1)^(t[1])*v[2]+(-1)^(t[2])*
v[3]+(-1)^(t[3])*v[4]+(-1)^(t[4])*v[5],2)^2 < Norm(v[1],2)^2) then \n \+
     print(\"not satisfied\",\"2*v_1\") \n   end if; \nend do:\nfor s \+
from 0 by 1 to 1 do\n   if (Norm(v[1]+(-1)^s*2*v[2]+v[3]+v[4]+v[5],2)^
2 < Norm(v[2],2)^2) then \n      print(\"not satisfied\",\"2*v_2\") \n
   end if;\nend do;\nfor s from 2 by 1 to 3 do\n   t:=convert(s,base,2
):\n   if (Norm(v[1]+(-1)^(t[1])*2*v[2]+(-1)^(t[2])*v[3]+v[4]+v[5],2)^
2 < Norm(v[2],2)^2) then \n      print(\"not satisfied\",\"2*v_2\") \n
   end if; \nend do:\nfor s from 4 by 1 to 7 do\n   t:=convert(s,base,
2):\n   if (Norm(v[1]+(-1)^(t[1])*2*v[2]+(-1)^(t[2])*v[3]+(-1)^(t[3])*
v[4]+v[5],2)^2 < Norm(v[2],2)^2) then \n      print(\"not satisfied\",
\"2*v_2\") \n   end if; \nend do:\nfor s from 8 by 1 to 15 do\n   t:=c
onvert(s,base,2):\n   if (Norm(v[1]+(-1)^(t[1])*2*v[2]+(-1)^(t[2])*v[3
]+(-1)^(t[3])*v[4]+(-1)^(t[4])*v[5],2)^2 < Norm(v[2],2)^2) then \n    \+
  print(\"not satisfied\",\"2*v_2\") \n   end if; \nend do:\nfor s fro
m 0 by 1 to 1 do\n   if (Norm(v[1]+(-1)^s*v[2]+2*v[3]+v[4]+v[5],2)^2 <
 Norm(v[3],2)^2) then \n      print(\"not satisfied\",\"2*v_3\") \n   \+
end if;\nend do;\nfor s from 2 by 1 to 3 do\n   t:=convert(s,base,2):
\n   if (Norm(v[1]+(-1)^(t[1])*v[2]+(-1)^(t[2])*2*v[3]+v[4]+v[5],2)^2 \+
< Norm(v[3],2)^2) then \n      print(\"not satisfied\",\"2*v_3\") \n  \+
 end if; \nend do:\nfor s from 4 by 1 to 7 do\n   t:=convert(s,base,2)
:\n   if (Norm(v[1]+(-1)^(t[1])*v[2]+(-1)^(t[2])*2*v[3]+(-1)^(t[3])*v[
4]+v[5],2)^2 < Norm(v[3],2)^2) then \n      print(\"not satisfied\",\"
2*v_3\") \n   end if; \nend do:\nfor s from 8 by 1 to 15 do\n   t:=con
vert(s,base,2):\n   if (Norm(v[1]+(-1)^(t[1])*v[2]+(-1)^(t[2])*2*v[3]+
(-1)^(t[3])*v[4]+(-1)^(t[4])*v[5],2)^2 < Norm(v[3],2)^2) then \n      \+
print(\"not satisfied\",\"2*v_3\") \n   end if; \nend do:\nfor s from \+
0 by 1 to 1 do\n   if (Norm(v[1]+(-1)^s*v[2]+v[3]+2*v[4]+v[5],2)^2 < N
orm(v[4],2)^2) then \n      print(\"not satisfied\",\"2*v_4\") \n   en
d if;\nend do;\nfor s from 2 by 1 to 3 do\n   t:=convert(s,base,2):\n \+
  if (Norm(v[1]+(-1)^(t[1])*v[2]+(-1)^(t[2])*v[3]+2*v[4]+v[5],2)^2 < N
orm(v[4],2)^2) then \n      print(\"not satisfied\",\"2*v_4\") \n   en
d if; \nend do:\nfor s from 4 by 1 to 7 do\n   t:=convert(s,base,2):\n
   if (Norm(v[1]+(-1)^(t[1])*v[2]+(-1)^(t[2])*v[3]+(-1)^(t[3])*2*v[4]+
v[5],2)^2 < Norm(v[4],2)^2) then \n      print(\"not satisfied\",\"2*v
_4\") \n   end if; \nend do:\nfor s from 8 by 1 to 15 do\n   t:=conver
t(s,base,2):\n   if (Norm(v[1]+(-1)^(t[1])*v[2]+(-1)^(t[2])*v[3]+(-1)^
(t[3])*2*v[4]+(-1)^(t[4])*v[5],2)^2 < Norm(v[4],2)^2) then \n      pri
nt(\"not satisfied\",\"2*v_4\") \n   end if; \nend do:\nfor s from 0 b
y 1 to 1 do\n   if (Norm(v[1]+(-1)^s*v[2]+v[3]+v[4]+2*v[5],2)^2 < Norm
(v[5],2)^2) then \n      print(\"not satisfied\",\"2*v_5\") \n   end i
f;\nend do;\nfor s from 2 by 1 to 3 do\n   t:=convert(s,base,2):\n   i
f (Norm(v[1]+(-1)^(t[1])*v[2]+(-1)^(t[2])*v[3]+v[4]+2*v[5],2)^2 < Norm
(v[5],2)^2) then \n      print(\"not satisfied\",\"2*v_5\") \n   end i
f; \nend do:\nfor s from 4 by 1 to 7 do\n   t:=convert(s,base,2):\n   \+
if (Norm(v[1]+(-1)^(t[1])*v[2]+(-1)^(t[2])*v[3]+(-1)^(t[3])*v[4]+2*v[5
],2)^2 < Norm(v[5],2)^2) then \n      print(\"not satisfied\",\"2*v_5
\") \n   end if; \nend do:\nfor s from 8 by 1 to 15 do\n   t:=convert(
s,base,2):\n   if (Norm(v[1]+(-1)^(t[1])*v[2]+(-1)^(t[2])*v[3]+(-1)^(t
[3])*v[4]+(-1)^(t[4])*2*v[5],2)^2 < Norm(v[5],2)^2) then \n      print
(\"not satisfied\",\"2*v_5\") \n   end if; \nend do:" }}{PARA 11 "" 1 
"" {XPPMATH 20 "6'Q.not~satisfied6\"Q,v_i,v_j,v_kF$\"\"\"\"\"$\"\"%" }
}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "> " 0 
"" {MPLTEXT 1 0 365 "v[1]:=Vector([4,1,-1,1,-1]):\nv[2]:=Vector([-1,4,
-1,-1,-1]):\nv[3]:=Vector([-1,1,4,1,-1]):\nv[4]:=Vector([-1,-1,-1,4,-1
]):\nv[5]:=Vector([-2,-2,-2,-2,-2]):\nv[1],v[2],v[3],v[4],v[5];\nprint
(\"|v[1]|^2\"=Norm(v[1],2)^2);\n#checking for decreasing order;\nfor i
 from 1 by 1 to 4 do \n   if (Norm(v[i],2)^2 > Norm(v[i+1],2)^2) then \+
print(\"not satisfied\",(i,i+1)) end if; \nend do;" }}{PARA 11 "" 1 "
" {XPPMATH 20 "6'-%'RTABLEG6%\"*?6,'=-%'MATRIXG6#7'7#\"\"%7#\"\"\"7#!
\"\"F-F/&%'VectorG6#%'columnG-F$6%\"*%=6g=-F(6#7'F/F+F/F/F/F1-F$6%\"*[
7,'=-F(6#7'F/F-F+F-F/F1-F$6%\"*78,'=-F(6#7'F/F/F/F+F/F1-F$6%\"*w8,'=-F
(6#7'7#!\"#FMFMFMFMF1" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#/Q)|grv[1]|gr
^26\"\"#?" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 6469 "#checking fo
r 2|v[j].v[i]|=<|v[i]|^2;\nL2:=choose(5, 2):\nfor i from 1 by 1 to num
bcomb(5, 2) do\n   if (2*abs(v[L2[i][2]].v[L2[i][1]]) > Norm(v[L2[i][1
]],2)^2) then \n      print(\"not satisfied\",\"v_i,v_j\",L2[i][1],L2[
i][2]) \n   end if;\nend do;\n#checking for 2|v[k].(v[i]+v[j])|=<|v[i]
+v[j]|^2;\nL3:=choose(5, 3):\nfor s from 0 by 1 to 1 do\n   for i from
 1 by 1 to numbcomb(5, 3) do\n      if (2*abs(v[L3[i][3]].(v[L3[i][1]]
+(-1)^s*v[L3[i][2]])) > Norm(v[L3[i][1]]+(-1)^s*v[L3[i][2]],2)^2) then
 \n         print(\"not satisfied\",\"v_i,v_j,v_k\",L3[i][1],(-1)^s*L3
[i][2],L3[i][3]); \n      end if;\n   end do;\nend do;\n#checking for \+
2|v[l].(v[i]+v[j]+v[k])|=<|v[i]+v[j]+v[k]|^2;\nL4:=choose(5, 4):\nfor \+
s from 0 by 1 to 1 do\n   for i from 1 by 1 to numbcomb(5, 4) do\n    \+
  if (2*abs(v[L4[i][4]].(v[L4[i][1]]+(-1)^s*v[L4[i][2]]+(-1)^0*v[L4[i]
[3]])) >\n         Norm(v[L4[i][1]]+(-1)^s*v[L4[i][2]]+(-1)^0*v[L4[i][
3]],2)^2) then \n         print(\"not satisfied\",\"v_i,v_j,v_k,v_l\",
L4[i][1],(-1)^s*L4[i][2],(-1)^0*L4[i][3],L4[i][4]); \n      end if;\n \+
  end do;\nend do;\nfor s from 2 by 1 to 3 do\n   t:=convert(s,base,2)
:\n   for i from 1 by 1 to numbcomb(5, 4) do\n      if (2*abs(v[L4[i][
4]].(v[L4[i][1]]+(-1)^(t[1])*v[L4[i][2]]+(-1)^(t[2])*v[L4[i][3]])) >\n
         Norm(v[L4[i][1]]+(-1)^(t[1])*v[L4[i][2]]+(-1)^(t[2])*v[L4[i][
3]],2)^2) then \n         print(\"not satisfied\",\"v_i,v_j,v_k,v_l\",
L4[i][1],(-1)^(t[1])*L4[i][2],(-1)^(t[2])*L4[i][3],L4[i][4]); \n      \+
end if;\n   end do;\nend do:\n#checking for 2|v[m].(v[i]+v[j]+v[k]+v[l
])|=<|v[i]+v[j]+v[k]+v[l]|^2;\nfor s from 0 by 1 to 1 do\n   if (2*abs
(v[5].(v[1]+(-1)^s*v[2]+(-1)^0*v[3]+(-1)^0*v[4])) > \n       Norm(v[1]
+(-1)^s*v[2]+(-1)^0*v[3]+(-1)^0*v[4],2)^2) then \n      print(\"not sa
tisfied\",\"v_i,v_j,v_k,v_l,v_m\",1,(-1)^s*2,3,4,5); \n   end if;\nend
 do;\nfor s from 2 by 1 to 3 do\n   t:=convert(s,base,2):\n   if (2*ab
s(v[5].(v[1]+(-1)^(t[1])*v[2]+(-1)^(t[2])*v[3]+(-1)^0*v[4])) > \n     \+
  Norm(v[1]+(-1)^(t[1])*v[2]+(-1)^(t[2])*v[3]+(-1)^0*v[4],2)^2) then \+
\n      print(\"not satisfied\",\"v_i,v_j,v_k,v_l,v_m\",1,+(-1)^(t[1])
*2,(-1)^(t[2])*3,(-1)^0*4,5); \n   end if;\nend do:\nfor s from 4 by 1
 to 7 do\n   t:=convert(s,base,2):\n   if (2*abs(v[5].(v[1]+(-1)^(t[1]
)*v[2]+(-1)^(t[2])*v[3]+(-1)^(t[3])*v[4])) > \n       Norm(v[1]+(-1)^(
t[1])*v[2]+(-1)^(t[2])*v[3]+(-1)^(t[3])*v[4],2)^2) then \n      print(
\"not satisfied\",\"v_i,v_j,v_k,v_l,v_m\",1,(-1)^(t[1])*2,+(-1)^(t[2])
*3,(-1)^(t[3])*4,5); \n   end if;\nend do:\n#checking for |v[i]+v[1]+v
[2]+v[3]+v[4]+v[5]|^2>=|v[i]|^2;\nfor s from 0 by 1 to 1 do\n   if (No
rm(2*v[1]+(-1)^s*v[2]+v[3]+v[4]+v[5],2)^2 < Norm(v[1],2)^2) then \n   \+
   print(\"not satisfied\",\"2*v_1\") \n   end if;\nend do;\nfor s fro
m 2 by 1 to 3 do\n   t:=convert(s,base,2):\n   if (Norm(2*v[1]+(-1)^(t
[1])*v[2]+(-1)^(t[2])*v[3]+v[4]+v[5],2)^2 < Norm(v[1],2)^2) then \n   \+
   print(\"not satisfied\",\"2*v_1\") \n   end if; \nend do:\nfor s fr
om 4 by 1 to 7 do\n   t:=convert(s,base,2):\n   if (Norm(2*v[1]+(-1)^(
t[1])*v[2]+(-1)^(t[2])*v[3]+(-1)^(t[3])*v[4]+v[5],2)^2 < Norm(v[1],2)^
2) then \n      print(\"not satisfied\",\"2*v_1\") \n   end if; \nend \+
do:\nfor s from 8 by 1 to 15 do\n   t:=convert(s,base,2):\n   if (Norm
(2*v[1]+(-1)^(t[1])*v[2]+(-1)^(t[2])*v[3]+(-1)^(t[3])*v[4]+(-1)^(t[4])
*v[5],2)^2 < Norm(v[1],2)^2) then \n      print(\"not satisfied\",\"2*
v_1\") \n   end if; \nend do:\nfor s from 0 by 1 to 1 do\n   if (Norm(
v[1]+(-1)^s*2*v[2]+v[3]+v[4]+v[5],2)^2 < Norm(v[2],2)^2) then \n      \+
print(\"not satisfied\",\"2*v_2\") \n   end if;\nend do;\nfor s from 2
 by 1 to 3 do\n   t:=convert(s,base,2):\n   if (Norm(v[1]+(-1)^(t[1])*
2*v[2]+(-1)^(t[2])*v[3]+v[4]+v[5],2)^2 < Norm(v[2],2)^2) then \n      \+
print(\"not satisfied\",\"2*v_2\") \n   end if; \nend do:\nfor s from \+
4 by 1 to 7 do\n   t:=convert(s,base,2):\n   if (Norm(v[1]+(-1)^(t[1])
*2*v[2]+(-1)^(t[2])*v[3]+(-1)^(t[3])*v[4]+v[5],2)^2 < Norm(v[2],2)^2) \+
then \n      print(\"not satisfied\",\"2*v_2\") \n   end if; \nend do:
\nfor s from 8 by 1 to 15 do\n   t:=convert(s,base,2):\n   if (Norm(v[
1]+(-1)^(t[1])*2*v[2]+(-1)^(t[2])*v[3]+(-1)^(t[3])*v[4]+(-1)^(t[4])*v[
5],2)^2 < Norm(v[2],2)^2) then \n      print(\"not satisfied\",\"2*v_2
\") \n   end if; \nend do:\nfor s from 0 by 1 to 1 do\n   if (Norm(v[1
]+(-1)^s*v[2]+2*v[3]+v[4]+v[5],2)^2 < Norm(v[3],2)^2) then \n      pri
nt(\"not satisfied\",\"2*v_3\") \n   end if;\nend do;\nfor s from 2 by
 1 to 3 do\n   t:=convert(s,base,2):\n   if (Norm(v[1]+(-1)^(t[1])*v[2
]+(-1)^(t[2])*2*v[3]+v[4]+v[5],2)^2 < Norm(v[3],2)^2) then \n      pri
nt(\"not satisfied\",\"2*v_3\") \n   end if; \nend do:\nfor s from 4 b
y 1 to 7 do\n   t:=convert(s,base,2):\n   if (Norm(v[1]+(-1)^(t[1])*v[
2]+(-1)^(t[2])*2*v[3]+(-1)^(t[3])*v[4]+v[5],2)^2 < Norm(v[3],2)^2) the
n \n      print(\"not satisfied\",\"2*v_3\") \n   end if; \nend do:\nf
or s from 8 by 1 to 15 do\n   t:=convert(s,base,2):\n   if (Norm(v[1]+
(-1)^(t[1])*v[2]+(-1)^(t[2])*2*v[3]+(-1)^(t[3])*v[4]+(-1)^(t[4])*v[5],
2)^2 < Norm(v[3],2)^2) then \n      print(\"not satisfied\",\"2*v_3\")
 \n   end if; \nend do:\nfor s from 0 by 1 to 1 do\n   if (Norm(v[1]+(
-1)^s*v[2]+v[3]+2*v[4]+v[5],2)^2 < Norm(v[4],2)^2) then \n      print(
\"not satisfied\",\"2*v_4\") \n   end if;\nend do;\nfor s from 2 by 1 \+
to 3 do\n   t:=convert(s,base,2):\n   if (Norm(v[1]+(-1)^(t[1])*v[2]+(
-1)^(t[2])*v[3]+2*v[4]+v[5],2)^2 < Norm(v[4],2)^2) then \n      print(
\"not satisfied\",\"2*v_4\") \n   end if; \nend do:\nfor s from 4 by 1
 to 7 do\n   t:=convert(s,base,2):\n   if (Norm(v[1]+(-1)^(t[1])*v[2]+
(-1)^(t[2])*v[3]+(-1)^(t[3])*2*v[4]+v[5],2)^2 < Norm(v[4],2)^2) then \+
\n      print(\"not satisfied\",\"2*v_4\") \n   end if; \nend do:\nfor
 s from 8 by 1 to 15 do\n   t:=convert(s,base,2):\n   if (Norm(v[1]+(-
1)^(t[1])*v[2]+(-1)^(t[2])*v[3]+(-1)^(t[3])*2*v[4]+(-1)^(t[4])*v[5],2)
^2 < Norm(v[4],2)^2) then \n      print(\"not satisfied\",\"2*v_4\") \+
\n   end if; \nend do:\nfor s from 0 by 1 to 1 do\n   if (Norm(v[1]+(-
1)^s*v[2]+v[3]+v[4]+2*v[5],2)^2 < Norm(v[5],2)^2) then \n      print(
\"not satisfied\",\"2*v_5\") \n   end if;\nend do;\nfor s from 2 by 1 \+
to 3 do\n   t:=convert(s,base,2):\n   if (Norm(v[1]+(-1)^(t[1])*v[2]+(
-1)^(t[2])*v[3]+v[4]+2*v[5],2)^2 < Norm(v[5],2)^2) then \n      print(
\"not satisfied\",\"2*v_5\") \n   end if; \nend do:\nfor s from 4 by 1
 to 7 do\n   t:=convert(s,base,2):\n   if (Norm(v[1]+(-1)^(t[1])*v[2]+
(-1)^(t[2])*v[3]+(-1)^(t[3])*v[4]+2*v[5],2)^2 < Norm(v[5],2)^2) then \+
\n      print(\"not satisfied\",\"2*v_5\") \n   end if; \nend do:\nfor
 s from 8 by 1 to 15 do\n   t:=convert(s,base,2):\n   if (Norm(v[1]+(-
1)^(t[1])*v[2]+(-1)^(t[2])*v[3]+(-1)^(t[3])*v[4]+(-1)^(t[4])*2*v[5],2)
^2 < Norm(v[5],2)^2) then \n      print(\"not satisfied\",\"2*v_5\") \+
\n   end if; \nend do:" }}{PARA 11 "" 1 "" {XPPMATH 20 "6'Q.not~satisf
ied6\"Q,v_i,v_j,v_kF$\"\"\"\"\"$\"\"&" }}}{EXCHG {PARA 0 "> " 0 "" 
{MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 365 "v[1]:=
Vector([4,1,1,-1,-1]):\nv[2]:=Vector([-1,4,-1,-1,-1]):\nv[3]:=Vector([
-1,-1,4,-1,-1]):\nv[4]:=Vector([-1,1,1,4,-1]):\nv[5]:=Vector([-2,-2,-2
,-2,-2]):\nv[1],v[2],v[3],v[4],v[5];\nprint(\"|v[1]|^2\"=Norm(v[1],2)^
2);\n#checking for decreasing order;\nfor i from 1 by 1 to 4 do \n   i
f (Norm(v[i],2)^2 > Norm(v[i+1],2)^2) then print(\"not satisfied\",(i,
i+1)) end if; \nend do;" }}{PARA 11 "" 1 "" {XPPMATH 20 "6'-%'RTABLEG6
%\"*WZH%>-%'MATRIXG6#7'7#\"\"%7#\"\"\"F-7#!\"\"F/&%'VectorG6#%'columnG
-F$6%\"*3[H%>-F(6#7'F/F+F/F/F/F1-F$6%\"*s[H%>-F(6#7'F/F/F+F/F/F1-F$6%
\"*O\\H%>-F(6#7'F/F-F-F+F/F1-F$6%\"*+]H%>-F(6#7'7#!\"#FMFMFMFMF1" }}
{PARA 11 "" 1 "" {XPPMATH 20 "6#/Q)|grv[1]|gr^26\"\"#?" }}}{EXCHG 
{PARA 0 "> " 0 "" {MPLTEXT 1 0 6469 "#checking for 2|v[j].v[i]|=<|v[i]
|^2;\nL2:=choose(5, 2):\nfor i from 1 by 1 to numbcomb(5, 2) do\n   if
 (2*abs(v[L2[i][2]].v[L2[i][1]]) > Norm(v[L2[i][1]],2)^2) then \n     \+
 print(\"not satisfied\",\"v_i,v_j\",L2[i][1],L2[i][2]) \n   end if;\n
end do;\n#checking for 2|v[k].(v[i]+v[j])|=<|v[i]+v[j]|^2;\nL3:=choose
(5, 3):\nfor s from 0 by 1 to 1 do\n   for i from 1 by 1 to numbcomb(5
, 3) do\n      if (2*abs(v[L3[i][3]].(v[L3[i][1]]+(-1)^s*v[L3[i][2]]))
 > Norm(v[L3[i][1]]+(-1)^s*v[L3[i][2]],2)^2) then \n         print(\"n
ot satisfied\",\"v_i,v_j,v_k\",L3[i][1],(-1)^s*L3[i][2],L3[i][3]); \n \+
     end if;\n   end do;\nend do;\n#checking for 2|v[l].(v[i]+v[j]+v[k
])|=<|v[i]+v[j]+v[k]|^2;\nL4:=choose(5, 4):\nfor s from 0 by 1 to 1 do
\n   for i from 1 by 1 to numbcomb(5, 4) do\n      if (2*abs(v[L4[i][4
]].(v[L4[i][1]]+(-1)^s*v[L4[i][2]]+(-1)^0*v[L4[i][3]])) >\n         No
rm(v[L4[i][1]]+(-1)^s*v[L4[i][2]]+(-1)^0*v[L4[i][3]],2)^2) then \n    \+
     print(\"not satisfied\",\"v_i,v_j,v_k,v_l\",L4[i][1],(-1)^s*L4[i]
[2],(-1)^0*L4[i][3],L4[i][4]); \n      end if;\n   end do;\nend do;\nf
or s from 2 by 1 to 3 do\n   t:=convert(s,base,2):\n   for i from 1 by
 1 to numbcomb(5, 4) do\n      if (2*abs(v[L4[i][4]].(v[L4[i][1]]+(-1)
^(t[1])*v[L4[i][2]]+(-1)^(t[2])*v[L4[i][3]])) >\n         Norm(v[L4[i]
[1]]+(-1)^(t[1])*v[L4[i][2]]+(-1)^(t[2])*v[L4[i][3]],2)^2) then \n    \+
     print(\"not satisfied\",\"v_i,v_j,v_k,v_l\",L4[i][1],(-1)^(t[1])*
L4[i][2],(-1)^(t[2])*L4[i][3],L4[i][4]); \n      end if;\n   end do;\n
end do:\n#checking for 2|v[m].(v[i]+v[j]+v[k]+v[l])|=<|v[i]+v[j]+v[k]+
v[l]|^2;\nfor s from 0 by 1 to 1 do\n   if (2*abs(v[5].(v[1]+(-1)^s*v[
2]+(-1)^0*v[3]+(-1)^0*v[4])) > \n       Norm(v[1]+(-1)^s*v[2]+(-1)^0*v
[3]+(-1)^0*v[4],2)^2) then \n      print(\"not satisfied\",\"v_i,v_j,v
_k,v_l,v_m\",1,(-1)^s*2,3,4,5); \n   end if;\nend do;\nfor s from 2 by
 1 to 3 do\n   t:=convert(s,base,2):\n   if (2*abs(v[5].(v[1]+(-1)^(t[
1])*v[2]+(-1)^(t[2])*v[3]+(-1)^0*v[4])) > \n       Norm(v[1]+(-1)^(t[1
])*v[2]+(-1)^(t[2])*v[3]+(-1)^0*v[4],2)^2) then \n      print(\"not sa
tisfied\",\"v_i,v_j,v_k,v_l,v_m\",1,+(-1)^(t[1])*2,(-1)^(t[2])*3,(-1)^
0*4,5); \n   end if;\nend do:\nfor s from 4 by 1 to 7 do\n   t:=conver
t(s,base,2):\n   if (2*abs(v[5].(v[1]+(-1)^(t[1])*v[2]+(-1)^(t[2])*v[3
]+(-1)^(t[3])*v[4])) > \n       Norm(v[1]+(-1)^(t[1])*v[2]+(-1)^(t[2])
*v[3]+(-1)^(t[3])*v[4],2)^2) then \n      print(\"not satisfied\",\"v_
i,v_j,v_k,v_l,v_m\",1,(-1)^(t[1])*2,+(-1)^(t[2])*3,(-1)^(t[3])*4,5); \+
\n   end if;\nend do:\n#checking for |v[i]+v[1]+v[2]+v[3]+v[4]+v[5]|^2
>=|v[i]|^2;\nfor s from 0 by 1 to 1 do\n   if (Norm(2*v[1]+(-1)^s*v[2]
+v[3]+v[4]+v[5],2)^2 < Norm(v[1],2)^2) then \n      print(\"not satisf
ied\",\"2*v_1\") \n   end if;\nend do;\nfor s from 2 by 1 to 3 do\n   \+
t:=convert(s,base,2):\n   if (Norm(2*v[1]+(-1)^(t[1])*v[2]+(-1)^(t[2])
*v[3]+v[4]+v[5],2)^2 < Norm(v[1],2)^2) then \n      print(\"not satisf
ied\",\"2*v_1\") \n   end if; \nend do:\nfor s from 4 by 1 to 7 do\n  \+
 t:=convert(s,base,2):\n   if (Norm(2*v[1]+(-1)^(t[1])*v[2]+(-1)^(t[2]
)*v[3]+(-1)^(t[3])*v[4]+v[5],2)^2 < Norm(v[1],2)^2) then \n      print
(\"not satisfied\",\"2*v_1\") \n   end if; \nend do:\nfor s from 8 by \+
1 to 15 do\n   t:=convert(s,base,2):\n   if (Norm(2*v[1]+(-1)^(t[1])*v
[2]+(-1)^(t[2])*v[3]+(-1)^(t[3])*v[4]+(-1)^(t[4])*v[5],2)^2 < Norm(v[1
],2)^2) then \n      print(\"not satisfied\",\"2*v_1\") \n   end if; \+
\nend do:\nfor s from 0 by 1 to 1 do\n   if (Norm(v[1]+(-1)^s*2*v[2]+v
[3]+v[4]+v[5],2)^2 < Norm(v[2],2)^2) then \n      print(\"not satisfie
d\",\"2*v_2\") \n   end if;\nend do;\nfor s from 2 by 1 to 3 do\n   t:
=convert(s,base,2):\n   if (Norm(v[1]+(-1)^(t[1])*2*v[2]+(-1)^(t[2])*v
[3]+v[4]+v[5],2)^2 < Norm(v[2],2)^2) then \n      print(\"not satisfie
d\",\"2*v_2\") \n   end if; \nend do:\nfor s from 4 by 1 to 7 do\n   t
:=convert(s,base,2):\n   if (Norm(v[1]+(-1)^(t[1])*2*v[2]+(-1)^(t[2])*
v[3]+(-1)^(t[3])*v[4]+v[5],2)^2 < Norm(v[2],2)^2) then \n      print(
