HUB is a system devoted to distribute computations in Algebraic Combinatorics from Maple. It was developped in collaboration with Christophe Carré (Université of Rouen). It has been demonstrated at the 9-th International Conference on Formal Power Series and Algebraic Combinatorics, 1997: HUB.SFCA97 (in French, 85Kb). HUB is not available even if it has shown its fantastic possibilities as illustrated by the following lines.
This file is a demonstration of the possibilities of the HUB system compared to some of the ACE 3.0 possibilities. HUB is able to contact several computers in order to distribute computations on different servers. Some ACE 3.0 functions are now recovered by SYMMETRICA or C functions. It has also the possibility to run several computations in parallel and in background (from a Maple session !!!). All these points are illustrated in the next lines. All computations were easily done with HUB:
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#
# ACE 3.0, for Maple V Release 1,2,3 and 4...
#
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> with(ACE):
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#
# New functionalities on permutations...
#
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> ListPerm(3, 'level');
[[[1, 2, 3]], [[1, 3, 2], [2, 1, 3]], [[3, 1, 2], [2, 3, 1]], [[3, 2, 1]]]
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> ListPerm(6, 'nb', 'level');
[1, 5, 14, 29, 49, 71, 90, 101, 101, 90, 71, 49, 29, 14, 5, 1]
> ListPerm(5, 'vexillary', 'nb', 'level');
[1, 4, 6, 11, 16, 18, 18, 15, 9, 4, 1]
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#
# New package on partitions (Vincent Prosper)...
#
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> ListPartIn([40,30,15,10,8,7,5,3,1], 'nb');
9631414
> ListPart(5, 'maxpart'=[3,2], 'maxlg'=3);
[[3, 2], [3, 1, 1], [2, 2, 1]]
> lsp:=ListSkewDiag(3);
lsp := [[[3], []], [[3, 1], [1]], [[3, 2], [2]], [[3, 2, 1], [2, 1]],
[[2, 1], []], [[2, 2], [1]], [[2, 2, 1], [1, 1]], [[2, 1, 1], [1]],
[[1, 1, 1], []]]
> map(SkewPart2Mat, lsp, 'alphabet'=[`*`,`.`,` `]);
[ * ]
[ * ] [ * * ] [ ] [ * ] [ * * ]
[[ * * * ], [ ], [ ], [ . * ], [ ], [ ],
[ . * * ] [ . . * ] [ ] [ * * ] [ . * ]
[ . . * ]
[ * ] [ * ] [ * ]
[ ] [ ] [ ]
[ . * ], [ * ], [ * ]]
[ ] [ ] [ ]
[ . * ] [ . * ] [ * ]
> ListSkewDiag(11, 'maxlg'=5, 'nb');
9695
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#
# New package to handle compositions (Vincent Prosper)...
#
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> lc:=ListCompo(4);
lc :=
[[4], [3, 1], [2, 2], [2, 1, 1], [1, 3], [1, 2, 1], [1, 1, 2], [1, 1, 1, 1]]
> map(Compo2Mat, lc, 'alphabet'=[`*`,`.`,` `]);
[ * ] [ * ]
[ * ] [ * * ] [ ] [ * * * ] [ ]
[[ * * * * ], [ ], [ ], [ * ], [ ], [ * * ],
[ * * * ] [ . * * ] [ ] [ . . * ] [ ]
[ * * ] [ . * ]
[ * ]
[ * * ] [ ]
[ ] [ * ]
[ . * ], [ ]]
[ ] [ * ]
[ . * ] [ ]
[ * ]
> ListCompo(20, 'lg'<=10, 'nb');
262144
> ListCompo(5, 'maxouter'=[4,3], 'allowzeros', 'lg'<=4);
[[4, 1], [4, 1, 0], [4, 1, 0, 0], [3, 2], [3, 2, 0], [3, 2, 0, 0], [2, 3],
[2, 3, 0], [2, 3, 0, 0]]
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#
# New package on words (Sebastien Veigneau)...
#
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> FreeShuffle(w[2,1] + w[2,1], w[1,1]);
6 w[2, 1, 1, 1] + 4 w[1, 2, 1, 1] + 2 w[1, 1, 2, 1]
> Free2Plax(");
12 w[2, 1, 1, 1]
> Free2PlaxClass(w[2,1,1,1]);
w[2, 1, 1, 1] + w[1, 2, 1, 1] + w[1, 1, 2, 1]
> wrd:=w[2,1,1]+w[3,1,1]+w[2,1,2]+w[3,1,2]+w[2,1,3]+w[3,1,3]+w[3,2,2]+w[3,2,3]:
> CLG_n(3): x2m_n(Free2Pol(wrd));
m[2, 1] + 2 m[1, 1, 1]
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#
# New functionalities on Schubert polynomials...
#
--------------------------------------------------------------------------------
> A:=TableX(3, Pe);
A := table([
[2, 3, 1] = Pe[2, 0, 0]
[1, 2, 3] = Pe[0]
[3, 2, 1] = Pe[2, 1, 0]
[3, 1, 2] = Pe[1, 1, 0] - Pe[2, 0, 0]
[2, 1, 3] = Pe[1, 0]
[1, 3, 2] = Pe[1, 0, 0]
])
> ToX(X[3,2,4,1]*X[1,4,3,2]);
X[3, 5, 4, 1, 2] + X[5, 2, 4, 1, 3] + X[4, 5, 2, 1, 3]
> ToXX(XX[2,3,4,1]*XX[4,1,3,2], 'collect');
2
(- y1 y3 + y3 y4 - y1 y4 + y1 ) XX[4, 2, 3, 1] + (y3 - y1) XX[5, 2, 3, 1, 4]
+ (y4 - y1) XX[4, 2, 5, 1, 3] + XX[5, 2, 4, 1, 3]
> ToX(X[4,5,1,7,2,6,3]^2*X[3,4,1,5,2]);
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#
# Too slow !!!! ..... maybe with HUB ????
#
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> restart:
> with(HUB):
> ipprefix:=`***.***.***.`: # does not matter for this example file...
