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{SECT 0 {EXCHG {PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT 
-1 42 "                                          " }{TEXT 256 7 "     \+
  " }{TEXT 257 7 "Crystal" }{TEXT 258 18 " test worksheet #1" }}{PARA 
0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 20 "12-5-96,cry2tst
1.mws" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 97 " This worksheet will pro
duce the crystal graphs of the standard repns of B5=SO(11) and C5=Sp(1
0)." }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 12 "with(share);" }}
{PARA 6 "" 1 "" {TEXT -1 70 "See ?share and ?share,contents for inform
ation about the share library" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#7\"" 
}}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 27 "readshare(coxeter,algebra
);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#%(coxeterG" }}}{EXCHG {PARA 0 ">
 " 0 "" {MPLTEXT 1 0 55 "read(`d:/maplev4/share/algebra/crystal/crysta
l2.mpl`);\n" }{TEXT -1 83 "This of course must be modified to whatever
 path your machine is using for crystal." }}{PARA 11 "" 1 "" {XPPMATH 
20 "6#%Dtype~init_crystal();~to~initialize.G" }}}{EXCHG {PARA 0 "> " 
0 "" {MPLTEXT 1 0 62 "libname:=libname,`d:\\\\MAPLEV4/share/algebra/cr
ystal/cryhelp`;\n" }{TEXT -1 68 "This changes the path so you can call
 up the crystal help database. " }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%(
libnameG6%%/D:\\MAPLEV4/libG%1D:\\MAPLEV4/shareG%Ic:\\MAPLEV4/share/al
gebra/crystal/cryhelpG" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 8 "?c
rystal" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 38 "coxeter[base](B5)
;\ncoxeter[base](C5);\n" }{TEXT -1 44 "Bases for the root lattices of \+
B5, C5, resp." }}{PARA 11 "" 1 "" {XPPMATH 20 "6#7'%#e1G,&%#e2G\"\"\"F
$!\"\",&%#e3GF'F&F(,&%#e4GF'F*F(,&%#e5GF'F,F(" }}{PARA 11 "" 1 "" 
{XPPMATH 20 "6#7',$%#e1G\"\"#,&%#e2G\"\"\"F%!\"\",&%#e3GF)F(F*,&%#e4GF
)F,F*,&%#e5GF)F.F*" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}
{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 15 "init_crystal():" }}{PARA 11 
"" 1 "" {XPPMATH 20 "6#%5Crystal~initialized.G" }}}{EXCHG {PARA 0 "> \+
" 0 "" {MPLTEXT 1 0 38 "weyl[weights](B5);\nweyl[weights](C5);\n" }
{TEXT -1 46 "Bases for the weight lattices of B5, C5, resp." }
{MPLTEXT 1 0 1 "\n" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#7',,%#e1G#\"\"\"
\"\"#%#e2GF&%#e3GF&%#e4GF&%#e5GF&,*F)F'F*F'F+F'F,F',(F*F'F+F'F,F',&F+F
'F,F'F," }}{PARA 11 "" 1 "" {XPPMATH 20 "6#7',,%#e1G\"\"\"%#e2GF&%#e3G
F&%#e4GF&%#e5GF&,*F'F&F(F&F)F&F*F&,(F(F&F)F&F*F&,&F)F&F*F&F*" }}}
{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 59 "weyl[weyl_dim](e5,B5);\nL1:=
crystal[weight_system](-e5,B5);\n" }{TEXT -1 157 "This assigns to L1 t
he weight system of B5 with highest weight e5. (Crystal, for technical
 reasons, uses the negative of the weights used in coxeter, weyl.) " }
}{PARA 11 "" 1 "" {XPPMATH 20 "6#\"#6" }}{PARA 12 "" 1 "" {XPPMATH 20 
"6#>%#L1G7-7'\"\"!F'F'F'\"\"\"7'F'F'F'F(!\"\"7'F'F'F(F*F'7'F'F(F*F'F'7
'\"\"#F*F'F'F'7'F'F'F'F'F'7'!\"#F(F'F'F'7'F'F*F(F'F'7'F'F'F*F(F'7'F'F'
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weyl_dim](e5,C5);\nL2:=crystal[weight_system](-e5,C5);\n" }}{PARA 11 "
" 1 "" {XPPMATH 20 "6#\"#5" }}{PARA 12 "" 1 "" {XPPMATH 20 "6#>%#L2G7,
7'\"\"!F'F'F'\"\"\"7'F'F'F'F(!\"\"7'F'F'F(F*F'7'F'F(F*F'F'7'F(F*F'F'F'
7'F*F(F'F'F'7'F'F*F(F'F'7'F'F'F*F(F'7'F'F'F'F*F(7'F'F'F'F'F*" }}}
{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 13 "with(plots):\n" }}}{EXCHG 
{PARA 0 "> " 0 "" {MPLTEXT 1 0 29 "crystal[graphrep](L1,B5,G1);\n" }
{TEXT -1 57 "This assigns to the weight system L1 the crystal graph G1
" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#%.Graph~formed.G" }}}{EXCHG {PARA 
0 "> " 0 "" {MPLTEXT 1 0 29 "crystal[graphrep](L2,C5,G2);\n" }{TEXT 
-1 57 "This assigns to the weight system L2 the crystal graph G2" }}
{PARA 11 "" 1 "" {XPPMATH 20 "6#%.Graph~formed.G" }}}{EXCHG {PARA 0 ">
 " 0 "" {MPLTEXT 1 0 28 "crystal[dynkin_diagram](B5);" }}{PARA 13 "" 
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