\"not satisfied\",\"2*v_2\") \n   end if; \nend do:\nfor s from 8 by 1
 to 15 do\n   t:=convert(s,base,2):\n   if (Norm(v[1]+(-1)^(t[1])*2*v[
2]+(-1)^(t[2])*v[3]+(-1)^(t[3])*v[4]+(-1)^(t[4])*v[5],2)^2 < Norm(v[2]
,2)^2) then \n      print(\"not satisfied\",\"2*v_2\") \n   end if; \n
end do:\nfor s from 0 by 1 to 1 do\n   if (Norm(v[1]+(-1)^s*v[2]+2*v[3
]+v[4]+v[5],2)^2 < Norm(v[3],2)^2) then \n      print(\"not satisfied
\",\"2*v_3\") \n   end if;\nend do;\nfor s from 2 by 1 to 3 do\n   t:=
convert(s,base,2):\n   if (Norm(v[1]+(-1)^(t[1])*v[2]+(-1)^(t[2])*2*v[
3]+v[4]+v[5],2)^2 < Norm(v[3],2)^2) then \n      print(\"not satisfied
\",\"2*v_3\") \n   end if; \nend do:\nfor s from 4 by 1 to 7 do\n   t:
=convert(s,base,2):\n   if (Norm(v[1]+(-1)^(t[1])*v[2]+(-1)^(t[2])*2*v
[3]+(-1)^(t[3])*v[4]+v[5],2)^2 < Norm(v[3],2)^2) then \n      print(\"
not satisfied\",\"2*v_3\") \n   end if; \nend do:\nfor s from 8 by 1 t
o 15 do\n   t:=convert(s,base,2):\n   if (Norm(v[1]+(-1)^(t[1])*v[2]+(
-1)^(t[2])*2*v[3]+(-1)^(t[3])*v[4]+(-1)^(t[4])*v[5],2)^2 < Norm(v[3],2
)^2) then \n      print(\"not satisfied\",\"2*v_3\") \n   end if; \nen
d do:\nfor s from 0 by 1 to 1 do\n   if (Norm(v[1]+(-1)^s*v[2]+v[3]+2*
v[4]+v[5],2)^2 < Norm(v[4],2)^2) then \n      print(\"not satisfied\",
\"2*v_4\") \n   end if;\nend do;\nfor s from 2 by 1 to 3 do\n   t:=con
vert(s,base,2):\n   if (Norm(v[1]+(-1)^(t[1])*v[2]+(-1)^(t[2])*v[3]+2*
v[4]+v[5],2)^2 < Norm(v[4],2)^2) then \n      print(\"not satisfied\",
\"2*v_4\") \n   end if; \nend do:\nfor s from 4 by 1 to 7 do\n   t:=co
nvert(s,base,2):\n   if (Norm(v[1]+(-1)^(t[1])*v[2]+(-1)^(t[2])*v[3]+(
-1)^(t[3])*2*v[4]+v[5],2)^2 < Norm(v[4],2)^2) then \n      print(\"not
 satisfied\",\"2*v_4\") \n   end if; \nend do:\nfor s from 8 by 1 to 1
5 do\n   t:=convert(s,base,2):\n   if (Norm(v[1]+(-1)^(t[1])*v[2]+(-1)
^(t[2])*v[3]+(-1)^(t[3])*2*v[4]+(-1)^(t[4])*v[5],2)^2 < Norm(v[4],2)^2
) then \n      print(\"not satisfied\",\"2*v_4\") \n   end if; \nend d
o:\nfor s from 0 by 1 to 1 do\n   if (Norm(v[1]+(-1)^s*v[2]+v[3]+v[4]+
2*v[5],2)^2 < Norm(v[5],2)^2) then \n      print(\"not satisfied\",\"2
*v_5\") \n   end if;\nend do;\nfor s from 2 by 1 to 3 do\n   t:=conver
t(s,base,2):\n   if (Norm(v[1]+(-1)^(t[1])*v[2]+(-1)^(t[2])*v[3]+v[4]+
2*v[5],2)^2 < Norm(v[5],2)^2) then \n      print(\"not satisfied\",\"2
*v_5\") \n   end if; \nend do:\nfor s from 4 by 1 to 7 do\n   t:=conve
rt(s,base,2):\n   if (Norm(v[1]+(-1)^(t[1])*v[2]+(-1)^(t[2])*v[3]+(-1)
^(t[3])*v[4]+2*v[5],2)^2 < Norm(v[5],2)^2) then \n      print(\"not sa
tisfied\",\"2*v_5\") \n   end if; \nend do:\nfor s from 8 by 1 to 15 d
o\n   t:=convert(s,base,2):\n   if (Norm(v[1]+(-1)^(t[1])*v[2]+(-1)^(t
[2])*v[3]+(-1)^(t[3])*v[4]+(-1)^(t[4])*2*v[5],2)^2 < Norm(v[5],2)^2) t
hen \n      print(\"not satisfied\",\"2*v_5\") \n   end if; \nend do:
" }}{PARA 11 "" 1 "" {XPPMATH 20 "6'Q.not~satisfied6\"Q,v_i,v_j,v_kF$
\"\"\"\"\"%\"\"&" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}
{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 365 "v[1]:=Vector([4,-1,-1,-1,-1
]):\nv[2]:=Vector([-1,4,-1,-1,-1]):\nv[3]:=Vector([1,-1,4,-1,-1]):\nv[
4]:=Vector([1,-1,-1,4,1]):\nv[5]:=Vector([-2,-2,-2,2,-2]):\nv[1],v[2],
v[3],v[4],v[5];\nprint(\"|v[1]|^2\"=Norm(v[1],2)^2);\n#checking for de
creasing order;\nfor i from 1 by 1 to 4 do \n   if (Norm(v[i],2)^2 > N
orm(v[i+1],2)^2) then print(\"not satisfied\",(i,i+1)) end if; \nend d
o;" }}{PARA 11 "" 1 "" {XPPMATH 20 "6'-%'RTABLEG6%\"*__I\"=-%'MATRIXG6
#7'7#\"\"%7#!\"\"F-F-F-&%'VectorG6#%'columnG-F$6%\"*;`I\"=-F(6#7'F-F+F
-F-F-F/-F$6%\"*!Q08=-F(6#7'7#\"\"\"F-F+F-F-F/-F$6%\"*WaI\"=-F(6#7'F?F-
F-F+F?F/-F$6%\"*3bI\"=-F(6#7'7#!\"#FMFM7#\"\"#FMF/" }}{PARA 11 "" 1 "
" {XPPMATH 20 "6#/Q)|grv[1]|gr^26\"\"#?" }}}{EXCHG {PARA 0 "> " 0 "" 
{MPLTEXT 1 0 6469 "#checking for 2|v[j].v[i]|=<|v[i]|^2;\nL2:=choose(5
, 2):\nfor i from 1 by 1 to numbcomb(5, 2) do\n   if (2*abs(v[L2[i][2]
].v[L2[i][1]]) > Norm(v[L2[i][1]],2)^2) then \n      print(\"not satis
fied\",\"v_i,v_j\",L2[i][1],L2[i][2]) \n   end if;\nend do;\n#checking
 for 2|v[k].(v[i]+v[j])|=<|v[i]+v[j]|^2;\nL3:=choose(5, 3):\nfor s fro
m 0 by 1 to 1 do\n   for i from 1 by 1 to numbcomb(5, 3) do\n      if \+
(2*abs(v[L3[i][3]].(v[L3[i][1]]+(-1)^s*v[L3[i][2]])) > Norm(v[L3[i][1]
]+(-1)^s*v[L3[i][2]],2)^2) then \n         print(\"not satisfied\",\"v
_i,v_j,v_k\",L3[i][1],(-1)^s*L3[i][2],L3[i][3]); \n      end if;\n   e
nd do;\nend do;\n#checking for 2|v[l].(v[i]+v[j]+v[k])|=<|v[i]+v[j]+v[
k]|^2;\nL4:=choose(5, 4):\nfor s from 0 by 1 to 1 do\n   for i from 1 \+
by 1 to numbcomb(5, 4) do\n      if (2*abs(v[L4[i][4]].(v[L4[i][1]]+(-
1)^s*v[L4[i][2]]+(-1)^0*v[L4[i][3]])) >\n         Norm(v[L4[i][1]]+(-1
)^s*v[L4[i][2]]+(-1)^0*v[L4[i][3]],2)^2) then \n         print(\"not s
atisfied\",\"v_i,v_j,v_k,v_l\",L4[i][1],(-1)^s*L4[i][2],(-1)^0*L4[i][3
],L4[i][4]); \n      end if;\n   end do;\nend do;\nfor s from 2 by 1 t
o 3 do\n   t:=convert(s,base,2):\n   for i from 1 by 1 to numbcomb(5, \+
4) do\n      if (2*abs(v[L4[i][4]].(v[L4[i][1]]+(-1)^(t[1])*v[L4[i][2]
]+(-1)^(t[2])*v[L4[i][3]])) >\n         Norm(v[L4[i][1]]+(-1)^(t[1])*v
[L4[i][2]]+(-1)^(t[2])*v[L4[i][3]],2)^2) then \n         print(\"not s
atisfied\",\"v_i,v_j,v_k,v_l\",L4[i][1],(-1)^(t[1])*L4[i][2],(-1)^(t[2
])*L4[i][3],L4[i][4]); \n      end if;\n   end do;\nend do:\n#checking
 for 2|v[m].(v[i]+v[j]+v[k]+v[l])|=<|v[i]+v[j]+v[k]+v[l]|^2;\nfor s fr
om 0 by 1 to 1 do\n   if (2*abs(v[5].(v[1]+(-1)^s*v[2]+(-1)^0*v[3]+(-1
)^0*v[4])) > \n       Norm(v[1]+(-1)^s*v[2]+(-1)^0*v[3]+(-1)^0*v[4],2)
^2) then \n      print(\"not satisfied\",\"v_i,v_j,v_k,v_l,v_m\",1,(-1
)^s*2,3,4,5); \n   end if;\nend do;\nfor s from 2 by 1 to 3 do\n   t:=
convert(s,base,2):\n   if (2*abs(v[5].(v[1]+(-1)^(t[1])*v[2]+(-1)^(t[2
])*v[3]+(-1)^0*v[4])) > \n       Norm(v[1]+(-1)^(t[1])*v[2]+(-1)^(t[2]
)*v[3]+(-1)^0*v[4],2)^2) then \n      print(\"not satisfied\",\"v_i,v_
j,v_k,v_l,v_m\",1,+(-1)^(t[1])*2,(-1)^(t[2])*3,(-1)^0*4,5); \n   end i
f;\nend do:\nfor s from 4 by 1 to 7 do\n   t:=convert(s,base,2):\n   i
f (2*abs(v[5].(v[1]+(-1)^(t[1])*v[2]+(-1)^(t[2])*v[3]+(-1)^(t[3])*v[4]
)) > \n       Norm(v[1]+(-1)^(t[1])*v[2]+(-1)^(t[2])*v[3]+(-1)^(t[3])*
v[4],2)^2) then \n      print(\"not satisfied\",\"v_i,v_j,v_k,v_l,v_m
\",1,(-1)^(t[1])*2,+(-1)^(t[2])*3,(-1)^(t[3])*4,5); \n   end if;\nend \+
do:\n#checking for |v[i]+v[1]+v[2]+v[3]+v[4]+v[5]|^2>=|v[i]|^2;\nfor s
 from 0 by 1 to 1 do\n   if (Norm(2*v[1]+(-1)^s*v[2]+v[3]+v[4]+v[5],2)
^2 < Norm(v[1],2)^2) then \n      print(\"not satisfied\",\"2*v_1\") \+
\n   end if;\nend do;\nfor s from 2 by 1 to 3 do\n   t:=convert(s,base
,2):\n   if (Norm(2*v[1]+(-1)^(t[1])*v[2]+(-1)^(t[2])*v[3]+v[4]+v[5],2
)^2 < Norm(v[1],2)^2) then \n      print(\"not satisfied\",\"2*v_1\") \+
\n   end if; \nend do:\nfor s from 4 by 1 to 7 do\n   t:=convert(s,bas
e,2):\n   if (Norm(2*v[1]+(-1)^(t[1])*v[2]+(-1)^(t[2])*v[3]+(-1)^(t[3]
)*v[4]+v[5],2)^2 < Norm(v[1],2)^2) then \n      print(\"not satisfied
\",\"2*v_1\") \n   end if; \nend do:\nfor s from 8 by 1 to 15 do\n   t
:=convert(s,base,2):\n   if (Norm(2*v[1]+(-1)^(t[1])*v[2]+(-1)^(t[2])*
v[3]+(-1)^(t[3])*v[4]+(-1)^(t[4])*v[5],2)^2 < Norm(v[1],2)^2) then \n \+
     print(\"not satisfied\",\"2*v_1\") \n   end if; \nend do:\nfor s \+
from 0 by 1 to 1 do\n   if (Norm(v[1]+(-1)^s*2*v[2]+v[3]+v[4]+v[5],2)^
2 < Norm(v[2],2)^2) then \n      print(\"not satisfied\",\"2*v_2\") \n
   end if;\nend do;\nfor s from 2 by 1 to 3 do\n   t:=convert(s,base,2
):\n   if (Norm(v[1]+(-1)^(t[1])*2*v[2]+(-1)^(t[2])*v[3]+v[4]+v[5],2)^
2 < Norm(v[2],2)^2) then \n      print(\"not satisfied\",\"2*v_2\") \n
   end if; \nend do:\nfor s from 4 by 1 to 7 do\n   t:=convert(s,base,
2):\n   if (Norm(v[1]+(-1)^(t[1])*2*v[2]+(-1)^(t[2])*v[3]+(-1)^(t[3])*
v[4]+v[5],2)^2 < Norm(v[2],2)^2) then \n      print(\"not satisfied\",
\"2*v_2\") \n   end if; \nend do:\nfor s from 8 by 1 to 15 do\n   t:=c
onvert(s,base,2):\n   if (Norm(v[1]+(-1)^(t[1])*2*v[2]+(-1)^(t[2])*v[3
]+(-1)^(t[3])*v[4]+(-1)^(t[4])*v[5],2)^2 < Norm(v[2],2)^2) then \n    \+
  print(\"not satisfied\",\"2*v_2\") \n   end if; \nend do:\nfor s fro
m 0 by 1 to 1 do\n   if (Norm(v[1]+(-1)^s*v[2]+2*v[3]+v[4]+v[5],2)^2 <
 Norm(v[3],2)^2) then \n      print(\"not satisfied\",\"2*v_3\") \n   \+
end if;\nend do;\nfor s from 2 by 1 to 3 do\n   t:=convert(s,base,2):
\n   if (Norm(v[1]+(-1)^(t[1])*v[2]+(-1)^(t[2])*2*v[3]+v[4]+v[5],2)^2 \+
< Norm(v[3],2)^2) then \n      print(\"not satisfied\",\"2*v_3\") \n  \+
 end if; \nend do:\nfor s from 4 by 1 to 7 do\n   t:=convert(s,base,2)
:\n   if (Norm(v[1]+(-1)^(t[1])*v[2]+(-1)^(t[2])*2*v[3]+(-1)^(t[3])*v[
4]+v[5],2)^2 < Norm(v[3],2)^2) then \n      print(\"not satisfied\",\"
2*v_3\") \n   end if; \nend do:\nfor s from 8 by 1 to 15 do\n   t:=con
vert(s,base,2):\n   if (Norm(v[1]+(-1)^(t[1])*v[2]+(-1)^(t[2])*2*v[3]+
(-1)^(t[3])*v[4]+(-1)^(t[4])*v[5],2)^2 < Norm(v[3],2)^2) then \n      \+
print(\"not satisfied\",\"2*v_3\") \n   end if; \nend do:\nfor s from \+
0 by 1 to 1 do\n   if (Norm(v[1]+(-1)^s*v[2]+v[3]+2*v[4]+v[5],2)^2 < N
orm(v[4],2)^2) then \n      print(\"not satisfied\",\"2*v_4\") \n   en
d if;\nend do;\nfor s from 2 by 1 to 3 do\n   t:=convert(s,base,2):\n \+
  if (Norm(v[1]+(-1)^(t[1])*v[2]+(-1)^(t[2])*v[3]+2*v[4]+v[5],2)^2 < N
orm(v[4],2)^2) then \n      print(\"not satisfied\",\"2*v_4\") \n   en
d if; \nend do:\nfor s from 4 by 1 to 7 do\n   t:=convert(s,base,2):\n
   if (Norm(v[1]+(-1)^(t[1])*v[2]+(-1)^(t[2])*v[3]+(-1)^(t[3])*2*v[4]+
v[5],2)^2 < Norm(v[4],2)^2) then \n      print(\"not satisfied\",\"2*v
_4\") \n   end if; \nend do:\nfor s from 8 by 1 to 15 do\n   t:=conver
t(s,base,2):\n   if (Norm(v[1]+(-1)^(t[1])*v[2]+(-1)^(t[2])*v[3]+(-1)^
(t[3])*2*v[4]+(-1)^(t[4])*v[5],2)^2 < Norm(v[4],2)^2) then \n      pri
nt(\"not satisfied\",\"2*v_4\") \n   end if; \nend do:\nfor s from 0 b
y 1 to 1 do\n   if (Norm(v[1]+(-1)^s*v[2]+v[3]+v[4]+2*v[5],2)^2 < Norm
(v[5],2)^2) then \n      print(\"not satisfied\",\"2*v_5\") \n   end i
f;\nend do;\nfor s from 2 by 1 to 3 do\n   t:=convert(s,base,2):\n   i
f (Norm(v[1]+(-1)^(t[1])*v[2]+(-1)^(t[2])*v[3]+v[4]+2*v[5],2)^2 < Norm
(v[5],2)^2) then \n      print(\"not satisfied\",\"2*v_5\") \n   end i
f; \nend do:\nfor s from 4 by 1 to 7 do\n   t:=convert(s,base,2):\n   \+
if (Norm(v[1]+(-1)^(t[1])*v[2]+(-1)^(t[2])*v[3]+(-1)^(t[3])*v[4]+2*v[5
],2)^2 < Norm(v[5],2)^2) then \n      print(\"not satisfied\",\"2*v_5
\") \n   end if; \nend do:\nfor s from 8 by 1 to 15 do\n   t:=convert(
s,base,2):\n   if (Norm(v[1]+(-1)^(t[1])*v[2]+(-1)^(t[2])*v[3]+(-1)^(t
[3])*v[4]+(-1)^(t[4])*2*v[5],2)^2 < Norm(v[5],2)^2) then \n      print
(\"not satisfied\",\"2*v_5\") \n   end if; \nend do:" }}{PARA 11 "" 1 
"" {XPPMATH 20 "6'Q.not~satisfied6\"Q,v_i,v_j,v_kF$\"\"#\"\"$\"\"%" }}
}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "> " 0 "
" {MPLTEXT 1 0 365 "v[1]:=Vector([4,-1,-1,-1,-1]):\nv[2]:=Vector([1,4,
-1,1,-1]):\nv[3]:=Vector([1,-1,4,1,-1]):\nv[4]:=Vector([-1,-1,-1,4,-1]
):\nv[5]:=Vector([-2,-2,-2,-2,-2]):\nv[1],v[2],v[3],v[4],v[5];\nprint(
\"|v[1]|^2\"=Norm(v[1],2)^2);\n#checking for decreasing order;\nfor i \+
from 1 by 1 to 4 do \n   if (Norm(v[i],2)^2 > Norm(v[i+1],2)^2) then p
rint(\"not satisfied\",(i,i+1)) end if; \nend do;" }}{PARA 11 "" 1 "" 
{XPPMATH 20 "6'-%'RTABLEG6%\"*ww9\">-%'MATRIXG6#7'7#\"\"%7#!\"\"F-F-F-
&%'VectorG6#%'columnG-F$6%\"*Sx9\">-F(6#7'7#\"\"\"F+F-F9F-F/-F$6%\"*/y
9\">-F(6#7'F9F-F+F9F-F/-F$6%\"*oy9\">-F(6#7'F-F-F-F+F-F/-F$6%\"*Kz9\">
-F(6#7'7#!\"#FMFMFMFMF/" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#/Q)|grv[1]|
gr^26\"\"#?" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 6469 "#checking \+
for 2|v[j].v[i]|=<|v[i]|^2;\nL2:=choose(5, 2):\nfor i from 1 by 1 to n
umbcomb(5, 2) do\n   if (2*abs(v[L2[i][2]].v[L2[i][1]]) > Norm(v[L2[i]
[1]],2)^2) then \n      print(\"not satisfied\",\"v_i,v_j\",L2[i][1],L
2[i][2]) \n   end if;\nend do;\n#checking for 2|v[k].(v[i]+v[j])|=<|v[
i]+v[j]|^2;\nL3:=choose(5, 3):\nfor s from 0 by 1 to 1 do\n   for i fr
om 1 by 1 to numbcomb(5, 3) do\n      if (2*abs(v[L3[i][3]].(v[L3[i][1
]]+(-1)^s*v[L3[i][2]])) > Norm(v[L3[i][1]]+(-1)^s*v[L3[i][2]],2)^2) th
en \n         print(\"not satisfied\",\"v_i,v_j,v_k\",L3[i][1],(-1)^s*
L3[i][2],L3[i][3]); \n      end if;\n   end do;\nend do;\n#checking fo
r 2|v[l].(v[i]+v[j]+v[k])|=<|v[i]+v[j]+v[k]|^2;\nL4:=choose(5, 4):\nfo
r s from 0 by 1 to 1 do\n   for i from 1 by 1 to numbcomb(5, 4) do\n  \+
    if (2*abs(v[L4[i][4]].(v[L4[i][1]]+(-1)^s*v[L4[i][2]]+(-1)^0*v[L4[
i][3]])) >\n         Norm(v[L4[i][1]]+(-1)^s*v[L4[i][2]]+(-1)^0*v[L4[i
][3]],2)^2) then \n         print(\"not satisfied\",\"v_i,v_j,v_k,v_l
\",L4[i][1],(-1)^s*L4[i][2],(-1)^0*L4[i][3],L4[i][4]); \n      end if;
\n   end do;\nend do;\nfor s from 2 by 1 to 3 do\n   t:=convert(s,base
,2):\n   for i from 1 by 1 to numbcomb(5, 4) do\n      if (2*abs(v[L4[
i][4]].(v[L4[i][1]]+(-1)^(t[1])*v[L4[i][2]]+(-1)^(t[2])*v[L4[i][3]])) \+
>\n         Norm(v[L4[i][1]]+(-1)^(t[1])*v[L4[i][2]]+(-1)^(t[2])*v[L4[
i][3]],2)^2) then \n         print(\"not satisfied\",\"v_i,v_j,v_k,v_l
\",L4[i][1],(-1)^(t[1])*L4[i][2],(-1)^(t[2])*L4[i][3],L4[i][4]); \n   \+
   end if;\n   end do;\nend do:\n#checking for 2|v[m].(v[i]+v[j]+v[k]+
v[l])|=<|v[i]+v[j]+v[k]+v[l]|^2;\nfor s from 0 by 1 to 1 do\n   if (2*
abs(v[5].(v[1]+(-1)^s*v[2]+(-1)^0*v[3]+(-1)^0*v[4])) > \n       Norm(v
[1]+(-1)^s*v[2]+(-1)^0*v[3]+(-1)^0*v[4],2)^2) then \n      print(\"not
 satisfied\",\"v_i,v_j,v_k,v_l,v_m\",1,(-1)^s*2,3,4,5); \n   end if;\n
end do;\nfor s from 2 by 1 to 3 do\n   t:=convert(s,base,2):\n   if (2
*abs(v[5].(v[1]+(-1)^(t[1])*v[2]+(-1)^(t[2])*v[3]+(-1)^0*v[4])) > \n  \+
     Norm(v[1]+(-1)^(t[1])*v[2]+(-1)^(t[2])*v[3]+(-1)^0*v[4],2)^2) the
n \n      print(\"not satisfied\",\"v_i,v_j,v_k,v_l,v_m\",1,+(-1)^(t[1
])*2,(-1)^(t[2])*3,(-1)^0*4,5); \n   end if;\nend do:\nfor s from 4 by
 1 to 7 do\n   t:=convert(s,base,2):\n   if (2*abs(v[5].(v[1]+(-1)^(t[
1])*v[2]+(-1)^(t[2])*v[3]+(-1)^(t[3])*v[4])) > \n       Norm(v[1]+(-1)
^(t[1])*v[2]+(-1)^(t[2])*v[3]+(-1)^(t[3])*v[4],2)^2) then \n      prin
t(\"not satisfied\",\"v_i,v_j,v_k,v_l,v_m\",1,(-1)^(t[1])*2,+(-1)^(t[2
])*3,(-1)^(t[3])*4,5); \n   end if;\nend do:\n#checking for |v[i]+v[1]
+v[2]+v[3]+v[4]+v[5]|^2>=|v[i]|^2;\nfor s from 0 by 1 to 1 do\n   if (
Norm(2*v[1]+(-1)^s*v[2]+v[3]+v[4]+v[5],2)^2 < Norm(v[1],2)^2) then \n \+
     print(\"not satisfied\",\"2*v_1\") \n   end if;\nend do;\nfor s f
rom 2 by 1 to 3 do\n   t:=convert(s,base,2):\n   if (Norm(2*v[1]+(-1)^
(t[1])*v[2]+(-1)^(t[2])*v[3]+v[4]+v[5],2)^2 < Norm(v[1],2)^2) then \n \+
     print(\"not satisfied\",\"2*v_1\") \n   end if; \nend do:\nfor s \+
from 4 by 1 to 7 do\n   t:=convert(s,base,2):\n   if (Norm(2*v[1]+(-1)
^(t[1])*v[2]+(-1)^(t[2])*v[3]+(-1)^(t[3])*v[4]+v[5],2)^2 < Norm(v[1],2
)^2) then \n      print(\"not satisfied\",\"2*v_1\") \n   end if; \nen
d do:\nfor s from 8 by 1 to 15 do\n   t:=convert(s,base,2):\n   if (No
rm(2*v[1]+(-1)^(t[1])*v[2]+(-1)^(t[2])*v[3]+(-1)^(t[3])*v[4]+(-1)^(t[4
])*v[5],2)^2 < Norm(v[1],2)^2) then \n      print(\"not satisfied\",\"
2*v_1\") \n   end if; \nend do:\nfor s from 0 by 1 to 1 do\n   if (Nor
m(v[1]+(-1)^s*2*v[2]+v[3]+v[4]+v[5],2)^2 < Norm(v[2],2)^2) then \n    \+
  print(\"not satisfied\",\"2*v_2\") \n   end if;\nend do;\nfor s from
 2 by 1 to 3 do\n   t:=convert(s,base,2):\n   if (Norm(v[1]+(-1)^(t[1]
)*2*v[2]+(-1)^(t[2])*v[3]+v[4]+v[5],2)^2 < Norm(v[2],2)^2) then \n    \+
  print(\"not satisfied\",\"2*v_2\") \n   end if; \nend do:\nfor s fro
m 4 by 1 to 7 do\n   t:=convert(s,base,2):\n   if (Norm(v[1]+(-1)^(t[1
])*2*v[2]+(-1)^(t[2])*v[3]+(-1)^(t[3])*v[4]+v[5],2)^2 < Norm(v[2],2)^2
) then \n      print(\"not satisfied\",\"2*v_2\") \n   end if; \nend d
o:\nfor s from 8 by 1 to 15 do\n   t:=convert(s,base,2):\n   if (Norm(
v[1]+(-1)^(t[1])*2*v[2]+(-1)^(t[2])*v[3]+(-1)^(t[3])*v[4]+(-1)^(t[4])*
v[5],2)^2 < Norm(v[2],2)^2) then \n      print(\"not satisfied\",\"2*v
_2\") \n   end if; \nend do:\nfor s from 0 by 1 to 1 do\n   if (Norm(v
[1]+(-1)^s*v[2]+2*v[3]+v[4]+v[5],2)^2 < Norm(v[3],2)^2) then \n      p
rint(\"not satisfied\",\"2*v_3\") \n   end if;\nend do;\nfor s from 2 \+
by 1 to 3 do\n   t:=convert(s,base,2):\n   if (Norm(v[1]+(-1)^(t[1])*v
[2]+(-1)^(t[2])*2*v[3]+v[4]+v[5],2)^2 < Norm(v[3],2)^2) then \n      p
rint(\"not satisfied\",\"2*v_3\") \n   end if; \nend do:\nfor s from 4