> HubInit(9999, [seq(cat(ipprefix,ip),\
ip=[`01`,`02`,`03`,`04`,`05`,`06`,`07`, 08])],\
[hub$8], [`HUB/BIN`$8], `rsh`,\
[2521$8], [2522$8]):
> HubSetEcho(1):
> for i from 1 to nops([indices(`HUB/__SERVERS/set`)]) do\
HubServer(enable=i)\
od:
> for i in `HUB/__PossiblyActivated` do\
HubEnable(i)\
od:
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#
# Services on Schubert polynomials...
#
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> res:=Tox(X[4,5,1,7,2,6,3]^2*X[3,4,1,5,2]):
*
> res;
8 9 4 2 8 9 3 3 8 8 5 2
20 x1 x2 x4 x5 x3 x6 + 24 x1 x2 x4 x5 x3 x6 + 10 x1 x2 x4 x5 x3 x6
8 10 2 4 9 9 3 4 8 10 2 2 3
+ 6 x1 x2 x3 x4 x5 + 6 x1 x2 x3 x4 + 5 x1 x2 x3 x5 x4
8 10 3 2 2 9 9 4 2 9 9 2 3 2
+ 5 x1 x2 x3 x5 x4 + 6 x1 x2 x3 x4 x6 + 10 x1 x2 x3 x4 x6
9 9 4 9 9 2 3
+ 12 x1 x2 x3 x4 x6 x5 + 20 x1 x2 x3 x4 x6 x5
9 9 3 2 9 9 4
+ 20 x1 x2 x3 x5 x4 x6 + 12 x1 x2 x3 x5 x4 x6
8 10 2 3 10 8 3 2
+ 10 x1 x2 x3 x5 x4 x6 + 10 x1 x2 x3 x4 x6 x5
8 10 3 2 9 9 5 10 8 5
+ 10 x1 x2 x3 x5 x4 x6 + 4 x1 x2 x4 x6 x5 + 2 x1 x2 x4 x6 x5
10 8 4 10 8 5 8 10 5 2
+ 6 x1 x2 x4 x6 x5 x3 + 2 x1 x2 x3 x5 x6 + x1 x2 x4 x6
8 10 4 2 8 10 5 8 10 4
+ 3 x1 x2 x4 x6 x3 + 2 x1 x2 x4 x6 x5 + 6 x1 x2 x4 x6 x5 x3
10 8 4 9 9 2 3 2 10 8 2 3 2
+ 6 x1 x2 x3 x5 x6 x4 + 10 x1 x2 x3 x4 x5 + 5 x1 x2 x3 x4 x5
10 8 3 3 10 8 3 2 2 9 9 5 2
+ 8 x1 x2 x3 x4 x5 + 5 x1 x2 x3 x4 x5 + 2 x1 x2 x4 x6
9 9 5 2 9 9 4 2 10 8 4 3
+ 2 x1 x2 x4 x5 + 6 x1 x2 x4 x5 x3 + 3 x1 x2 x3 x4
9 9 3 2 2 10 8 5 2 10 8 4 2
+ 10 x1 x2 x3 x5 x4 + x1 x2 x4 x5 + 3 x1 x2 x4 x5 x3
10 8 5 10 8 4 2 8 10 5 2
+ 2 x1 x2 x4 x5 x3 + 6 x1 x2 x4 x5 x3 + x1 x2 x4 x5
10 8 5 2 9 9 5 8 10 4 2
+ x1 x2 x3 x6 + 4 x1 x2 x4 x5 x3 + 3 x1 x2 x4 x5 x3
10 8 4 2 10 8 5 10 8 5 2
+ 6 x1 x2 x3 x4 x6 + 2 x1 x2 x3 x4 x6 + x1 x2 x3 x4
10 8 4 2 10 8 5 2 10 8 4 2
+ 3 x1 x2 x3 x5 x4 + x1 x2 x3 x5 + 6 x1 x2 x3 x5 x4
10 8 5 8 9 6 8 8 4 4
+ 2 x1 x2 x3 x5 x4 + 4 x1 x2 x4 x5 x3 + 12 x1 x2 x4 x5 x3
8 10 3 4 8 9 5 3 8 9 6 2
+ 3 x1 x2 x3 x4 + 6 x1 x2 x3 x4 + 2 x1 x2 x3 x4
10 8 2 5 10 8 3 4 10 8 4 2
+ x1 x2 x3 x4 + 3 x1 x2 x3 x4 + 3 x1 x2 x3 x6 x4
8 8 7 8 8 5 3 8 10 4 3
+ 2 x1 x2 x4 x5 x3 + 10 x1 x2 x4 x5 x3 + 3 x1 x2 x3 x4
8 10 5 2 8 9 5 2 8 9 4 3
+ x1 x2 x3 x4 + 12 x1 x2 x4 x5 x3 + 18 x1 x2 x4 x5 x3
8 8 7 8 8 6 9 8 6 2
+ 2 x1 x2 x4 x5 x6 + 6 x1 x2 x4 x5 x6 x3 + 2 x1 x2 x4 x5
8 8 7 2 8 8 6 2 9 8 6
+ x1 x2 x4 x5 + 3 x1 x2 x4 x5 x3 + 4 x1 x2 x4 x5 x6
8 9 4 2 2 8 9 3 2 3 9 8 5
+ 10 x1 x2 x4 x5 x3 + 12 x1 x2 x4 x5 x3 + 12 x1 x2 x4 x5 x3 x6
8 8 6 2 8 8 3 4 9 9 5
+ 6 x1 x2 x4 x5 x3 + 14 x1 x2 x4 x5 x3 x6 + 4 x1 x2 x3 x4 x6
9 9 2 4 8 9 6 8 9 5
+ 12 x1 x2 x3 x4 x5 + 4 x1 x2 x4 x5 x6 + 12 x1 x2 x4 x5 x6 x3
9 8 6 9 8 4 2 9 8 3 3
+ 4 x1 x2 x4 x5 x3 + 20 x1 x2 x4 x5 x3 x6 + 24 x1 x2 x4 x5 x3 x6
9 9 2 4 9 9 4 2 9 9 5
+ 12 x1 x2 x3 x4 x6 + 12 x1 x2 x3 x4 x5 + 4 x1 x2 x3 x4 x5
9 9 4 3 9 9 5 2 8 10 5
+ 6 x1 x2 x3 x4 + 2 x1 x2 x3 x4 + 2 x1 x2 x3 x4 x5
8 10 2 4 10 8 3 3 10 8 5
+ 6 x1 x2 x3 x4 x6 + 8 x1 x2 x4 x6 x3 + 2 x1 x2 x4 x6 x3
9 8 4 3 8 9 5 2 10 8 4 2
+ 18 x1 x2 x4 x5 x3 + 6 x1 x2 x4 x5 x3 + 3 x1 x2 x4 x6 x3
8 9 2 5 8 9 3 4 9 8 5 2
+ 12 x1 x2 x3 x4 x6 + 18 x1 x2 x3 x4 x6 + 6 x1 x2 x4 x5 x3
