{VERSION 6 0 "IBM INTEL NT" "6.0" }
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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 42 "# proof of the mobil
ity for the 1st family" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" 
}}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 28 "restart:with(LinearAlgebr
a):" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "
> " 0 "" {MPLTEXT 1 0 21 "# entries of matrix R" }}}{EXCHG {PARA 0 "> \+
" 0 "" {MPLTEXT 1 0 25 "r11:=e0^2+e1^2-e2^2-e3^2:" }}}{EXCHG {PARA 0 "
> " 0 "" {MPLTEXT 1 0 21 "r12:=2*(e1*e2-e0*e3):" }}}{EXCHG {PARA 0 "> \+
" 0 "" {MPLTEXT 1 0 21 "r13:=2*(e1*e3+e0*e2):" }}}{EXCHG {PARA 0 "> " 
0 "" {MPLTEXT 1 0 21 "r21:=2*(e1*e2+e0*e3):" }}}{EXCHG {PARA 0 "> " 0 
"" {MPLTEXT 1 0 25 "r22:=e0^2-e1^2+e2^2-e3^2:" }}}{EXCHG {PARA 0 "> " 
0 "" {MPLTEXT 1 0 21 "r23:=2*(e2*e3-e0*e1):" }}}{EXCHG {PARA 0 "> " 0 
"" {MPLTEXT 1 0 21 "r31:=2*(e1*e3-e0*e2):" }}}{EXCHG {PARA 0 "> " 0 "
" {MPLTEXT 1 0 21 "r32:=2*(e2*e3+e0*e1):" }}}{EXCHG {PARA 0 "> " 0 "" 
{MPLTEXT 1 0 25 "r33:=e0^2-e1^2-e2^2+e3^2:" }}}{EXCHG {PARA 0 "> " 0 "
" {MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 20 "# tra
nslational part" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 32 "t1:=2*(f
1*e0-f0*e1+f3*e2-f2*e3):" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 32 
"t2:=2*(f2*e0-f0*e2+f1*e3-f3*e1):" }}}{EXCHG {PARA 0 "> " 0 "" 
{MPLTEXT 1 0 32 "t3:=2*(f3*e0-f0*e3+f2*e1-f1*e2):" }}}{EXCHG {PARA 0 "
> " 0 "" {MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 
125 "# direct isometry: (AA,BB,CC) are the coordinates of the point (Y
1,Y2,Y3) in the moving frame with respect to the fixed frame" }}}
{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 28 "AA:=t1+r11*Y1+r12*Y2+r13*Y3:
" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 28 "BB:=t2+r21*Y1+r22*Y2+r2
3*Y3:" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 28 "CC:=t3+r31*Y1+r32*
Y2+r33*Y3:" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{EXCHG 
{PARA 0 "> " 0 "" {MPLTEXT 1 0 119 "# computation of the sphere condit
ion Lambda with base point (X1,X2,X3), platform point (Y1,Y2,Y3) and s
quard radius dd" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 23 "N:=e0^2+
e1^2+e2^2+e3^2:" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 71 "Sphere:=
AA^2+BB^2+CC^2-2*N*(AA*X1+BB*X2+CC*X3)+N^2*(X1^2+X2^2+X3^2-dd):" }}}
{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 29 "psi:=e0*f0+e1*f1+e2*f2+e3*f3
:" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 43 "Lambda:=factor(Sphere \+
+ 4*psi^2)/N:nops(%);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#\"#!)" }}}
{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 31 "# parametrisation of the fam
ily" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 12 "B1:=0:C1:=0:" }}}
{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 23 "A2:=mu1*A1:B2:=0:C2:=0:" }}}
{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 6 "C3:=0:" }}}{EXCHG {PARA 0 "> \+
" 0 "" {MPLTEXT 1 0 28 "A4:=mu3*A3:B4:=mu3*B3:C4:=0:" }}}{EXCHG {PARA 
0 "> " 0 "" {MPLTEXT 1 0 33 "A6:=mu5*A5:B6:=mu5*B5:C6:=mu5*C5:" }}}
{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 24 "a1:=-A2:b1:=-B2:c1:=-C2:" }}
}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 24 "a2:=-A1:b2:=-B1:c2:=-C1:" }
}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 24 "a3:=-A4:b3:=-B4:c3:=-C4:" 
}}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 24 "a4:=-A3:b4:=-B3:c4:=-C3:
" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 24 "a5:=-A6:b5:=-B6:c5:=-C6
:" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 24 "a6:=-A5:b6:=-B5:c6:=-C
5:" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 ">
 " 0 "" {MPLTEXT 1 0 32 "# defining Lambda1, ..., Lambda6" }}}{EXCHG 
{PARA 0 "> " 0 "" {MPLTEXT 1 0 75 "Lambda1:=simplify(subs(X1=A1,X2=B1,
X3=C1,Y1=a1,Y2=b1,Y3=c1,dd=dd1,Lambda)):" }}}{EXCHG {PARA 0 "> " 0 "" 
{MPLTEXT 1 0 75 "Lambda2:=simplify(subs(X1=A2,X2=B2,X3=C2,Y1=a2,Y2=b2,
Y3=c2,dd=dd2,Lambda)):" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 75 "L
ambda3:=simplify(subs(X1=A3,X2=B3,X3=C3,Y1=a3,Y2=b3,Y3=c3,dd=dd3,Lambd
a)):" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 75 "Lambda4:=simplify(s
ubs(X1=A4,X2=B4,X3=C4,Y1=a4,Y2=b4,Y3=c4,dd=dd4,Lambda)):" }}}{EXCHG 
{PARA 0 "> " 0 "" {MPLTEXT 1 0 75 "Lambda5:=simplify(subs(X1=A5,X2=B5,
X3=C5,Y1=a5,Y2=b5,Y3=c5,dd=dd5,Lambda)):" }}}{EXCHG {PARA 0 "> " 0 "" 
{MPLTEXT 1 0 75 "Lambda6:=simplify(subs(X1=A6,X2=B6,X3=C6,Y1=a6,Y2=b6,
Y3=c6,dd=dd6,Lambda)):" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" 
}}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 23 "# defining Delata12,..." 
}}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 35 "Delta12:=simplify(Lambda1
-Lambda2):" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 35 "Delta13:=simp
lify(Lambda1-Lambda3):" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 35 "D
elta14:=simplify(Lambda1-Lambda4):" }}}{EXCHG {PARA 0 "> " 0 "" 
{MPLTEXT 1 0 35 "Delta15:=simplify(Lambda1-Lambda5):" }}}{EXCHG {PARA 
0 "> " 0 "" {MPLTEXT 1 0 35 "Delta16:=simplify(Lambda1-Lambda6):" }}}
{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 35 "Delta23:=simplify(Lambda1-La
mbda3):" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 35 "Delta24:=simplif
y(Lambda1-Lambda4):" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 35 "Delt
a25:=simplify(Lambda1-Lambda5):" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 
1 0 35 "Delta26:=simplify(Lambda1-Lambda6):" }}}{EXCHG {PARA 0 "> " 0 
"" {MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 34 "# de
fining Sij, Tij, Uij, Vij, Wij" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 
1 0 49 "S12:=simplify(select(has,Lambda1-Lambda2,f0)/f0):" }}}{EXCHG 
{PARA 0 "> " 0 "" {MPLTEXT 1 0 49 "T12:=simplify(select(has,Lambda1-La
mbda2,f1)/f1):" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 49 "U12:=simp
lify(select(has,Lambda1-Lambda2,f2)/f2):" }}}{EXCHG {PARA 0 "> " 0 "" 
{MPLTEXT 1 0 49 "V12:=simplify(select(has,Lambda1-Lambda2,f3)/f3):" }}
}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 59 "W12:=simplify(Lambda1-Lambd
a2-S12*f0-T12*f1-U12*f2-V12*f3):" }}}{EXCHG {PARA 0 "> " 0 "" 
{MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 49 "S13:=si
mplify(select(has,Lambda1-Lambda3,f0)/f0):" }}}{EXCHG {PARA 0 "> " 0 "
" {MPLTEXT 1 0 49 "T13:=simplify(select(has,Lambda1-Lambda3,f1)/f1):" 
}}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 49 "U13:=simplify(select(has,
Lambda1-Lambda3,f2)/f2):" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 49 
"V13:=simplify(select(has,Lambda1-Lambda3,f3)/f3):" }}}{EXCHG {PARA 0 
"> " 0 "" {MPLTEXT 1 0 59 "W13:=simplify(Lambda1-Lambda3-S13*f0-T13*f1
-U13*f2-V13*f3):" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}
{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 49 "S14:=simplify(select(has,Lam
bda1-Lambda4,f0)/f0):" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 49 "T1
4:=simplify(select(has,Lambda1-Lambda4,f1)/f1):" }}}{EXCHG {PARA 0 "> \+
" 0 "" {MPLTEXT 1 0 49 "U14:=simplify(select(has,Lambda1-Lambda4,f2)/f
2):" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 49 "V14:=simplify(select
(has,Lambda1-Lambda4,f3)/f3):" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 