 by 1 to 7 do\n   t:=convert(s,base,2):\n   if (Norm(v[1]+(-1)^(t[1])*
v[2]+(-1)^(t[2])*2*v[3]+(-1)^(t[3])*v[4]+v[5],2)^2 < Norm(v[3],2)^2) t
hen \n      print(\"not satisfied\",\"2*v_3\") \n   end if; \nend do:
\nfor s from 8 by 1 to 15 do\n   t:=convert(s,base,2):\n   if (Norm(v[
1]+(-1)^(t[1])*v[2]+(-1)^(t[2])*2*v[3]+(-1)^(t[3])*v[4]+(-1)^(t[4])*v[
5],2)^2 < Norm(v[3],2)^2) then \n      print(\"not satisfied\",\"2*v_3
\") \n   end if; \nend do:\nfor s from 0 by 1 to 1 do\n   if (Norm(v[1
]+(-1)^s*v[2]+v[3]+2*v[4]+v[5],2)^2 < Norm(v[4],2)^2) then \n      pri
nt(\"not satisfied\",\"2*v_4\") \n   end if;\nend do;\nfor s from 2 by
 1 to 3 do\n   t:=convert(s,base,2):\n   if (Norm(v[1]+(-1)^(t[1])*v[2
]+(-1)^(t[2])*v[3]+2*v[4]+v[5],2)^2 < Norm(v[4],2)^2) then \n      pri
nt(\"not satisfied\",\"2*v_4\") \n   end if; \nend do:\nfor s from 4 b
y 1 to 7 do\n   t:=convert(s,base,2):\n   if (Norm(v[1]+(-1)^(t[1])*v[
2]+(-1)^(t[2])*v[3]+(-1)^(t[3])*2*v[4]+v[5],2)^2 < Norm(v[4],2)^2) the
n \n      print(\"not satisfied\",\"2*v_4\") \n   end if; \nend do:\nf
or s from 8 by 1 to 15 do\n   t:=convert(s,base,2):\n   if (Norm(v[1]+
(-1)^(t[1])*v[2]+(-1)^(t[2])*v[3]+(-1)^(t[3])*2*v[4]+(-1)^(t[4])*v[5],
2)^2 < Norm(v[4],2)^2) then \n      print(\"not satisfied\",\"2*v_4\")
 \n   end if; \nend do:\nfor s from 0 by 1 to 1 do\n   if (Norm(v[1]+(
-1)^s*v[2]+v[3]+v[4]+2*v[5],2)^2 < Norm(v[5],2)^2) then \n      print(
\"not satisfied\",\"2*v_5\") \n   end if;\nend do;\nfor s from 2 by 1 \+
to 3 do\n   t:=convert(s,base,2):\n   if (Norm(v[1]+(-1)^(t[1])*v[2]+(
-1)^(t[2])*v[3]+v[4]+2*v[5],2)^2 < Norm(v[5],2)^2) then \n      print(
\"not satisfied\",\"2*v_5\") \n   end if; \nend do:\nfor s from 4 by 1
 to 7 do\n   t:=convert(s,base,2):\n   if (Norm(v[1]+(-1)^(t[1])*v[2]+
(-1)^(t[2])*v[3]+(-1)^(t[3])*v[4]+2*v[5],2)^2 < Norm(v[5],2)^2) then \+
\n      print(\"not satisfied\",\"2*v_5\") \n   end if; \nend do:\nfor
 s from 8 by 1 to 15 do\n   t:=convert(s,base,2):\n   if (Norm(v[1]+(-
1)^(t[1])*v[2]+(-1)^(t[2])*v[3]+(-1)^(t[3])*v[4]+(-1)^(t[4])*2*v[5],2)
^2 < Norm(v[5],2)^2) then \n      print(\"not satisfied\",\"2*v_5\") \+
\n   end if; \nend do:" }}{PARA 11 "" 1 "" {XPPMATH 20 "6'Q.not~satisf
ied6\"Q,v_i,v_j,v_kF$\"\"#\"\"$\"\"&" }}}{EXCHG {PARA 0 "> " 0 "" 
{MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 365 "v[1]:=
Vector([4,-1,-1,-1,-1]):\nv[2]:=Vector([1,4,1,-1,-1]):\nv[3]:=Vector([
-1,-1,4,-1,-1]):\nv[4]:=Vector([1,-1,1,4,-1]):\nv[5]:=Vector([-2,-2,-2
,-2,-2]):\nv[1],v[2],v[3],v[4],v[5];\nprint(\"|v[1]|^2\"=Norm(v[1],2)^
2);\n#checking for decreasing order;\nfor i from 1 by 1 to 4 do \n   i
f (Norm(v[i],2)^2 > Norm(v[i+1],2)^2) then print(\"not satisfied\",(i,
i+1)) end if; \nend do;" }}{PARA 11 "" 1 "" {XPPMATH 20 "6'-%'RTABLEG6
%\"*?!>&3#-%'MATRIXG6#7'7#\"\"%7#!\"\"F-F-F-&%'VectorG6#%'columnG-F$6%
\"*%3>&3#-F(6#7'7#\"\"\"F+F9F-F-F/-F$6%\"*[\">&3#-F(6#7'F-F-F+F-F-F/-F
$6%\"*7#>&3#-F(6#7'F9F-F9F+F-F/-F$6%\"*w#>&3#-F(6#7'7#!\"#FMFMFMFMF/" 
}}{PARA 11 "" 1 "" {XPPMATH 20 "6#/Q)|grv[1]|gr^26\"\"#?" }}}{EXCHG 
{PARA 0 "> " 0 "" {MPLTEXT 1 0 6469 "#checking for 2|v[j].v[i]|=<|v[i]
|^2;\nL2:=choose(5, 2):\nfor i from 1 by 1 to numbcomb(5, 2) do\n   if
 (2*abs(v[L2[i][2]].v[L2[i][1]]) > Norm(v[L2[i][1]],2)^2) then \n     \+
 print(\"not satisfied\",\"v_i,v_j\",L2[i][1],L2[i][2]) \n   end if;\n
end do;\n#checking for 2|v[k].(v[i]+v[j])|=<|v[i]+v[j]|^2;\nL3:=choose
(5, 3):\nfor s from 0 by 1 to 1 do\n   for i from 1 by 1 to numbcomb(5
, 3) do\n      if (2*abs(v[L3[i][3]].(v[L3[i][1]]+(-1)^s*v[L3[i][2]]))
 > Norm(v[L3[i][1]]+(-1)^s*v[L3[i][2]],2)^2) then \n         print(\"n
ot satisfied\",\"v_i,v_j,v_k\",L3[i][1],(-1)^s*L3[i][2],L3[i][3]); \n \+
     end if;\n   end do;\nend do;\n#checking for 2|v[l].(v[i]+v[j]+v[k
])|=<|v[i]+v[j]+v[k]|^2;\nL4:=choose(5, 4):\nfor s from 0 by 1 to 1 do
\n   for i from 1 by 1 to numbcomb(5, 4) do\n      if (2*abs(v[L4[i][4
]].(v[L4[i][1]]+(-1)^s*v[L4[i][2]]+(-1)^0*v[L4[i][3]])) >\n         No
rm(v[L4[i][1]]+(-1)^s*v[L4[i][2]]+(-1)^0*v[L4[i][3]],2)^2) then \n    \+
     print(\"not satisfied\",\"v_i,v_j,v_k,v_l\",L4[i][1],(-1)^s*L4[i]
[2],(-1)^0*L4[i][3],L4[i][4]); \n      end if;\n   end do;\nend do;\nf
or s from 2 by 1 to 3 do\n   t:=convert(s,base,2):\n   for i from 1 by
 1 to numbcomb(5, 4) do\n      if (2*abs(v[L4[i][4]].(v[L4[i][1]]+(-1)
^(t[1])*v[L4[i][2]]+(-1)^(t[2])*v[L4[i][3]])) >\n         Norm(v[L4[i]
[1]]+(-1)^(t[1])*v[L4[i][2]]+(-1)^(t[2])*v[L4[i][3]],2)^2) then \n    \+
     print(\"not satisfied\",\"v_i,v_j,v_k,v_l\",L4[i][1],(-1)^(t[1])*
L4[i][2],(-1)^(t[2])*L4[i][3],L4[i][4]); \n      end if;\n   end do;\n
end do:\n#checking for 2|v[m].(v[i]+v[j]+v[k]+v[l])|=<|v[i]+v[j]+v[k]+
v[l]|^2;\nfor s from 0 by 1 to 1 do\n   if (2*abs(v[5].(v[1]+(-1)^s*v[
2]+(-1)^0*v[3]+(-1)^0*v[4])) > \n       Norm(v[1]+(-1)^s*v[2]+(-1)^0*v
[3]+(-1)^0*v[4],2)^2) then \n      print(\"not satisfied\",\"v_i,v_j,v
_k,v_l,v_m\",1,(-1)^s*2,3,4,5); \n   end if;\nend do;\nfor s from 2 by
 1 to 3 do\n   t:=convert(s,base,2):\n   if (2*abs(v[5].(v[1]+(-1)^(t[
1])*v[2]+(-1)^(t[2])*v[3]+(-1)^0*v[4])) > \n       Norm(v[1]+(-1)^(t[1
])*v[2]+(-1)^(t[2])*v[3]+(-1)^0*v[4],2)^2) then \n      print(\"not sa
tisfied\",\"v_i,v_j,v_k,v_l,v_m\",1,+(-1)^(t[1])*2,(-1)^(t[2])*3,(-1)^
0*4,5); \n   end if;\nend do:\nfor s from 4 by 1 to 7 do\n   t:=conver
t(s,base,2):\n   if (2*abs(v[5].(v[1]+(-1)^(t[1])*v[2]+(-1)^(t[2])*v[3
]+(-1)^(t[3])*v[4])) > \n       Norm(v[1]+(-1)^(t[1])*v[2]+(-1)^(t[2])
*v[3]+(-1)^(t[3])*v[4],2)^2) then \n      print(\"not satisfied\",\"v_
i,v_j,v_k,v_l,v_m\",1,(-1)^(t[1])*2,+(-1)^(t[2])*3,(-1)^(t[3])*4,5); \+
\n   end if;\nend do:\n#checking for |v[i]+v[1]+v[2]+v[3]+v[4]+v[5]|^2
>=|v[i]|^2;\nfor s from 0 by 1 to 1 do\n   if (Norm(2*v[1]+(-1)^s*v[2]
+v[3]+v[4]+v[5],2)^2 < Norm(v[1],2)^2) then \n      print(\"not satisf
ied\",\"2*v_1\") \n   end if;\nend do;\nfor s from 2 by 1 to 3 do\n   \+
t:=convert(s,base,2):\n   if (Norm(2*v[1]+(-1)^(t[1])*v[2]+(-1)^(t[2])
*v[3]+v[4]+v[5],2)^2 < Norm(v[1],2)^2) then \n      print(\"not satisf
ied\",\"2*v_1\") \n   end if; \nend do:\nfor s from 4 by 1 to 7 do\n  \+
 t:=convert(s,base,2):\n   if (Norm(2*v[1]+(-1)^(t[1])*v[2]+(-1)^(t[2]
)*v[3]+(-1)^(t[3])*v[4]+v[5],2)^2 < Norm(v[1],2)^2) then \n      print
(\"not satisfied\",\"2*v_1\") \n   end if; \nend do:\nfor s from 8 by \+
1 to 15 do\n   t:=convert(s,base,2):\n   if (Norm(2*v[1]+(-1)^(t[1])*v
[2]+(-1)^(t[2])*v[3]+(-1)^(t[3])*v[4]+(-1)^(t[4])*v[5],2)^2 < Norm(v[1
],2)^2) then \n      print(\"not satisfied\",\"2*v_1\") \n   end if; \+
\nend do:\nfor s from 0 by 1 to 1 do\n   if (Norm(v[1]+(-1)^s*2*v[2]+v
[3]+v[4]+v[5],2)^2 < Norm(v[2],2)^2) then \n      print(\"not satisfie
d\",\"2*v_2\") \n   end if;\nend do;\nfor s from 2 by 1 to 3 do\n   t:
=convert(s,base,2):\n   if (Norm(v[1]+(-1)^(t[1])*2*v[2]+(-1)^(t[2])*v
[3]+v[4]+v[5],2)^2 < Norm(v[2],2)^2) then \n      print(\"not satisfie
d\",\"2*v_2\") \n   end if; \nend do:\nfor s from 4 by 1 to 7 do\n   t
:=convert(s,base,2):\n   if (Norm(v[1]+(-1)^(t[1])*2*v[2]+(-1)^(t[2])*
v[3]+(-1)^(t[3])*v[4]+v[5],2)^2 < Norm(v[2],2)^2) then \n      print(
\"not satisfied\",\"2*v_2\") \n   end if; \nend do:\nfor s from 8 by 1
 to 15 do\n   t:=convert(s,base,2):\n   if (Norm(v[1]+(-1)^(t[1])*2*v[
2]+(-1)^(t[2])*v[3]+(-1)^(t[3])*v[4]+(-1)^(t[4])*v[5],2)^2 < Norm(v[2]
,2)^2) then \n      print(\"not satisfied\",\"2*v_2\") \n   end if; \n
end do:\nfor s from 0 by 1 to 1 do\n   if (Norm(v[1]+(-1)^s*v[2]+2*v[3
]+v[4]+v[5],2)^2 < Norm(v[3],2)^2) then \n      print(\"not satisfied
\",\"2*v_3\") \n   end if;\nend do;\nfor s from 2 by 1 to 3 do\n   t:=
convert(s,base,2):\n   if (Norm(v[1]+(-1)^(t[1])*v[2]+(-1)^(t[2])*2*v[
3]+v[4]+v[5],2)^2 < Norm(v[3],2)^2) then \n      print(\"not satisfied
\",\"2*v_3\") \n   end if; \nend do:\nfor s from 4 by 1 to 7 do\n   t:
=convert(s,base,2):\n   if (Norm(v[1]+(-1)^(t[1])*v[2]+(-1)^(t[2])*2*v
[3]+(-1)^(t[3])*v[4]+v[5],2)^2 < Norm(v[3],2)^2) then \n      print(\"
not satisfied\",\"2*v_3\") \n   end if; \nend do:\nfor s from 8 by 1 t
o 15 do\n   t:=convert(s,base,2):\n   if (Norm(v[1]+(-1)^(t[1])*v[2]+(
-1)^(t[2])*2*v[3]+(-1)^(t[3])*v[4]+(-1)^(t[4])*v[5],2)^2 < Norm(v[3],2
)^2) then \n      print(\"not satisfied\",\"2*v_3\") \n   end if; \nen
d do:\nfor s from 0 by 1 to 1 do\n   if (Norm(v[1]+(-1)^s*v[2]+v[3]+2*
v[4]+v[5],2)^2 < Norm(v[4],2)^2) then \n      print(\"not satisfied\",
\"2*v_4\") \n   end if;\nend do;\nfor s from 2 by 1 to 3 do\n   t:=con
vert(s,base,2):\n   if (Norm(v[1]+(-1)^(t[1])*v[2]+(-1)^(t[2])*v[3]+2*
v[4]+v[5],2)^2 < Norm(v[4],2)^2) then \n      print(\"not satisfied\",
\"2*v_4\") \n   end if; \nend do:\nfor s from 4 by 1 to 7 do\n   t:=co
nvert(s,base,2):\n   if (Norm(v[1]+(-1)^(t[1])*v[2]+(-1)^(t[2])*v[3]+(
-1)^(t[3])*2*v[4]+v[5],2)^2 < Norm(v[4],2)^2) then \n      print(\"not
 satisfied\",\"2*v_4\") \n   end if; \nend do:\nfor s from 8 by 1 to 1
5 do\n   t:=convert(s,base,2):\n   if (Norm(v[1]+(-1)^(t[1])*v[2]+(-1)
^(t[2])*v[3]+(-1)^(t[3])*2*v[4]+(-1)^(t[4])*v[5],2)^2 < Norm(v[4],2)^2
) then \n      print(\"not satisfied\",\"2*v_4\") \n   end if; \nend d
o:\nfor s from 0 by 1 to 1 do\n   if (Norm(v[1]+(-1)^s*v[2]+v[3]+v[4]+
2*v[5],2)^2 < Norm(v[5],2)^2) then \n      print(\"not satisfied\",\"2
*v_5\") \n   end if;\nend do;\nfor s from 2 by 1 to 3 do\n   t:=conver
t(s,base,2):\n   if (Norm(v[1]+(-1)^(t[1])*v[2]+(-1)^(t[2])*v[3]+v[4]+
2*v[5],2)^2 < Norm(v[5],2)^2) then \n      print(\"not satisfied\",\"2
*v_5\") \n   end if; \nend do:\nfor s from 4 by 1 to 7 do\n   t:=conve
rt(s,base,2):\n   if (Norm(v[1]+(-1)^(t[1])*v[2]+(-1)^(t[2])*v[3]+(-1)
^(t[3])*v[4]+2*v[5],2)^2 < Norm(v[5],2)^2) then \n      print(\"not sa
tisfied\",\"2*v_5\") \n   end if; \nend do:\nfor s from 8 by 1 to 15 d
o\n   t:=convert(s,base,2):\n   if (Norm(v[1]+(-1)^(t[1])*v[2]+(-1)^(t
[2])*v[3]+(-1)^(t[3])*v[4]+(-1)^(t[4])*2*v[5],2)^2 < Norm(v[5],2)^2) t
hen \n      print(\"not satisfied\",\"2*v_5\") \n   end if; \nend do:
" }}{PARA 11 "" 1 "" {XPPMATH 20 "6'Q.not~satisfied6\"Q,v_i,v_j,v_kF$
\"\"#\"\"%\"\"&" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}
{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 365 "v[1]:=Vector([4,-1,-1,-1,-1
]):\nv[2]:=Vector([-1,4,-1,-1,-1]):\nv[3]:=Vector([1,1,4,-1,-1]):\nv[4
]:=Vector([1,1,-1,4,-1]):\nv[5]:=Vector([-2,-2,-2,-2,-2]):\nv[1],v[2],
v[3],v[4],v[5];\nprint(\"|v[1]|^2\"=Norm(v[1],2)^2);\n#checking for de
creasing order;\nfor i from 1 by 1 to 4 do \n   if (Norm(v[i],2)^2 > N
orm(v[i+1],2)^2) then print(\"not satisfied\",(i,i+1)) end if; \nend d
o;" }}{PARA 11 "" 1 "" {XPPMATH 20 "6'-%'RTABLEG6%\"*ScQ>#-%'MATRIXG6#
7'7#\"\"%7#!\"\"F-F-F-&%'VectorG6#%'columnG-F$6%\"*/dQ>#-F(6#7'F-F+F-F
-F-F/-F$6%\"*odQ>#-F(6#7'7#\"\"\"F?F+F-F-F/-F$6%\"*KeQ>#-F(6#7'F?F?F-F
+F-F/-F$6%\"*'*eQ>#-F(6#7'7#!\"#FMFMFMFMF/" }}{PARA 11 "" 1 "" 
{XPPMATH 20 "6#/Q)|grv[1]|gr^26\"\"#?" }}}{EXCHG {PARA 0 "> " 0 "" 
{MPLTEXT 1 0 6470 "#checking for 2|v[j].v[i]|=<|v[i]|^2;\nL2:=choose(5
, 2):\nfor i from 1 by 1 to numbcomb(5, 2) do\n   if (2*abs(v[L2[i][2]
].v[L2[i][1]]) > Norm(v[L2[i][1]],2)^2) then \n      print(\"not satis
fied\",\"v_i,v_j\",L2[i][1],L2[i][2]) \n   end if;\nend do;\n#checking
 for 2|v[k].(v[i]+v[j])|=<|v[i]+v[j]|^2;\nL3:=choose(5, 3):\nfor s fro
m 0 by 1 to 1 do\n   for i from 1 by 1 to numbcomb(5, 3) do\n      if \+
(2*abs(v[L3[i][3]].(v[L3[i][1]]+(-1)^s*v[L3[i][2]])) > Norm(v[L3[i][1]
]+(-1)^s*v[L3[i][2]],2)^2) then \n         print(\"not satisfied\",\"v
_i,v_j,v_k\",L3[i][1],(-1)^s*L3[i][2],L3[i][3]); \n      end if;\n   e
nd do;\nend do;\n#checking for 2|v[l].(v[i]+v[j]+v[k])|=<|v[i]+v[j]+v[
k]|^2;\nL4:=choose(5, 4):\nfor s from 0 by 1 to 1 do\n   for i from 1 \+
by 1 to numbcomb(5, 4) do\n      if (2*abs(v[L4[i][4]].(v[L4[i][1]]+(-
1)^s*v[L4[i][2]]+(-1)^0*v[L4[i][3]])) >\n         Norm(v[L4[i][1]]+(-1
)^s*v[L4[i][2]]+(-1)^0*v[L4[i][3]],2)^2) then \n         print(\"not s
atisfied\",\"v_i,v_j,v_k,v_l\",L4[i][1],(-1)^s*L4[i][2],(-1)^0*L4[i][3
],L4[i][4]); \n      end if;\n   end do;\nend do;\nfor s from 2 by 1 t
o 3 do\n   t:=convert(s,base,2):\n   for i from 1 by 1 to numbcomb(5, \+
4) do\n      if (2*abs(v[L4[i][4]].(v[L4[i][1]]+(-1)^(t[1])*v[L4[i][2]
]+(-1)^(t[2])*v[L4[i][3]])) >\n         Norm(v[L4[i][1]]+(-1)^(t[1])*v
[L4[i][2]]+(-1)^(t[2])*v[L4[i][3]],2)^2) then \n         print(\"not s
atisfied\",\"v_i,v_j,v_k,v_l\",L4[i][1],(-1)^(t[1])*L4[i][2],(-1)^(t[2
])*L4[i][3],L4[i][4]); \n      end if;\n   end do;\nend do:\n#checking
 for 2|v[m].(v[i]+v[j]+v[k]+v[l])|=<|v[i]+v[j]+v[k]+v[l]|^2;\nfor s fr
om 0 by 1 to 1 do\n   if (2*abs(v[5].(v[1]+(-1)^s*v[2]+(-1)^0*v[3]+(-1
)^0*v[4])) > \n       Norm(v[1]+(-1)^s*v[2]+(-1)^0*v[3]+(-1)^0*v[4],2)
^2) then \n      print(\"not satisfied\",\"v_i,v_j,v_k,v_l,v_m\",1,(-1
)^s*2,3,4,5); \n   end if;\nend do;\nfor s from 2 by 1 to 3 do\n   t:=
convert(s,base,2):\n   if (2*abs(v[5].(v[1]+(-1)^(t[1])*v[2]+(-1)^(t[2
])*v[3]+(-1)^0*v[4])) > \n       Norm(v[1]+(-1)^(t[1])*v[2]+(-1)^(t[2]
)*v[3]+(-1)^0*v[4],2)^2) then \n      print(\"not satisfied\",\"v_i,v_
j,v_k,v_l,v_m\",1,+(-1)^(t[1])*2,(-1)^(t[2])*3,(-1)^0*4,5); \n   end i
f;\nend do:\nfor s from 4 by 1 to 7 do\n   t:=convert(s,base,2):\n   i
f (2*abs(v[5].(v[1]+(-1)^(t[1])*v[2]+(-1)^(t[2])*v[3]+(-1)^(t[3])*v[4]
)) > \n       Norm(v[1]+(-1)^(t[1])*v[2]+(-1)^(t[2])*v[3]+(-1)^(t[3])*
v[4],2)^2) then \n      print(\"not satisfied\",\"v_i,v_j,v_k,v_l,v_m
\",1,(-1)^(t[1])*2,+(-1)^(t[2])*3,(-1)^(t[3])*4,5); \n   end if;\nend \+
do:\n\n#checking for |v[i]+v[1]+v[2]+v[3]+v[4]+v[5]|^2>=|v[i]|^2;\nfor
 s from 0 by 1 to 1 do\n   if (Norm(2*v[1]+(-1)^s*v[2]+v[3]+v[4]+v[5],
2)^2 < Norm(v[1],2)^2) then \n      print(\"not satisfied\",\"2*v_1\")
 \n   end if;\nend do;\nfor s from 2 by 1 to 3 do\n   t:=convert(s,bas
e,2):\n   if (Norm(2*v[1]+(-1)^(t[1])*v[2]+(-1)^(t[2])*v[3]+v[4]+v[5],
2)^2 < Norm(v[1],2)^2) then \n      print(\"not satisfied\",\"2*v_1\")
 \n   end if; \nend do:\nfor s from 4 by 1 to 7 do\n   t:=convert(s,ba
se,2):\n   if (Norm(2*v[1]+(-1)^(t[1])*v[2]+(-1)^(t[2])*v[3]+(-1)^(t[3
])*v[4]+v[5],2)^2 < Norm(v[1],2)^2) then \n      print(\"not satisfied
\",\"2*v_1\") \n   end if; \nend do:\nfor s from 8 by 1 to 15 do\n   t
:=convert(s,base,2):\n   if (Norm(2*v[1]+(-1)^(t[1])*v[2]+(-1)^(t[2])*
v[3]+(-1)^(t[3])*v[4]+(-1)^(t[4])*v[5],2)^2 < Norm(v[1],2)^2) then \n \+
     print(\"not satisfied\",\"2*v_1\") \n   end if; \nend do:\nfor s \+
from 0 by 1 to 1 do\n   if (Norm(v[1]+(-1)^s*2*v[2]+v[3]+v[4]+v[5],2)^
2 < Norm(v[2],2)^2) then \n      print(\"not satisfied\",\"2*v_2\") \n
   end if;\nend do;\nfor s from 2 by 1 to 3 do\n   t:=convert(s,base,2
):\n   if (Norm(v[1]+(-1)^(t[1])*2*v[2]+(-1)^(t[2])*v[3]+v[4]+v[5],2)^
2 < Norm(v[2],2)^2) then \n      print(\"not satisfied\",\"2*v_2\") \n
   end if; \nend do:\nfor s from 4 by 1 to 7 do\n   t:=convert(s,base,
2):\n   if (Norm(v[1]+(-1)^(t[1])*2*v[2]+(-1)^(t[2])*v[3]+(-1)^(t[3])*
v[4]+v[5],2)^2 < Norm(v[2],2)^2) then \n      print(\"not satisfied\",
\"2*v_2\") \n   end if; \nend do:\nfor s from 8 by 1 to 15 do\n   t:=c
onvert(s,base,2):\n   if (Norm(v[1]+(-1)^(t[1])*2*v[2]+(-1)^(t[2])*v[3
]+(-1)^(t[3])*v[4]+(-1)^(t[4])*v[5],2)^2 < Norm(v[2],2)^2) then \n    \+
  print(\"not satisfied\",\"2*v_2\") \n   end if; \nend do:\nfor s fro
m 0 by 1 to 1 do\n   if (Norm(v[1]+(-1)^s*v[2]+2*v[3]+v[4]+v[5],2)^2 <
 Norm(v[3],2)^2) then \n      print(\"not satisfied\",\"2*v_3\") \n   \+
end if;\nend do;\nfor s from 2 by 1 to 3 do\n   t:=convert(s,base,2):
\n   if (Norm(v[1]+(-1)^(t[1])*v[2]+(-1)^(t[2])*2*v[3]+v[4]+v[5],2)^2 \+
< Norm(v[3],2)^2) then \n      print(\"not satisfied\",\"2*v_3\") \n  \+
 end if; \nend do:\nfor s from 4 by 1 to 7 do\n   t:=convert(s,base,2)
:\n   if (Norm(v[1]+(-1)^(t[1])*v[2]+(-1)^(t[2])*2*v[3]+(-1)^(t[3])*v[
4]+v[5],2)^2 < Norm(v[3],2)^2) then \n      print(\"not satisfied\",\"
2*v_3\") \n   end if; \nend do:\nfor s from 8 by 1 to 15 do\n   t:=con
vert(s,base,2):\n   if (Norm(v[1]+(-1)^(t[1])*v[2]+(-1)^(t[2])*2*v[3]+
(-1)^(t[3])*v[4]+(-1)^(t[4])*v[5],2)^2 < Norm(v[3],2)^2) then \n      \+
print(\"not satisfied\",\"2*v_3\") \n   end if; \nend do:\nfor s from \+
0 by 1 to 1 do\n   if (Norm(v[1]+(-1)^s*v[2]+v[3]+2*v[4]+v[5],2)^2 < N
orm(v[4],2)^2) then \n      print(\"not satisfied\",\"2*v_4\") \n   en
d if;\nend do;\nfor s from 2 by 1 to 3 do\n   t:=convert(s,base,2):\n \+
  if (Norm(v[1]+(-1)^(t[1])*v[2]+(-1)^(t[2])*v[3]+2*v[4]+v[5],2)^2 < N
