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{PARA 0 "> " 0 "" {MPLTEXT 1 0 53 "for n from 3 to 14 do SteinhausRota
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" 1 "" {XPPMATH 20 "6#7+\"\"!,(&%\"xG6#\"\"$\"\"\"&F'6#\"\"%F*&F'6#\"
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" {XPPMATH 20 "6#7.,&&%\"xG6#\"\"%\"\"\"&F&6#\"\"(F),(&F&6#\"\"&F)&F&6
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{XPPMATH 20 "6#7/,&&%\"xG6#\"\"%\"\"\"&F&6#\"\")F),(&F&6#\"\"&F)&F&6#
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0 69 "for n from 3 to 25 do if testSR(n)=false then print(n) end if en
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{XPPMATH 20 "6#7/\"\"!&%\"xG6#\"\"%F%,(F%\"\"\"&F&6#\"\"&F*&F&6#\"\"'F
*F%F+F.F+F%F)F%F%F$" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#70\"\"!&%\"xG6#
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{MPLTEXT 1 0 69 "for n from 3 to 25 do if testSD(n)=false then print(n
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6 "Pascal" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 49 "for k from 3 t
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#7%&%\"aG6#\"\"!F'&F%6#\"\"#" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#7&&%\"
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"" 1 "" {XPPMATH 20 "6#7(&%\"aG6#\"\"!&F%6#\"\"\",(F$F*F(F*&F%6#\"\"&F
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" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#7*&%\"aG6#\"\"!&F%6#\"\"\"&F%6#\"
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{PARA 11 "" 1 "" {XPPMATH 20 "6#7,&%\"aG6#\"\"!&F%6#\"\"\"&F%6#\"\"#,&
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%6#\"\"#&F%6#\"\"$,.F$F*F+F*F.F*&F%6#\"#5F*&F%6#\"\"*F*&F%6#\"\"(F*,&F
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{XPPMATH 20 "6#7.&%\"aG6#\"\"!&F%6#\"\"\"&F%6#\"\"#&F%6#\"\"$,,F$F*F.F
*&F%6#\"#6F*&F%6#\"#5F*&F%6#\"\"*F*,.F(F*F+F*F.F*F5F*F8F*&F%6#\"\")F*F
;,,F$F*F(F*F+F*F2F*F<F*F<F8F5F2" }}{PARA 12 "" 1 "" {XPPMATH 20 "6#7/&
%\"aG6#\"\"!&F%6#\"\"\"&F%6#\"\"#&F%6#\"\"$,,F$F*&F%6#\"#7F*&F%6#\"#6F
*&F%6#\"#5F*&F%6#\"\"*F*,(F(F*F.F*F5F*,&F.F*F;F*,(F(F*F5F*F;F*,,F$F*F(
F*F+F*F.F*F2F*F;F8F5F2" }}{PARA 12 "" 1 "" {XPPMATH 20 "6#70&%\"aG6#\"
\"!&F%6#\"\"\"&F%6#\"\"#&F%6#\"\"$&F%6#\"\"%,0F$F*F+F*F.F*&F%6#\"#8F*&
F%6#\"#7F*&F%6#\"#5F*&F%6#\"\"*F*,(F+F*F.F*&F%6#\"#6F*,(F+F*FBF*F;F*,0
F$F*F(F*F.F*F1F*F5F*FBF*F;F*F>F;FBF8F5" }}}{EXCHG {PARA 0 "> " 0 "" 
{MPLTEXT 1 0 69 "for k from 3 to 25 do if testPR(k)=false then print(k
) end if end do;" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 48 "for k f
rom 3 to 14 do PascalDihedral(k); end do;" }}{PARA 11 "" 1 "" 
{XPPMATH 20 "6#7%&%\"aG6#\"\"!F'F$" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#
7&&%\"aG6#\"\"!F'F'F$" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#7'&%\"aG6#\"
\"!&F%6#\"\"\"F'F(F$" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#7(&%\"aG6#\"\"
!&F%6#\"\"\"F(F(F(F$" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#7)&%\"aG6#\"\"
!&F%6#\"\"\"F(F'F(F(F$" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#7*&%\"aG6#\"
\"!&F%6#\"\"\"&F%6#\"\"#,&F(F*F+F*F.F+F(F$" }}{PARA 11 "" 1 "" 
{XPPMATH 20 "6#7+&%\"aG6#\"\"!&F%6#\"\"\"&F%6#\"\"#F'F'F'F+F(F$" }}