9 8 4 2 2 9 8 3 2 3 8 10 4 2
+ 10 x1 x2 x4 x5 x3 + 12 x1 x2 x4 x5 x3 + 6 x1 x2 x3 x4 x6
8 10 3 3 8 10 4 2 8 9 6 2
+ 8 x1 x2 x3 x4 x5 + 6 x1 x2 x3 x4 x5 + 2 x1 x2 x4 x5
8 8 4 3 8 8 4 2 3 8 8 3 2 4
+ 14 x1 x2 x4 x5 x3 x6 + 7 x1 x2 x4 x5 x3 + 7 x1 x2 x4 x5 x3
8 8 5 2 2 10 8 5 2 8 10 3 3
+ 5 x1 x2 x4 x5 x3 + x1 x2 x4 x6 + 8 x1 x2 x3 x4 x6
8 10 5 9 8 5 2 10 8 4 2
+ 2 x1 x2 x3 x4 x6 + 12 x1 x2 x4 x5 x3 + 6 x1 x2 x4 x6 x3
10 8 3 2 2 10 8 2 2 3 9 9 4 2
+ 5 x1 x2 x4 x6 x3 + 5 x1 x2 x4 x6 x3 + 6 x1 x2 x3 x5 x4
9 9 5 2 9 9 3 3 9 9 4 2
+ 2 x1 x2 x3 x5 + 16 x1 x2 x3 x4 x6 + 12 x1 x2 x3 x4 x6
9 9 3 3 8 8 7 8 8 2 7
+ 16 x1 x2 x3 x4 x5 + 2 x1 x2 x3 x6 x5 + x1 x2 x3 x4
8 8 6 2 8 8 7 2 8 8 5 2 2
+ 3 x1 x2 x3 x5 x4 + x1 x2 x3 x5 + 5 x1 x2 x3 x5 x4
8 8 6 8 8 4 2 3 8 8 7
+ 6 x1 x2 x3 x6 x4 x5 + 7 x1 x2 x4 x6 x3 + 2 x1 x2 x3 x4 x5
8 8 7 8 8 6 3 8 9 6 2
+ 2 x1 x2 x4 x6 x3 + 3 x1 x2 x3 x4 + 2 x1 x2 x3 x6
8 10 5 2 8 9 2 6 8 8 7 2
+ x1 x2 x3 x6 + 2 x1 x2 x3 x4 + x1 x2 x3 x4
8 8 5 3 8 8 6 2 8 8 5 2 2
+ 10 x1 x2 x4 x6 x3 + 3 x1 x2 x4 x6 x3 + 5 x1 x2 x4 x6 x3
8 8 5 3 8 8 6 2 8 8 4 4
+ 10 x1 x2 x3 x4 x5 + 6 x1 x2 x3 x4 x5 + 12 x1 x2 x3 x4 x6
8 8 5 3 8 8 5 2 8 8 6 2
+ 10 x1 x2 x3 x4 x6 + 10 x1 x2 x3 x4 x6 x5 + 3 x1 x2 x3 x6 x4
8 8 7 2 8 8 3 6 8 8 4 5
+ x1 x2 x3 x6 + 3 x1 x2 x3 x4 + 5 x1 x2 x3 x4
8 8 6 2 8 8 5 4 8 8 6 2
+ 6 x1 x2 x4 x6 x3 + 5 x1 x2 x3 x4 + 6 x1 x2 x3 x4 x6
8 8 7 8 8 7 2 8 10 5
+ 2 x1 x2 x3 x4 x6 + x1 x2 x4 x6 + 2 x1 x2 x4 x5 x3
9 8 2 6 9 8 3 5 8 9 6
+ 2 x1 x2 x3 x4 + 6 x1 x2 x3 x4 + 4 x1 x2 x4 x6 x3
9 8 4 4 9 9 2 5 9 9 5 2
+ 8 x1 x2 x3 x4 + 2 x1 x2 x3 x4 + 2 x1 x2 x3 x6
9 8 5 3 8 9 3 2 3 8 10 4 2
+ 6 x1 x2 x3 x4 + 12 x1 x2 x4 x6 x3 + 3 x1 x2 x3 x4 x6
9 8 6 2 9 8 6 8 9 6 2
+ 2 x1 x2 x3 x4 + 4 x1 x2 x3 x4 x6 + 2 x1 x2 x4 x6
8 8 4 3 2 8 8 5 2 2 9 8 5 2
+ 7 x1 x2 x3 x4 x6 + 5 x1 x2 x3 x4 x6 + 12 x1 x2 x3 x4 x6
8 9 4 2 2 8 9 5 2 8 9 3 5
+ 10 x1 x2 x3 x4 x6 + 6 x1 x2 x3 x4 x6 + 6 x1 x2 x3 x4
8 9 4 4 9 8 4 3 9 8 5 2
+ 8 x1 x2 x3 x4 + 18 x1 x2 x3 x4 x5 + 6 x1 x2 x3 x4 x6
9 8 6 9 8 5 2 9 8 6
+ 4 x1 x2 x3 x5 x6 + 12 x1 x2 x3 x5 x4 + 4 x1 x2 x3 x5 x4
9 8 4 2 2 8 10 5 8 10 3 2 2
+ 10 x1 x2 x3 x4 x5 + 2 x1 x2 x4 x6 x3 + 5 x1 x2 x4 x6 x3
8 10 2 2 3 8 9 5 2 9 8 6 2
+ 5 x1 x2 x4 x6 x3 + 6 x1 x2 x4 x6 x3 + 2 x1 x2 x3 x5
8 9 4 2 2 9 8 5 2 9 9 4 2
+ 10 x1 x2 x4 x6 x3 + 6 x1 x2 x3 x5 x4 + 6 x1 x2 x3 x4 x6
8 10 2 5 9 8 5 9 8 2 4
+ x1 x2 x3 x4 + 12 x1 x2 x3 x4 x6 x5 + 20 x1 x2 x4 x6 x3 x5
8 9 6 8 9 6 8 9 5 2
+ 4 x1 x2 x3 x4 x6 + 4 x1 x2 x3 x4 x5 + 12 x1 x2 x3 x4 x5
9 8 6 2 8 9 4 3 8 9 4 3
+ 2 x1 x2 x4 x6 + 18 x1 x2 x3 x4 x6 + 18 x1 x2 x3 x4 x5
8 9 5 2 9 9 5 9 9 2 2 3
+ 12 x1 x2 x3 x4 x6 + 4 x1 x2 x4 x6 x3 + 10 x1 x2 x4 x6 x3
9 8 5 2 9 8 4 2 2 9 8 6
+ 6 x1 x2 x4 x6 x3 + 10 x1 x2 x4 x6 x3 + 4 x1 x2 x4 x6 x3
9 8 5 2 9 8 3 2 3 9 8 2 2 4
+ 12 x1 x2 x4 x6 x3 + 12 x1 x2 x4 x6 x3 + 10 x1 x2 x4 x6 x3
9 8 4 3 9 8 3 4 8 10 4
+ 18 x1 x2 x4 x6 x3 + 18 x1 x2 x4 x6 x3 + 6 x1 x2 x3 x5 x6 x4
8 10 5 9 9 5 8 10 4 2
+ 2 x1 x2 x3 x5 x6 + 4 x1 x2 x3 x5 x6 + 3 x1 x2 x3 x5 x4
8 10 5 2 10 8 3 2 8 9 4 2 2
+ x1 x2 x3 x5 + 10 x1 x2 x4 x6 x3 x5 + 10 x1 x2 x3 x5 x4
8 9 5 8 9 6 8 9 4 2