orm(v[4],2)^2) then \n      print(\"not satisfied\",\"2*v_4\") \n   en
d if; \nend do:\nfor s from 4 by 1 to 7 do\n   t:=convert(s,base,2):\n
   if (Norm(v[1]+(-1)^(t[1])*v[2]+(-1)^(t[2])*v[3]+(-1)^(t[3])*2*v[4]+
v[5],2)^2 < Norm(v[4],2)^2) then \n      print(\"not satisfied\",\"2*v
_4\") \n   end if; \nend do:\nfor s from 8 by 1 to 15 do\n   t:=conver
t(s,base,2):\n   if (Norm(v[1]+(-1)^(t[1])*v[2]+(-1)^(t[2])*v[3]+(-1)^
(t[3])*2*v[4]+(-1)^(t[4])*v[5],2)^2 < Norm(v[4],2)^2) then \n      pri
nt(\"not satisfied\",\"2*v_4\") \n   end if; \nend do:\nfor s from 0 b
y 1 to 1 do\n   if (Norm(v[1]+(-1)^s*v[2]+v[3]+v[4]+2*v[5],2)^2 < Norm
(v[5],2)^2) then \n      print(\"not satisfied\",\"2*v_5\") \n   end i
f;\nend do;\nfor s from 2 by 1 to 3 do\n   t:=convert(s,base,2):\n   i
f (Norm(v[1]+(-1)^(t[1])*v[2]+(-1)^(t[2])*v[3]+v[4]+2*v[5],2)^2 < Norm
(v[5],2)^2) then \n      print(\"not satisfied\",\"2*v_5\") \n   end i
f; \nend do:\nfor s from 4 by 1 to 7 do\n   t:=convert(s,base,2):\n   \+
if (Norm(v[1]+(-1)^(t[1])*v[2]+(-1)^(t[2])*v[3]+(-1)^(t[3])*v[4]+2*v[5
],2)^2 < Norm(v[5],2)^2) then \n      print(\"not satisfied\",\"2*v_5
\") \n   end if; \nend do:\nfor s from 8 by 1 to 15 do\n   t:=convert(
s,base,2):\n   if (Norm(v[1]+(-1)^(t[1])*v[2]+(-1)^(t[2])*v[3]+(-1)^(t
[3])*v[4]+(-1)^(t[4])*2*v[5],2)^2 < Norm(v[5],2)^2) then \n      print
(\"not satisfied\",\"2*v_5\") \n   end if; \nend do:" }}{PARA 11 "" 1 
"" {XPPMATH 20 "6'Q.not~satisfied6\"Q,v_i,v_j,v_kF$\"\"$\"\"%\"\"&" }}
}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "> " 0 "
" {MPLTEXT 1 0 368 "v[1]:=Vector([4,-1,-1,-1,-1]):\nv[2]:=Vector([-1,4
,-1,-1,-1]):\nv[3]:=Vector([-1,-1,4,-1,-1]):\nv[4]:=Vector([-1,-1,-1,4
,1]):\nv[5]:=Vector([-2,-2,-2,-2,-2]):\nv[1],v[2],v[3],v[4],v[5];\npri
nt(\"|v[1]|^2\"=Norm(v[1],2)^2);\n#checking for decreasing order;\nfor
 i from 1 by 1 to 4 do \n   if (Norm(v[i],2)^2 > Norm(v[i+1],2)^2) the
n print(\"not satisfied\",(i,i+1)) end if; \nend do;" }}{PARA 11 "" 1 
"" {XPPMATH 20 "6'-%'RTABLEG6%\"*![+!=#-%'MATRIXG6#7'7#\"\"%7#!\"\"F-F
-F-&%'VectorG6#%'columnG-F$6%\"*W0+=#-F(6#7'F-F+F-F-F-F/-F$6%\"*31+=#-
F(6#7'F-F-F+F-F-F/-F$6%\"*s1+=#-F(6#7'F-F-F-F+7#\"\"\"F/-F$6%\"*O2+=#-
F(6#7'7#!\"#FMFMFMFMF/" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#/Q)|grv[1]|g
r^26\"\"#?" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 6469 "#checking f
or 2|v[j].v[i]|=<|v[i]|^2;\nL2:=choose(5, 2):\nfor i from 1 by 1 to nu
mbcomb(5, 2) do\n   if (2*abs(v[L2[i][2]].v[L2[i][1]]) > Norm(v[L2[i][
1]],2)^2) then \n      print(\"not satisfied\",\"v_i,v_j\",L2[i][1],L2
[i][2]) \n   end if;\nend do;\n#checking for 2|v[k].(v[i]+v[j])|=<|v[i
]+v[j]|^2;\nL3:=choose(5, 3):\nfor s from 0 by 1 to 1 do\n   for i fro
m 1 by 1 to numbcomb(5, 3) do\n      if (2*abs(v[L3[i][3]].(v[L3[i][1]
]+(-1)^s*v[L3[i][2]])) > Norm(v[L3[i][1]]+(-1)^s*v[L3[i][2]],2)^2) the
n \n         print(\"not satisfied\",\"v_i,v_j,v_k\",L3[i][1],(-1)^s*L
3[i][2],L3[i][3]); \n      end if;\n   end do;\nend do;\n#checking for
 2|v[l].(v[i]+v[j]+v[k])|=<|v[i]+v[j]+v[k]|^2;\nL4:=choose(5, 4):\nfor
 s from 0 by 1 to 1 do\n   for i from 1 by 1 to numbcomb(5, 4) do\n   \+
   if (2*abs(v[L4[i][4]].(v[L4[i][1]]+(-1)^s*v[L4[i][2]]+(-1)^0*v[L4[i
][3]])) >\n         Norm(v[L4[i][1]]+(-1)^s*v[L4[i][2]]+(-1)^0*v[L4[i]
[3]],2)^2) then \n         print(\"not satisfied\",\"v_i,v_j,v_k,v_l\"
,L4[i][1],(-1)^s*L4[i][2],(-1)^0*L4[i][3],L4[i][4]); \n      end if;\n
   end do;\nend do;\nfor s from 2 by 1 to 3 do\n   t:=convert(s,base,2
):\n   for i from 1 by 1 to numbcomb(5, 4) do\n      if (2*abs(v[L4[i]
[4]].(v[L4[i][1]]+(-1)^(t[1])*v[L4[i][2]]+(-1)^(t[2])*v[L4[i][3]])) >
\n         Norm(v[L4[i][1]]+(-1)^(t[1])*v[L4[i][2]]+(-1)^(t[2])*v[L4[i
][3]],2)^2) then \n         print(\"not satisfied\",\"v_i,v_j,v_k,v_l
\",L4[i][1],(-1)^(t[1])*L4[i][2],(-1)^(t[2])*L4[i][3],L4[i][4]); \n   \+
   end if;\n   end do;\nend do:\n#checking for 2|v[m].(v[i]+v[j]+v[k]+
v[l])|=<|v[i]+v[j]+v[k]+v[l]|^2;\nfor s from 0 by 1 to 1 do\n   if (2*
abs(v[5].(v[1]+(-1)^s*v[2]+(-1)^0*v[3]+(-1)^0*v[4])) > \n       Norm(v
[1]+(-1)^s*v[2]+(-1)^0*v[3]+(-1)^0*v[4],2)^2) then \n      print(\"not
 satisfied\",\"v_i,v_j,v_k,v_l,v_m\",1,(-1)^s*2,3,4,5); \n   end if;\n
end do;\nfor s from 2 by 1 to 3 do\n   t:=convert(s,base,2):\n   if (2
*abs(v[5].(v[1]+(-1)^(t[1])*v[2]+(-1)^(t[2])*v[3]+(-1)^0*v[4])) > \n  \+
     Norm(v[1]+(-1)^(t[1])*v[2]+(-1)^(t[2])*v[3]+(-1)^0*v[4],2)^2) the
n \n      print(\"not satisfied\",\"v_i,v_j,v_k,v_l,v_m\",1,+(-1)^(t[1
])*2,(-1)^(t[2])*3,(-1)^0*4,5); \n   end if;\nend do:\nfor s from 4 by
 1 to 7 do\n   t:=convert(s,base,2):\n   if (2*abs(v[5].(v[1]+(-1)^(t[
1])*v[2]+(-1)^(t[2])*v[3]+(-1)^(t[3])*v[4])) > \n       Norm(v[1]+(-1)
^(t[1])*v[2]+(-1)^(t[2])*v[3]+(-1)^(t[3])*v[4],2)^2) then \n      prin
t(\"not satisfied\",\"v_i,v_j,v_k,v_l,v_m\",1,(-1)^(t[1])*2,+(-1)^(t[2
])*3,(-1)^(t[3])*4,5); \n   end if;\nend do:\n#checking for |v[i]+v[1]
+v[2]+v[3]+v[4]+v[5]|^2>=|v[i]|^2;\nfor s from 0 by 1 to 1 do\n   if (
Norm(2*v[1]+(-1)^s*v[2]+v[3]+v[4]+v[5],2)^2 < Norm(v[1],2)^2) then \n \+
     print(\"not satisfied\",\"2*v_1\") \n   end if;\nend do;\nfor s f
rom 2 by 1 to 3 do\n   t:=convert(s,base,2):\n   if (Norm(2*v[1]+(-1)^
(t[1])*v[2]+(-1)^(t[2])*v[3]+v[4]+v[5],2)^2 < Norm(v[1],2)^2) then \n \+
     print(\"not satisfied\",\"2*v_1\") \n   end if; \nend do:\nfor s \+
from 4 by 1 to 7 do\n   t:=convert(s,base,2):\n   if (Norm(2*v[1]+(-1)
^(t[1])*v[2]+(-1)^(t[2])*v[3]+(-1)^(t[3])*v[4]+v[5],2)^2 < Norm(v[1],2
)^2) then \n      print(\"not satisfied\",\"2*v_1\") \n   end if; \nen
d do:\nfor s from 8 by 1 to 15 do\n   t:=convert(s,base,2):\n   if (No
rm(2*v[1]+(-1)^(t[1])*v[2]+(-1)^(t[2])*v[3]+(-1)^(t[3])*v[4]+(-1)^(t[4
])*v[5],2)^2 < Norm(v[1],2)^2) then \n      print(\"not satisfied\",\"
2*v_1\") \n   end if; \nend do:\nfor s from 0 by 1 to 1 do\n   if (Nor
m(v[1]+(-1)^s*2*v[2]+v[3]+v[4]+v[5],2)^2 < Norm(v[2],2)^2) then \n    \+
  print(\"not satisfied\",\"2*v_2\") \n   end if;\nend do;\nfor s from
 2 by 1 to 3 do\n   t:=convert(s,base,2):\n   if (Norm(v[1]+(-1)^(t[1]
)*2*v[2]+(-1)^(t[2])*v[3]+v[4]+v[5],2)^2 < Norm(v[2],2)^2) then \n    \+
  print(\"not satisfied\",\"2*v_2\") \n   end if; \nend do:\nfor s fro
m 4 by 1 to 7 do\n   t:=convert(s,base,2):\n   if (Norm(v[1]+(-1)^(t[1
])*2*v[2]+(-1)^(t[2])*v[3]+(-1)^(t[3])*v[4]+v[5],2)^2 < Norm(v[2],2)^2
) then \n      print(\"not satisfied\",\"2*v_2\") \n   end if; \nend d
o:\nfor s from 8 by 1 to 15 do\n   t:=convert(s,base,2):\n   if (Norm(
v[1]+(-1)^(t[1])*2*v[2]+(-1)^(t[2])*v[3]+(-1)^(t[3])*v[4]+(-1)^(t[4])*
v[5],2)^2 < Norm(v[2],2)^2) then \n      print(\"not satisfied\",\"2*v
_2\") \n   end if; \nend do:\nfor s from 0 by 1 to 1 do\n   if (Norm(v
[1]+(-1)^s*v[2]+2*v[3]+v[4]+v[5],2)^2 < Norm(v[3],2)^2) then \n      p
rint(\"not satisfied\",\"2*v_3\") \n   end if;\nend do;\nfor s from 2 \+
by 1 to 3 do\n   t:=convert(s,base,2):\n   if (Norm(v[1]+(-1)^(t[1])*v
[2]+(-1)^(t[2])*2*v[3]+v[4]+v[5],2)^2 < Norm(v[3],2)^2) then \n      p
rint(\"not satisfied\",\"2*v_3\") \n   end if; \nend do:\nfor s from 4
 by 1 to 7 do\n   t:=convert(s,base,2):\n   if (Norm(v[1]+(-1)^(t[1])*
v[2]+(-1)^(t[2])*2*v[3]+(-1)^(t[3])*v[4]+v[5],2)^2 < Norm(v[3],2)^2) t
hen \n      print(\"not satisfied\",\"2*v_3\") \n   end if; \nend do:
\nfor s from 8 by 1 to 15 do\n   t:=convert(s,base,2):\n   if (Norm(v[
1]+(-1)^(t[1])*v[2]+(-1)^(t[2])*2*v[3]+(-1)^(t[3])*v[4]+(-1)^(t[4])*v[
5],2)^2 < Norm(v[3],2)^2) then \n      print(\"not satisfied\",\"2*v_3
\") \n   end if; \nend do:\nfor s from 0 by 1 to 1 do\n   if (Norm(v[1
]+(-1)^s*v[2]+v[3]+2*v[4]+v[5],2)^2 < Norm(v[4],2)^2) then \n      pri
nt(\"not satisfied\",\"2*v_4\") \n   end if;\nend do;\nfor s from 2 by
 1 to 3 do\n   t:=convert(s,base,2):\n   if (Norm(v[1]+(-1)^(t[1])*v[2
]+(-1)^(t[2])*v[3]+2*v[4]+v[5],2)^2 < Norm(v[4],2)^2) then \n      pri
nt(\"not satisfied\",\"2*v_4\") \n   end if; \nend do:\nfor s from 4 b
y 1 to 7 do\n   t:=convert(s,base,2):\n   if (Norm(v[1]+(-1)^(t[1])*v[
2]+(-1)^(t[2])*v[3]+(-1)^(t[3])*2*v[4]+v[5],2)^2 < Norm(v[4],2)^2) the
n \n      print(\"not satisfied\",\"2*v_4\") \n   end if; \nend do:\nf
or s from 8 by 1 to 15 do\n   t:=convert(s,base,2):\n   if (Norm(v[1]+
(-1)^(t[1])*v[2]+(-1)^(t[2])*v[3]+(-1)^(t[3])*2*v[4]+(-1)^(t[4])*v[5],
2)^2 < Norm(v[4],2)^2) then \n      print(\"not satisfied\",\"2*v_4\")
 \n   end if; \nend do:\nfor s from 0 by 1 to 1 do\n   if (Norm(v[1]+(
-1)^s*v[2]+v[3]+v[4]+2*v[5],2)^2 < Norm(v[5],2)^2) then \n      print(
\"not satisfied\",\"2*v_5\") \n   end if;\nend do;\nfor s from 2 by 1 \+
to 3 do\n   t:=convert(s,base,2):\n   if (Norm(v[1]+(-1)^(t[1])*v[2]+(
-1)^(t[2])*v[3]+v[4]+2*v[5],2)^2 < Norm(v[5],2)^2) then \n      print(
\"not satisfied\",\"2*v_5\") \n   end if; \nend do:\nfor s from 4 by 1
 to 7 do\n   t:=convert(s,base,2):\n   if (Norm(v[1]+(-1)^(t[1])*v[2]+
(-1)^(t[2])*v[3]+(-1)^(t[3])*v[4]+2*v[5],2)^2 < Norm(v[5],2)^2) then \+
\n      print(\"not satisfied\",\"2*v_5\") \n   end if; \nend do:\nfor
 s from 8 by 1 to 15 do\n   t:=convert(s,base,2):\n   if (Norm(v[1]+(-
1)^(t[1])*v[2]+(-1)^(t[2])*v[3]+(-1)^(t[3])*v[4]+(-1)^(t[4])*2*v[5],2)
^2 < Norm(v[5],2)^2) then \n      print(\"not satisfied\",\"2*v_5\") \+
\n   end if; \nend do:" }}{PARA 11 "" 1 "" {XPPMATH 20 "6(Q.not~satisf
ied6\"Q0v_i,v_j,v_k,v_lF$\"\"\"\"\"#\"\"$\"\"%" }}}{EXCHG {PARA 0 "> \+
" 0 "" {MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 365 
"v[1]:=Vector([4,-1,-1,1,1]):\nv[2]:=Vector([1,4,-1,1,-1]):\nv[3]:=Vec
tor([-1,-1,4,-1,-1]):\nv[4]:=Vector([-1,-1,-1,4,-1]):\nv[5]:=Vector([-
2,-2,-2,-2,-2]):\nv[1],v[2],v[3],v[4],v[5];\nprint(\"|v[1]|^2\"=Norm(v
[1],2)^2);\n#checking for decreasing order;\nfor i from 1 by 1 to 4 do
 \n   if (Norm(v[i],2)^2 > Norm(v[i+1],2)^2) then print(\"not satisfie
d\",(i,i+1)) end if; \nend do;" }}{PARA 11 "" 1 "" {XPPMATH 20 "6'-%'R
TABLEG6%\"*3nV#=-%'MATRIXG6#7'7#\"\"%7#!\"\"F-7#\"\"\"F/&%'VectorG6#%'
columnG-F$6%\"*snV#=-F(6#7'F/F+F-F/F-F1-F$6%\"*OoV#=-F(6#7'F-F-F+F-F-F
1-F$6%\"*+pV#=-F(6#7'F-F-F-F+F-F1-F$6%\"*kpV#=-F(6#7'7#!\"#FMFMFMFMF1
" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#/Q)|grv[1]|gr^26\"\"#?" }}}{EXCHG 
{PARA 0 "> " 0 "" {MPLTEXT 1 0 6469 "#checking for 2|v[j].v[i]|=<|v[i]
|^2;\nL2:=choose(5, 2):\nfor i from 1 by 1 to numbcomb(5, 2) do\n   if
 (2*abs(v[L2[i][2]].v[L2[i][1]]) > Norm(v[L2[i][1]],2)^2) then \n     \+
 print(\"not satisfied\",\"v_i,v_j\",L2[i][1],L2[i][2]) \n   end if;\n
end do;\n#checking for 2|v[k].(v[i]+v[j])|=<|v[i]+v[j]|^2;\nL3:=choose
(5, 3):\nfor s from 0 by 1 to 1 do\n   for i from 1 by 1 to numbcomb(5
, 3) do\n      if (2*abs(v[L3[i][3]].(v[L3[i][1]]+(-1)^s*v[L3[i][2]]))
 > Norm(v[L3[i][1]]+(-1)^s*v[L3[i][2]],2)^2) then \n         print(\"n
ot satisfied\",\"v_i,v_j,v_k\",L3[i][1],(-1)^s*L3[i][2],L3[i][3]); \n \+
     end if;\n   end do;\nend do;\n#checking for 2|v[l].(v[i]+v[j]+v[k
])|=<|v[i]+v[j]+v[k]|^2;\nL4:=choose(5, 4):\nfor s from 0 by 1 to 1 do
\n   for i from 1 by 1 to numbcomb(5, 4) do\n      if (2*abs(v[L4[i][4
]].(v[L4[i][1]]+(-1)^s*v[L4[i][2]]+(-1)^0*v[L4[i][3]])) >\n         No
rm(v[L4[i][1]]+(-1)^s*v[L4[i][2]]+(-1)^0*v[L4[i][3]],2)^2) then \n    \+
     print(\"not satisfied\",\"v_i,v_j,v_k,v_l\",L4[i][1],(-1)^s*L4[i]
[2],(-1)^0*L4[i][3],L4[i][4]); \n      end if;\n   end do;\nend do;\nf
or s from 2 by 1 to 3 do\n   t:=convert(s,base,2):\n   for i from 1 by
 1 to numbcomb(5, 4) do\n      if (2*abs(v[L4[i][4]].(v[L4[i][1]]+(-1)
^(t[1])*v[L4[i][2]]+(-1)^(t[2])*v[L4[i][3]])) >\n         Norm(v[L4[i]
[1]]+(-1)^(t[1])*v[L4[i][2]]+(-1)^(t[2])*v[L4[i][3]],2)^2) then \n    \+
     print(\"not satisfied\",\"v_i,v_j,v_k,v_l\",L4[i][1],(-1)^(t[1])*
L4[i][2],(-1)^(t[2])*L4[i][3],L4[i][4]); \n      end if;\n   end do;\n
end do:\n#checking for 2|v[m].(v[i]+v[j]+v[k]+v[l])|=<|v[i]+v[j]+v[k]+
v[l]|^2;\nfor s from 0 by 1 to 1 do\n   if (2*abs(v[5].(v[1]+(-1)^s*v[
2]+(-1)^0*v[3]+(-1)^0*v[4])) > \n       Norm(v[1]+(-1)^s*v[2]+(-1)^0*v
[3]+(-1)^0*v[4],2)^2) then \n      print(\"not satisfied\",\"v_i,v_j,v
_k,v_l,v_m\",1,(-1)^s*2,3,4,5); \n   end if;\nend do;\nfor s from 2 by
 1 to 3 do\n   t:=convert(s,base,2):\n   if (2*abs(v[5].(v[1]+(-1)^(t[
1])*v[2]+(-1)^(t[2])*v[3]+(-1)^0*v[4])) > \n       Norm(v[1]+(-1)^(t[1
])*v[2]+(-1)^(t[2])*v[3]+(-1)^0*v[4],2)^2) then \n      print(\"not sa
tisfied\",\"v_i,v_j,v_k,v_l,v_m\",1,+(-1)^(t[1])*2,(-1)^(t[2])*3,(-1)^
0*4,5); \n   end if;\nend do:\nfor s from 4 by 1 to 7 do\n   t:=conver
t(s,base,2):\n   if (2*abs(v[5].(v[1]+(-1)^(t[1])*v[2]+(-1)^(t[2])*v[3
]+(-1)^(t[3])*v[4])) > \n       Norm(v[1]+(-1)^(t[1])*v[2]+(-1)^(t[2])
*v[3]+(-1)^(t[3])*v[4],2)^2) then \n      print(\"not satisfied\",\"v_
i,v_j,v_k,v_l,v_m\",1,(-1)^(t[1])*2,+(-1)^(t[2])*3,(-1)^(t[3])*4,5); \+
\n   end if;\nend do:\n#checking for |v[i]+v[1]+v[2]+v[3]+v[4]+v[5]|^2
>=|v[i]|^2;\nfor s from 0 by 1 to 1 do\n   if (Norm(2*v[1]+(-1)^s*v[2]
+v[3]+v[4]+v[5],2)^2 < Norm(v[1],2)^2) then \n      print(\"not satisf
ied\",\"2*v_1\") \n   end if;\nend do;\nfor s from 2 by 1 to 3 do\n   \+
t:=convert(s,base,2):\n   if (Norm(2*v[1]+(-1)^(t[1])*v[2]+(-1)^(t[2])
*v[3]+v[4]+v[5],2)^2 < Norm(v[1],2)^2) then \n      print(\"not satisf
ied\",\"2*v_1\") \n   end if; \nend do:\nfor s from 4 by 1 to 7 do\n  \+
 t:=convert(s,base,2):\n   if (Norm(2*v[1]+(-1)^(t[1])*v[2]+(-1)^(t[2]
)*v[3]+(-1)^(t[3])*v[4]+v[5],2)^2 < Norm(v[1],2)^2) then \n      print
(\"not satisfied\",\"2*v_1\") \n   end if; \nend do:\nfor s from 8 by \+
1 to 15 do\n   t:=convert(s,base,2):\n   if (Norm(2*v[1]+(-1)^(t[1])*v
[2]+(-1)^(t[2])*v[3]+(-1)^(t[3])*v[4]+(-1)^(t[4])*v[5],2)^2 < Norm(v[1
],2)^2) then \n      print(\"not satisfied\",\"2*v_1\") \n   end if; \+
\nend do:\nfor s from 0 by 1 to 1 do\n   if (Norm(v[1]+(-1)^s*2*v[2]+v
[3]+v[4]+v[5],2)^2 < Norm(v[2],2)^2) then \n      print(\"not satisfie
d\",\"2*v_2\") \n   end if;\nend do;\nfor s from 2 by 1 to 3 do\n   t:
=convert(s,base,2):\n   if (Norm(v[1]+(-1)^(t[1])*2*v[2]+(-1)^(t[2])*v
[3]+v[4]+v[5],2)^2 < Norm(v[2],2)^2) then \n      print(\"not satisfie
d\",\"2*v_2\") \n   end if; \nend do:\nfor s from 4 by 1 to 7 do\n   t
:=convert(s,base,2):\n   if (Norm(v[1]+(-1)^(t[1])*2*v[2]+(-1)^(t[2])*
v[3]+(-1)^(t[3])*v[4]+v[5],2)^2 < Norm(v[2],2)^2) then \n      print(
\"not satisfied\",\"2*v_2\") \n   end if; \nend do:\nfor s from 8 by 1
 to 15 do\n   t:=convert(s,base,2):\n   if (Norm(v[1]+(-1)^(t[1])*2*v[
2]+(-1)^(t[2])*v[3]+(-1)^(t[3])*v[4]+(-1)^(t[4])*v[5],2)^2 < Norm(v[2]
,2)^2) then \n      print(\"not satisfied\",\"2*v_2\") \n   end if; \n
end do:\nfor s from 0 by 1 to 1 do\n   if (Norm(v[1]+(-1)^s*v[2]+2*v[3
]+v[4]+v[5],2)^2 < Norm(v[3],2)^2) then \n      print(\"not satisfied
\",\"2*v_3\") \n   end if;\nend do;\nfor s from 2 by 1 to 3 do\n   t:=
convert(s,base,2):\n   if (Norm(v[1]+(-1)^(t[1])*v[2]+(-1)^(t[2])*2*v[
3]+v[4]+v[5],2)^2 < Norm(v[3],2)^2) then \n      print(\"not satisfied
\",\"2*v_3\") \n   end if; \nend do:\nfor s from 4 by 1 to 7 do\n   t:
=convert(s,base,2):\n   if (Norm(v[1]+(-1)^(t[1])*v[2]+(-1)^(t[2])*2*v
[3]+(-1)^(t[3])*v[4]+v[5],2)^2 < Norm(v[3],2)^2) then \n      print(\"
not satisfied\",\"2*v_3\") \n   end if; \nend do:\nfor s from 8 by 1 t
o 15 do\n   t:=convert(s,base,2):\n   if (Norm(v[1]+(-1)^(t[1])*v[2]+(
-1)^(t[2])*2*v[3]+(-1)^(t[3])*v[4]+(-1)^(t[4])*v[5],2)^2 < Norm(v[3],2
)^2) then \n      print(\"not satisfied\",\"2*v_3\") \n   end if; \nen
d do:\nfor s from 0 by 1 to 1 do\n   if (Norm(v[1]+(-1)^s*v[2]+v[3]+2*
v[4]+v[5],2)^2 < Norm(v[4],2)^2) then \n      print(\"not satisfied\",
\"2*v_4\") \n   end if;\nend do;\nfor s from 2 by 1 to 3 do\n   t:=con
vert(s,base,2):\n   if (Norm(v[1]+(-1)^(t[1])*v[2]+(-1)^(t[2])*v[3]+2*
v[4]+v[5],2)^2 < Norm(v[4],2)^2) then \n      print(\"not satisfied\",
\"2*v_4\") \n   end if; \nend do:\nfor s from 4 by 1 to 7 do\n   t:=co
nvert(s,base,2):\n   if (Norm(v[1]+(-1)^(t[1])*v[2]+(-1)^(t[2])*v[3]+(
-1)^(t[3])*2*v[4]+v[5],2)^2 < Norm(v[4],2)^2) then \n      print(\"not
 satisfied\",\"2*v_4\") \n   end if; \nend do:\nfor s from 8 by 1 to 1
5 do\n   t:=convert(s,base,2):\n   if (Norm(v[1]+(-1)^(t[1])*v[2]+(-1)
^(t[2])*v[3]+(-1)^(t[3])*2*v[4]+(-1)^(t[4])*v[5],2)^2 < Norm(v[4],2)^2
) then \n      print(\"not satisfied\",\"2*v_4\") \n   end if; \nend d
o:\nfor s from 0 by 1 to 1 do\n   if (Norm(v[1]+(-1)^s*v[2]+v[3]+v[4]+
2*v[5],2)^2 < Norm(v[5],2)^2) then \n      print(\"not satisfied\",\"2
