{VERSION 5 0 "IBM INTEL LINUX" "5.0" }
{USTYLETAB {CSTYLE "Maple Input" -1 0 "CG Times" 1 12 255 0 0 1 0 1 0 
0 1 0 0 0 0 0 }{CSTYLE "2D Math" -1 2 "Times" 0 1 0 0 0 0 0 0 2 0 0 0 
0 0 0 1 }{CSTYLE "2D Output" 2 20 "" 0 1 0 0 255 1 0 0 0 0 0 0 0 0 0 
1 }{CSTYLE "" -1 256 "" 1 18 10 0 0 0 0 1 0 0 0 0 0 0 0 0 }{CSTYLE "" 
-1 257 "System" 0 1 0 0 80 0 0 0 0 0 0 0 0 0 0 0 }{CSTYLE "" -1 258 "
" 0 1 0 0 0 0 0 1 0 0 0 0 0 0 0 0 }{PSTYLE "Normal" -1 0 1 {CSTYLE "" 
-1 -1 "" 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 }0 0 0 -1 -1 -1 0 0 0 0 0 0 
-1 0 }{PSTYLE "Heading 1" 0 3 1 {CSTYLE "" -1 -1 "" 1 18 0 0 0 0 0 1 
0 0 0 0 0 0 0 0 }1 0 0 0 6 6 0 0 0 0 0 0 -1 0 }{PSTYLE "Maple Output" 
0 11 1 {CSTYLE "" -1 -1 "" 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 }3 3 0 -1 
-1 -1 0 0 0 0 0 0 -1 0 }{PSTYLE "Maple Plot" 0 13 1 {CSTYLE "" -1 -1 "
" 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 }3 0 0 -1 -1 -1 0 0 0 0 0 0 -1 0 }}
{SECT 0 {EXCHG {PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT 
-1 50 "                                                  " }{TEXT 256 
21 "     Help for rainbow" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "
" 0 "" {TEXT -1 338 "FUNCTION : rb(L,A0);\n\nCALLING SEQUENCE :  rb(L,
A0);\n\nPARAMETERS : L is a list of powers of the generators r1,r2,r3,
r4,f1,f2,f3,f4,f5,f6,f7,f8 of the masterball.\nA0 is a 4x8 array of in
tegers in the range 1, ..., 8 (the \"color array\").\n\nSYNOPSIS : Thi
s program creates a 3d polygonplot of a sphere representing a \"geomas
ter\" masterball (c)" }}{PARA 0 "" 0 "" {TEXT -1 66 "obtained by movin
g the masterball associated to A0 by the move L.\n" }}{PARA 0 "" 0 "" 
{TEXT -1 5 "Uses " }{TEXT 257 11 "rainbow.mpl" }{TEXT -1 9 " and the \+
" }{TEXT 258 5 "plots" }{TEXT -1 9 " package\n" }}}{EXCHG {PARA 0 "> \+
" 0 "" {MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 26 "
with(plots):\nwith(linalg):" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 
44 "read(`/home/wdj/maplefiles/rainbow_v7.mpl`):" }}}{SECT 0 {PARA 3 "
" 0 "" {TEXT -1 8 "Examples" }}{EXCHG {PARA 0 "" 0 "" {TEXT -1 50 "To \+
see the masterball in the solved position, type" }}}{EXCHG {PARA 0 "> \+
" 0 "" {MPLTEXT 1 0 9 "rb(1,A0);" }}{PARA 13 "" 1 "" {GLPLOT3D 400 
300 300 {PLOTDATA 3 "6B-%)POLYGONSG6%7&7%$\"+[U&ol&!\"*F($\"+5y1rqF*7%
$\"\"!F/$\"\")F/F+7%F.$\"#5F/F.7%F+F+F.-%'COLOURG6&%$RGBG$\"*++++\"!\"
)F.F.-%&STYLEG6#%&PATCHG-F$6%7&F-7%$!+[U&ol&F*F(F+7%$!+5y1rqF*F+F.F2-F
76&F9F.F.F:F=-F$6%7&FD7%$F<F/F.F+7%$!#5F/F.F.FG-F76&F9F:$\")AR!)\\F<F.