+ 12 x1 x2 x3 x5 x6 x4 + 4 x1 x2 x3 x5 x6 + 20 x1 x2 x3 x5 x4 x6
8 9 5 2 8 9 6 2 9 8 6 2
+ 6 x1 x2 x3 x5 x4 + 2 x1 x2 x3 x5 + 2 x1 x2 x3 x6
> res:=ToX(X[4,5,1,7,2,6,3]^2*X[3,4,1,5,2]):
*
> res;
2 X[10, 11, 3, 5, 2, 4, 1, 6, 7, 8, 9] + 2 X[10, 11, 3, 6, 1, 4, 2, 5, 7, 8, 9]
+ 2 X[9, 12, 3, 5, 1, 6, 2, 4, 7, 8, 10, 11]
+ X[10, 11, 1, 7, 3, 4, 2, 5, 6, 8, 9]
+ 2 X[10, 11, 2, 6, 1, 5, 3, 4, 7, 8, 9]
+ 2 X[10, 11, 2, 6, 3, 4, 1, 5, 7, 8, 9]
+ 2 X[10, 11, 3, 5, 1, 6, 2, 4, 7, 8, 9]
+ 2 X[9, 12, 3, 6, 1, 4, 2, 5, 7, 8, 10, 11]
+ X[10, 11, 1, 7, 2, 5, 3, 4, 6, 8, 9]
+ 2 X[9, 11, 4, 6, 1, 3, 2, 5, 7, 8, 10]
+ 2 X[9, 10, 4, 7, 1, 3, 2, 5, 6, 8]
+ 2 X[9, 12, 2, 6, 3, 4, 1, 5, 7, 8, 10, 11]
+ 2 X[9, 12, 3, 5, 2, 4, 1, 6, 7, 8, 10, 11]
+ X[9, 10, 1, 11, 2, 5, 3, 4, 6, 7, 8]
+ X[9, 10, 1, 11, 3, 4, 2, 5, 6, 7, 8] + 2 X[9, 10, 2, 8, 1, 5, 3, 4, 6, 7]
+ 2 X[9, 10, 2, 8, 3, 4, 1, 5, 6, 7] + 2 X[9, 10, 3, 7, 1, 5, 2, 4, 6, 8]
+ 2 X[9, 10, 3, 7, 2, 4, 1, 5, 6, 8] + 2 X[9, 10, 3, 8, 1, 4, 2, 5, 6, 7]
+ 2 X[9, 10, 4, 6, 1, 5, 2, 3, 7, 8] + 2 X[9, 10, 4, 6, 2, 3, 1, 5, 7, 8]
+ 2 X[9, 10, 5, 6, 1, 3, 2, 4, 7, 8] + 2 X[9, 10, 5, 7, 1, 2, 3, 4, 6, 8]
+ 2 X[9, 11, 1, 8, 2, 5, 3, 4, 6, 7, 10]
+ 2 X[9, 11, 1, 8, 3, 4, 2, 5, 6, 7, 10]
+ 4 X[9, 11, 2, 7, 1, 5, 3, 4, 6, 8, 10]
+ 4 X[9, 11, 2, 7, 3, 4, 1, 5, 6, 8, 10]
+ 4 X[9, 11, 3, 6, 1, 5, 2, 4, 7, 8, 10]
+ 4 X[9, 11, 3, 6, 2, 4, 1, 5, 7, 8, 10]
+ 4 X[9, 11, 3, 7, 1, 4, 2, 5, 6, 8, 10]
+ 2 X[9, 11, 4, 5, 1, 6, 2, 3, 7, 8, 10]
+ 2 X[9, 11, 4, 5, 2, 3, 1, 6, 7, 8, 10]
+ 2 X[9, 11, 5, 6, 1, 2, 3, 4, 7, 8, 10]
+ X[9, 12, 1, 7, 2, 5, 3, 4, 6, 8, 10, 11]
+ X[9, 12, 1, 7, 3, 4, 2, 5, 6, 8, 10, 11]
+ 2 X[9, 12, 2, 6, 1, 5, 3, 4, 7, 8, 10, 11]
> res:=ToX(X[3,4,8,1,2,6,7,5]*X[4,6,1,7,8,5,2,3]):
*
> res;
X[6, 11, 5, 3, 7, 4, 2, 1, 8, 9, 10] + X[6, 11, 5, 3, 7, 8, 1, 2, 4, 9, 10]
+ X[6, 11, 5, 2, 8, 4, 3, 1, 7, 9, 10]
+ X[6, 11, 5, 2, 8, 7, 1, 3, 4, 9, 10]
+ X[6, 11, 5, 3, 8, 4, 1, 2, 7, 9, 10]
+ X[6, 11, 5, 4, 7, 2, 3, 1, 8, 9, 10]
+ X[6, 11, 4, 7, 8, 2, 1, 3, 5, 9, 10]
+ X[6, 11, 5, 2, 7, 8, 3, 1, 4, 9, 10] + X[6, 9, 10, 2, 7, 4, 1, 3, 5, 8]
+ X[6, 9, 10, 3, 5, 4, 1, 2, 7, 8] + X[6, 10, 5, 7, 8, 2, 1, 3, 4, 9]
+ X[6, 10, 4, 5, 8, 3, 2, 1, 7, 9] + X[6, 10, 4, 7, 8, 3, 1, 2, 5, 9]
+ X[6, 10, 5, 3, 7, 8, 2, 1, 4, 9] + X[6, 10, 5, 3, 8, 4, 2, 1, 7, 9]
+ X[6, 10, 5, 3, 8, 7, 1, 2, 4, 9] + X[6, 10, 5, 4, 7, 3, 2, 1, 8, 9]
+ X[6, 10, 5, 4, 7, 8, 1, 2, 3, 9] + X[6, 10, 5, 4, 8, 2, 3, 1, 7, 9]
+ X[6, 10, 5, 4, 8, 3, 1, 2, 7, 9] + X[6, 10, 7, 2, 5, 8, 3, 1, 4, 9]
+ X[6, 10, 7, 2, 8, 4, 3, 1, 5, 9] + X[6, 10, 7, 2, 8, 5, 1, 3, 4, 9]
+ X[6, 10, 7, 3, 5, 4, 2, 1, 8, 9] + X[6, 10, 7, 3, 5, 8, 1, 2, 4, 9]
+ 2 X[6, 10, 7, 3, 8, 4, 1, 2, 5, 9] + X[6, 10, 7, 4, 5, 2, 3, 1, 8, 9]
+ X[6, 10, 7, 4, 8, 1, 3, 2, 5, 9] + X[6, 10, 7, 4, 8, 2, 1, 3, 5, 9]
+ X[6, 10, 7, 5, 8, 1, 2, 3, 4, 9] + X[6, 10, 8, 2, 5, 4, 3, 1, 7, 9]
+ X[6, 10, 8, 2, 5, 7, 1, 3, 4, 9] + X[6, 10, 8, 2, 7, 4, 1, 3, 5, 9]
+ X[6, 10, 8, 3, 5, 4, 1, 2, 7, 9] + X[6, 10, 8, 4, 5, 1, 3, 2, 7, 9]
+ X[6, 10, 8, 4, 7, 1, 2, 3, 5, 9] + X[6, 11, 3, 5, 7, 8, 2, 1, 4, 9, 10]