*v_5\") \n   end if;\nend do;\nfor s from 2 by 1 to 3 do\n   t:=conver
t(s,base,2):\n   if (Norm(v[1]+(-1)^(t[1])*v[2]+(-1)^(t[2])*v[3]+v[4]+
2*v[5],2)^2 < Norm(v[5],2)^2) then \n      print(\"not satisfied\",\"2
*v_5\") \n   end if; \nend do:\nfor s from 4 by 1 to 7 do\n   t:=conve
rt(s,base,2):\n   if (Norm(v[1]+(-1)^(t[1])*v[2]+(-1)^(t[2])*v[3]+(-1)
^(t[3])*v[4]+2*v[5],2)^2 < Norm(v[5],2)^2) then \n      print(\"not sa
tisfied\",\"2*v_5\") \n   end if; \nend do:\nfor s from 8 by 1 to 15 d
o\n   t:=convert(s,base,2):\n   if (Norm(v[1]+(-1)^(t[1])*v[2]+(-1)^(t
[2])*v[3]+(-1)^(t[3])*v[4]+(-1)^(t[4])*2*v[5],2)^2 < Norm(v[5],2)^2) t
hen \n      print(\"not satisfied\",\"2*v_5\") \n   end if; \nend do:
" }}{PARA 11 "" 1 "" {XPPMATH 20 "6(Q.not~satisfied6\"Q0v_i,v_j,v_k,v_
lF$\"\"\"\"\"#\"\"$\"\"&" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "
" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 365 "v[1]:=Vector([4,-1,1,-
1,1]):\nv[2]:=Vector([1,4,1,-1,-1]):\nv[3]:=Vector([-1,-1,4,-1,-1]):\n
v[4]:=Vector([-1,-1,-1,4,-1]):\nv[5]:=Vector([-2,-2,-2,-2,-2]):\nv[1],
v[2],v[3],v[4],v[5];\nprint(\"|v[1]|^2\"=Norm(v[1],2)^2);\n#checking f
or decreasing order;\nfor i from 1 by 1 to 4 do \n   if (Norm(v[i],2)^
2 > Norm(v[i+1],2)^2) then print(\"not satisfied\",(i,i+1)) end if; \n
end do;" }}{PARA 11 "" 1 "" {XPPMATH 20 "6'-%'RTABLEG6%\"*/4c4#-%'MATR
IXG6#7'7#\"\"%7#!\"\"7#\"\"\"F-F/&%'VectorG6#%'columnG-F$6%\"*o4c4#-F(
6#7'F/F+F/F-F-F1-F$6%\"*K5c4#-F(6#7'F-F-F+F-F-F1-F$6%\"*'4h&4#-F(6#7'F
-F-F-F+F-F1-F$6%\"*g6c4#-F(6#7'7#!\"#FMFMFMFMF1" }}{PARA 11 "" 1 "" 
{XPPMATH 20 "6#/Q)|grv[1]|gr^26\"\"#?" }}}{EXCHG {PARA 0 "> " 0 "" 
{MPLTEXT 1 0 6469 "#checking for 2|v[j].v[i]|=<|v[i]|^2;\nL2:=choose(5
, 2):\nfor i from 1 by 1 to numbcomb(5, 2) do\n   if (2*abs(v[L2[i][2]
].v[L2[i][1]]) > Norm(v[L2[i][1]],2)^2) then \n      print(\"not satis
fied\",\"v_i,v_j\",L2[i][1],L2[i][2]) \n   end if;\nend do;\n#checking
 for 2|v[k].(v[i]+v[j])|=<|v[i]+v[j]|^2;\nL3:=choose(5, 3):\nfor s fro
m 0 by 1 to 1 do\n   for i from 1 by 1 to numbcomb(5, 3) do\n      if \+
(2*abs(v[L3[i][3]].(v[L3[i][1]]+(-1)^s*v[L3[i][2]])) > Norm(v[L3[i][1]
]+(-1)^s*v[L3[i][2]],2)^2) then \n         print(\"not satisfied\",\"v
_i,v_j,v_k\",L3[i][1],(-1)^s*L3[i][2],L3[i][3]); \n      end if;\n   e
nd do;\nend do;\n#checking for 2|v[l].(v[i]+v[j]+v[k])|=<|v[i]+v[j]+v[
k]|^2;\nL4:=choose(5, 4):\nfor s from 0 by 1 to 1 do\n   for i from 1 \+
by 1 to numbcomb(5, 4) do\n      if (2*abs(v[L4[i][4]].(v[L4[i][1]]+(-
1)^s*v[L4[i][2]]+(-1)^0*v[L4[i][3]])) >\n         Norm(v[L4[i][1]]+(-1
)^s*v[L4[i][2]]+(-1)^0*v[L4[i][3]],2)^2) then \n         print(\"not s
atisfied\",\"v_i,v_j,v_k,v_l\",L4[i][1],(-1)^s*L4[i][2],(-1)^0*L4[i][3
],L4[i][4]); \n      end if;\n   end do;\nend do;\nfor s from 2 by 1 t
o 3 do\n   t:=convert(s,base,2):\n   for i from 1 by 1 to numbcomb(5, \+
4) do\n      if (2*abs(v[L4[i][4]].(v[L4[i][1]]+(-1)^(t[1])*v[L4[i][2]
]+(-1)^(t[2])*v[L4[i][3]])) >\n         Norm(v[L4[i][1]]+(-1)^(t[1])*v
[L4[i][2]]+(-1)^(t[2])*v[L4[i][3]],2)^2) then \n         print(\"not s
atisfied\",\"v_i,v_j,v_k,v_l\",L4[i][1],(-1)^(t[1])*L4[i][2],(-1)^(t[2
])*L4[i][3],L4[i][4]); \n      end if;\n   end do;\nend do:\n#checking
 for 2|v[m].(v[i]+v[j]+v[k]+v[l])|=<|v[i]+v[j]+v[k]+v[l]|^2;\nfor s fr
om 0 by 1 to 1 do\n   if (2*abs(v[5].(v[1]+(-1)^s*v[2]+(-1)^0*v[3]+(-1
)^0*v[4])) > \n       Norm(v[1]+(-1)^s*v[2]+(-1)^0*v[3]+(-1)^0*v[4],2)
^2) then \n      print(\"not satisfied\",\"v_i,v_j,v_k,v_l,v_m\",1,(-1
)^s*2,3,4,5); \n   end if;\nend do;\nfor s from 2 by 1 to 3 do\n   t:=
convert(s,base,2):\n   if (2*abs(v[5].(v[1]+(-1)^(t[1])*v[2]+(-1)^(t[2
])*v[3]+(-1)^0*v[4])) > \n       Norm(v[1]+(-1)^(t[1])*v[2]+(-1)^(t[2]
)*v[3]+(-1)^0*v[4],2)^2) then \n      print(\"not satisfied\",\"v_i,v_
j,v_k,v_l,v_m\",1,+(-1)^(t[1])*2,(-1)^(t[2])*3,(-1)^0*4,5); \n   end i
f;\nend do:\nfor s from 4 by 1 to 7 do\n   t:=convert(s,base,2):\n   i
f (2*abs(v[5].(v[1]+(-1)^(t[1])*v[2]+(-1)^(t[2])*v[3]+(-1)^(t[3])*v[4]
)) > \n       Norm(v[1]+(-1)^(t[1])*v[2]+(-1)^(t[2])*v[3]+(-1)^(t[3])*
v[4],2)^2) then \n      print(\"not satisfied\",\"v_i,v_j,v_k,v_l,v_m
\",1,(-1)^(t[1])*2,+(-1)^(t[2])*3,(-1)^(t[3])*4,5); \n   end if;\nend \+
do:\n#checking for |v[i]+v[1]+v[2]+v[3]+v[4]+v[5]|^2>=|v[i]|^2;\nfor s
 from 0 by 1 to 1 do\n   if (Norm(2*v[1]+(-1)^s*v[2]+v[3]+v[4]+v[5],2)
^2 < Norm(v[1],2)^2) then \n      print(\"not satisfied\",\"2*v_1\") \+
\n   end if;\nend do;\nfor s from 2 by 1 to 3 do\n   t:=convert(s,base
,2):\n   if (Norm(2*v[1]+(-1)^(t[1])*v[2]+(-1)^(t[2])*v[3]+v[4]+v[5],2
)^2 < Norm(v[1],2)^2) then \n      print(\"not satisfied\",\"2*v_1\") \+
\n   end if; \nend do:\nfor s from 4 by 1 to 7 do\n   t:=convert(s,bas
e,2):\n   if (Norm(2*v[1]+(-1)^(t[1])*v[2]+(-1)^(t[2])*v[3]+(-1)^(t[3]
)*v[4]+v[5],2)^2 < Norm(v[1],2)^2) then \n      print(\"not satisfied
\",\"2*v_1\") \n   end if; \nend do:\nfor s from 8 by 1 to 15 do\n   t
:=convert(s,base,2):\n   if (Norm(2*v[1]+(-1)^(t[1])*v[2]+(-1)^(t[2])*
v[3]+(-1)^(t[3])*v[4]+(-1)^(t[4])*v[5],2)^2 < Norm(v[1],2)^2) then \n \+
     print(\"not satisfied\",\"2*v_1\") \n   end if; \nend do:\nfor s \+
from 0 by 1 to 1 do\n   if (Norm(v[1]+(-1)^s*2*v[2]+v[3]+v[4]+v[5],2)^
2 < Norm(v[2],2)^2) then \n      print(\"not satisfied\",\"2*v_2\") \n
   end if;\nend do;\nfor s from 2 by 1 to 3 do\n   t:=convert(s,base,2
):\n   if (Norm(v[1]+(-1)^(t[1])*2*v[2]+(-1)^(t[2])*v[3]+v[4]+v[5],2)^
2 < Norm(v[2],2)^2) then \n      print(\"not satisfied\",\"2*v_2\") \n
   end if; \nend do:\nfor s from 4 by 1 to 7 do\n   t:=convert(s,base,
2):\n   if (Norm(v[1]+(-1)^(t[1])*2*v[2]+(-1)^(t[2])*v[3]+(-1)^(t[3])*
v[4]+v[5],2)^2 < Norm(v[2],2)^2) then \n      print(\"not satisfied\",
\"2*v_2\") \n   end if; \nend do:\nfor s from 8 by 1 to 15 do\n   t:=c
onvert(s,base,2):\n   if (Norm(v[1]+(-1)^(t[1])*2*v[2]+(-1)^(t[2])*v[3
]+(-1)^(t[3])*v[4]+(-1)^(t[4])*v[5],2)^2 < Norm(v[2],2)^2) then \n    \+
  print(\"not satisfied\",\"2*v_2\") \n   end if; \nend do:\nfor s fro
m 0 by 1 to 1 do\n   if (Norm(v[1]+(-1)^s*v[2]+2*v[3]+v[4]+v[5],2)^2 <
 Norm(v[3],2)^2) then \n      print(\"not satisfied\",\"2*v_3\") \n   \+
end if;\nend do;\nfor s from 2 by 1 to 3 do\n   t:=convert(s,base,2):
\n   if (Norm(v[1]+(-1)^(t[1])*v[2]+(-1)^(t[2])*2*v[3]+v[4]+v[5],2)^2 \+
< Norm(v[3],2)^2) then \n      print(\"not satisfied\",\"2*v_3\") \n  \+
 end if; \nend do:\nfor s from 4 by 1 to 7 do\n   t:=convert(s,base,2)
:\n   if (Norm(v[1]+(-1)^(t[1])*v[2]+(-1)^(t[2])*2*v[3]+(-1)^(t[3])*v[
4]+v[5],2)^2 < Norm(v[3],2)^2) then \n      print(\"not satisfied\",\"
2*v_3\") \n   end if; \nend do:\nfor s from 8 by 1 to 15 do\n   t:=con
vert(s,base,2):\n   if (Norm(v[1]+(-1)^(t[1])*v[2]+(-1)^(t[2])*2*v[3]+
(-1)^(t[3])*v[4]+(-1)^(t[4])*v[5],2)^2 < Norm(v[3],2)^2) then \n      \+
print(\"not satisfied\",\"2*v_3\") \n   end if; \nend do:\nfor s from \+
0 by 1 to 1 do\n   if (Norm(v[1]+(-1)^s*v[2]+v[3]+2*v[4]+v[5],2)^2 < N
orm(v[4],2)^2) then \n      print(\"not satisfied\",\"2*v_4\") \n   en
d if;\nend do;\nfor s from 2 by 1 to 3 do\n   t:=convert(s,base,2):\n \+
  if (Norm(v[1]+(-1)^(t[1])*v[2]+(-1)^(t[2])*v[3]+2*v[4]+v[5],2)^2 < N
orm(v[4],2)^2) then \n      print(\"not satisfied\",\"2*v_4\") \n   en
d if; \nend do:\nfor s from 4 by 1 to 7 do\n   t:=convert(s,base,2):\n
   if (Norm(v[1]+(-1)^(t[1])*v[2]+(-1)^(t[2])*v[3]+(-1)^(t[3])*2*v[4]+
v[5],2)^2 < Norm(v[4],2)^2) then \n      print(\"not satisfied\",\"2*v
_4\") \n   end if; \nend do:\nfor s from 8 by 1 to 15 do\n   t:=conver
t(s,base,2):\n   if (Norm(v[1]+(-1)^(t[1])*v[2]+(-1)^(t[2])*v[3]+(-1)^
(t[3])*2*v[4]+(-1)^(t[4])*v[5],2)^2 < Norm(v[4],2)^2) then \n      pri
nt(\"not satisfied\",\"2*v_4\") \n   end if; \nend do:\nfor s from 0 b
y 1 to 1 do\n   if (Norm(v[1]+(-1)^s*v[2]+v[3]+v[4]+2*v[5],2)^2 < Norm
(v[5],2)^2) then \n      print(\"not satisfied\",\"2*v_5\") \n   end i
f;\nend do;\nfor s from 2 by 1 to 3 do\n   t:=convert(s,base,2):\n   i
f (Norm(v[1]+(-1)^(t[1])*v[2]+(-1)^(t[2])*v[3]+v[4]+2*v[5],2)^2 < Norm
(v[5],2)^2) then \n      print(\"not satisfied\",\"2*v_5\") \n   end i
f; \nend do:\nfor s from 4 by 1 to 7 do\n   t:=convert(s,base,2):\n   \+
if (Norm(v[1]+(-1)^(t[1])*v[2]+(-1)^(t[2])*v[3]+(-1)^(t[3])*v[4]+2*v[5
],2)^2 < Norm(v[5],2)^2) then \n      print(\"not satisfied\",\"2*v_5
\") \n   end if; \nend do:\nfor s from 8 by 1 to 15 do\n   t:=convert(
s,base,2):\n   if (Norm(v[1]+(-1)^(t[1])*v[2]+(-1)^(t[2])*v[3]+(-1)^(t
[3])*v[4]+(-1)^(t[4])*2*v[5],2)^2 < Norm(v[5],2)^2) then \n      print
(\"not satisfied\",\"2*v_5\") \n   end if; \nend do:" }}{PARA 11 "" 1 
"" {XPPMATH 20 "6(Q.not~satisfied6\"Q0v_i,v_j,v_k,v_lF$\"\"\"\"\"#\"\"
%\"\"&" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 
0 "> " 0 "" {MPLTEXT 1 0 365 "v[1]:=Vector([4,1,-1,-1,1]):\nv[2]:=Vect
or([-1,4,-1,-1,-1]):\nv[3]:=Vector([1,1,4,-1,-1]):\nv[4]:=Vector([-1,-
1,-1,4,-1]):\nv[5]:=Vector([-2,-2,-2,-2,-2]):\nv[1],v[2],v[3],v[4],v[5
];\nprint(\"|v[1]|^2\"=Norm(v[1],2)^2);\n#checking for decreasing orde
r;\nfor i from 1 by 1 to 4 do \n   if (Norm(v[i],2)^2 > Norm(v[i+1],2)
^2) then print(\"not satisfied\",(i,i+1)) end if; \nend do;" }}{PARA 
11 "" 1 "" {XPPMATH 20 "6'-%'RTABLEG6%\"*SzJy\"-%'MATRIXG6#7'7#\"\"%7#
\"\"\"7#!\"\"F/F-&%'VectorG6#%'columnG-F$6%\"*/!=$y\"-F(6#7'F/F+F/F/F/
F1-F$6%\"*o!=$y\"-F(6#7'F-F-F+F/F/F1-F$6%\"*K\"=$y\"-F(6#7'F/F/F/F+F/F
1-F$6%\"*'>=$y\"-F(6#7'7#!\"#FMFMFMFMF1" }}{PARA 11 "" 1 "" {XPPMATH 
20 "6#/Q)|grv[1]|gr^26\"\"#?" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 
0 6469 "#checking for 2|v[j].v[i]|=<|v[i]|^2;\nL2:=choose(5, 2):\nfor \+
i from 1 by 1 to numbcomb(5, 2) do\n   if (2*abs(v[L2[i][2]].v[L2[i][1
]]) > Norm(v[L2[i][1]],2)^2) then \n      print(\"not satisfied\",\"v_
i,v_j\",L2[i][1],L2[i][2]) \n   end if;\nend do;\n#checking for 2|v[k]
.(v[i]+v[j])|=<|v[i]+v[j]|^2;\nL3:=choose(5, 3):\nfor s from 0 by 1 to
 1 do\n   for i from 1 by 1 to numbcomb(5, 3) do\n      if (2*abs(v[L3
[i][3]].(v[L3[i][1]]+(-1)^s*v[L3[i][2]])) > Norm(v[L3[i][1]]+(-1)^s*v[
L3[i][2]],2)^2) then \n         print(\"not satisfied\",\"v_i,v_j,v_k
\",L3[i][1],(-1)^s*L3[i][2],L3[i][3]); \n      end if;\n   end do;\nen
d do;\n#checking for 2|v[l].(v[i]+v[j]+v[k])|=<|v[i]+v[j]+v[k]|^2;\nL4
:=choose(5, 4):\nfor s from 0 by 1 to 1 do\n   for i from 1 by 1 to nu
mbcomb(5, 4) do\n      if (2*abs(v[L4[i][4]].(v[L4[i][1]]+(-1)^s*v[L4[
i][2]]+(-1)^0*v[L4[i][3]])) >\n         Norm(v[L4[i][1]]+(-1)^s*v[L4[i
][2]]+(-1)^0*v[L4[i][3]],2)^2) then \n         print(\"not satisfied\"
,\"v_i,v_j,v_k,v_l\",L4[i][1],(-1)^s*L4[i][2],(-1)^0*L4[i][3],L4[i][4]
); \n      end if;\n   end do;\nend do;\nfor s from 2 by 1 to 3 do\n  \+
 t:=convert(s,base,2):\n   for i from 1 by 1 to numbcomb(5, 4) do\n   \+
   if (2*abs(v[L4[i][4]].(v[L4[i][1]]+(-1)^(t[1])*v[L4[i][2]]+(-1)^(t[
2])*v[L4[i][3]])) >\n         Norm(v[L4[i][1]]+(-1)^(t[1])*v[L4[i][2]]
+(-1)^(t[2])*v[L4[i][3]],2)^2) then \n         print(\"not satisfied\"
,\"v_i,v_j,v_k,v_l\",L4[i][1],(-1)^(t[1])*L4[i][2],(-1)^(t[2])*L4[i][3
],L4[i][4]); \n      end if;\n   end do;\nend do:\n#checking for 2|v[m
].(v[i]+v[j]+v[k]+v[l])|=<|v[i]+v[j]+v[k]+v[l]|^2;\nfor s from 0 by 1 \+
to 1 do\n   if (2*abs(v[5].(v[1]+(-1)^s*v[2]+(-1)^0*v[3]+(-1)^0*v[4]))
 > \n       Norm(v[1]+(-1)^s*v[2]+(-1)^0*v[3]+(-1)^0*v[4],2)^2) then \+
\n      print(\"not satisfied\",\"v_i,v_j,v_k,v_l,v_m\",1,(-1)^s*2,3,4
,5); \n   end if;\nend do;\nfor s from 2 by 1 to 3 do\n   t:=convert(s
,base,2):\n   if (2*abs(v[5].(v[1]+(-1)^(t[1])*v[2]+(-1)^(t[2])*v[3]+(
-1)^0*v[4])) > \n       Norm(v[1]+(-1)^(t[1])*v[2]+(-1)^(t[2])*v[3]+(-
1)^0*v[4],2)^2) then \n      print(\"not satisfied\",\"v_i,v_j,v_k,v_l
,v_m\",1,+(-1)^(t[1])*2,(-1)^(t[2])*3,(-1)^0*4,5); \n   end if;\nend d
o:\nfor s from 4 by 1 to 7 do\n   t:=convert(s,base,2):\n   if (2*abs(
v[5].(v[1]+(-1)^(t[1])*v[2]+(-1)^(t[2])*v[3]+(-1)^(t[3])*v[4])) > \n  \+
     Norm(v[1]+(-1)^(t[1])*v[2]+(-1)^(t[2])*v[3]+(-1)^(t[3])*v[4],2)^2
) then \n      print(\"not satisfied\",\"v_i,v_j,v_k,v_l,v_m\",1,(-1)^
(t[1])*2,+(-1)^(t[2])*3,(-1)^(t[3])*4,5); \n   end if;\nend do:\n#chec
king for |v[i]+v[1]+v[2]+v[3]+v[4]+v[5]|^2>=|v[i]|^2;\nfor s from 0 by
 1 to 1 do\n   if (Norm(2*v[1]+(-1)^s*v[2]+v[3]+v[4]+v[5],2)^2 < Norm(
v[1],2)^2) then \n      print(\"not satisfied\",\"2*v_1\") \n   end if
;\nend do;\nfor s from 2 by 1 to 3 do\n   t:=convert(s,base,2):\n   if
 (Norm(2*v[1]+(-1)^(t[1])*v[2]+(-1)^(t[2])*v[3]+v[4]+v[5],2)^2 < Norm(
v[1],2)^2) then \n      print(\"not satisfied\",\"2*v_1\") \n   end if
; \nend do:\nfor s from 4 by 1 to 7 do\n   t:=convert(s,base,2):\n   i
f (Norm(2*v[1]+(-1)^(t[1])*v[2]+(-1)^(t[2])*v[3]+(-1)^(t[3])*v[4]+v[5]
,2)^2 < Norm(v[1],2)^2) then \n      print(\"not satisfied\",\"2*v_1\"
) \n   end if; \nend do:\nfor s from 8 by 1 to 15 do\n   t:=convert(s,
base,2):\n   if (Norm(2*v[1]+(-1)^(t[1])*v[2]+(-1)^(t[2])*v[3]+(-1)^(t
[3])*v[4]+(-1)^(t[4])*v[5],2)^2 < Norm(v[1],2)^2) then \n      print(
\"not satisfied\",\"2*v_1\") \n   end if; \nend do:\nfor s from 0 by 1
 to 1 do\n   if (Norm(v[1]+(-1)^s*2*v[2]+v[3]+v[4]+v[5],2)^2 < Norm(v[
2],2)^2) then \n      print(\"not satisfied\",\"2*v_2\") \n   end if;
\nend do;\nfor s from 2 by 1 to 3 do\n   t:=convert(s,base,2):\n   if \+
(Norm(v[1]+(-1)^(t[1])*2*v[2]+(-1)^(t[2])*v[3]+v[4]+v[5],2)^2 < Norm(v
[2],2)^2) then \n      print(\"not satisfied\",\"2*v_2\") \n   end if;
 \nend do:\nfor s from 4 by 1 to 7 do\n   t:=convert(s,base,2):\n   if
 (Norm(v[1]+(-1)^(t[1])*2*v[2]+(-1)^(t[2])*v[3]+(-1)^(t[3])*v[4]+v[5],
2)^2 < Norm(v[2],2)^2) then \n      print(\"not satisfied\",\"2*v_2\")
 \n   end if; \nend do:\nfor s from 8 by 1 to 15 do\n   t:=convert(s,b
ase,2):\n   if (Norm(v[1]+(-1)^(t[1])*2*v[2]+(-1)^(t[2])*v[3]+(-1)^(t[
3])*v[4]+(-1)^(t[4])*v[5],2)^2 < Norm(v[2],2)^2) then \n      print(\"
not satisfied\",\"2*v_2\") \n   end if; \nend do:\nfor s from 0 by 1 t
o 1 do\n   if (Norm(v[1]+(-1)^s*v[2]+2*v[3]+v[4]+v[5],2)^2 < Norm(v[3]
,2)^2) then \n      print(\"not satisfied\",\"2*v_3\") \n   end if;\ne
nd do;\nfor s from 2 by 1 to 3 do\n   t:=convert(s,base,2):\n   if (No
rm(v[1]+(-1)^(t[1])*v[2]+(-1)^(t[2])*2*v[3]+v[4]+v[5],2)^2 < Norm(v[3]
,2)^2) then \n      print(\"not satisfied\",\"2*v_3\") \n   end if; \n
end do:\nfor s from 4 by 1 to 7 do\n   t:=convert(s,base,2):\n   if (N
orm(v[1]+(-1)^(t[1])*v[2]+(-1)^(t[2])*2*v[3]+(-1)^(t[3])*v[4]+v[5],2)^
2 < Norm(v[3],2)^2) then \n      print(\"not satisfied\",\"2*v_3\") \n
   end if; \nend do:\nfor s from 8 by 1 to 15 do\n   t:=convert(s,base
,2):\n   if (Norm(v[1]+(-1)^(t[1])*v[2]+(-1)^(t[2])*2*v[3]+(-1)^(t[3])
*v[4]+(-1)^(t[4])*v[5],2)^2 < Norm(v[3],2)^2) then \n      print(\"not
 satisfied\",\"2*v_3\") \n   end if; \nend do:\nfor s from 0 by 1 to 1
 do\n   if (Norm(v[1]+(-1)^s*v[2]+v[3]+2*v[4]+v[5],2)^2 < Norm(v[4],2)
^2) then \n      print(\"not satisfied\",\"2*v_4\") \n   end if;\nend \+
do;\nfor s from 2 by 1 to 3 do\n   t:=convert(s,base,2):\n   if (Norm(
v[1]+(-1)^(t[1])*v[2]+(-1)^(t[2])*v[3]+2*v[4]+v[5],2)^2 < Norm(v[4],2)
^2) then \n      print(\"not satisfied\",\"2*v_4\") \n   end if; \nend
 do:\nfor s from 4 by 1 to 7 do\n   t:=convert(s,base,2):\n   if (Norm
(v[1]+(-1)^(t[1])*v[2]+(-1)^(t[2])*v[3]+(-1)^(t[3])*2*v[4]+v[5],2)^2 <
 Norm(v[4],2)^2) then \n      print(\"not satisfied\",\"2*v_4\") \n   \+
end if; \nend do:\nfor s from 8 by 1 to 15 do\n   t:=convert(s,base,2)
:\n   if (Norm(v[1]+(-1)^(t[1])*v[2]+(-1)^(t[2])*v[3]+(-1)^(t[3])*2*v[
4]+(-1)^(t[4])*v[5],2)^2 < Norm(v[4],2)^2) then \n      print(\"not sa
tisfied\",\"2*v_4\") \n   end if; \nend do:\nfor s from 0 by 1 to 1 do
\n   if (Norm(v[1]+(-1)^s*v[2]+v[3]+v[4]+2*v[5],2)^2 < Norm(v[5],2)^2)
 then \n      print(\"not satisfied\",\"2*v_5\") \n   end if;\nend do;
\nfor s from 2 by 1 to 3 do\n   t:=convert(s,base,2):\n   if (Norm(v[1
]+(-1)^(t[1])*v[2]+(-1)^(t[2])*v[3]+v[4]+2*v[5],2)^2 < Norm(v[5],2)^2)
 then \n      print(\"not satisfied\",\"2*v_5\") \n   end if; \nend do
:\nfor s from 4 by 1 to 7 do\n   t:=convert(s,base,2):\n   if (Norm(v[
1]+(-1)^(t[1])*v[2]+(-1)^(t[2])*v[3]+(-1)^(t[3])*v[4]+2*v[5],2)^2 < No
rm(v[5],2)^2) then \n      print(\"not satisfied\",\"2*v_5\") \n   end
 if; \nend do:\nfor s from 8 by 1 to 15 do\n   t:=convert(s,base,2):\n
   if (Norm(v[1]+(-1)^(t[1])*v[2]+(-1)^(t[2])*v[3]+(-1)^(t[3])*v[4]+(-
1)^(t[4])*2*v[5],2)^2 < Norm(v[5],2)^2) then \n      print(\"not satis