F=-F$6%7&FO7%FEFEF+7%FHFHF.FQ-F76&F9$\")1Zw\"*F<$\")PJ%y'F<FinF=-F$6%7
&Fen7%F.FPF+7%F.FRF.Ffn-F76&F9F.F:F.F=-F$6%7&F`o7%F(FEF+7%F+FHF.Fao-F7
6&F9F:F:F.F=-F$6%7&Fgo7%F0F.F+7%F3F.F.Fho-F76&F9F.F:F:F=-F$6%7&F^pF'F5
F_p-%&COLORG6&F9$\"%2c!\"%$\"%stFjpFhpF=-F$6%7%F'F-7%F.F.F3F6F=-F$6%7%
F-FDF`qFJF=-F$6%7%FDFOF`qFTF=-F$6%7%FOFenF`qFgnF=-F$6%7%FenF`oF`qFboF=
-F$6%7%F`oFgoF`qFioF=-F$6%7%FgoF^pF`qF`pF=-F$6%7%F^pF'F`qFepF=-F$6%7&7
%F(F(FH7%F.F0FHF2F5F6F=-F$6%7&Fjr7%FEF(FHFGF2FJF=-F$6%7&F^s7%FPF.FHFQF
GFTF=-F$6%7&Fbs7%FEFEFHFfnFQFgnF=-F$6%7&Ffs7%F.FPFHFaoFfnFboF=-F$6%7&F
js7%F(FEFHFhoFaoFioF=-F$6%7&F^t7%F0F.FHF_pFhoF`pF=-F$6%7&FbtFirF5F_pFe
pF=-F$6%7%FirFjr7%F.F.FRF6F=-F$6%7%FjrF^sFitFJF=-F$6%7%F^sFbsFitFTF=-F
$6%7%FbsFfsFitFgnF=-F$6%7%FfsFjsFitFboF=-F$6%7%FjsF^tFitFioF=-F$6%7%F^
tFbtFitF`pF=-F$6%7%FbtFirFitFepF=" 1 2 0 1 10 0 2 1 1 1 2 1.000000 
84.000000 33.000000 0 0 "Curve 1" "Curve 2" "Curve 3" "Curve 4" "Curve
 5" "Curve 6" "Curve 7" "Curve 8" "Curve 9" "Curve 10" "Curve 11" "Cur
ve 12" "Curve 13" "Curve 14" "Curve 15" "Curve 16" "Curve 17" "Curve 1
8" "Curve 19" "Curve 20" "Curve 21" "Curve 22" "Curve 23" "Curve 24" "
Curve 25" "Curve 26" "Curve 27" "Curve 28" "Curve 29" "Curve 30" "Curv
e 31" "Curve 32" }}}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 76 "To see the ma
sterball after moving r1 then r2 from the solved position, type" }}}
{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 15 "rb([r1,r2],A0);" }}{PARA 13 
"" 1 "" {GLPLOT3D 400 300 300 {PLOTDATA 3 "6B-%)POLYGONSG6%7&7%$\"+[U&
ol&!\"*F($\"+5y1rqF*7%$\"\"!F/$\"\")F/F+7%F.$\"#5F/F.7%F+F+F.-%'COLOUR
G6&%$RGBGF.F.$\"*++++\"!\")-%&STYLEG6#%&PATCHG-F$6%7&F-7%$!+[U&ol&F*F(
F+7%$!+5y1rqF*F+F.F2-F76&F9F:$\")AR!)\\F<F.F=-F$6%7&FD7%$F<F/F.F+7%$!#
5F/F.F.FG-F76&F9$\")1Zw\"*F<$\")PJ%y'F<FXF=-F$6%7&FQ7%FEFEF+7%FHFHF.FS
-F76&F9F.F:F.F=-F$6%7&Fin7%F.FRF+7%F.FTF.Fjn-F76&F9F:F:F.F=-F$6%7&F`o7
%F(FEF+7%F+FHF.Fao-F76&F9F.F:F:F=-F$6%7&Fgo7%F0F.F+7%F3F.F.Fho-%&COLOR
G6&F9$\"%2c!\"%$\"%stFepFcpF=-F$6%7&F^pF'F5F_p-F76&F9F:F.F.F=-F$6%7%F'
F-7%F.F.F3F6F=-F$6%7%F-FDF`qFJF=-F$6%7%FDFQF`qFVF=-F$6%7%FQFinF`qF[oF=
-F$6%7%FinF`oF`qFboF=-F$6%7%F`oFgoF`qFioF=-F$6%7%FgoF^pF`qF`pF=-F$6%7%