+ X[6, 11, 3, 5, 8, 4, 2, 1, 7, 9, 10]
+ X[6, 11, 3, 5, 8, 7, 1, 2, 4, 9, 10]
+ X[6, 11, 3, 7, 8, 4, 1, 2, 5, 9, 10]
+ X[6, 11, 4, 5, 7, 3, 2, 1, 8, 9, 10]
+ X[6, 11, 4, 5, 7, 8, 1, 2, 3, 9, 10]
+ X[6, 11, 4, 5, 8, 2, 3, 1, 7, 9, 10]
+ X[6, 11, 4, 5, 8, 3, 1, 2, 7, 9, 10] + X[6, 10, 4, 5, 8, 7, 1, 2, 3, 9]
+ X[6, 9, 10, 4, 5, 1, 3, 2, 7, 8] + X[6, 9, 10, 4, 7, 1, 2, 3, 5, 8]
+ X[6, 9, 11, 1, 5, 4, 3, 2, 7, 8, 10] + X[6, 9, 7, 4, 8, 2, 3, 1, 5]
+ 2 X[6, 9, 7, 4, 8, 3, 1, 2, 5] + X[6, 9, 11, 1, 5, 7, 2, 3, 4, 8, 10]
+ X[6, 10, 4, 5, 7, 8, 2, 1, 3, 9] + X[6, 9, 11, 1, 7, 4, 2, 3, 5, 8, 10]
+ X[6, 9, 7, 4, 5, 3, 2, 1, 8] + X[6, 9, 7, 4, 5, 8, 1, 2, 3]
+ X[6, 9, 7, 5, 8, 2, 1, 3, 4] + X[6, 9, 8, 3, 5, 4, 2, 1, 7]
+ X[6, 9, 8, 3, 5, 7, 1, 2, 4] + X[6, 9, 8, 3, 7, 4, 1, 2, 5]
+ X[6, 9, 8, 4, 5, 2, 3, 1, 7] + X[6, 9, 8, 4, 5, 3, 1, 2, 7]
+ X[6, 9, 8, 4, 7, 2, 1, 3, 5] + X[6, 9, 10, 2, 5, 4, 3, 1, 7, 8]
+ X[6, 9, 10, 2, 5, 7, 1, 3, 4, 8] + X[6, 9, 5, 4, 8, 3, 2, 1, 7]
+ X[6, 9, 5, 7, 8, 3, 1, 2, 4] + X[6, 9, 7, 3, 5, 8, 2, 1, 4]
+ X[6, 9, 7, 3, 8, 4, 2, 1, 5] + X[6, 9, 7, 3, 8, 5, 1, 2, 4]
+ X[6, 9, 5, 4, 8, 7, 1, 2, 3] + X[6, 8, 10, 2, 7, 5, 1, 3, 4, 9]
+ X[6, 8, 10, 4, 5, 2, 3, 1, 7, 9] + X[6, 8, 10, 4, 7, 1, 3, 2, 5, 9]
+ X[6, 8, 11, 2, 5, 4, 3, 1, 7, 9, 10] + X[6, 9, 5, 4, 7, 8, 2, 1, 3]
+ X[6, 8, 7, 4, 5, 9, 2, 1, 3] + X[6, 8, 7, 4, 9, 3, 2, 1, 5]
+ X[6, 8, 7, 4, 9, 5, 1, 2, 3] + X[6, 8, 7, 5, 9, 3, 1, 2, 4]
+ X[6, 8, 9, 3, 5, 7, 2, 1, 4] + X[6, 8, 9, 3, 7, 4, 2, 1, 5]
+ X[6, 8, 9, 3, 7, 5, 1, 2, 4] + X[6, 8, 9, 4, 5, 3, 2, 1, 7]
+ X[6, 8, 9, 4, 5, 7, 1, 2, 3] + X[6, 8, 9, 4, 7, 2, 3, 1, 5]
+ X[6, 8, 9, 4, 7, 3, 1, 2, 5] + X[6, 8, 9, 5, 7, 2, 1, 3, 4]
+ X[6, 8, 10, 2, 5, 7, 3, 1, 4, 9] + X[6, 8, 10, 2, 7, 4, 3, 1, 5, 9]
+ X[6, 8, 10, 3, 5, 4, 2, 1, 7, 9] + X[6, 8, 10, 3, 5, 7, 1, 2, 4, 9]
+ X[6, 8, 10, 3, 7, 4, 1, 2, 5, 9] + X[6, 8, 10, 5, 7, 1, 2, 3, 4, 9]
+ X[6, 8, 11, 1, 7, 4, 3, 2, 5, 9, 10]
+ X[6, 8, 11, 1, 7, 5, 2, 3, 4, 9, 10]
+ X[6, 8, 11, 1, 5, 7, 3, 2, 4, 9, 10] + X[8, 9, 4, 5, 7, 3, 1, 2, 6]
+ 2 X[8, 9, 5, 3, 6, 4, 2, 1, 7] + 2 X[8, 9, 5, 3, 6, 7, 1, 2, 4]
+ 2 X[8, 9, 5, 3, 7, 4, 1, 2, 6] + X[8, 9, 5, 4, 6, 2, 3, 1, 7]
+ X[8, 9, 5, 4, 6, 3, 1, 2, 7] + X[8, 9, 5, 4, 7, 2, 1, 3, 6]
+ X[8, 9, 6, 2, 5, 4, 3, 1, 7] + X[8, 9, 6, 2, 5, 7, 1, 3, 4]
+ X[8, 9, 6, 3, 4, 5, 2, 1, 7] + X[8, 9, 6, 3, 4, 7, 1, 2, 5]
+ X[8, 9, 6, 3, 5, 4, 1, 2, 7] + X[7, 11, 8, 1, 4, 6, 2, 3, 5, 9, 10]
+ X[7, 11, 8, 1, 5, 4, 2, 3, 6, 9, 10]
+ X[7, 11, 6, 2, 4, 5, 3, 1, 8, 9, 10]
+ X[7, 11, 8, 1, 4, 5, 3, 2, 6, 9, 10]
+ X[7, 11, 6, 1, 5, 8, 2, 3, 4, 9, 10]
+ X[7, 11, 6, 1, 8, 4, 2, 3, 5, 9, 10] + X[8, 9, 4, 5, 6, 3, 2, 1, 7]
+ X[8, 9, 4, 5, 6, 7, 1, 2, 3] + X[7, 11, 4, 3, 6, 8, 1, 2, 5, 9, 10]
+ X[7, 11, 3, 4, 6, 8, 2, 1, 5, 9, 10] + X[7, 10, 8, 1, 5, 4, 3, 2, 6, 9]
+ X[7, 10, 8, 1, 6, 4, 2, 3, 5, 9] + X[7, 10, 8, 2, 4, 5, 3, 1, 6, 9]
+ X[7, 10, 8, 2, 4, 6, 1, 3, 5, 9] + X[7, 10, 8, 2, 5, 4, 1, 3, 6, 9]
+ X[7, 10, 8, 3, 4, 5, 1, 2, 6, 9] + X[7, 10, 8, 4, 5, 1, 2, 3, 6, 9]
+ X[7, 11, 3, 4, 8, 5, 2, 1, 6, 9, 10]
+ X[7, 11, 3, 4, 8, 6, 1, 2, 5, 9, 10]
+ X[7, 11, 3, 5, 6, 8, 1, 2, 4, 9, 10]