fied\",\"2*v_5\") \n   end if; \nend do:" }}{PARA 11 "" 1 "" {XPPMATH 
20 "6(Q.not~satisfied6\"Q0v_i,v_j,v_k,v_lF$\"\"\"\"\"$\"\"%\"\"&" }}}
{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "> " 0 "
" {MPLTEXT 1 0 364 "v[1]:=Vector([4,-1,-1,-1,1]):\nv[2]:=Vector([1,4,-
1,-1,1]):\nv[3]:=Vector([1,-1,4,-1,-1]):\nv[4]:=Vector([1,-1,-1,4,-1])
:\nv[5]:=Vector([-2,-2,-2,-2,-2]):\nv[1],v[2],v[3],v[4],v[5];\nprint(
\"|v[1]|^2\"=Norm(v[1],2)^2);\n#checking for decreasing order;\nfor i \+
from 1 by 1 to 4 do \n   if (Norm(v[i],2)^2 > Norm(v[i+1],2)^2) then p
rint(\"not satisfied\",(i,i+1)) end if; \nend do;" }}{PARA 11 "" 1 "" 
{XPPMATH 20 "6'-%'RTABLEG6%\"*oM<;#-%'MATRIXG6#7'7#\"\"%7#!\"\"F-F-7#
\"\"\"&%'VectorG6#%'columnG-F$6%\"*KN<;#-F(6#7'F/F+F-F-F/F1-F$6%\"*'ft
h@-F(6#7'F/F-F+F-F-F1-F$6%\"*gO<;#-F(6#7'F/F-F-F+F-F1-F$6%\"*CP<;#-F(6
#7'7#!\"#FMFMFMFMF1" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#/Q)|grv[1]|gr^2
6\"\"#?" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 6469 "#checking for \+
2|v[j].v[i]|=<|v[i]|^2;\nL2:=choose(5, 2):\nfor i from 1 by 1 to numbc
omb(5, 2) do\n   if (2*abs(v[L2[i][2]].v[L2[i][1]]) > Norm(v[L2[i][1]]
,2)^2) then \n      print(\"not satisfied\",\"v_i,v_j\",L2[i][1],L2[i]
[2]) \n   end if;\nend do;\n#checking for 2|v[k].(v[i]+v[j])|=<|v[i]+v
[j]|^2;\nL3:=choose(5, 3):\nfor s from 0 by 1 to 1 do\n   for i from 1
 by 1 to numbcomb(5, 3) do\n      if (2*abs(v[L3[i][3]].(v[L3[i][1]]+(
-1)^s*v[L3[i][2]])) > Norm(v[L3[i][1]]+(-1)^s*v[L3[i][2]],2)^2) then \+
\n         print(\"not satisfied\",\"v_i,v_j,v_k\",L3[i][1],(-1)^s*L3[
i][2],L3[i][3]); \n      end if;\n   end do;\nend do;\n#checking for 2
|v[l].(v[i]+v[j]+v[k])|=<|v[i]+v[j]+v[k]|^2;\nL4:=choose(5, 4):\nfor s
 from 0 by 1 to 1 do\n   for i from 1 by 1 to numbcomb(5, 4) do\n     \+
 if (2*abs(v[L4[i][4]].(v[L4[i][1]]+(-1)^s*v[L4[i][2]]+(-1)^0*v[L4[i][
3]])) >\n         Norm(v[L4[i][1]]+(-1)^s*v[L4[i][2]]+(-1)^0*v[L4[i][3
]],2)^2) then \n         print(\"not satisfied\",\"v_i,v_j,v_k,v_l\",L
4[i][1],(-1)^s*L4[i][2],(-1)^0*L4[i][3],L4[i][4]); \n      end if;\n  \+
 end do;\nend do;\nfor s from 2 by 1 to 3 do\n   t:=convert(s,base,2):
\n   for i from 1 by 1 to numbcomb(5, 4) do\n      if (2*abs(v[L4[i][4
]].(v[L4[i][1]]+(-1)^(t[1])*v[L4[i][2]]+(-1)^(t[2])*v[L4[i][3]])) >\n \+
        Norm(v[L4[i][1]]+(-1)^(t[1])*v[L4[i][2]]+(-1)^(t[2])*v[L4[i][3
]],2)^2) then \n         print(\"not satisfied\",\"v_i,v_j,v_k,v_l\",L
4[i][1],(-1)^(t[1])*L4[i][2],(-1)^(t[2])*L4[i][3],L4[i][4]); \n      e
nd if;\n   end do;\nend do:\n#checking for 2|v[m].(v[i]+v[j]+v[k]+v[l]
)|=<|v[i]+v[j]+v[k]+v[l]|^2;\nfor s from 0 by 1 to 1 do\n   if (2*abs(
v[5].(v[1]+(-1)^s*v[2]+(-1)^0*v[3]+(-1)^0*v[4])) > \n       Norm(v[1]+
(-1)^s*v[2]+(-1)^0*v[3]+(-1)^0*v[4],2)^2) then \n      print(\"not sat
isfied\",\"v_i,v_j,v_k,v_l,v_m\",1,(-1)^s*2,3,4,5); \n   end if;\nend \+
do;\nfor s from 2 by 1 to 3 do\n   t:=convert(s,base,2):\n   if (2*abs
(v[5].(v[1]+(-1)^(t[1])*v[2]+(-1)^(t[2])*v[3]+(-1)^0*v[4])) > \n      \+
 Norm(v[1]+(-1)^(t[1])*v[2]+(-1)^(t[2])*v[3]+(-1)^0*v[4],2)^2) then \n
      print(\"not satisfied\",\"v_i,v_j,v_k,v_l,v_m\",1,+(-1)^(t[1])*2
,(-1)^(t[2])*3,(-1)^0*4,5); \n   end if;\nend do:\nfor s from 4 by 1 t
o 7 do\n   t:=convert(s,base,2):\n   if (2*abs(v[5].(v[1]+(-1)^(t[1])*
v[2]+(-1)^(t[2])*v[3]+(-1)^(t[3])*v[4])) > \n       Norm(v[1]+(-1)^(t[
1])*v[2]+(-1)^(t[2])*v[3]+(-1)^(t[3])*v[4],2)^2) then \n      print(\"
not satisfied\",\"v_i,v_j,v_k,v_l,v_m\",1,(-1)^(t[1])*2,+(-1)^(t[2])*3
,(-1)^(t[3])*4,5); \n   end if;\nend do:\n#checking for |v[i]+v[1]+v[2
]+v[3]+v[4]+v[5]|^2>=|v[i]|^2;\nfor s from 0 by 1 to 1 do\n   if (Norm
(2*v[1]+(-1)^s*v[2]+v[3]+v[4]+v[5],2)^2 < Norm(v[1],2)^2) then \n     \+
 print(\"not satisfied\",\"2*v_1\") \n   end if;\nend do;\nfor s from \+
2 by 1 to 3 do\n   t:=convert(s,base,2):\n   if (Norm(2*v[1]+(-1)^(t[1
])*v[2]+(-1)^(t[2])*v[3]+v[4]+v[5],2)^2 < Norm(v[1],2)^2) then \n     \+
 print(\"not satisfied\",\"2*v_1\") \n   end if; \nend do:\nfor s from
 4 by 1 to 7 do\n   t:=convert(s,base,2):\n   if (Norm(2*v[1]+(-1)^(t[
1])*v[2]+(-1)^(t[2])*v[3]+(-1)^(t[3])*v[4]+v[5],2)^2 < Norm(v[1],2)^2)
 then \n      print(\"not satisfied\",\"2*v_1\") \n   end if; \nend do
:\nfor s from 8 by 1 to 15 do\n   t:=convert(s,base,2):\n   if (Norm(2
*v[1]+(-1)^(t[1])*v[2]+(-1)^(t[2])*v[3]+(-1)^(t[3])*v[4]+(-1)^(t[4])*v
[5],2)^2 < Norm(v[1],2)^2) then \n      print(\"not satisfied\",\"2*v_
1\") \n   end if; \nend do:\nfor s from 0 by 1 to 1 do\n   if (Norm(v[
1]+(-1)^s*2*v[2]+v[3]+v[4]+v[5],2)^2 < Norm(v[2],2)^2) then \n      pr
int(\"not satisfied\",\"2*v_2\") \n   end if;\nend do;\nfor s from 2 b
y 1 to 3 do\n   t:=convert(s,base,2):\n   if (Norm(v[1]+(-1)^(t[1])*2*
v[2]+(-1)^(t[2])*v[3]+v[4]+v[5],2)^2 < Norm(v[2],2)^2) then \n      pr
int(\"not satisfied\",\"2*v_2\") \n   end if; \nend do:\nfor s from 4 \+
by 1 to 7 do\n   t:=convert(s,base,2):\n   if (Norm(v[1]+(-1)^(t[1])*2
*v[2]+(-1)^(t[2])*v[3]+(-1)^(t[3])*v[4]+v[5],2)^2 < Norm(v[2],2)^2) th
en \n      print(\"not satisfied\",\"2*v_2\") \n   end if; \nend do:\n
for s from 8 by 1 to 15 do\n   t:=convert(s,base,2):\n   if (Norm(v[1]
+(-1)^(t[1])*2*v[2]+(-1)^(t[2])*v[3]+(-1)^(t[3])*v[4]+(-1)^(t[4])*v[5]
,2)^2 < Norm(v[2],2)^2) then \n      print(\"not satisfied\",\"2*v_2\"
) \n   end if; \nend do:\nfor s from 0 by 1 to 1 do\n   if (Norm(v[1]+
(-1)^s*v[2]+2*v[3]+v[4]+v[5],2)^2 < Norm(v[3],2)^2) then \n      print
(\"not satisfied\",\"2*v_3\") \n   end if;\nend do;\nfor s from 2 by 1
 to 3 do\n   t:=convert(s,base,2):\n   if (Norm(v[1]+(-1)^(t[1])*v[2]+
(-1)^(t[2])*2*v[3]+v[4]+v[5],2)^2 < Norm(v[3],2)^2) then \n      print
(\"not satisfied\",\"2*v_3\") \n   end if; \nend do:\nfor s from 4 by \+
1 to 7 do\n   t:=convert(s,base,2):\n   if (Norm(v[1]+(-1)^(t[1])*v[2]
+(-1)^(t[2])*2*v[3]+(-1)^(t[3])*v[4]+v[5],2)^2 < Norm(v[3],2)^2) then \+
\n      print(\"not satisfied\",\"2*v_3\") \n   end if; \nend do:\nfor
 s from 8 by 1 to 15 do\n   t:=convert(s,base,2):\n   if (Norm(v[1]+(-
1)^(t[1])*v[2]+(-1)^(t[2])*2*v[3]+(-1)^(t[3])*v[4]+(-1)^(t[4])*v[5],2)
^2 < Norm(v[3],2)^2) then \n      print(\"not satisfied\",\"2*v_3\") \+
\n   end if; \nend do:\nfor s from 0 by 1 to 1 do\n   if (Norm(v[1]+(-
1)^s*v[2]+v[3]+2*v[4]+v[5],2)^2 < Norm(v[4],2)^2) then \n      print(
\"not satisfied\",\"2*v_4\") \n   end if;\nend do;\nfor s from 2 by 1 \+
to 3 do\n   t:=convert(s,base,2):\n   if (Norm(v[1]+(-1)^(t[1])*v[2]+(
-1)^(t[2])*v[3]+2*v[4]+v[5],2)^2 < Norm(v[4],2)^2) then \n      print(
\"not satisfied\",\"2*v_4\") \n   end if; \nend do:\nfor s from 4 by 1
 to 7 do\n   t:=convert(s,base,2):\n   if (Norm(v[1]+(-1)^(t[1])*v[2]+
(-1)^(t[2])*v[3]+(-1)^(t[3])*2*v[4]+v[5],2)^2 < Norm(v[4],2)^2) then \+
\n      print(\"not satisfied\",\"2*v_4\") \n   end if; \nend do:\nfor
 s from 8 by 1 to 15 do\n   t:=convert(s,base,2):\n   if (Norm(v[1]+(-
1)^(t[1])*v[2]+(-1)^(t[2])*v[3]+(-1)^(t[3])*2*v[4]+(-1)^(t[4])*v[5],2)
^2 < Norm(v[4],2)^2) then \n      print(\"not satisfied\",\"2*v_4\") \+
\n   end if; \nend do:\nfor s from 0 by 1 to 1 do\n   if (Norm(v[1]+(-
1)^s*v[2]+v[3]+v[4]+2*v[5],2)^2 < Norm(v[5],2)^2) then \n      print(
\"not satisfied\",\"2*v_5\") \n   end if;\nend do;\nfor s from 2 by 1 \+
to 3 do\n   t:=convert(s,base,2):\n   if (Norm(v[1]+(-1)^(t[1])*v[2]+(
-1)^(t[2])*v[3]+v[4]+2*v[5],2)^2 < Norm(v[5],2)^2) then \n      print(
\"not satisfied\",\"2*v_5\") \n   end if; \nend do:\nfor s from 4 by 1
 to 7 do\n   t:=convert(s,base,2):\n   if (Norm(v[1]+(-1)^(t[1])*v[2]+
(-1)^(t[2])*v[3]+(-1)^(t[3])*v[4]+2*v[5],2)^2 < Norm(v[5],2)^2) then \+
\n      print(\"not satisfied\",\"2*v_5\") \n   end if; \nend do:\nfor
 s from 8 by 1 to 15 do\n   t:=convert(s,base,2):\n   if (Norm(v[1]+(-
1)^(t[1])*v[2]+(-1)^(t[2])*v[3]+(-1)^(t[3])*v[4]+(-1)^(t[4])*2*v[5],2)
^2 < Norm(v[5],2)^2) then \n      print(\"not satisfied\",\"2*v_5\") \+
\n   end if; \nend do:" }}{PARA 11 "" 1 "" {XPPMATH 20 "6(Q.not~satisf
ied6\"Q0v_i,v_j,v_k,v_lF$\"\"#\"\"$\"\"%\"\"&" }}}{EXCHG {PARA 0 "> " 
0 "" {MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 365 "v
[1]:=Vector([4,-1,-1,-1,1]):\nv[2]:=Vector([-1,4,-1,-1,1]):\nv[3]:=Vec
tor([-1,-1,4,-1,1]):\nv[4]:=Vector([-1,-1,-1,4,1]):\nv[5]:=Vector([-2,
-2,-2,-2,-2]):\nv[1],v[2],v[3],v[4],v[5];\nprint(\"|v[1]|^2\"=Norm(v[1
],2)^2);\n#checking for decreasing order;\nfor i from 1 by 1 to 4 do \+
\n   if (Norm(v[i],2)^2 > Norm(v[i+1],2)^2) then print(\"not satisfied
\",(i,i+1)) end if; \nend do;" }}{PARA 11 "" 1 "" {XPPMATH 20 "6'-%'RT
ABLEG6%\"*#Hgk=-%'MATRIXG6#7'7#\"\"%7#!\"\"F-F-7#\"\"\"&%'VectorG6#%'c
olumnG-F$6%\"*c.Y'=-F(6#7'F-F+F-F-F/F1-F$6%\"*?/Y'=-F(6#7'F-F-F+F-F/F1
-F$6%\"*%[gk=-F(6#7'F-F-F-F+F/F1-F$6%\"*[0Y'=-F(6#7'7#!\"#FMFMFMFMF1" 
}}{PARA 11 "" 1 "" {XPPMATH 20 "6#/Q)|grv[1]|gr^26\"\"#?" }}}{EXCHG 
{PARA 0 "> " 0 "" {MPLTEXT 1 0 6469 "#checking for 2|v[j].v[i]|=<|v[i]
|^2;\nL2:=choose(5, 2):\nfor i from 1 by 1 to numbcomb(5, 2) do\n   if
 (2*abs(v[L2[i][2]].v[L2[i][1]]) > Norm(v[L2[i][1]],2)^2) then \n     \+
 print(\"not satisfied\",\"v_i,v_j\",L2[i][1],L2[i][2]) \n   end if;\n
end do;\n#checking for 2|v[k].(v[i]+v[j])|=<|v[i]+v[j]|^2;\nL3:=choose
(5, 3):\nfor s from 0 by 1 to 1 do\n   for i from 1 by 1 to numbcomb(5
, 3) do\n      if (2*abs(v[L3[i][3]].(v[L3[i][1]]+(-1)^s*v[L3[i][2]]))
 > Norm(v[L3[i][1]]+(-1)^s*v[L3[i][2]],2)^2) then \n         print(\"n
ot satisfied\",\"v_i,v_j,v_k\",L3[i][1],(-1)^s*L3[i][2],L3[i][3]); \n \+
     end if;\n   end do;\nend do;\n#checking for 2|v[l].(v[i]+v[j]+v[k
])|=<|v[i]+v[j]+v[k]|^2;\nL4:=choose(5, 4):\nfor s from 0 by 1 to 1 do
\n   for i from 1 by 1 to numbcomb(5, 4) do\n      if (2*abs(v[L4[i][4
]].(v[L4[i][1]]+(-1)^s*v[L4[i][2]]+(-1)^0*v[L4[i][3]])) >\n         No
rm(v[L4[i][1]]+(-1)^s*v[L4[i][2]]+(-1)^0*v[L4[i][3]],2)^2) then \n    \+
     print(\"not satisfied\",\"v_i,v_j,v_k,v_l\",L4[i][1],(-1)^s*L4[i]
[2],(-1)^0*L4[i][3],L4[i][4]); \n      end if;\n   end do;\nend do;\nf
or s from 2 by 1 to 3 do\n   t:=convert(s,base,2):\n   for i from 1 by
 1 to numbcomb(5, 4) do\n      if (2*abs(v[L4[i][4]].(v[L4[i][1]]+(-1)
^(t[1])*v[L4[i][2]]+(-1)^(t[2])*v[L4[i][3]])) >\n         Norm(v[L4[i]
[1]]+(-1)^(t[1])*v[L4[i][2]]+(-1)^(t[2])*v[L4[i][3]],2)^2) then \n    \+
     print(\"not satisfied\",\"v_i,v_j,v_k,v_l\",L4[i][1],(-1)^(t[1])*
L4[i][2],(-1)^(t[2])*L4[i][3],L4[i][4]); \n      end if;\n   end do;\n
end do:\n#checking for 2|v[m].(v[i]+v[j]+v[k]+v[l])|=<|v[i]+v[j]+v[k]+
v[l]|^2;\nfor s from 0 by 1 to 1 do\n   if (2*abs(v[5].(v[1]+(-1)^s*v[
2]+(-1)^0*v[3]+(-1)^0*v[4])) > \n       Norm(v[1]+(-1)^s*v[2]+(-1)^0*v
[3]+(-1)^0*v[4],2)^2) then \n      print(\"not satisfied\",\"v_i,v_j,v
_k,v_l,v_m\",1,(-1)^s*2,3,4,5); \n   end if;\nend do;\nfor s from 2 by
 1 to 3 do\n   t:=convert(s,base,2):\n   if (2*abs(v[5].(v[1]+(-1)^(t[
1])*v[2]+(-1)^(t[2])*v[3]+(-1)^0*v[4])) > \n       Norm(v[1]+(-1)^(t[1
])*v[2]+(-1)^(t[2])*v[3]+(-1)^0*v[4],2)^2) then \n      print(\"not sa
tisfied\",\"v_i,v_j,v_k,v_l,v_m\",1,+(-1)^(t[1])*2,(-1)^(t[2])*3,(-1)^
0*4,5); \n   end if;\nend do:\nfor s from 4 by 1 to 7 do\n   t:=conver
t(s,base,2):\n   if (2*abs(v[5].(v[1]+(-1)^(t[1])*v[2]+(-1)^(t[2])*v[3
]+(-1)^(t[3])*v[4])) > \n       Norm(v[1]+(-1)^(t[1])*v[2]+(-1)^(t[2])
*v[3]+(-1)^(t[3])*v[4],2)^2) then \n      print(\"not satisfied\",\"v_
i,v_j,v_k,v_l,v_m\",1,(-1)^(t[1])*2,+(-1)^(t[2])*3,(-1)^(t[3])*4,5); \+
\n   end if;\nend do:\n#checking for |v[i]+v[1]+v[2]+v[3]+v[4]+v[5]|^2
>=|v[i]|^2;\nfor s from 0 by 1 to 1 do\n   if (Norm(2*v[1]+(-1)^s*v[2]
+v[3]+v[4]+v[5],2)^2 < Norm(v[1],2)^2) then \n      print(\"not satisf
ied\",\"2*v_1\") \n   end if;\nend do;\nfor s from 2 by 1 to 3 do\n   \+
t:=convert(s,base,2):\n   if (Norm(2*v[1]+(-1)^(t[1])*v[2]+(-1)^(t[2])
*v[3]+v[4]+v[5],2)^2 < Norm(v[1],2)^2) then \n      print(\"not satisf
ied\",\"2*v_1\") \n   end if; \nend do:\nfor s from 4 by 1 to 7 do\n  \+
 t:=convert(s,base,2):\n   if (Norm(2*v[1]+(-1)^(t[1])*v[2]+(-1)^(t[2]
)*v[3]+(-1)^(t[3])*v[4]+v[5],2)^2 < Norm(v[1],2)^2) then \n      print
(\"not satisfied\",\"2*v_1\") \n   end if; \nend do:\nfor s from 8 by \+
1 to 15 do\n   t:=convert(s,base,2):\n   if (Norm(2*v[1]+(-1)^(t[1])*v
[2]+(-1)^(t[2])*v[3]+(-1)^(t[3])*v[4]+(-1)^(t[4])*v[5],2)^2 < Norm(v[1
],2)^2) then \n      print(\"not satisfied\",\"2*v_1\") \n   end if; \+
\nend do:\nfor s from 0 by 1 to 1 do\n   if (Norm(v[1]+(-1)^s*2*v[2]+v
[3]+v[4]+v[5],2)^2 < Norm(v[2],2)^2) then \n      print(\"not satisfie
d\",\"2*v_2\") \n   end if;\nend do;\nfor s from 2 by 1 to 3 do\n   t:
=convert(s,base,2):\n   if (Norm(v[1]+(-1)^(t[1])*2*v[2]+(-1)^(t[2])*v
[3]+v[4]+v[5],2)^2 < Norm(v[2],2)^2) then \n      print(\"not satisfie
d\",\"2*v_2\") \n   end if; \nend do:\nfor s from 4 by 1 to 7 do\n   t
:=convert(s,base,2):\n   if (Norm(v[1]+(-1)^(t[1])*2*v[2]+(-1)^(t[2])*
v[3]+(-1)^(t[3])*v[4]+v[5],2)^2 < Norm(v[2],2)^2) then \n      print(
\"not satisfied\",\"2*v_2\") \n   end if; \nend do:\nfor s from 8 by 1
 to 15 do\n   t:=convert(s,base,2):\n   if (Norm(v[1]+(-1)^(t[1])*2*v[
2]+(-1)^(t[2])*v[3]+(-1)^(t[3])*v[4]+(-1)^(t[4])*v[5],2)^2 < Norm(v[2]
,2)^2) then \n      print(\"not satisfied\",\"2*v_2\") \n   end if; \n
end do:\nfor s from 0 by 1 to 1 do\n   if (Norm(v[1]+(-1)^s*v[2]+2*v[3
]+v[4]+v[5],2)^2 < Norm(v[3],2)^2) then \n      print(\"not satisfied
\",\"2*v_3\") \n   end if;\nend do;\nfor s from 2 by 1 to 3 do\n   t:=
convert(s,base,2):\n   if (Norm(v[1]+(-1)^(t[1])*v[2]+(-1)^(t[2])*2*v[
3]+v[4]+v[5],2)^2 < Norm(v[3],2)^2) then \n      print(\"not satisfied
\",\"2*v_3\") \n   end if; \nend do:\nfor s from 4 by 1 to 7 do\n   t:
=convert(s,base,2):\n   if (Norm(v[1]+(-1)^(t[1])*v[2]+(-1)^(t[2])*2*v
[3]+(-1)^(t[3])*v[4]+v[5],2)^2 < Norm(v[3],2)^2) then \n      print(\"
not satisfied\",\"2*v_3\") \n   end if; \nend do:\nfor s from 8 by 1 t
o 15 do\n   t:=convert(s,base,2):\n   if (Norm(v[1]+(-1)^(t[1])*v[2]+(
-1)^(t[2])*2*v[3]+(-1)^(t[3])*v[4]+(-1)^(t[4])*v[5],2)^2 < Norm(v[3],2
)^2) then \n      print(\"not satisfied\",\"2*v_3\") \n   end if; \nen
d do:\nfor s from 0 by 1 to 1 do\n   if (Norm(v[1]+(-1)^s*v[2]+v[3]+2*
v[4]+v[5],2)^2 < Norm(v[4],2)^2) then \n      print(\"not satisfied\",
\"2*v_4\") \n   end if;\nend do;\nfor s from 2 by 1 to 3 do\n   t:=con
vert(s,base,2):\n   if (Norm(v[1]+(-1)^(t[1])*v[2]+(-1)^(t[2])*v[3]+2*
v[4]+v[5],2)^2 < Norm(v[4],2)^2) then \n      print(\"not satisfied\",
\"2*v_4\") \n   end if; \nend do:\nfor s from 4 by 1 to 7 do\n   t:=co
nvert(s,base,2):\n   if (Norm(v[1]+(-1)^(t[1])*v[2]+(-1)^(t[2])*v[3]+(
-1)^(t[3])*2*v[4]+v[5],2)^2 < Norm(v[4],2)^2) then \n      print(\"not
 satisfied\",\"2*v_4\") \n   end if; \nend do:\nfor s from 8 by 1 to 1
5 do\n   t:=convert(s,base,2):\n   if (Norm(v[1]+(-1)^(t[1])*v[2]+(-1)
^(t[2])*v[3]+(-1)^(t[3])*2*v[4]+(-1)^(t[4])*v[5],2)^2 < Norm(v[4],2)^2
) then \n      print(\"not satisfied\",\"2*v_4\") \n   end if; \nend d
o:\nfor s from 0 by 1 to 1 do\n   if (Norm(v[1]+(-1)^s*v[2]+v[3]+v[4]+
2*v[5],2)^2 < Norm(v[5],2)^2) then \n      print(\"not satisfied\",\"2
*v_5\") \n   end if;\nend do;\nfor s from 2 by 1 to 3 do\n   t:=conver
t(s,base,2):\n   if (Norm(v[1]+(-1)^(t[1])*v[2]+(-1)^(t[2])*v[3]+v[4]+
2*v[5],2)^2 < Norm(v[5],2)^2) then \n      print(\"not satisfied\",\"2
*v_5\") \n   end if; \nend do:\nfor s from 4 by 1 to 7 do\n   t:=conve
rt(s,base,2):\n   if (Norm(v[1]+(-1)^(t[1])*v[2]+(-1)^(t[2])*v[3]+(-1)
^(t[3])*v[4]+2*v[5],2)^2 < Norm(v[5],2)^2) then \n      print(\"not sa
tisfied\",\"2*v_5\") \n   end if; \nend do:\nfor s from 8 by 1 to 15 d
o\n   t:=convert(s,base,2):\n   if (Norm(v[1]+(-1)^(t[1])*v[2]+(-1)^(t
[2])*v[3]+(-1)^(t[3])*v[4]+(-1)^(t[4])*2*v[5],2)^2 < Norm(v[5],2)^2) t
hen \n      print(\"not satisfied\",\"2*v_5\") \n   end if; \nend do:
" }}{PARA 11 "" 1 "" {XPPMATH 20 "6)Q.not~satisfied6\"Q4v_i,v_j,v_k,v_
l,v_mF$\"\"\"\"\"#\"\"$\"\"%\"\"&" }}}{EXCHG {PARA 0 "> " 0 "" 
{MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 361 "v[1]:=
Vector([-1,-5,-5,-5,-5]):\nv[2]:=Vector([-1,10,0,0,0]):\nv[3]:=Vector(
[-1,0,10,0,0]):\nv[4]:=Vector([-1,0,0,10,0]):\nv[5]:=Vector([-1,0,0,0,
10]):\nv[1],v[2],v[3],v[4],v[5];\nprint(\"|v[1]|^2\"=Norm(v[1],2)^2);
\n#checking for decreasing order;\nfor i from 1 by 1 to 4 do \n   if (
Norm(v[i],2)^2 > Norm(v[i+1],2)^2) then print(\"not satisfied\",(i,i+1
)) end if; \nend do;" }}{PARA 11 "" 1 "" {XPPMATH 20 "6'-%'RTABLEG6%\"
*'H]G>-%'MATRIXG6#7'7#!\"\"7#!\"&F-F-F-&%'VectorG6#%'columnG-F$6%\"*g.