F^pF'F`qF[qF=-F$6%7&7%F(F(FH7%F.F0FHF2F5F[qF=-F$6%7&Fjr7%FEF(FHFGF2F6F
=-F$6%7&F^s7%FRF.FHFSFGFJF=-F$6%7&Fbs7%FEFEFHFjnFSFVF=-F$6%7&Ffs7%F.FR
FHFaoFjnF[oF=-F$6%7&Fjs7%F(FEFHFhoFaoFboF=-F$6%7&F^t7%F0F.FHF_pFhoFioF
=-F$6%7&FbtFirF5F_pF`pF=-F$6%7%FirFjr7%F.F.FTF[qF=-F$6%7%FjrF^sFitF6F=
-F$6%7%F^sFbsFitFJF=-F$6%7%FbsFfsFitFVF=-F$6%7%FfsFjsFitF[oF=-F$6%7%Fj
sF^tFitFboF=-F$6%7%F^tFbtFitFioF=-F$6%7%FbtFirFitF`pF=" 1 2 0 1 10 0 
2 1 1 1 2 1.000000 45.000000 45.000000 0 0 "Curve 1" "Curve 2" "Curve \+
3" "Curve 4" "Curve 5" "Curve 6" "Curve 7" "Curve 8" "Curve 9" "Curve \+
10" "Curve 11" "Curve 12" "Curve 13" "Curve 14" "Curve 15" "Curve 16" 
"Curve 17" "Curve 18" "Curve 19" "Curve 20" "Curve 21" "Curve 22" "Cur
ve 23" "Curve 24" "Curve 25" "Curve 26" "Curve 27" "Curve 28" "Curve 2
9" "Curve 30" "Curve 31" "Curve 32" }}}}{EXCHG {PARA 0 "" 0 "" {TEXT 
-1 173 " To see more precisely how a move affects the individual facet
s, there is a \"text only\" option. We use the matrix for the solved m
asterball already entered into rainbow.mpl:" }}}{EXCHG {PARA 0 "> " 0 
"" {MPLTEXT 1 0 10 "evalm(A0);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#-%'m
atrixG6#7&7*\"\"\"\"\"#\"\"$\"\"%\"\"&\"\"'\"\"(\"\")F'F'F'" }}}
{EXCHG {PARA 0 "" 0 "" {TEXT -1 45 "To see the effect of r1 then r2 on
 this, type" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 32 "A1:=move([r1
,r2],A0): evalm(A1);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#-%'matrixG6#7&
7*\"\"#\"\"$\"\"%\"\"&\"\"'\"\"(\"\")\"\"\"F'7*F/F(F)F*F+F,F-F.F0" }}}
{EXCHG {PARA 0 "" 0 "" {TEXT -1 78 "Some prettier examples (the ideas \+
for these moves are due to Andrew Southern):" }}}{EXCHG {PARA 0 "> " 
0 "" {MPLTEXT 1 0 78 "banded:=[r3^(-4),r1^(-4),f1,r3^(2),r1^(2),f2,r3^
(2),r1^(2),f3]:\nrb(banded,A0);" }}{PARA 13 "" 1 "" {GLPLOT3D 400 300 
300 {PLOTDATA 3 "6B-%)POLYGONSG6%7&7%$\"+[U&ol&!\"*F($\"+5y1rqF*7%$\"
\"!F/$\"\")F/F+7%F.$\"#5F/F.7%F+F+F.-%&COLORG6&%$RGBG$\"%2c!\"%$\"%stF
<F:-%&STYLEG6#%&PATCHG-F$6%7&F-7%$!+[U&ol&F*F(F+7%$!+5y1rqF*F+F.F2-%'C
OLOURG6&F9$\"*++++\"!\")$\")AR!)\\FQF.F?-F$6%7&FF7%$FQF/F.F+7%$!#5F/F.