+ X[7, 11, 3, 5, 8, 4, 1, 2, 6, 9, 10]
+ X[7, 11, 4, 2, 6, 8, 3, 1, 5, 9, 10]
+ X[7, 11, 4, 2, 8, 5, 3, 1, 6, 9, 10]
+ X[7, 11, 4, 2, 8, 6, 1, 3, 5, 9, 10]
+ X[7, 11, 4, 3, 6, 5, 2, 1, 8, 9, 10]
+ X[7, 11, 4, 3, 8, 5, 1, 2, 6, 9, 10]
+ X[7, 11, 4, 5, 8, 2, 1, 3, 6, 9, 10]
+ X[7, 11, 5, 1, 6, 8, 3, 2, 4, 9, 10]
+ X[7, 11, 5, 1, 8, 4, 3, 2, 6, 9, 10]
+ X[7, 11, 5, 1, 8, 6, 2, 3, 4, 9, 10]
+ X[7, 11, 5, 2, 6, 4, 3, 1, 8, 9, 10]
+ X[7, 11, 5, 2, 6, 8, 1, 3, 4, 9, 10]
+ X[7, 11, 5, 2, 8, 4, 1, 3, 6, 9, 10]
+ X[7, 11, 5, 4, 8, 1, 2, 3, 6, 9, 10]
+ X[7, 11, 6, 1, 4, 8, 3, 2, 5, 9, 10] + X[7, 10, 8, 1, 5, 6, 2, 3, 4, 9]
+ X[7, 10, 6, 2, 5, 8, 1, 3, 4, 9] + 2 X[7, 10, 4, 5, 8, 3, 1, 2, 6, 9]
+ X[7, 10, 4, 3, 6, 8, 2, 1, 5, 9] + X[7, 10, 4, 3, 8, 5, 2, 1, 6, 9]
+ X[7, 10, 4, 3, 8, 6, 1, 2, 5, 9] + X[7, 10, 4, 5, 6, 3, 2, 1, 8, 9]
+ 2 X[7, 10, 4, 5, 6, 8, 1, 2, 3, 9] + X[7, 10, 4, 5, 8, 2, 3, 1, 6, 9]
+ X[7, 10, 4, 6, 8, 2, 1, 3, 5, 9] + 2 X[7, 10, 5, 2, 6, 8, 3, 1, 4, 9]
+ 2 X[7, 10, 5, 2, 8, 4, 3, 1, 6, 9] + 2 X[7, 10, 5, 2, 8, 6, 1, 3, 4, 9]
+ 2 X[7, 10, 5, 3, 6, 4, 2, 1, 8, 9] + 3 X[7, 10, 5, 3, 6, 8, 1, 2, 4, 9]
+ 3 X[7, 10, 5, 3, 8, 4, 1, 2, 6, 9] + X[7, 10, 5, 4, 6, 2, 3, 1, 8, 9]
+ X[7, 10, 5, 4, 8, 1, 3, 2, 6, 9] + X[7, 10, 5, 4, 8, 2, 1, 3, 6, 9]
+ X[7, 10, 5, 6, 8, 1, 2, 3, 4, 9] + X[7, 10, 6, 1, 5, 8, 3, 2, 4, 9]
+ X[7, 10, 6, 1, 8, 4, 3, 2, 5, 9] + X[7, 10, 6, 1, 8, 5, 2, 3, 4, 9]
+ X[7, 10, 6, 2, 4, 8, 3, 1, 5, 9] + X[7, 10, 6, 2, 5, 4, 3, 1, 8, 9]
+ 2 X[7, 10, 6, 2, 8, 4, 1, 3, 5, 9] + X[7, 10, 6, 3, 4, 5, 2, 1, 8, 9]
+ X[7, 10, 6, 3, 4, 8, 1, 2, 5, 9] + X[7, 10, 6, 4, 8, 1, 2, 3, 5, 9]
+ X[7, 9, 6, 2, 8, 4, 3, 1, 5] + X[7, 9, 6, 3, 4, 8, 2, 1, 5]
+ X[7, 9, 6, 3, 5, 4, 2, 1, 8] + 2 X[7, 9, 6, 3, 5, 8, 1, 2, 4]
+ 3 X[7, 9, 6, 3, 8, 4, 1, 2, 5] + X[7, 9, 6, 4, 8, 2, 1, 3, 5]
+ X[7, 9, 8, 2, 5, 4, 3, 1, 6] + X[7, 9, 8, 2, 5, 6, 1, 3, 4]
+ X[7, 9, 8, 2, 6, 4, 1, 3, 5] + X[7, 9, 8, 3, 4, 5, 2, 1, 6]
+ X[7, 9, 8, 3, 4, 6, 1, 2, 5] + 2 X[7, 9, 8, 3, 5, 4, 1, 2, 6]
+ X[7, 9, 8, 4, 5, 2, 1, 3, 6] + X[7, 9, 10, 1, 5, 4, 3, 2, 6, 8]
+ X[7, 9, 6, 2, 8, 5, 1, 3, 4] + X[7, 9, 10, 1, 5, 6, 2, 3, 4, 8]
+ X[7, 9, 10, 2, 4, 5, 3, 1, 6, 8] + X[7, 9, 10, 2, 4, 6, 1, 3, 5, 8]
+ X[7, 9, 10, 2, 5, 4, 1, 3, 6, 8] + X[7, 9, 10, 3, 4, 5, 1, 2, 6, 8]
+ X[7, 9, 10, 4, 5, 1, 2, 3, 6, 8] + X[7, 9, 11, 1, 4, 5, 3, 2, 6, 8, 10]
+ X[7, 9, 11, 1, 4, 6, 2, 3, 5, 8, 10]
+ X[7, 9, 11, 1, 5, 4, 2, 3, 6, 8, 10] + X[7, 10, 3, 5, 6, 8, 2, 1, 4, 9]
+ X[7, 10, 3, 5, 8, 4, 2, 1, 6, 9] + X[7, 10, 3, 5, 8, 6, 1, 2, 4, 9]
+ X[7, 10, 3, 6, 8, 4, 1, 2, 5, 9] + X[7, 9, 10, 1, 6, 4, 2, 3, 5, 8]
+ 2 X[7, 8, 10, 2, 5, 4, 3, 1, 6, 9] + X[7, 8, 10, 2, 6, 4, 1, 3, 5, 9]
+ X[7, 8, 10, 3, 4, 5, 2, 1, 6, 9] + 2 X[7, 8, 10, 2, 5, 6, 1, 3, 4, 9]
+ X[7, 9, 4, 5, 8, 6, 1, 2, 3] + X[7, 8, 10, 4, 6, 1, 2, 3, 5, 9]
+ X[7, 8, 11, 1, 5, 4, 3, 2, 6, 9, 10]
+ 2 X[7, 8, 11, 1, 5, 6, 2, 3, 4, 9, 10]
+ X[7, 8, 11, 1, 6, 4, 2, 3, 5, 9, 10]
+ X[7, 8, 11, 2, 4, 5, 3, 1, 6, 9, 10] + X[7, 9, 4, 5, 6, 8, 2, 1, 3]
+ X[7, 9, 4, 5, 8, 3, 2, 1, 6] + X[7, 9, 4, 6, 8, 3, 1, 2, 5]