&G>-F(6#7'F+7#\"#57#\"\"!F;F;F/-F$6%\"*C/&G>-F(6#7'F+F;F9F;F;F/-F$6%\"
*)[]G>-F(6#7'F+F;F;F9F;F/-F$6%\"*_0&G>-F(6#7'F+F;F;F;F9F/" }}{PARA 11 
"" 1 "" {XPPMATH 20 "6#/Q)|grv[1]|gr^26\"\"$,\"" }}}{EXCHG {PARA 0 "> \+
" 0 "" {MPLTEXT 1 0 6469 "#checking for 2|v[j].v[i]|=<|v[i]|^2;\nL2:=c
hoose(5, 2):\nfor i from 1 by 1 to numbcomb(5, 2) do\n   if (2*abs(v[L
2[i][2]].v[L2[i][1]]) > Norm(v[L2[i][1]],2)^2) then \n      print(\"no
t satisfied\",\"v_i,v_j\",L2[i][1],L2[i][2]) \n   end if;\nend do;\n#c
hecking for 2|v[k].(v[i]+v[j])|=<|v[i]+v[j]|^2;\nL3:=choose(5, 3):\nfo
r s from 0 by 1 to 1 do\n   for i from 1 by 1 to numbcomb(5, 3) do\n  \+
    if (2*abs(v[L3[i][3]].(v[L3[i][1]]+(-1)^s*v[L3[i][2]])) > Norm(v[L
3[i][1]]+(-1)^s*v[L3[i][2]],2)^2) then \n         print(\"not satisfie
d\",\"v_i,v_j,v_k\",L3[i][1],(-1)^s*L3[i][2],L3[i][3]); \n      end if
;\n   end do;\nend do;\n#checking for 2|v[l].(v[i]+v[j]+v[k])|=<|v[i]+
v[j]+v[k]|^2;\nL4:=choose(5, 4):\nfor s from 0 by 1 to 1 do\n   for i \+
from 1 by 1 to numbcomb(5, 4) do\n      if (2*abs(v[L4[i][4]].(v[L4[i]
[1]]+(-1)^s*v[L4[i][2]]+(-1)^0*v[L4[i][3]])) >\n         Norm(v[L4[i][
1]]+(-1)^s*v[L4[i][2]]+(-1)^0*v[L4[i][3]],2)^2) then \n         print(
\"not satisfied\",\"v_i,v_j,v_k,v_l\",L4[i][1],(-1)^s*L4[i][2],(-1)^0*
L4[i][3],L4[i][4]); \n      end if;\n   end do;\nend do;\nfor s from 2
 by 1 to 3 do\n   t:=convert(s,base,2):\n   for i from 1 by 1 to numbc
omb(5, 4) do\n      if (2*abs(v[L4[i][4]].(v[L4[i][1]]+(-1)^(t[1])*v[L
4[i][2]]+(-1)^(t[2])*v[L4[i][3]])) >\n         Norm(v[L4[i][1]]+(-1)^(
t[1])*v[L4[i][2]]+(-1)^(t[2])*v[L4[i][3]],2)^2) then \n         print(
\"not satisfied\",\"v_i,v_j,v_k,v_l\",L4[i][1],(-1)^(t[1])*L4[i][2],(-
1)^(t[2])*L4[i][3],L4[i][4]); \n      end if;\n   end do;\nend do:\n#c
hecking for 2|v[m].(v[i]+v[j]+v[k]+v[l])|=<|v[i]+v[j]+v[k]+v[l]|^2;\nf
or s from 0 by 1 to 1 do\n   if (2*abs(v[5].(v[1]+(-1)^s*v[2]+(-1)^0*v
[3]+(-1)^0*v[4])) > \n       Norm(v[1]+(-1)^s*v[2]+(-1)^0*v[3]+(-1)^0*
v[4],2)^2) then \n      print(\"not satisfied\",\"v_i,v_j,v_k,v_l,v_m
\",1,(-1)^s*2,3,4,5); \n   end if;\nend do;\nfor s from 2 by 1 to 3 do
\n   t:=convert(s,base,2):\n   if (2*abs(v[5].(v[1]+(-1)^(t[1])*v[2]+(
-1)^(t[2])*v[3]+(-1)^0*v[4])) > \n       Norm(v[1]+(-1)^(t[1])*v[2]+(-
1)^(t[2])*v[3]+(-1)^0*v[4],2)^2) then \n      print(\"not satisfied\",
\"v_i,v_j,v_k,v_l,v_m\",1,+(-1)^(t[1])*2,(-1)^(t[2])*3,(-1)^0*4,5); \n
   end if;\nend do:\nfor s from 4 by 1 to 7 do\n   t:=convert(s,base,2
):\n   if (2*abs(v[5].(v[1]+(-1)^(t[1])*v[2]+(-1)^(t[2])*v[3]+(-1)^(t[
3])*v[4])) > \n       Norm(v[1]+(-1)^(t[1])*v[2]+(-1)^(t[2])*v[3]+(-1)
^(t[3])*v[4],2)^2) then \n      print(\"not satisfied\",\"v_i,v_j,v_k,
v_l,v_m\",1,(-1)^(t[1])*2,+(-1)^(t[2])*3,(-1)^(t[3])*4,5); \n   end if
;\nend do:\n#checking for |v[i]+v[1]+v[2]+v[3]+v[4]+v[5]|^2>=|v[i]|^2;
\nfor s from 0 by 1 to 1 do\n   if (Norm(2*v[1]+(-1)^s*v[2]+v[3]+v[4]+
v[5],2)^2 < Norm(v[1],2)^2) then \n      print(\"not satisfied\",\"2*v
_1\") \n   end if;\nend do;\nfor s from 2 by 1 to 3 do\n   t:=convert(
s,base,2):\n   if (Norm(2*v[1]+(-1)^(t[1])*v[2]+(-1)^(t[2])*v[3]+v[4]+
v[5],2)^2 < Norm(v[1],2)^2) then \n      print(\"not satisfied\",\"2*v
_1\") \n   end if; \nend do:\nfor s from 4 by 1 to 7 do\n   t:=convert
(s,base,2):\n   if (Norm(2*v[1]+(-1)^(t[1])*v[2]+(-1)^(t[2])*v[3]+(-1)
^(t[3])*v[4]+v[5],2)^2 < Norm(v[1],2)^2) then \n      print(\"not sati
sfied\",\"2*v_1\") \n   end if; \nend do:\nfor s from 8 by 1 to 15 do
\n   t:=convert(s,base,2):\n   if (Norm(2*v[1]+(-1)^(t[1])*v[2]+(-1)^(
t[2])*v[3]+(-1)^(t[3])*v[4]+(-1)^(t[4])*v[5],2)^2 < Norm(v[1],2)^2) th
en \n      print(\"not satisfied\",\"2*v_1\") \n   end if; \nend do:\n
for s from 0 by 1 to 1 do\n   if (Norm(v[1]+(-1)^s*2*v[2]+v[3]+v[4]+v[
5],2)^2 < Norm(v[2],2)^2) then \n      print(\"not satisfied\",\"2*v_2
\") \n   end if;\nend do;\nfor s from 2 by 1 to 3 do\n   t:=convert(s,
base,2):\n   if (Norm(v[1]+(-1)^(t[1])*2*v[2]+(-1)^(t[2])*v[3]+v[4]+v[
5],2)^2 < Norm(v[2],2)^2) then \n      print(\"not satisfied\",\"2*v_2
\") \n   end if; \nend do:\nfor s from 4 by 1 to 7 do\n   t:=convert(s
,base,2):\n   if (Norm(v[1]+(-1)^(t[1])*2*v[2]+(-1)^(t[2])*v[3]+(-1)^(
t[3])*v[4]+v[5],2)^2 < Norm(v[2],2)^2) then \n      print(\"not satisf
ied\",\"2*v_2\") \n   end if; \nend do:\nfor s from 8 by 1 to 15 do\n \+
  t:=convert(s,base,2):\n   if (Norm(v[1]+(-1)^(t[1])*2*v[2]+(-1)^(t[2
])*v[3]+(-1)^(t[3])*v[4]+(-1)^(t[4])*v[5],2)^2 < Norm(v[2],2)^2) then \+
\n      print(\"not satisfied\",\"2*v_2\") \n   end if; \nend do:\nfor
 s from 0 by 1 to 1 do\n   if (Norm(v[1]+(-1)^s*v[2]+2*v[3]+v[4]+v[5],
2)^2 < Norm(v[3],2)^2) then \n      print(\"not satisfied\",\"2*v_3\")
 \n   end if;\nend do;\nfor s from 2 by 1 to 3 do\n   t:=convert(s,bas
e,2):\n   if (Norm(v[1]+(-1)^(t[1])*v[2]+(-1)^(t[2])*2*v[3]+v[4]+v[5],
2)^2 < Norm(v[3],2)^2) then \n      print(\"not satisfied\",\"2*v_3\")
 \n   end if; \nend do:\nfor s from 4 by 1 to 7 do\n   t:=convert(s,ba
se,2):\n   if (Norm(v[1]+(-1)^(t[1])*v[2]+(-1)^(t[2])*2*v[3]+(-1)^(t[3
])*v[4]+v[5],2)^2 < Norm(v[3],2)^2) then \n      print(\"not satisfied
\",\"2*v_3\") \n   end if; \nend do:\nfor s from 8 by 1 to 15 do\n   t
:=convert(s,base,2):\n   if (Norm(v[1]+(-1)^(t[1])*v[2]+(-1)^(t[2])*2*
v[3]+(-1)^(t[3])*v[4]+(-1)^(t[4])*v[5],2)^2 < Norm(v[3],2)^2) then \n \+
     print(\"not satisfied\",\"2*v_3\") \n   end if; \nend do:\nfor s \+
from 0 by 1 to 1 do\n   if (Norm(v[1]+(-1)^s*v[2]+v[3]+2*v[4]+v[5],2)^
2 < Norm(v[4],2)^2) then \n      print(\"not satisfied\",\"2*v_4\") \n
   end if;\nend do;\nfor s from 2 by 1 to 3 do\n   t:=convert(s,base,2
):\n   if (Norm(v[1]+(-1)^(t[1])*v[2]+(-1)^(t[2])*v[3]+2*v[4]+v[5],2)^
2 < Norm(v[4],2)^2) then \n      print(\"not satisfied\",\"2*v_4\") \n
   end if; \nend do:\nfor s from 4 by 1 to 7 do\n   t:=convert(s,base,
2):\n   if (Norm(v[1]+(-1)^(t[1])*v[2]+(-1)^(t[2])*v[3]+(-1)^(t[3])*2*
v[4]+v[5],2)^2 < Norm(v[4],2)^2) then \n      print(\"not satisfied\",
\"2*v_4\") \n   end if; \nend do:\nfor s from 8 by 1 to 15 do\n   t:=c
onvert(s,base,2):\n   if (Norm(v[1]+(-1)^(t[1])*v[2]+(-1)^(t[2])*v[3]+
(-1)^(t[3])*2*v[4]+(-1)^(t[4])*v[5],2)^2 < Norm(v[4],2)^2) then \n    \+
  print(\"not satisfied\",\"2*v_4\") \n   end if; \nend do:\nfor s fro
m 0 by 1 to 1 do\n   if (Norm(v[1]+(-1)^s*v[2]+v[3]+v[4]+2*v[5],2)^2 <
 Norm(v[5],2)^2) then \n      print(\"not satisfied\",\"2*v_5\") \n   \+
end if;\nend do;\nfor s from 2 by 1 to 3 do\n   t:=convert(s,base,2):
\n   if (Norm(v[1]+(-1)^(t[1])*v[2]+(-1)^(t[2])*v[3]+v[4]+2*v[5],2)^2 \+
< Norm(v[5],2)^2) then \n      print(\"not satisfied\",\"2*v_5\") \n  \+
 end if; \nend do:\nfor s from 4 by 1 to 7 do\n   t:=convert(s,base,2)
:\n   if (Norm(v[1]+(-1)^(t[1])*v[2]+(-1)^(t[2])*v[3]+(-1)^(t[3])*v[4]
+2*v[5],2)^2 < Norm(v[5],2)^2) then \n      print(\"not satisfied\",\"
2*v_5\") \n   end if; \nend do:\nfor s from 8 by 1 to 15 do\n   t:=con
vert(s,base,2):\n   if (Norm(v[1]+(-1)^(t[1])*v[2]+(-1)^(t[2])*v[3]+(-
1)^(t[3])*v[4]+(-1)^(t[4])*2*v[5],2)^2 < Norm(v[5],2)^2) then \n      \+
print(\"not satisfied\",\"2*v_5\") \n   end if; \nend do:" }}{PARA 11 
"" 1 "" {XPPMATH 20 "6$Q.not~satisfied6\"Q&2*v_1F$" }}}{EXCHG {PARA 0 
"> " 0 "" {MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 
360 "v[1]:=Vector([10,0,0,0,0]):\nv[2]:=Vector([-5,-1,-5,-5,-5]):\nv[3
]:=Vector([0,-1,10,0,0]):\nv[4]:=Vector([0,-1,0,10,0]):\nv[5]:=Vector(
[0,-1,0,0,10]):\nv[1],v[2],v[3],v[4],v[5];\nprint(\"|v[1]|^2\"=Norm(v[
1],2)^2);\n#checking for decreasing order;\nfor i from 1 by 1 to 4 do \+
\n   if (Norm(v[i],2)^2 > Norm(v[i+1],2)^2) then print(\"not satisfied
\",(i,i+1)) end if; \nend do;" }}{PARA 11 "" 1 "" {XPPMATH 20 "6'-%'RT
ABLEG6%\"*!o7C>-%'MATRIXG6#7'7#\"#57#\"\"!F-F-F-&%'VectorG6#%'columnG-
F$6%\"*WFT#>-F(6#7'7#!\"&7#!\"\"F9F9F9F/-F$6%\"*3GT#>-F(6#7'F-F;F+F-F-
F/-F$6%\"*sGT#>-F(6#7'F-F;F-F+F-F/-F$6%\"*OHT#>-F(6#7'F-F;F-F-F+F/" }}
{PARA 11 "" 1 "" {XPPMATH 20 "6#/Q)|grv[1]|gr^26\"\"$+\"" }}}{EXCHG 
{PARA 0 "> " 0 "" {MPLTEXT 1 0 6469 "#checking for 2|v[j].v[i]|=<|v[i]
|^2;\nL2:=choose(5, 2):\nfor i from 1 by 1 to numbcomb(5, 2) do\n   if
 (2*abs(v[L2[i][2]].v[L2[i][1]]) > Norm(v[L2[i][1]],2)^2) then \n     \+
 print(\"not satisfied\",\"v_i,v_j\",L2[i][1],L2[i][2]) \n   end if;\n
end do;\n#checking for 2|v[k].(v[i]+v[j])|=<|v[i]+v[j]|^2;\nL3:=choose
(5, 3):\nfor s from 0 by 1 to 1 do\n   for i from 1 by 1 to numbcomb(5
, 3) do\n      if (2*abs(v[L3[i][3]].(v[L3[i][1]]+(-1)^s*v[L3[i][2]]))
 > Norm(v[L3[i][1]]+(-1)^s*v[L3[i][2]],2)^2) then \n         print(\"n
ot satisfied\",\"v_i,v_j,v_k\",L3[i][1],(-1)^s*L3[i][2],L3[i][3]); \n \+
     end if;\n   end do;\nend do;\n#checking for 2|v[l].(v[i]+v[j]+v[k
])|=<|v[i]+v[j]+v[k]|^2;\nL4:=choose(5, 4):\nfor s from 0 by 1 to 1 do
\n   for i from 1 by 1 to numbcomb(5, 4) do\n      if (2*abs(v[L4[i][4
]].(v[L4[i][1]]+(-1)^s*v[L4[i][2]]+(-1)^0*v[L4[i][3]])) >\n         No
rm(v[L4[i][1]]+(-1)^s*v[L4[i][2]]+(-1)^0*v[L4[i][3]],2)^2) then \n    \+
     print(\"not satisfied\",\"v_i,v_j,v_k,v_l\",L4[i][1],(-1)^s*L4[i]
[2],(-1)^0*L4[i][3],L4[i][4]); \n      end if;\n   end do;\nend do;\nf
or s from 2 by 1 to 3 do\n   t:=convert(s,base,2):\n   for i from 1 by
 1 to numbcomb(5, 4) do\n      if (2*abs(v[L4[i][4]].(v[L4[i][1]]+(-1)
^(t[1])*v[L4[i][2]]+(-1)^(t[2])*v[L4[i][3]])) >\n         Norm(v[L4[i]
[1]]+(-1)^(t[1])*v[L4[i][2]]+(-1)^(t[2])*v[L4[i][3]],2)^2) then \n    \+
     print(\"not satisfied\",\"v_i,v_j,v_k,v_l\",L4[i][1],(-1)^(t[1])*
L4[i][2],(-1)^(t[2])*L4[i][3],L4[i][4]); \n      end if;\n   end do;\n
end do:\n#checking for 2|v[m].(v[i]+v[j]+v[k]+v[l])|=<|v[i]+v[j]+v[k]+
v[l]|^2;\nfor s from 0 by 1 to 1 do\n   if (2*abs(v[5].(v[1]+(-1)^s*v[
2]+(-1)^0*v[3]+(-1)^0*v[4])) > \n       Norm(v[1]+(-1)^s*v[2]+(-1)^0*v
[3]+(-1)^0*v[4],2)^2) then \n      print(\"not satisfied\",\"v_i,v_j,v
_k,v_l,v_m\",1,(-1)^s*2,3,4,5); \n   end if;\nend do;\nfor s from 2 by
 1 to 3 do\n   t:=convert(s,base,2):\n   if (2*abs(v[5].(v[1]+(-1)^(t[
1])*v[2]+(-1)^(t[2])*v[3]+(-1)^0*v[4])) > \n       Norm(v[1]+(-1)^(t[1
])*v[2]+(-1)^(t[2])*v[3]+(-1)^0*v[4],2)^2) then \n      print(\"not sa
tisfied\",\"v_i,v_j,v_k,v_l,v_m\",1,+(-1)^(t[1])*2,(-1)^(t[2])*3,(-1)^
0*4,5); \n   end if;\nend do:\nfor s from 4 by 1 to 7 do\n   t:=conver
t(s,base,2):\n   if (2*abs(v[5].(v[1]+(-1)^(t[1])*v[2]+(-1)^(t[2])*v[3
]+(-1)^(t[3])*v[4])) > \n       Norm(v[1]+(-1)^(t[1])*v[2]+(-1)^(t[2])
*v[3]+(-1)^(t[3])*v[4],2)^2) then \n      print(\"not satisfied\",\"v_
i,v_j,v_k,v_l,v_m\",1,(-1)^(t[1])*2,+(-1)^(t[2])*3,(-1)^(t[3])*4,5); \+
\n   end if;\nend do:\n#checking for |v[i]+v[1]+v[2]+v[3]+v[4]+v[5]|^2
>=|v[i]|^2;\nfor s from 0 by 1 to 1 do\n   if (Norm(2*v[1]+(-1)^s*v[2]
+v[3]+v[4]+v[5],2)^2 < Norm(v[1],2)^2) then \n      print(\"not satisf
ied\",\"2*v_1\") \n   end if;\nend do;\nfor s from 2 by 1 to 3 do\n   \+
t:=convert(s,base,2):\n   if (Norm(2*v[1]+(-1)^(t[1])*v[2]+(-1)^(t[2])
*v[3]+v[4]+v[5],2)^2 < Norm(v[1],2)^2) then \n      print(\"not satisf
ied\",\"2*v_1\") \n   end if; \nend do:\nfor s from 4 by 1 to 7 do\n  \+
 t:=convert(s,base,2):\n   if (Norm(2*v[1]+(-1)^(t[1])*v[2]+(-1)^(t[2]
)*v[3]+(-1)^(t[3])*v[4]+v[5],2)^2 < Norm(v[1],2)^2) then \n      print
(\"not satisfied\",\"2*v_1\") \n   end if; \nend do:\nfor s from 8 by \+
1 to 15 do\n   t:=convert(s,base,2):\n   if (Norm(2*v[1]+(-1)^(t[1])*v
[2]+(-1)^(t[2])*v[3]+(-1)^(t[3])*v[4]+(-1)^(t[4])*v[5],2)^2 < Norm(v[1
],2)^2) then \n      print(\"not satisfied\",\"2*v_1\") \n   end if; \+
\nend do:\nfor s from 0 by 1 to 1 do\n   if (Norm(v[1]+(-1)^s*2*v[2]+v
[3]+v[4]+v[5],2)^2 < Norm(v[2],2)^2) then \n      print(\"not satisfie
d\",\"2*v_2\") \n   end if;\nend do;\nfor s from 2 by 1 to 3 do\n   t:
=convert(s,base,2):\n   if (Norm(v[1]+(-1)^(t[1])*2*v[2]+(-1)^(t[2])*v
[3]+v[4]+v[5],2)^2 < Norm(v[2],2)^2) then \n      print(\"not satisfie
d\",\"2*v_2\") \n   end if; \nend do:\nfor s from 4 by 1 to 7 do\n   t
:=convert(s,base,2):\n   if (Norm(v[1]+(-1)^(t[1])*2*v[2]+(-1)^(t[2])*
v[3]+(-1)^(t[3])*v[4]+v[5],2)^2 < Norm(v[2],2)^2) then \n      print(
\"not satisfied\",\"2*v_2\") \n   end if; \nend do:\nfor s from 8 by 1
 to 15 do\n   t:=convert(s,base,2):\n   if (Norm(v[1]+(-1)^(t[1])*2*v[
2]+(-1)^(t[2])*v[3]+(-1)^(t[3])*v[4]+(-1)^(t[4])*v[5],2)^2 < Norm(v[2]
,2)^2) then \n      print(\"not satisfied\",\"2*v_2\") \n   end if; \n
end do:\nfor s from 0 by 1 to 1 do\n   if (Norm(v[1]+(-1)^s*v[2]+2*v[3
]+v[4]+v[5],2)^2 < Norm(v[3],2)^2) then \n      print(\"not satisfied
\",\"2*v_3\") \n   end if;\nend do;\nfor s from 2 by 1 to 3 do\n   t:=
convert(s,base,2):\n   if (Norm(v[1]+(-1)^(t[1])*v[2]+(-1)^(t[2])*2*v[
3]+v[4]+v[5],2)^2 < Norm(v[3],2)^2) then \n      print(\"not satisfied
\",\"2*v_3\") \n   end if; \nend do:\nfor s from 4 by 1 to 7 do\n   t:
=convert(s,base,2):\n   if (Norm(v[1]+(-1)^(t[1])*v[2]+(-1)^(t[2])*2*v
[3]+(-1)^(t[3])*v[4]+v[5],2)^2 < Norm(v[3],2)^2) then \n      print(\"
not satisfied\",\"2*v_3\") \n   end if; \nend do:\nfor s from 8 by 1 t
o 15 do\n   t:=convert(s,base,2):\n   if (Norm(v[1]+(-1)^(t[1])*v[2]+(
-1)^(t[2])*2*v[3]+(-1)^(t[3])*v[4]+(-1)^(t[4])*v[5],2)^2 < Norm(v[3],2
)^2) then \n      print(\"not satisfied\",\"2*v_3\") \n   end if; \nen
d do:\nfor s from 0 by 1 to 1 do\n   if (Norm(v[1]+(-1)^s*v[2]+v[3]+2*
v[4]+v[5],2)^2 < Norm(v[4],2)^2) then \n      print(\"not satisfied\",
\"2*v_4\") \n   end if;\nend do;\nfor s from 2 by 1 to 3 do\n   t:=con
vert(s,base,2):\n   if (Norm(v[1]+(-1)^(t[1])*v[2]+(-1)^(t[2])*v[3]+2*
v[4]+v[5],2)^2 < Norm(v[4],2)^2) then \n      print(\"not satisfied\",
\"2*v_4\") \n   end if; \nend do:\nfor s from 4 by 1 to 7 do\n   t:=co
nvert(s,base,2):\n   if (Norm(v[1]+(-1)^(t[1])*v[2]+(-1)^(t[2])*v[3]+(
-1)^(t[3])*2*v[4]+v[5],2)^2 < Norm(v[4],2)^2) then \n      print(\"not
 satisfied\",\"2*v_4\") \n   end if; \nend do:\nfor s from 8 by 1 to 1
5 do\n   t:=convert(s,base,2):\n   if (Norm(v[1]+(-1)^(t[1])*v[2]+(-1)
^(t[2])*v[3]+(-1)^(t[3])*2*v[4]+(-1)^(t[4])*v[5],2)^2 < Norm(v[4],2)^2
) then \n      print(\"not satisfied\",\"2*v_4\") \n   end if; \nend d
o:\nfor s from 0 by 1 to 1 do\n   if (Norm(v[1]+(-1)^s*v[2]+v[3]+v[4]+
2*v[5],2)^2 < Norm(v[5],2)^2) then \n      print(\"not satisfied\",\"2
*v_5\") \n   end if;\nend do;\nfor s from 2 by 1 to 3 do\n   t:=conver
t(s,base,2):\n   if (Norm(v[1]+(-1)^(t[1])*v[2]+(-1)^(t[2])*v[3]+v[4]+
2*v[5],2)^2 < Norm(v[5],2)^2) then \n      print(\"not satisfied\",\"2
*v_5\") \n   end if; \nend do:\nfor s from 4 by 1 to 7 do\n   t:=conve
rt(s,base,2):\n   if (Norm(v[1]+(-1)^(t[1])*v[2]+(-1)^(t[2])*v[3]+(-1)
^(t[3])*v[4]+2*v[5],2)^2 < Norm(v[5],2)^2) then \n      print(\"not sa
tisfied\",\"2*v_5\") \n   end if; \nend do:\nfor s from 8 by 1 to 15 d
o\n   t:=convert(s,base,2):\n   if (Norm(v[1]+(-1)^(t[1])*v[2]+(-1)^(t
[2])*v[3]+(-1)^(t[3])*v[4]+(-1)^(t[4])*2*v[5],2)^2 < Norm(v[5],2)^2) t
hen \n      print(\"not satisfied\",\"2*v_5\") \n   end if; \nend do:
" }}{PARA 11 "" 1 "" {XPPMATH 20 "6$Q.not~satisfied6\"Q&2*v_2F$" }}}
{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "> " 0 "
" {MPLTEXT 1 0 359 "v[1]:=Vector([10,0,0,0,0]):\nv[2]:=Vector([0,10,0,
0,0]):\nv[3]:=Vector([-5,-5,-1,-5,-5]):\nv[4]:=Vector([0,0,-1,10,0]):
\nv[5]:=Vector([0,0,-1,0,10]):\nv[1],v[2],v[3],v[4],v[5];\nprint(\"|v[
1]|^2\"=Norm(v[1],2)^2);\n#checking for decreasing order;\nfor i from \+
1 by 1 to 4 do \n   if (Norm(v[i],2)^2 > Norm(v[i+1],2)^2) then print(
\"not satisfied\",(i,i+1)) end if; \nend do;" }}{PARA 11 "" 1 "" 
{XPPMATH 20 "6'-%'RTABLEG6%\"*W(4S=-%'MATRIXG6#7'7#\"#57#\"\"!F-F-F-&%
'VectorG6#%'columnG-F$6%\"*3)4S=-F(6#7'F-F+F-F-F-F/-F$6%\"*s)4S=-F(6#7
'7#!\"&F?7#!\"\"F?F?F/-F$6%\"*O*4S=-F(6#7'F-F-FAF+F-F/-F$6%\"*++,%=-F(
6#7'F-F-FAF-F+F/" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#/Q)|grv[1]|gr^26\"
\"$+\"" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 6469 "#checking for 2
|v[j].v[i]|=<|v[i]|^2;\nL2:=choose(5, 2):\nfor i from 1 by 1 to numbco
mb(5, 2) do\n   if (2*abs(v[L2[i][2]].v[L2[i][1]]) > Norm(v[L2[i][1]],
2)^2) then \n      print(\"not satisfied\",\"v_i,v_j\",L2[i][1],L2[i][
2]) \n   end if;\nend do;\n#checking for 2|v[k].(v[i]+v[j])|=<|v[i]+v[
j]|^2;\nL3:=choose(5, 3):\nfor s from 0 by 1 to 1 do\n   for i from 1 \+
by 1 to numbcomb(5, 3) do\n      if (2*abs(v[L3[i][3]].(v[L3[i][1]]+(-
1)^s*v[L3[i][2]])) > Norm(v[L3[i][1]]+(-1)^s*v[L3[i][2]],2)^2) then \n
         print(\"not satisfied\",\"v_i,v_j,v_k\",L3[i][1],(-1)^s*L3[i]
[2],L3[i][3]); \n      end if;\n   end do;\nend do;\n#checking for 2|v
[l].(v[i]+v[j]+v[k])|=<|v[i]+v[j]+v[k]|^2;\nL4:=choose(5, 4):\nfor s f
rom 0 by 1 to 1 do\n   for i from 1 by 1 to numbcomb(5, 4) do\n      i
f (2*abs(v[L4[i][4]].(v[L4[i][1]]+(-1)^s*v[L4[i][2]]+(-1)^0*v[L4[i][3]
])) >\n         Norm(v[L4[i][1]]+(-1)^s*v[L4[i][2]]+(-1)^0*v[L4[i][3]]
,2)^2) then \n         print(\"not satisfied\",\"v_i,v_j,v_k,v_l\",L4[
i][1],(-1)^s*L4[i][2],(-1)^0*L4[i][3],L4[i][4]); \n      end if;\n   e
nd do;\nend do;\nfor s from 2 by 1 to 3 do\n   t:=convert(s,base,2):\n
   for i from 1 by 1 to numbcomb(5, 4) do\n      if (2*abs(v[L4[i][4]]
.(v[L4[i][1]]+(-1)^(t[1])*v[L4[i][2]]+(-1)^(t[2])*v[L4[i][3]])) >\n   \+
      Norm(v[L4[i][1]]+(-1)^(t[1])*v[L4[i][2]]+(-1)^(t[2])*v[L4[i][3]]
,2)^2) then \n         print(\"not satisfied\",\"v_i,v_j,v_k,v_l\",L4[
i][1],(-1)^(t[1])*L4[i][2],(-1)^(t[2])*L4[i][3],L4[i][4]); \n      end
 if;\n   end do;\nend do:\n#checking for 2|v[m].(v[i]+v[j]+v[k]+v[l])|
=<|v[i]+v[j]+v[k]+v[l]|^2;\nfor s from 0 by 1 to 1 do\n   if (2*abs(v[
5].(v[1]+(-1)^s*v[2]+(-1)^0*v[3]+(-1)^0*v[4])) > \n       Norm(v[1]+(-
1)^s*v[2]+(-1)^0*v[3]+(-1)^0*v[4],2)^2) then \n      print(\"not satis
fied\",\"v_i,v_j,v_k,v_l,v_m\",1,(-1)^s*2,3,4,5); \n   end if;\nend do
;\nfor s from 2 by 1 to 3 do\n   t:=convert(s,base,2):\n   if (2*abs(v
[5].(v[1]+(-1)^(t[1])*v[2]+(-1)^(t[2])*v[3]+(-1)^0*v[4])) > \n       N
orm(v[1]+(-1)^(t[1])*v[2]+(-1)^(t[2])*v[3]+(-1)^0*v[4],2)^2) then \n  \+
    print(\"not satisfied\",\"v_i,v_j,v_k,v_l,v_m\",1,+(-1)^(t[1])*2,(
-1)^(t[2])*3,(-1)^0*4,5); \n   end if;\nend do:\nfor s from 4 by 1 to \+
7 do\n   t:=convert(s,base,2):\n   if (2*abs(v[5].(v[1]+(-1)^(t[1])*v[
2]+(-1)^(t[2])*v[3]+(-1)^(t[3])*v[4])) > \n       Norm(v[1]+(-1)^(t[1]
)*v[2]+(-1)^(t[2])*v[3]+(-1)^(t[3])*v[4],2)^2) then \n      print(\"no
t satisfied\",\"v_i,v_j,v_k,v_l,v_m\",1,(-1)^(t[1])*2,+(-1)^(t[2])*3,(
-1)^(t[3])*4,5); \n   end if;\nend do:\n#checking for |v[i]+v[1]+v[2]+
v[3]+v[4]+v[5]|^2>=|v[i]|^2;\nfor s from 0 by 1 to 1 do\n   if (Norm(2
*v[1]+(-1)^s*v[2]+v[3]+v[4]+v[5],2)^2 < Norm(v[1],2)^2) then \n      p
rint(\"not satisfied\",\"2*v_1\") \n   end if;\nend do;\nfor s from 2 \+
by 1 to 3 do\n   t:=convert(s,base,2):\n   if (Norm(2*v[1]+(-1)^(t[1])
*v[2]+(-1)^(t[2])*v[3]+v[4]+v[5],2)^2 < Norm(v[1],2)^2) then \n      p
rint(\"not satisfied\",\"2*v_1\") \n   end if; \nend do:\nfor s from 4
 by 1 to 7 do\n   t:=convert(s,base,2):\n   if (Norm(2*v[1]+(-1)^(t[1]
)*v[2]+(-1)^(t[2])*v[3]+(-1)^(t[3])*v[4]+v[5],2)^2 < Norm(v[1],2)^2) t
hen \n      print(\"not satisfied\",\"2*v_1\") \n   end if; \nend do:
\nfor s from 8 by 1 to 15 do\n   t:=convert(s,base,2):\n   if (Norm(2*
v[1]+(-1)^(t[1])*v[2]+(-1)^(t[2])*v[3]+(-1)^(t[3])*v[4]+(-1)^(t[4])*v[
5],2)^2 < Norm(v[1],2)^2) then \n      print(\"not satisfied\",\"2*v_1
\") \n   end if; \nend do:\nfor s from 0 by 1 to 1 do\n   if (Norm(v[1
]+(-1)^s*2*v[2]+v[3]+v[4]+v[5],2)^2 < Norm(v[2],2)^2) then \n      pri
nt(\"not satisfied\",\"2*v_2\") \n   end if;\nend do;\nfor s from 2 by
 1 to 3 do\n   t:=convert(s,base,2):\n   if (Norm(v[1]+(-1)^(t[1])*2*v
[2]+(-1)^(t[2])*v[3]+v[4]+v[5],2)^2 < Norm(v[2],2)^2) then \n      pri
nt(\"not satisfied\",\"2*v_2\") \n   end if; \nend do:\nfor s from 4 b
y 1 to 7 do\n   t:=convert(s,base,2):\n   if (Norm(v[1]+(-1)^(t[1])*2*
v[2]+(-1)^(t[2])*v[3]+(-1)^(t[3])*v[4]+v[5],2)^2 < Norm(v[2],2)^2) the
n \n      print(\"not satisfied\",\"2*v_2\") \n   end if; \nend do:\nf
or s from 8 by 1 to 15 do\n   t:=convert(s,base,2):\n   if (Norm(v[1]+
(-1)^(t[1])*2*v[2]+(-1)^(t[2])*v[3]+(-1)^(t[3])*v[4]+(-1)^(t[4])*v[5],
2)^2 < Norm(v[2],2)^2) then \n      print(\"not satisfied\",\"2*v_2\")
 \n   end if; \nend do:\nfor s from 0 by 1 to 1 do\n   if (Norm(v[1]+(
-1)^s*v[2]+2*v[3]+v[4]+v[5],2)^2 < Norm(v[3],2)^2) then \n      print(
\"not satisfied\",\"2*v_3\") \n   end if;\nend do;\nfor s from 2 by 1 \+