F.FIFLF?-F$6%7&FW7%FGFGF+7%FJFJF.FY-FM6&F9$\")1Zw\"*FQ$\")PJ%y'FQF]oF?
-F$6%7&Fin7%F.FXF+7%F.FZF.FjnF[oF?-F$6%7&Fdo7%F(FGF+7%F+FJF.Feo-FM6&F9
F.FOFOF?-F$6%7&Fio7%F0F.F+7%F3F.F.FjoF[pF?-F$6%7&F`pF'F5FapF6F?-F$6%7%
F'F-7%F.F.F3-FM6&F9F.FOF.F?-F$6%7%F-FFFhp-FM6&F9FOFOF.F?-F$6%7%FFFWFhp
F^qF?-F$6%7%FWFinFhp-FM6&F9FOF.F.F?-F$6%7%FinFdoFhpFfqF?-F$6%7%FdoFioF
hp-FM6&F9F.F.FOF?-F$6%7%FioF`pFhpF^rF?-F$6%7%F`pF'FhpFipF?-F$6%7&7%F(F
(FJ7%F.F0FJF2F5FipF?-F$6%7&Fjr7%FGF(FJFIF2F^qF?-F$6%7&F^s7%FXF.FJFYFIF
^qF?-F$6%7&Fbs7%FGFGFJFjnFYFfqF?-F$6%7&Ffs7%F.FXFJFeoFjnFfqF?-F$6%7&Fj
s7%F(FGFJFjoFeoF^rF?-F$6%7&F^t7%F0F.FJFapFjoF^rF?-F$6%7&FbtFirF5FapFip
F?-F$6%7%FirFjr7%F.F.FZF6F?-F$6%7%FjrF^sFitFLF?-F$6%7%F^sFbsFitFLF?-F$
6%7%FbsFfsFitF[oF?-F$6%7%FfsFjsFitF[oF?-F$6%7%FjsF^tFitF[pF?-F$6%7%F^t
FbtFitF[pF?-F$6%7%FbtFirFitF6F?" 1 2 0 1 10 0 2 1 1 1 2 1.000000 
65.000000 -58.000000 0 0 "Curve 1" "Curve 2" "Curve 3" "Curve 4" "Curv
e 5" "Curve 6" "Curve 7" "Curve 8" "Curve 9" "Curve 10" "Curve 11" "Cu
rve 12" "Curve 13" "Curve 14" "Curve 15" "Curve 16" "Curve 17" "Curve \+
18" "Curve 19" "Curve 20" "Curve 21" "Curve 22" "Curve 23" "Curve 24" 
"Curve 25" "Curve 26" "Curve 27" "Curve 28" "Curve 29" "Curve 30" "Cur
ve 31" "Curve 32" }}}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 3 "and" }}}
{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 82 "quadrant:=[r3^(-4),r4^(-4),f
1,r3^(2),r4^(2),f2,r3^(2),r4^(2),f3]:\nrb(quadrant,A0);" }}{PARA 13 "
" 1 "" {GLPLOT3D 400 300 300 {PLOTDATA 3 "6B-%)POLYGONSG6%7&7%$\"+[U&o
l&!\"*F($\"+5y1rqF*7%$\"\"!F/$\"\")F/F+7%F.$\"#5F/F.7%F+F+F.-%&COLORG6
&%$RGBG$\"%2c!\"%$\"%stF<F:-%&STYLEG6#%&PATCHG-F$6%7&F-7%$!+[U&ol&F*F(
F+7%$!+5y1rqF*F+F.F2-%'COLOURG6&F9$\"*++++\"!\")$\")AR!)\\FQF.F?-F$6%7