+ 2 X[7, 9, 5, 3, 6, 8, 2, 1, 4] + 2 X[7, 9, 5, 3, 8, 4, 2, 1, 6]
+ 2 X[7, 9, 5, 3, 8, 6, 1, 2, 4] + X[7, 9, 5, 4, 6, 3, 2, 1, 8]
+ 2 X[7, 9, 5, 4, 6, 8, 1, 2, 3] + X[7, 9, 5, 4, 8, 2, 3, 1, 6]
+ 2 X[7, 9, 5, 4, 8, 3, 1, 2, 6] + X[7, 9, 5, 6, 8, 2, 1, 3, 4]
+ X[7, 9, 6, 2, 5, 8, 3, 1, 4] + X[7, 8, 11, 1, 4, 6, 3, 2, 5, 9, 10]
+ X[6, 11, 5, 4, 8, 1, 3, 2, 7, 9, 10]
+ X[6, 11, 5, 7, 8, 1, 2, 3, 4, 9, 10] + X[7, 8, 10, 3, 4, 6, 1, 2, 5, 9]
+ X[7, 8, 10, 4, 5, 1, 3, 2, 6, 9] + X[7, 8, 10, 3, 5, 4, 1, 2, 6, 9]
+ X[7, 8, 6, 3, 9, 5, 1, 2, 4] + X[7, 8, 6, 4, 5, 9, 1, 2, 3]
+ X[7, 8, 6, 4, 9, 3, 1, 2, 5] + X[7, 8, 9, 2, 5, 6, 3, 1, 4]
+ X[7, 8, 9, 2, 6, 4, 3, 1, 5] + X[7, 8, 9, 2, 6, 5, 1, 3, 4]
+ X[7, 8, 9, 3, 4, 6, 2, 1, 5] + 2 X[7, 8, 9, 3, 5, 4, 2, 1, 6]
+ 3 X[7, 8, 9, 3, 5, 6, 1, 2, 4] + 2 X[7, 8, 9, 3, 6, 4, 1, 2, 5]
+ X[7, 8, 9, 4, 5, 2, 3, 1, 6] + X[7, 8, 9, 4, 5, 3, 1, 2, 6]
+ X[7, 8, 9, 4, 6, 2, 1, 3, 5] + X[7, 8, 10, 1, 5, 6, 3, 2, 4, 9]
+ X[7, 8, 10, 1, 6, 4, 3, 2, 5, 9] + X[7, 8, 10, 1, 6, 5, 2, 3, 4, 9]
+ X[7, 8, 10, 2, 4, 6, 3, 1, 5, 9] + X[6, 11, 7, 4, 8, 1, 2, 3, 5, 9, 10]
+ X[6, 11, 8, 1, 5, 4, 3, 2, 7, 9, 10] + X[7, 8, 5, 4, 9, 6, 1, 2, 3]
+ X[7, 8, 6, 3, 5, 9, 2, 1, 4] + X[7, 8, 6, 3, 9, 4, 2, 1, 5]
+ X[7, 8, 5, 6, 9, 3, 1, 2, 4] + X[6, 11, 7, 2, 5, 4, 3, 1, 8, 9, 10]
+ X[6, 11, 7, 1, 5, 8, 3, 2, 4, 9, 10]
+ X[6, 11, 7, 1, 8, 4, 3, 2, 5, 9, 10]
+ X[6, 11, 7, 1, 8, 5, 2, 3, 4, 9, 10]
+ X[6, 11, 7, 2, 8, 4, 1, 3, 5, 9, 10]
+ X[6, 11, 8, 1, 5, 7, 2, 3, 4, 9, 10]
+ X[6, 11, 8, 1, 7, 4, 2, 3, 5, 9, 10] + X[7, 8, 5, 4, 6, 9, 2, 1, 3]
+ X[7, 8, 5, 4, 9, 3, 2, 1, 6] + X[8, 10, 6, 1, 7, 4, 2, 3, 5, 9]
+ X[8, 10, 6, 2, 4, 7, 1, 3, 5, 9] + X[8, 10, 6, 3, 4, 5, 1, 2, 7, 9]
+ X[8, 10, 6, 2, 4, 5, 3, 1, 7, 9] + X[8, 10, 7, 1, 5, 4, 2, 3, 6, 9]
+ X[8, 11, 3, 4, 6, 5, 2, 1, 7, 9, 10]
+ X[8, 11, 3, 4, 6, 7, 1, 2, 5, 9, 10]
+ X[8, 11, 3, 4, 7, 5, 1, 2, 6, 9, 10]
+ X[8, 11, 4, 2, 6, 5, 3, 1, 7, 9, 10]
+ X[8, 11, 4, 2, 6, 7, 1, 3, 5, 9, 10]
+ X[8, 11, 4, 2, 7, 5, 1, 3, 6, 9, 10]
+ X[8, 11, 4, 3, 6, 5, 1, 2, 7, 9, 10]
+ X[8, 11, 5, 1, 6, 4, 3, 2, 7, 9, 10]
+ X[8, 11, 5, 1, 6, 7, 2, 3, 4, 9, 10]
+ X[8, 11, 5, 1, 7, 4, 2, 3, 6, 9, 10]
+ X[8, 11, 6, 1, 4, 5, 3, 2, 7, 9, 10]
+ X[8, 11, 6, 1, 4, 7, 2, 3, 5, 9, 10]
+ X[8, 11, 7, 1, 4, 5, 2, 3, 6, 9, 10] + X[8, 10, 7, 2, 4, 5, 1, 3, 6, 9]
+ X[8, 9, 7, 2, 5, 4, 1, 3, 6] + X[8, 9, 7, 3, 4, 5, 1, 2, 6]
+ X[8, 9, 10, 1, 5, 4, 2, 3, 6, 7] + X[8, 9, 10, 2, 4, 5, 1, 3, 6, 7]
+ X[8, 9, 11, 1, 4, 5, 2, 3, 6, 7, 10] + X[8, 10, 3, 5, 6, 4, 2, 1, 7, 9]
+ X[8, 10, 3, 5, 6, 7, 1, 2, 4, 9] + X[8, 10, 3, 5, 7, 4, 1, 2, 6, 9]
+ X[8, 10, 4, 3, 6, 5, 2, 1, 7, 9] + X[8, 10, 4, 3, 6, 7, 1, 2, 5, 9]
+ X[8, 10, 4, 3, 7, 5, 1, 2, 6, 9] + X[8, 10, 4, 5, 6, 2, 3, 1, 7, 9]
+ X[8, 10, 4, 5, 6, 3, 1, 2, 7, 9] + X[8, 10, 4, 5, 7, 2, 1, 3, 6, 9]
+ 2 X[8, 10, 5, 2, 6, 4, 3, 1, 7, 9] + 2 X[8, 10, 5, 2, 6, 7, 1, 3, 4, 9]
+ 2 X[8, 10, 5, 2, 7, 4, 1, 3, 6, 9] + 2 X[8, 10, 5, 3, 6, 4, 1, 2, 7, 9]
+ X[8, 10, 5, 4, 6, 1, 3, 2, 7, 9] + X[8, 10, 5, 4, 7, 1, 2, 3, 6, 9]
+ X[8, 10, 6, 1, 5, 4, 3, 2, 7, 9] + X[8, 10, 6, 1, 5, 7, 2, 3, 4, 9]
+ X[8, 9, 6, 2, 7, 4, 1, 3, 5]