to 3 do\n   t:=convert(s,base,2):\n   if (Norm(v[1]+(-1)^(t[1])*v[2]+(
-1)^(t[2])*2*v[3]+v[4]+v[5],2)^2 < Norm(v[3],2)^2) then \n      print(
\"not satisfied\",\"2*v_3\") \n   end if; \nend do:\nfor s from 4 by 1
 to 7 do\n   t:=convert(s,base,2):\n   if (Norm(v[1]+(-1)^(t[1])*v[2]+
(-1)^(t[2])*2*v[3]+(-1)^(t[3])*v[4]+v[5],2)^2 < Norm(v[3],2)^2) then \+
\n      print(\"not satisfied\",\"2*v_3\") \n   end if; \nend do:\nfor
 s from 8 by 1 to 15 do\n   t:=convert(s,base,2):\n   if (Norm(v[1]+(-
1)^(t[1])*v[2]+(-1)^(t[2])*2*v[3]+(-1)^(t[3])*v[4]+(-1)^(t[4])*v[5],2)
^2 < Norm(v[3],2)^2) then \n      print(\"not satisfied\",\"2*v_3\") \+
\n   end if; \nend do:\nfor s from 0 by 1 to 1 do\n   if (Norm(v[1]+(-
1)^s*v[2]+v[3]+2*v[4]+v[5],2)^2 < Norm(v[4],2)^2) then \n      print(
\"not satisfied\",\"2*v_4\") \n   end if;\nend do;\nfor s from 2 by 1 \+
to 3 do\n   t:=convert(s,base,2):\n   if (Norm(v[1]+(-1)^(t[1])*v[2]+(
-1)^(t[2])*v[3]+2*v[4]+v[5],2)^2 < Norm(v[4],2)^2) then \n      print(
\"not satisfied\",\"2*v_4\") \n   end if; \nend do:\nfor s from 4 by 1
 to 7 do\n   t:=convert(s,base,2):\n   if (Norm(v[1]+(-1)^(t[1])*v[2]+
(-1)^(t[2])*v[3]+(-1)^(t[3])*2*v[4]+v[5],2)^2 < Norm(v[4],2)^2) then \+
\n      print(\"not satisfied\",\"2*v_4\") \n   end if; \nend do:\nfor
 s from 8 by 1 to 15 do\n   t:=convert(s,base,2):\n   if (Norm(v[1]+(-
1)^(t[1])*v[2]+(-1)^(t[2])*v[3]+(-1)^(t[3])*2*v[4]+(-1)^(t[4])*v[5],2)
^2 < Norm(v[4],2)^2) then \n      print(\"not satisfied\",\"2*v_4\") \+
\n   end if; \nend do:\nfor s from 0 by 1 to 1 do\n   if (Norm(v[1]+(-
1)^s*v[2]+v[3]+v[4]+2*v[5],2)^2 < Norm(v[5],2)^2) then \n      print(
\"not satisfied\",\"2*v_5\") \n   end if;\nend do;\nfor s from 2 by 1 \+
to 3 do\n   t:=convert(s,base,2):\n   if (Norm(v[1]+(-1)^(t[1])*v[2]+(
-1)^(t[2])*v[3]+v[4]+2*v[5],2)^2 < Norm(v[5],2)^2) then \n      print(
\"not satisfied\",\"2*v_5\") \n   end if; \nend do:\nfor s from 4 by 1
 to 7 do\n   t:=convert(s,base,2):\n   if (Norm(v[1]+(-1)^(t[1])*v[2]+
(-1)^(t[2])*v[3]+(-1)^(t[3])*v[4]+2*v[5],2)^2 < Norm(v[5],2)^2) then \+
\n      print(\"not satisfied\",\"2*v_5\") \n   end if; \nend do:\nfor
 s from 8 by 1 to 15 do\n   t:=convert(s,base,2):\n   if (Norm(v[1]+(-
1)^(t[1])*v[2]+(-1)^(t[2])*v[3]+(-1)^(t[3])*v[4]+(-1)^(t[4])*2*v[5],2)
^2 < Norm(v[5],2)^2) then \n      print(\"not satisfied\",\"2*v_5\") \+
\n   end if; \nend do:" }}{PARA 11 "" 1 "" {XPPMATH 20 "6$Q.not~satisf
ied6\"Q&2*v_3F$" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}
{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 358 "v[1]:=Vector([10,0,0,0,0]):
\nv[2]:=Vector([0,10,0,0,0]):\nv[3]:=Vector([0,0,10,0,0]):\nv[4]:=Vect
or([-5,-5,-5,-1,-5]):\nv[5]:=Vector([0,0,0,-1,10]):\nv[1],v[2],v[3],v[
4],v[5];\nprint(\"|v[1]|^2\"=Norm(v[1],2)^2);\n#checking for decreasin
g order;\nfor i from 1 by 1 to 4 do \n   if (Norm(v[i],2)^2 > Norm(v[i
+1],2)^2) then print(\"not satisfied\",(i,i+1)) end if; \nend do;" }}
{PARA 11 "" 1 "" {XPPMATH 20 "6'-%'RTABLEG6%\"*/u[(=-%'MATRIXG6#7'7#\"
#57#\"\"!F-F-F-&%'VectorG6#%'columnG-F$6%\"*ou[(=-F(6#7'F-F+F-F-F-F/-F
$6%\"*Kv[(=-F(6#7'F-F-F+F-F-F/-F$6%\"*'f([(=-F(6#7'7#!\"&FEFE7#!\"\"FE
F/-F$6%\"*gw[(=-F(6#7'F-F-F-FGF+F/" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#
/Q)|grv[1]|gr^26\"\"$+\"" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 
6469 "#checking for 2|v[j].v[i]|=<|v[i]|^2;\nL2:=choose(5, 2):\nfor i \+
from 1 by 1 to numbcomb(5, 2) do\n   if (2*abs(v[L2[i][2]].v[L2[i][1]]
) > Norm(v[L2[i][1]],2)^2) then \n      print(\"not satisfied\",\"v_i,
v_j\",L2[i][1],L2[i][2]) \n   end if;\nend do;\n#checking for 2|v[k].(
v[i]+v[j])|=<|v[i]+v[j]|^2;\nL3:=choose(5, 3):\nfor s from 0 by 1 to 1
 do\n   for i from 1 by 1 to numbcomb(5, 3) do\n      if (2*abs(v[L3[i
][3]].(v[L3[i][1]]+(-1)^s*v[L3[i][2]])) > Norm(v[L3[i][1]]+(-1)^s*v[L3
[i][2]],2)^2) then \n         print(\"not satisfied\",\"v_i,v_j,v_k\",
L3[i][1],(-1)^s*L3[i][2],L3[i][3]); \n      end if;\n   end do;\nend d
o;\n#checking for 2|v[l].(v[i]+v[j]+v[k])|=<|v[i]+v[j]+v[k]|^2;\nL4:=c
hoose(5, 4):\nfor s from 0 by 1 to 1 do\n   for i from 1 by 1 to numbc
omb(5, 4) do\n      if (2*abs(v[L4[i][4]].(v[L4[i][1]]+(-1)^s*v[L4[i][
2]]+(-1)^0*v[L4[i][3]])) >\n         Norm(v[L4[i][1]]+(-1)^s*v[L4[i][2
]]+(-1)^0*v[L4[i][3]],2)^2) then \n         print(\"not satisfied\",\"
v_i,v_j,v_k,v_l\",L4[i][1],(-1)^s*L4[i][2],(-1)^0*L4[i][3],L4[i][4]); \+
\n      end if;\n   end do;\nend do;\nfor s from 2 by 1 to 3 do\n   t:
=convert(s,base,2):\n   for i from 1 by 1 to numbcomb(5, 4) do\n      \+
if (2*abs(v[L4[i][4]].(v[L4[i][1]]+(-1)^(t[1])*v[L4[i][2]]+(-1)^(t[2])
*v[L4[i][3]])) >\n         Norm(v[L4[i][1]]+(-1)^(t[1])*v[L4[i][2]]+(-
1)^(t[2])*v[L4[i][3]],2)^2) then \n         print(\"not satisfied\",\"
v_i,v_j,v_k,v_l\",L4[i][1],(-1)^(t[1])*L4[i][2],(-1)^(t[2])*L4[i][3],L
4[i][4]); \n      end if;\n   end do;\nend do:\n#checking for 2|v[m].(
v[i]+v[j]+v[k]+v[l])|=<|v[i]+v[j]+v[k]+v[l]|^2;\nfor s from 0 by 1 to \+
1 do\n   if (2*abs(v[5].(v[1]+(-1)^s*v[2]+(-1)^0*v[3]+(-1)^0*v[4])) > \+
\n       Norm(v[1]+(-1)^s*v[2]+(-1)^0*v[3]+(-1)^0*v[4],2)^2) then \n  \+
    print(\"not satisfied\",\"v_i,v_j,v_k,v_l,v_m\",1,(-1)^s*2,3,4,5);
 \n   end if;\nend do;\nfor s from 2 by 1 to 3 do\n   t:=convert(s,bas
e,2):\n   if (2*abs(v[5].(v[1]+(-1)^(t[1])*v[2]+(-1)^(t[2])*v[3]+(-1)^
0*v[4])) > \n       Norm(v[1]+(-1)^(t[1])*v[2]+(-1)^(t[2])*v[3]+(-1)^0
*v[4],2)^2) then \n      print(\"not satisfied\",\"v_i,v_j,v_k,v_l,v_m
\",1,+(-1)^(t[1])*2,(-1)^(t[2])*3,(-1)^0*4,5); \n   end if;\nend do:\n
for s from 4 by 1 to 7 do\n   t:=convert(s,base,2):\n   if (2*abs(v[5]
.(v[1]+(-1)^(t[1])*v[2]+(-1)^(t[2])*v[3]+(-1)^(t[3])*v[4])) > \n      \+
 Norm(v[1]+(-1)^(t[1])*v[2]+(-1)^(t[2])*v[3]+(-1)^(t[3])*v[4],2)^2) th
en \n      print(\"not satisfied\",\"v_i,v_j,v_k,v_l,v_m\",1,(-1)^(t[1
])*2,+(-1)^(t[2])*3,(-1)^(t[3])*4,5); \n   end if;\nend do:\n#checking
 for |v[i]+v[1]+v[2]+v[3]+v[4]+v[5]|^2>=|v[i]|^2;\nfor s from 0 by 1 t
o 1 do\n   if (Norm(2*v[1]+(-1)^s*v[2]+v[3]+v[4]+v[5],2)^2 < Norm(v[1]
,2)^2) then \n      print(\"not satisfied\",\"2*v_1\") \n   end if;\ne
nd do;\nfor s from 2 by 1 to 3 do\n   t:=convert(s,base,2):\n   if (No
rm(2*v[1]+(-1)^(t[1])*v[2]+(-1)^(t[2])*v[3]+v[4]+v[5],2)^2 < Norm(v[1]
,2)^2) then \n      print(\"not satisfied\",\"2*v_1\") \n   end if; \n
end do:\nfor s from 4 by 1 to 7 do\n   t:=convert(s,base,2):\n   if (N
orm(2*v[1]+(-1)^(t[1])*v[2]+(-1)^(t[2])*v[3]+(-1)^(t[3])*v[4]+v[5],2)^
2 < Norm(v[1],2)^2) then \n      print(\"not satisfied\",\"2*v_1\") \n
   end if; \nend do:\nfor s from 8 by 1 to 15 do\n   t:=convert(s,base
,2):\n   if (Norm(2*v[1]+(-1)^(t[1])*v[2]+(-1)^(t[2])*v[3]+(-1)^(t[3])
*v[4]+(-1)^(t[4])*v[5],2)^2 < Norm(v[1],2)^2) then \n      print(\"not
 satisfied\",\"2*v_1\") \n   end if; \nend do:\nfor s from 0 by 1 to 1
 do\n   if (Norm(v[1]+(-1)^s*2*v[2]+v[3]+v[4]+v[5],2)^2 < Norm(v[2],2)
^2) then \n      print(\"not satisfied\",\"2*v_2\") \n   end if;\nend \+
do;\nfor s from 2 by 1 to 3 do\n   t:=convert(s,base,2):\n   if (Norm(
v[1]+(-1)^(t[1])*2*v[2]+(-1)^(t[2])*v[3]+v[4]+v[5],2)^2 < Norm(v[2],2)
^2) then \n      print(\"not satisfied\",\"2*v_2\") \n   end if; \nend
 do:\nfor s from 4 by 1 to 7 do\n   t:=convert(s,base,2):\n   if (Norm
(v[1]+(-1)^(t[1])*2*v[2]+(-1)^(t[2])*v[3]+(-1)^(t[3])*v[4]+v[5],2)^2 <
 Norm(v[2],2)^2) then \n      print(\"not satisfied\",\"2*v_2\") \n   \+
end if; \nend do:\nfor s from 8 by 1 to 15 do\n   t:=convert(s,base,2)
:\n   if (Norm(v[1]+(-1)^(t[1])*2*v[2]+(-1)^(t[2])*v[3]+(-1)^(t[3])*v[
4]+(-1)^(t[4])*v[5],2)^2 < Norm(v[2],2)^2) then \n      print(\"not sa
tisfied\",\"2*v_2\") \n   end if; \nend do:\nfor s from 0 by 1 to 1 do
\n   if (Norm(v[1]+(-1)^s*v[2]+2*v[3]+v[4]+v[5],2)^2 < Norm(v[3],2)^2)
 then \n      print(\"not satisfied\",\"2*v_3\") \n   end if;\nend do;
\nfor s from 2 by 1 to 3 do\n   t:=convert(s,base,2):\n   if (Norm(v[1
]+(-1)^(t[1])*v[2]+(-1)^(t[2])*2*v[3]+v[4]+v[5],2)^2 < Norm(v[3],2)^2)
 then \n      print(\"not satisfied\",\"2*v_3\") \n   end if; \nend do
:\nfor s from 4 by 1 to 7 do\n   t:=convert(s,base,2):\n   if (Norm(v[
1]+(-1)^(t[1])*v[2]+(-1)^(t[2])*2*v[3]+(-1)^(t[3])*v[4]+v[5],2)^2 < No
rm(v[3],2)^2) then \n      print(\"not satisfied\",\"2*v_3\") \n   end
 if; \nend do:\nfor s from 8 by 1 to 15 do\n   t:=convert(s,base,2):\n
   if (Norm(v[1]+(-1)^(t[1])*v[2]+(-1)^(t[2])*2*v[3]+(-1)^(t[3])*v[4]+
(-1)^(t[4])*v[5],2)^2 < Norm(v[3],2)^2) then \n      print(\"not satis
fied\",\"2*v_3\") \n   end if; \nend do:\nfor s from 0 by 1 to 1 do\n \+
  if (Norm(v[1]+(-1)^s*v[2]+v[3]+2*v[4]+v[5],2)^2 < Norm(v[4],2)^2) th
en \n      print(\"not satisfied\",\"2*v_4\") \n   end if;\nend do;\nf
or s from 2 by 1 to 3 do\n   t:=convert(s,base,2):\n   if (Norm(v[1]+(
-1)^(t[1])*v[2]+(-1)^(t[2])*v[3]+2*v[4]+v[5],2)^2 < Norm(v[4],2)^2) th
en \n      print(\"not satisfied\",\"2*v_4\") \n   end if; \nend do:\n
for s from 4 by 1 to 7 do\n   t:=convert(s,base,2):\n   if (Norm(v[1]+
(-1)^(t[1])*v[2]+(-1)^(t[2])*v[3]+(-1)^(t[3])*2*v[4]+v[5],2)^2 < Norm(
v[4],2)^2) then \n      print(\"not satisfied\",\"2*v_4\") \n   end if
; \nend do:\nfor s from 8 by 1 to 15 do\n   t:=convert(s,base,2):\n   \+
if (Norm(v[1]+(-1)^(t[1])*v[2]+(-1)^(t[2])*v[3]+(-1)^(t[3])*2*v[4]+(-1
)^(t[4])*v[5],2)^2 < Norm(v[4],2)^2) then \n      print(\"not satisfie
d\",\"2*v_4\") \n   end if; \nend do:\nfor s from 0 by 1 to 1 do\n   i
f (Norm(v[1]+(-1)^s*v[2]+v[3]+v[4]+2*v[5],2)^2 < Norm(v[5],2)^2) then \+
\n      print(\"not satisfied\",\"2*v_5\") \n   end if;\nend do;\nfor \+
s from 2 by 1 to 3 do\n   t:=convert(s,base,2):\n   if (Norm(v[1]+(-1)
^(t[1])*v[2]+(-1)^(t[2])*v[3]+v[4]+2*v[5],2)^2 < Norm(v[5],2)^2) then \+
\n      print(\"not satisfied\",\"2*v_5\") \n   end if; \nend do:\nfor
 s from 4 by 1 to 7 do\n   t:=convert(s,base,2):\n   if (Norm(v[1]+(-1
)^(t[1])*v[2]+(-1)^(t[2])*v[3]+(-1)^(t[3])*v[4]+2*v[5],2)^2 < Norm(v[5
],2)^2) then \n      print(\"not satisfied\",\"2*v_5\") \n   end if; \+
\nend do:\nfor s from 8 by 1 to 15 do\n   t:=convert(s,base,2):\n   if
 (Norm(v[1]+(-1)^(t[1])*v[2]+(-1)^(t[2])*v[3]+(-1)^(t[3])*v[4]+(-1)^(t
[4])*2*v[5],2)^2 < Norm(v[5],2)^2) then \n      print(\"not satisfied
\",\"2*v_5\") \n   end if; \nend do:" }}{PARA 11 "" 1 "" {XPPMATH 20 "
6$Q.not~satisfied6\"Q&2*v_4F$" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 
0 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 357 "v[1]:=Vector([10,
0,0,0,0]):\nv[2]:=Vector([0,10,0,0,0]):\nv[3]:=Vector([0,0,10,0,0]):\n
v[4]:=Vector([0,0,0,10,0]):\nv[5]:=Vector([-5,-5,-5,-5,-1]):\nv[1],v[2
],v[3],v[4],v[5];\nprint(\"|v[1]|^2\"=Norm(v[1],2)^2);\n#checking for \+
decreasing order;\nfor i from 1 by 1 to 4 do \n   if (Norm(v[i],2)^2 >
 Norm(v[i+1],2)^2) then print(\"not satisfied\",(i,i+1)) end if; \nend
 do;" }}{PARA 11 "" 1 "" {XPPMATH 20 "6'-%'RTABLEG6%\"*#4s^<-%'MATRIXG
6#7'7#\"#57#\"\"!F-F-F-&%'VectorG6#%'columnG-F$6%\"*c@<v\"-F(6#7'F-F+F
-F-F-F/-F$6%\"*?A<v\"-F(6#7'F-F-F+F-F-F/-F$6%\"*%Gs^<-F(6#7'F-F-F-F+F-
F/-F$6%\"*[B<v\"-F(6#7'7#!\"&FKFKFK7#!\"\"F/" }}{PARA 11 "" 1 "" 
{XPPMATH 20 "6#/Q)|grv[1]|gr^26\"\"$+\"" }}}{EXCHG {PARA 0 "> " 0 "" 
{MPLTEXT 1 0 6469 "#checking for 2|v[j].v[i]|=<|v[i]|^2;\nL2:=choose(5
, 2):\nfor i from 1 by 1 to numbcomb(5, 2) do\n   if (2*abs(v[L2[i][2]
].v[L2[i][1]]) > Norm(v[L2[i][1]],2)^2) then \n      print(\"not satis
fied\",\"v_i,v_j\",L2[i][1],L2[i][2]) \n   end if;\nend do;\n#checking
 for 2|v[k].(v[i]+v[j])|=<|v[i]+v[j]|^2;\nL3:=choose(5, 3):\nfor s fro
m 0 by 1 to 1 do\n   for i from 1 by 1 to numbcomb(5, 3) do\n      if \+
(2*abs(v[L3[i][3]].(v[L3[i][1]]+(-1)^s*v[L3[i][2]])) > Norm(v[L3[i][1]
]+(-1)^s*v[L3[i][2]],2)^2) then \n         print(\"not satisfied\",\"v
_i,v_j,v_k\",L3[i][1],(-1)^s*L3[i][2],L3[i][3]); \n      end if;\n   e
nd do;\nend do;\n#checking for 2|v[l].(v[i]+v[j]+v[k])|=<|v[i]+v[j]+v[
k]|^2;\nL4:=choose(5, 4):\nfor s from 0 by 1 to 1 do\n   for i from 1 \+
by 1 to numbcomb(5, 4) do\n      if (2*abs(v[L4[i][4]].(v[L4[i][1]]+(-
1)^s*v[L4[i][2]]+(-1)^0*v[L4[i][3]])) >\n         Norm(v[L4[i][1]]+(-1
)^s*v[L4[i][2]]+(-1)^0*v[L4[i][3]],2)^2) then \n         print(\"not s
atisfied\",\"v_i,v_j,v_k,v_l\",L4[i][1],(-1)^s*L4[i][2],(-1)^0*L4[i][3
],L4[i][4]); \n      end if;\n   end do;\nend do;\nfor s from 2 by 1 t
o 3 do\n   t:=convert(s,base,2):\n   for i from 1 by 1 to numbcomb(5, \+
4) do\n      if (2*abs(v[L4[i][4]].(v[L4[i][1]]+(-1)^(t[1])*v[L4[i][2]
]+(-1)^(t[2])*v[L4[i][3]])) >\n         Norm(v[L4[i][1]]+(-1)^(t[1])*v
[L4[i][2]]+(-1)^(t[2])*v[L4[i][3]],2)^2) then \n         print(\"not s
atisfied\",\"v_i,v_j,v_k,v_l\",L4[i][1],(-1)^(t[1])*L4[i][2],(-1)^(t[2
])*L4[i][3],L4[i][4]); \n      end if;\n   end do;\nend do:\n#checking
 for 2|v[m].(v[i]+v[j]+v[k]+v[l])|=<|v[i]+v[j]+v[k]+v[l]|^2;\nfor s fr
om 0 by 1 to 1 do\n   if (2*abs(v[5].(v[1]+(-1)^s*v[2]+(-1)^0*v[3]+(-1
)^0*v[4])) > \n       Norm(v[1]+(-1)^s*v[2]+(-1)^0*v[3]+(-1)^0*v[4],2)
^2) then \n      print(\"not satisfied\",\"v_i,v_j,v_k,v_l,v_m\",1,(-1
)^s*2,3,4,5); \n   end if;\nend do;\nfor s from 2 by 1 to 3 do\n   t:=
convert(s,base,2):\n   if (2*abs(v[5].(v[1]+(-1)^(t[1])*v[2]+(-1)^(t[2
])*v[3]+(-1)^0*v[4])) > \n       Norm(v[1]+(-1)^(t[1])*v[2]+(-1)^(t[2]
)*v[3]+(-1)^0*v[4],2)^2) then \n      print(\"not satisfied\",\"v_i,v_
j,v_k,v_l,v_m\",1,+(-1)^(t[1])*2,(-1)^(t[2])*3,(-1)^0*4,5); \n   end i
f;\nend do:\nfor s from 4 by 1 to 7 do\n   t:=convert(s,base,2):\n   i
f (2*abs(v[5].(v[1]+(-1)^(t[1])*v[2]+(-1)^(t[2])*v[3]+(-1)^(t[3])*v[4]
)) > \n       Norm(v[1]+(-1)^(t[1])*v[2]+(-1)^(t[2])*v[3]+(-1)^(t[3])*
v[4],2)^2) then \n      print(\"not satisfied\",\"v_i,v_j,v_k,v_l,v_m
\",1,(-1)^(t[1])*2,+(-1)^(t[2])*3,(-1)^(t[3])*4,5); \n   end if;\nend \+
do:\n#checking for |v[i]+v[1]+v[2]+v[3]+v[4]+v[5]|^2>=|v[i]|^2;\nfor s
 from 0 by 1 to 1 do\n   if (Norm(2*v[1]+(-1)^s*v[2]+v[3]+v[4]+v[5],2)
^2 < Norm(v[1],2)^2) then \n      print(\"not satisfied\",\"2*v_1\") \+
\n   end if;\nend do;\nfor s from 2 by 1 to 3 do\n   t:=convert(s,base
,2):\n   if (Norm(2*v[1]+(-1)^(t[1])*v[2]+(-1)^(t[2])*v[3]+v[4]+v[5],2
)^2 < Norm(v[1],2)^2) then \n      print(\"not satisfied\",\"2*v_1\") \+
\n   end if; \nend do:\nfor s from 4 by 1 to 7 do\n   t:=convert(s,bas
e,2):\n   if (Norm(2*v[1]+(-1)^(t[1])*v[2]+(-1)^(t[2])*v[3]+(-1)^(t[3]
)*v[4]+v[5],2)^2 < Norm(v[1],2)^2) then \n      print(\"not satisfied
\",\"2*v_1\") \n   end if; \nend do:\nfor s from 8 by 1 to 15 do\n   t
:=convert(s,base,2):\n   if (Norm(2*v[1]+(-1)^(t[1])*v[2]+(-1)^(t[2])*
v[3]+(-1)^(t[3])*v[4]+(-1)^(t[4])*v[5],2)^2 < Norm(v[1],2)^2) then \n \+
     print(\"not satisfied\",\"2*v_1\") \n   end if; \nend do:\nfor s \+
from 0 by 1 to 1 do\n   if (Norm(v[1]+(-1)^s*2*v[2]+v[3]+v[4]+v[5],2)^
2 < Norm(v[2],2)^2) then \n      print(\"not satisfied\",\"2*v_2\") \n
   end if;\nend do;\nfor s from 2 by 1 to 3 do\n   t:=convert(s,base,2
):\n   if (Norm(v[1]+(-1)^(t[1])*2*v[2]+(-1)^(t[2])*v[3]+v[4]+v[5],2)^
2 < Norm(v[2],2)^2) then \n      print(\"not satisfied\",\"2*v_2\") \n
   end if; \nend do:\nfor s from 4 by 1 to 7 do\n   t:=convert(s,base,
2):\n   if (Norm(v[1]+(-1)^(t[1])*2*v[2]+(-1)^(t[2])*v[3]+(-1)^(t[3])*
v[4]+v[5],2)^2 < Norm(v[2],2)^2) then \n      print(\"not satisfied\",
\"2*v_2\") \n   end if; \nend do:\nfor s from 8 by 1 to 15 do\n   t:=c
onvert(s,base,2):\n   if (Norm(v[1]+(-1)^(t[1])*2*v[2]+(-1)^(t[2])*v[3
]+(-1)^(t[3])*v[4]+(-1)^(t[4])*v[5],2)^2 < Norm(v[2],2)^2) then \n    \+
  print(\"not satisfied\",\"2*v_2\") \n   end if; \nend do:\nfor s fro
m 0 by 1 to 1 do\n   if (Norm(v[1]+(-1)^s*v[2]+2*v[3]+v[4]+v[5],2)^2 <
 Norm(v[3],2)^2) then \n      print(\"not satisfied\",\"2*v_3\") \n   \+
end if;\nend do;\nfor s from 2 by 1 to 3 do\n   t:=convert(s,base,2):
\n   if (Norm(v[1]+(-1)^(t[1])*v[2]+(-1)^(t[2])*2*v[3]+v[4]+v[5],2)^2 \+
< Norm(v[3],2)^2) then \n      print(\"not satisfied\",\"2*v_3\") \n  \+
 end if; \nend do:\nfor s from 4 by 1 to 7 do\n   t:=convert(s,base,2)
:\n   if (Norm(v[1]+(-1)^(t[1])*v[2]+(-1)^(t[2])*2*v[3]+(-1)^(t[3])*v[
4]+v[5],2)^2 < Norm(v[3],2)^2) then \n      print(\"not satisfied\",\"
2*v_3\") \n   end if; \nend do:\nfor s from 8 by 1 to 15 do\n   t:=con
vert(s,base,2):\n   if (Norm(v[1]+(-1)^(t[1])*v[2]+(-1)^(t[2])*2*v[3]+
(-1)^(t[3])*v[4]+(-1)^(t[4])*v[5],2)^2 < Norm(v[3],2)^2) then \n      \+
print(\"not satisfied\",\"2*v_3\") \n   end if; \nend do:\nfor s from \+
0 by 1 to 1 do\n   if (Norm(v[1]+(-1)^s*v[2]+v[3]+2*v[4]+v[5],2)^2 < N
orm(v[4],2)^2) then \n      print(\"not satisfied\",\"2*v_4\") \n   en
d if;\nend do;\nfor s from 2 by 1 to 3 do\n   t:=convert(s,base,2):\n \+
  if (Norm(v[1]+(-1)^(t[1])*v[2]+(-1)^(t[2])*v[3]+2*v[4]+v[5],2)^2 < N
orm(v[4],2)^2) then \n      print(\"not satisfied\",\"2*v_4\") \n   en
d if; \nend do:\nfor s from 4 by 1 to 7 do\n   t:=convert(s,base,2):\n
   if (Norm(v[1]+(-1)^(t[1])*v[2]+(-1)^(t[2])*v[3]+(-1)^(t[3])*2*v[4]+
v[5],2)^2 < Norm(v[4],2)^2) then \n      print(\"not satisfied\",\"2*v
_4\") \n   end if; \nend do:\nfor s from 8 by 1 to 15 do\n   t:=conver
t(s,base,2):\n   if (Norm(v[1]+(-1)^(t[1])*v[2]+(-1)^(t[2])*v[3]+(-1)^
(t[3])*2*v[4]+(-1)^(t[4])*v[5],2)^2 < Norm(v[4],2)^2) then \n      pri
nt(\"not satisfied\",\"2*v_4\") \n   end if; \nend do:\nfor s from 0 b
y 1 to 1 do\n   if (Norm(v[1]+(-1)^s*v[2]+v[3]+v[4]+2*v[5],2)^2 < Norm
(v[5],2)^2) then \n      print(\"not satisfied\",\"2*v_5\") \n   end i
f;\nend do;\nfor s from 2 by 1 to 3 do\n   t:=convert(s,base,2):\n   i
f (Norm(v[1]+(-1)^(t[1])*v[2]+(-1)^(t[2])*v[3]+v[4]+2*v[5],2)^2 < Norm
(v[5],2)^2) then \n      print(\"not satisfied\",\"2*v_5\") \n   end i
f; \nend do:\nfor s from 4 by 1 to 7 do\n   t:=convert(s,base,2):\n   \+
if (Norm(v[1]+(-1)^(t[1])*v[2]+(-1)^(t[2])*v[3]+(-1)^(t[3])*v[4]+2*v[5
],2)^2 < Norm(v[5],2)^2) then \n      print(\"not satisfied\",\"2*v_5
\") \n   end if; \nend do:\nfor s from 8 by 1 to 15 do\n   t:=convert(
s,base,2):\n   if (Norm(v[1]+(-1)^(t[1])*v[2]+(-1)^(t[2])*v[3]+(-1)^(t
[3])*v[4]+(-1)^(t[4])*2*v[5],2)^2 < Norm(v[5],2)^2) then \n      print
(\"not satisfied\",\"2*v_5\") \n   end if; \nend do:" }}{PARA 11 "" 1 
"" {XPPMATH 20 "6$Q.not~satisfied6\"Q&2*v_5F$" }}}{EXCHG {PARA 0 "> " 
0 "" {MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }
}}}{MARK "0 0 0" 8 }{VIEWOPTS 1 1 0 1 1 1803 1 1 1 1 }{PAGENUMBERS 0 
1 2 33 1 1 }{RTABLE_HANDLES 212269040 212269104 212269168 212269232 
212269296 182796228 182796292 182796356 182796420 182796484 223913152 
223913216 223913280 223913344 223913408 210884852 210884916 210884980 
210885044 210885108 217658012 217658076 217658140 217658204 217658268 
211736276 211736340 211736404 211736468 211736532 223380820 223380884 
223380948 223381012 223381076 217048016 217048080 217048144 217048208 
217048272 183921796 183921860 183921924 183921988 183922052 192976600 
192976664 192976728 192976792 192976856 177313656 177313720 177313784 
177313848 177313912 173786064 173786128 173786192 173786256 173786320 
216047240 216047304 216047368 216047432 216047496 193298156 193298220 
193298284 193298348 193298412 186011120 186011184 186011248 186011312 
186011376 194294744 194294808 194294872 194294936 194295000 181305252 
181305316 181305380 181305444 181305508 191147676 191147740 191147804 
191147868 191147932 208519020 208519084 208519148 208519212 208519276 
219385640 219385704 219385768 219385832 219385896 218000480 218000544 
218000608 218000672 218000736 182436708 182436772 182436836 182436900 
182436964 209560904 209560968 209561032 209561096 209561160 178317940 
178318004 178318068 178318132 178318196 216173468 216173532 216173596 
216173660 216173724 186460292 186460356 186460420 186460484 186460548 
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I6RTABLE_SAVE/210884916X*%)anythingG6"6"[gl!#%!!!"&"&!""""%F'F'F'F&
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I6RTABLE_SAVE/210884980X*%)anythingG6"6"[gl!#%!!!"&"&!""F'""%F'F'F&
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I6RTABLE_SAVE/217658204X*%)anythingG6"6"[gl!#%!!!"&"&!""F'F'""%F'F&
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I6RTABLE_SAVE/183921988X*%)anythingG6"6"[gl!#%!!!"&"&!""F'F'""%F'F&
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I6RTABLE_SAVE/183922052X*%)anythingG6"6"[gl!#%!!!"&"&!"#F'F'F'F'F&
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