0 59 "W14:=simplify(Lambda1-Lambda4-S14*f0-T14*f1-U14*f2-V14*f3):" }}}
{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "> " 0 "
" {MPLTEXT 1 0 49 "S15:=simplify(select(has,Lambda1-Lambda5,f0)/f0):" 
}}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 49 "T15:=simplify(select(has,
Lambda1-Lambda5,f1)/f1):" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 49 
"U15:=simplify(select(has,Lambda1-Lambda5,f2)/f2):" }}}{EXCHG {PARA 0 
"> " 0 "" {MPLTEXT 1 0 49 "V15:=simplify(select(has,Lambda1-Lambda5,f3
)/f3):" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 59 "W15:=simplify(Lam
bda1-Lambda5-S15*f0-T15*f1-U15*f2-V15*f3):" }}}{EXCHG {PARA 0 "> " 0 "
" {MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 49 "S16:=
simplify(select(has,Lambda1-Lambda6,f0)/f0):" }}}{EXCHG {PARA 0 "> " 
0 "" {MPLTEXT 1 0 49 "T16:=simplify(select(has,Lambda1-Lambda6,f1)/f1)
:" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 49 "U16:=simplify(select(h
as,Lambda1-Lambda6,f2)/f2):" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 
49 "V16:=simplify(select(has,Lambda1-Lambda6,f3)/f3):" }}}{EXCHG 
{PARA 0 "> " 0 "" {MPLTEXT 1 0 59 "W16:=simplify(Lambda1-Lambda6-S16*f
0-T16*f1-U16*f2-V16*f3):" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "
" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 49 "S23:=simplify(select(ha
s,Lambda2-Lambda3,f0)/f0):" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 
49 "T23:=simplify(select(has,Lambda2-Lambda3,f1)/f1):" }}}{EXCHG 
{PARA 0 "> " 0 "" {MPLTEXT 1 0 49 "U23:=simplify(select(has,Lambda2-La
mbda3,f2)/f2):" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 49 "V23:=simp
lify(select(has,Lambda2-Lambda3,f3)/f3):" }}}{EXCHG {PARA 0 "> " 0 "" 
{MPLTEXT 1 0 59 "W23:=simplify(Lambda2-Lambda3-S23*f0-T23*f1-U23*f2-V2
3*f3):" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 
0 "> " 0 "" {MPLTEXT 1 0 49 "S24:=simplify(select(has,Lambda2-Lambda4,
f0)/f0):" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 49 "T24:=simplify(s
elect(has,Lambda2-Lambda4,f1)/f1):" }}}{EXCHG {PARA 0 "> " 0 "" 
{MPLTEXT 1 0 49 "U24:=simplify(select(has,Lambda2-Lambda4,f2)/f2):" }}
}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 49 "V24:=simplify(select(has,La
mbda2-Lambda4,f3)/f3):" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 59 "W
24:=simplify(Lambda2-Lambda4-S24*f0-T24*f1-U24*f2-V24*f3):" }}}{EXCHG 
{PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "> " 0 "" 
{MPLTEXT 1 0 49 "S25:=simplify(select(has,Lambda2-Lambda5,f0)/f0):" }}
}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 49 "T25:=simplify(select(has,La
mbda2-Lambda5,f1)/f1):" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 49 "U
25:=simplify(select(has,Lambda2-Lambda5,f2)/f2):" }}}{EXCHG {PARA 0 ">
 " 0 "" {MPLTEXT 1 0 49 "V25:=simplify(select(has,Lambda2-Lambda5,f3)/
f3):" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 59 "W25:=simplify(Lambd
a2-Lambda5-S25*f0-T25*f1-U25*f2-V25*f3):" }}}{EXCHG {PARA 0 "> " 0 "" 
{MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 49 "S26:=si
mplify(select(has,Lambda2-Lambda6,f0)/f0):" }}}{EXCHG {PARA 0 "> " 0 "
" {MPLTEXT 1 0 49 "T26:=simplify(select(has,Lambda2-Lambda6,f1)/f1):" 
}}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 49 "U26:=simplify(select(has,
Lambda2-Lambda6,f2)/f2):" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 49 
"V26:=simplify(select(has,Lambda2-Lambda6,f3)/f3):" }}}{EXCHG {PARA 0 
"> " 0 "" {MPLTEXT 1 0 59 "W26:=simplify(Lambda2-Lambda6-S26*f0-T26*f1
-U26*f2-V26*f3):" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}
{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 52 "# collecting Sij, Tij, Uij, \+