&FF7%$FQF/F.F+7%$!#5F/F.F.FIFLF?-F$6%7&FW7%FGFGF+7%FJFJF.FY-FM6&F9$\")
1Zw\"*FQ$\")PJ%y'FQF]oF?-F$6%7&Fin7%F.FXF+7%F.FZF.FjnF[oF?-F$6%7&Fdo7%
F(FGF+7%F+FJF.Feo-FM6&F9F.FOFOF?-F$6%7&Fio7%F0F.F+7%F3F.F.FjoF[pF?-F$6
%7&F`pF'F5FapF6F?-F$6%7%F'F-7%F.F.F3F6F?-F$6%7%F-FFFhpFLF?-F$6%7%FFFWF
hpFLF?-F$6%7%FWFinFhpF[oF?-F$6%7%FinFdoFhpF[oF?-F$6%7%FdoFioFhpF[pF?-F
$6%7%FioF`pFhpF[pF?-F$6%7%F`pF'FhpF6F?-F$6%7&7%F(F(FJ7%F.F0FJF2F5-FM6&
F9F.FOF.F?-F$6%7&Fbr7%FGF(FJFIF2-FM6&F9FOFOF.F?-F$6%7&Fhr7%FXF.FJFYFIF
irF?-F$6%7&F^s7%FGFGFJFjnFY-FM6&F9FOF.F.F?-F$6%7&Fbs7%F.FXFJFeoFjnFcsF
?-F$6%7&Fhs7%F(FGFJFjoFeo-FM6&F9F.F.FOF?-F$6%7&F\\t7%F0F.FJFapFjoF]tF?
-F$6%7&FbtFarF5FapFcrF?-F$6%7%FarFbr7%F.F.FZFcrF?-F$6%7%FbrFhrFitFirF?
-F$6%7%FhrF^sFitFirF?-F$6%7%F^sFbsFitFcsF?-F$6%7%FbsFhsFitFcsF?-F$6%7%
FhsF\\tFitF]tF?-F$6%7%F\\tFbtFitF]tF?-F$6%7%FbtFarFitFcrF?" 1 2 0 1 
10 0 2 1 1 1 2 1.000000 45.000000 45.000000 0 0 "Curve 1" "Curve 2" "C
urve 3" "Curve 4" "Curve 5" "Curve 6" "Curve 7" "Curve 8" "Curve 9" "C
urve 10" "Curve 11" "Curve 12" "Curve 13" "Curve 14" "Curve 15" "Curve
 16" "Curve 17" "Curve 18" "Curve 19" "Curve 20" "Curve 21" "Curve 22
" "Curve 23" "Curve 24" "Curve 25" "Curve 26" "Curve 27" "Curve 28" "C
urve 29" "Curve 30" "Curve 31" "Curve 32" }}}}{EXCHG {PARA 0 "" 0 "" 
{TEXT -1 3 "and" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 389 "move1:=
[r1,r3,f1,r3^(-1),r1^(-1),f7,f2]:\nmove2:=[r1,r3,f1,r3^(-1),r1^(-1),f1
]:\nmove3:=[r1,r3,f3,r1^(-1),r3^(-1),f4,f5]:\nmove4:=[r1,r3,f2,r1^(-1)
,r3^(-1),f2]:\nmove5:=[f3,f4,f5,f6,f3,f4,f5,f6,r1,r2,r3,r4]: #this swa
ps columns 1,2\nmove6:=[f4,f5,f6,f7,f4,f5,f6,f7,r1,r2,r3,r4]: #this sw
aps columns 2,3\ncheckered:=[op(move1),op(move2),op(move3),op(move4),o