{PARA 11 "" 1 "" {XPPMATH 20 "6#7,&%\"aG6#\"\"!&F%6#\"\"\"&F%6#\"\"#F'
,&F(F*F+F*F.F'F+F(F$" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#7-&%\"aG6#\"\"
!&F%6#\"\"\"&F%6#\"\"#&F%6#\"\"$,&F(F*F+F*F'F1F.F+F(F$" }}{PARA 11 "" 
1 "" {XPPMATH 20 "6#7.&%\"aG6#\"\"!&F%6#\"\"\"&F%6#\"\"#&F%6#\"\"$,(F(
F*F+F*F.F*F'F'F1F.F+F(F$" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#7/&%\"aG6#
\"\"!&F%6#\"\"\"&F%6#\"\"#&F%6#\"\"$,(F(F*F+F*F.F*F.F'F.F1F.F+F(F$" }}
{PARA 11 "" 1 "" {XPPMATH 20 "6#70&%\"aG6#\"\"!&F%6#\"\"\"&F%6#\"\"#&F
%6#\"\"$&F%6#\"\"%,(F(F*F+F*F1F*F.F.F4F1F.F+F(F$" }}}{EXCHG {PARA 0 ">
 " 0 "" {MPLTEXT 1 0 69 "for k from 3 to 25 do if testPD(k)=false then
 print(k) end if end do;" }}}{EXCHG {PARA 257 "" 0 "" {TEXT -1 37 "Gen
erating random symmetric triangles" }}}{EXCHG {PARA 0 "> " 0 "" 
{MPLTEXT 1 0 92 "n:=10: L:=RandomSteinhausRotational(n); \nfor i from \+
1 to n do print(steinhaus(L)[i]) end do;" }}{PARA 11 "" 1 "" {XPPMATH 
20 "6#>%\"LG7,\"\"!F&\"\"\"F&F&F&F'F'F&F&" }}{PARA 11 "" 1 "" 
{XPPMATH 20 "6#7,\"\"!F$\"\"\"F$F$F$F%F%F$F$" }}{PARA 11 "" 1 "" 
{XPPMATH 20 "6#7+\"\"!\"\"\"F%F$F$F%F$F%F$" }}{PARA 11 "" 1 "" 
{XPPMATH 20 "6#7*\"\"\"\"\"!F$F%F$F$F$F$" }}{PARA 11 "" 1 "" {XPPMATH 
20 "6#7)\"\"\"F$F$F$\"\"!F%F%" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#7(\"
\"!F$F$\"\"\"F$F$" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#7'\"\"!F$\"\"\"F%
F$" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#7&\"\"!\"\"\"F$F%" }}{PARA 11 "
" 1 "" {XPPMATH 20 "6#7%\"\"\"F$F$" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#
7$\"\"!F$" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#7#\"\"!" }}}{EXCHG {PARA 
0 "> " 0 "" {MPLTEXT 1 0 90 "n:=10: L:=RandomSteinhausDihedral(n); \nf
or i from 1 to n do print(steinhaus(L)[i]) end do;" }}{PARA 11 "" 1 "
" {XPPMATH 20 "6#>%\"LG7,\"\"!F&F&\"\"\"F&F&F'F&F&F&" }}{PARA 11 "" 1 
"" {XPPMATH 20 "6#7,\"\"!F$F$\"\"\"F$F$F%F$F$F$" }}{PARA 11 "" 1 "" 
{XPPMATH 20 "6#7+\"\"!F$\"\"\"F%F$F%F%F$F$" }}{PARA 11 "" 1 "" 
{XPPMATH 20 "6#7*\"\"!\"\"\"F$F%F%F$F%F$" }}{PARA 11 "" 1 "" {XPPMATH 
20 "6#7)\"\"\"F$F$\"\"!F$F$F$" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#7(\"
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F$" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#7&\"\"\"F$F$F$" }}{PARA 11 "" 1 
"" {XPPMATH 20 "6#7%\"\"!F$F$" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#7$\"
\"!F$" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#7#\"\"!" }}}{EXCHG {PARA 0 ">
 " 0 "" {MPLTEXT 1 0 88 "k:=10: L:=RandomPascalRotational(k): \nfor i \+
from 1 to k+1 do print(pascal(L)[i]) end do;" }}{PARA 11 "" 1 "" 
{XPPMATH 20 "6#7$\"\"!\"\"\"" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#7%\"\"
\"F$F$" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#7&\"\"\"\"\"!F%F%" }}{PARA 
11 "" 1 "" {XPPMATH 20 "6#7'\"\"\"F$\"\"!F%F$" }}{PARA 11 "" 1 "" 
{XPPMATH 20 "6#7(\"\"!F$\"\"\"F$F%F%" }}{PARA 11 "" 1 "" {XPPMATH 20 "
6#7)\"\"\"\"\"!F$F$F$F%F%" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#7*\"\"\"F
$F$\"\"!F%F$F%F$" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#7+\"\"!F$F$\"\"\"F
$F%F%F%F%" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#7,\"\"\"\"\"!F%F$F$F$F%F%
F%F$" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#7-\"\"\"F$\"\"!F$F%F%F$F%F%F$F
%" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#7,\"\"!\"\"\"F%F%F$F%F%F$F%F%" }}
}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 86 "k:=10: L:=RandomPascalDihed
ral(k): \nfor i from 1 to k+1 do print(pascal(L)[i]) end do;" }}{PARA 
11 "" 1 "" {XPPMATH 20 "6#7$\"\"\"F$" }}{PARA 11 "" 1 "" {XPPMATH 20 "
6#7%\"\"\"\"\"!F$" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#7&\"\"!\"\"\"F%F$
" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#7'\"\"!\"\"\"F$F%F$" }}{PARA 11 "
" 1 "" {XPPMATH 20 "6#7(\"\"\"F$F$F$F$F$" }}{PARA 11 "" 1 "" {XPPMATH 
20 "6#7)\"\"\"\"\"!F%F%F%F%F$" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#7*\"
\"!\"\"\"F$F$F$F$F%F$" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#7+\"\"!\"\"\"
F%F$F$F$F%F%F$" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#7,\"\"\"F$\"\"!F$F%F
%F$F%F$F$" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#7-\"\"\"\"\"!F$F$F$F%F$F$
F$F%F$" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#7,\"\"\"F$\"\"!F%F$F$F%F%F$F
$" }}}{EXCHG {PARA 0 "" 0 "" {TEXT 256 45 "Generating all symmetric tr
iangles of a class" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 310 "# Ac
cording to the dimension, the number of structures.\n# N:nomber  S:Ste
inhaus  P:Pascal  R:Rotational  D:dihedral\nNSR:=proc(k) 2^(floor(k/3)
+((k mod 3) mod 2)) end: \nNSD:=proc(k)  2^ceil((floor(k/3)+((k mod 3)
 mod 2))/2) end: \nNPR:=proc(k) 2^(2*floor((k+1)/3)) end: \nNPD:=proc(
k) 2^(floor((2*k+3)/6)) end:   " }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 
1 0 45 "n:=11: T:=GeneratingAllSR(n); nops(T)=NSR(n);" }}{PARA 12 "" 
1 "" {XPPMATH 20 "6#>%\"TG7*7-\"\"!F'F'F'F'F'F'F'F'F'F'7-\"\"\"F'F)F)F
)F'F'F)F'F)F)7-F'F'F'F)F'F)F'F)F'F'F'7-F)F'F)F'F)F)F'F'F'F)F)7-F)F)F'F
)F'F'F)F)F)F'F)7-F'F)F)F'F)F'F)F'F)F)F'7-F)F)F'F'F'F)F)F'F)F'F)7-F'F)F
)F)F)F)F)F)F)F)F'" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#/\"\")F$" }}}
{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 45 "n:=12: T:=GeneratingAllSD(n)
; nops(T)=NSD(n);" }}{PARA 12 "" 1 "" {XPPMATH 20 "6#>%\"TG7&7.\"\"!F'
F'F'F'F'F'F'F'F'F'F'7.F'\"\"\"F)F)F)F'F'F)F)F)F)F'7.F'F'F'F'F'F)F)F'F'
F'F'F'7.F'F)F)F)F)F)F)F)F)F)F)F'" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#/
\"\"%F$" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 44 "k:=7: T:=Generat
ingAllPR(k); nops(T)=NPR(k);" }}{PARA 12 "" 1 "" {XPPMATH 20 "6#>%\"TG
727)\"\"!F'F'F'F'F'F'7)\"\"\"F'F)F'F)F'F'7)F'F)F'F'F)F'F'7)F)F)F)F'F'F
'F'7)F'F'F)F'F'F)F'7)F)F'F'F'F)F)F'7)F'F)F)F'F)F)F'7)F)F)F'F'F'F)F'7)F
'F'F)F'F)F'F)7)F)F'F'F'F'F'F)7)F'F)F)F'F'F'F)7)F)F)F'F'F)F'F)7)F'F'F'F
'F)F)F)7)F)F'F)F'F'F)F)7)F'F)F'F'F'F)F)7)F)F)F)F'F)F)F)" }}{PARA 11 "
" 1 "" {XPPMATH 20 "6#/\"#;F$" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 
0 44 "k:=8: T:=GeneratingAllPD(k); nops(T)=NPD(k);" }}{PARA 12 "" 1 "
" {XPPMATH 20 "6#>%\"TG7*7*\"\"!F'F'F'F'F'F'F'7*\"\"\"F'F'F'F'F'F'F)7*
F'F)F'F)F)F'F)F'7*F)F)F'F)F)F'F)F)7*F'F'F)F)F)F)F'F'7*F)F'F)F)F)F)F'F)
7*F'F)F)F'F'F)F)F'7*F)F)F)F'F'F)F)F)" }}{PARA 11 "" 1 "" {XPPMATH 20 "
6#/\"\")F$" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{PARA 11 
"" 1 "" {TEXT -1 0 "" }}}{MARK "20 0 0" 0 }{VIEWOPTS 0 1 0 1 1 1803 1 
1 1 1 }{PAGENUMBERS 0 1 2 33 1 1 }