Vij, Wij in a vector Hij" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 27 
"H12:=<S12,T12,U12,V12,W12>:" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 
0 27 "H13:=<S13,T13,U13,V13,W13>:" }}}{EXCHG {PARA 0 "> " 0 "" 
{MPLTEXT 1 0 27 "H14:=<S14,T14,U14,V14,W14>:" }}}{EXCHG {PARA 0 "> " 
0 "" {MPLTEXT 1 0 27 "H15:=<S15,T15,U15,V15,W15>:" }}}{EXCHG {PARA 0 "
> " 0 "" {MPLTEXT 1 0 27 "H16:=<S16,T16,U16,V16,W16>:" }}}{EXCHG 
{PARA 0 "> " 0 "" {MPLTEXT 1 0 27 "H23:=<S23,T23,U23,V23,W23>:" }}}
{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 27 "H24:=<S24,T24,U24,V24,W24>:
" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 27 "H25:=<S25,T25,U25,V25,W
25>:" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 27 "H26:=<S26,T26,U26,V
26,W26>:" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{EXCHG 
{PARA 0 "> " 0 "" {MPLTEXT 1 0 44 "# the coefficients of psi are colle
cted in H" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 19 "H:=<e0,e1,e2,e
3,0>:" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 
0 "> " 0 "" {MPLTEXT 1 0 31 "# computing Omega1, ..., Omega6" }}}
{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 41 "Omega1:=Determinant(<H23|H24
|H25|H26|H>):" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 41 "Omega2:=De
terminant(<H13|H14|H15|H16|H>):" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 
1 0 41 "Omega3:=Determinant(<H12|H14|H15|H16|H>):" }}}{EXCHG {PARA 0 "
> " 0 "" {MPLTEXT 1 0 41 "Omega4:=Determinant(<H12|H13|H15|H16|H>):" }
}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 41 "Omega5:=Determinant(<H12|H
13|H14|H16|H>):" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 41 "Omega6:=
Determinant(<H12|H13|H14|H15|H>):" }}}{EXCHG {PARA 0 "> " 0 "" 
{MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 23 "# compu
ting G1, ..., G6" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 21 "G1:=fac
tor(Omega1/N):" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 21 "G2:=facto
r(Omega2/N):" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 21 "G3:=factor(
Omega3/N):" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 21 "G4:=factor(Om
ega4/N):" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 21 "G5:=factor(Omeg
a5/N):" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 21 "G6:=factor(Omega6
/N):" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 
"> " 0 "" {MPLTEXT 1 0 6 "# test" }}}{EXCHG {PARA 0 "> " 0 "" 
{MPLTEXT 1 0 28 "simplify(G1-G2+G3-G4+G5-G6);" }}{PARA 11 "" 1 "" 
{XPPMATH 20 "6#\"\"!" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 28 "# s
pecifying the leg lengths" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 
27 "dd2:=dd1:dd4:=dd3:dd6:=dd5:" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 
1 0 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 22 "# completing the
 proof" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 33 "G2n:=factor(numer
(simplify(G2))):" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 33 "G3n:=fa
ctor(numer(simplify(G3))):" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 
33 "G4n:=factor(numer(simplify(G4))):" }}}{EXCHG {PARA 0 "> " 0 "" 
{MPLTEXT 1 0 33 "G5n:=factor(numer(simplify(G5))):" }}}{EXCHG {PARA 0 
"> " 0 "" {MPLTEXT 1 0 33 "G6n:=factor(numer(simplify(G6))):" }}}
{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "> " 0 "
" {MPLTEXT 1 0 51 "S:=gcd(gcd(gcd(G2n,G3n),gcd(G4n,G5n)),G6n):nops(%);
" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#\"$]'" }}}{EXCHG {PARA 0 "> " 0 "
" {MPLTEXT 1 0 0 "" }}}}{MARK "1 0 0" 0 }{VIEWOPTS 1 1 0 1 1 1803 1 1 
1 1 }{PAGENUMBERS 0 1 2 33 1 1 }