p(move5),op(move6)]:\nrb(checkered,A0);" }}{PARA 13 "" 1 "" {GLPLOT3D 
400 300 300 {PLOTDATA 3 "6B-%)POLYGONSG6%7&7%$\"+[U&ol&!\"*F($\"+5y1rq
F*7%$\"\"!F/$\"\")F/F+7%F.$\"#5F/F.7%F+F+F.-%'COLOURG6&%$RGBG$\"*++++
\"!\")$\")AR!)\\F<F.-%&STYLEG6#%&PATCHG-F$6%7&F-7%$!+[U&ol&F*F(F+7%$!+
5y1rqF*F+F.F2-F76&F9$\")1Zw\"*F<$\")PJ%y'F<FNF?-F$6%7&FF7%$F<F/F.F+7%$
!#5F/F.F.FI-F76&F9F:F.F.F?-F$6%7&FU7%FGFGF+7%FJFJF.FW-F76&F9F.F:F.F?-F
$6%7&Fin7%F.FVF+7%F.FXF.Fjn-F76&F9F.F.F:F?-F$6%7&F`o7%F(FGF+7%F+FJF.Fa
o-F76&F9F:F:F.F?-F$6%7&Fgo7%F0F.F+7%F3F.F.Fho-%&COLORG6&F9$\"%2c!\"%$
\"%stFepFcpF?-F$6%7&F^pF'F5F_p-F76&F9F.F:F:F?-F$6%7%F'F-7%F.F.F3FLF?-F
$6%7%F-FFF`qF6F?-F$6%7%FFFUF`qF[oF?-F$6%7%FUFinF`qFZF?-F$6%7%FinF`oF`q
FioF?-F$6%7%F`oFgoF`qFboF?-F$6%7%FgoF^pF`qF[qF?-F$6%7%F^pF'F`qF`pF?-F$
6%7&7%F(F(FJ7%F.F0FJF2F5FLF?-F$6%7&Fjr7%FGF(FJFIF2F6F?-F$6%7&F^s7%FVF.
FJFWFIF[oF?-F$6%7&Fbs7%FGFGFJFjnFWFZF?-F$6%7&Ffs7%F.FVFJFaoFjnFioF?-F$
6%7&Fjs7%F(FGFJFhoFaoFboF?-F$6%7&F^t7%F0F.FJF_pFhoF[qF?-F$6%7&FbtFirF5
F_pF`pF?-F$6%7%FirFjr7%F.F.FXF6F?-F$6%7%FjrF^sFitFLF?-F$6%7%F^sFbsFitF
ZF?-F$6%7%FbsFfsFitF[oF?-F$6%7%FfsFjsFitFboF?-F$6%7%FjsF^tFitFioF?-F$6
%7%F^tFbtFitF`pF?-F$6%7%FbtFirFitF[qF?" 1 2 0 1 10 0 2 1 1 1 2 
1.000000 64.000000 0.000000 0 0 "Curve 1" "Curve 2" "Curve 3" "Curve 4
" "Curve 5" "Curve 6" "Curve 7" "Curve 8" "Curve 9" "Curve 10" "Curve \+
11" "Curve 12" "Curve 13" "Curve 14" "Curve 15" "Curve 16" "Curve 17" 
"Curve 18" "Curve 19" "Curve 20" "Curve 21" "Curve 22" "Curve 23" "Cur
ve 24" "Curve 25" "Curve 26" "Curve 27" "Curve 28" "Curve 29" "Curve 3
0" "Curve 31" "Curve 32" }}}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "
" }}}{PARA 0 "" 0 "" {TEXT -1 0 "" }}}}{MARK "0 5 4" 9 }{VIEWOPTS 1 1 
0 1 1 1803 1 1 1 1 }{PAGENUMBERS 0 1 2 33 1 1 }