--------------------------------------------------------------------------------
#
# ACE says: ``I can do it................but I need time and memory...''
#
# P.S.: feel free to send your contribution ($)
#
--------------------------------------------------------------------------------
> HubDisable(SYMMETRICA):
> ToX(X[3,4,2,1]^3);
X[7, 8, 4, 1, 2, 3, 5, 6]
> ToX(X[4,5,1,7,2,6,3]^3);
> HubEnable(SYMMETRICA):
--------------------------------------------------------------------------------
#
# Using several computers in parallel...
#
--------------------------------------------------------------------------------
> PowerX:=proc(schub, n) local ind,i,out_res,rec_res;\
if (n=1) then\
schub\
else\
rec_res:=PowerX(schub, n-1);\
ind:=indets(rec_res);\
out_res:=HubParallel([14$nops(ind)],\
map(proc(schub1, schub2)\
[schub1*schub2]\
end, [op(ind)], schub));\
subs(seq(op(i, ind)=op(i, out_res), i=1..nops(ind)), rec_res)\
fi\
end:
> res:=PowerX(X[4,5,1,7,2,6,3], 3):
##
> res;
2 X[10, 11, 1, 13, 3, 5, 2, 4, 6, 7, 8, 9, 12]
+ 4 X[10, 11, 2, 12, 3, 5, 1, 4, 6, 7, 8, 9]
+ 3 X[10, 11, 3, 9, 1, 6, 2, 4, 5, 7, 8]
+ 6 X[10, 11, 3, 9, 2, 5, 1, 4, 6, 7, 8]
+ 4 X[10, 11, 3, 12, 1, 5, 2, 4, 6, 7, 8, 9]
+ 4 X[10, 11, 4, 8, 1, 6, 2, 3, 5, 7, 9]
+ 8 X[10, 11, 4, 8, 2, 5, 1, 3, 6, 7, 9]
+ 6 X[10, 11, 4, 9, 1, 5, 2, 3, 6, 7, 8]
+ 9 X[10, 11, 5, 8, 2, 3, 1, 4, 6, 7, 9]
+ 6 X[10, 11, 5, 9, 1, 3, 2, 4, 6, 7, 8]
+ 6 X[10, 11, 6, 8, 1, 3, 2, 4, 5, 7, 9]
+ 3 X[10, 11, 6, 9, 1, 2, 3, 4, 5, 7, 8]
+ 2 X[10, 12, 1, 11, 2, 6, 3, 4, 5, 7, 8, 9]
+ 4 X[10, 12, 1, 11, 3, 5, 2, 4, 6, 7, 8, 9]
+ 6 X[10, 12, 2, 9, 1, 6, 3, 4, 5, 7, 8, 11]
+ 12 X[10, 12, 2, 9, 3, 5, 1, 4, 6, 7, 8, 11]
+ 9 X[10, 12, 3, 8, 1, 6, 2, 4, 5, 7, 9, 11]
+ 18 X[10, 12, 3, 8, 2, 5, 1, 4, 6, 7, 9, 11]
+ 9 X[10, 12, 4, 7, 1, 6, 2, 3, 5, 8, 9, 11]
+ 18 X[10, 12, 4, 7, 2, 5, 1, 3, 6, 8, 9, 11]
+ 15 X[10, 12, 4, 8, 1, 5, 2, 3, 6, 7, 9, 11]
+ 18 X[10, 12, 5, 7, 2, 3, 1, 4, 6, 8, 9, 11]
+ 12 X[10, 12, 5, 8, 1, 3, 2, 4, 6, 7, 9, 11]
+ 9 X[10, 12, 6, 7, 1, 3, 2, 4, 5, 8, 9, 11]
+ 6 X[10, 12, 6, 8, 1, 2, 3, 4, 5, 7, 9, 11]
+ 3 X[10, 13, 1, 9, 2, 6, 3, 4, 5, 7, 8, 11, 12]
+ 6 X[10, 13, 1, 9, 3, 5, 2, 4, 6, 7, 8, 11, 12]
+ 6 X[10, 13, 2, 8, 1, 6, 3, 4, 5, 7, 9, 11, 12]
+ 12 X[10, 13, 2, 8, 3, 5, 1, 4, 6, 7, 9, 11, 12]
+ 9 X[10, 13, 3, 7, 1, 6, 2, 4, 5, 8, 9, 11, 12]
+ 18 X[10, 13, 3, 7, 2, 5, 1, 4, 6, 8, 9, 11, 12]
+ 12 X[10, 13, 3, 8, 1, 5, 2, 4, 6, 7, 9, 11, 12]
+ 3 X[11, 12, 1, 9, 2, 6, 3, 4, 5, 7, 8, 10]
+ 6 X[11, 12, 1, 9, 3, 5, 2, 4, 6, 7, 8, 10]
+ 6 X[11, 12, 2, 8, 1, 6, 3, 4, 5, 7, 9, 10]
+ 12 X[11, 12, 2, 8, 3, 5, 1, 4, 6, 7, 9, 10]
+ 9 X[11, 12, 3, 7, 1, 6, 2, 4, 5, 8, 9, 10]
+ 18 X[11, 12, 3, 7, 2, 5, 1, 4, 6, 8, 9, 10]
+ 12 X[11, 12, 3, 8, 1, 5, 2, 4, 6, 7, 9, 10]
+ 2 X[10, 11, 2, 12, 1, 6, 3, 4, 5, 7, 8, 9]
+ 2 X[10, 14, 4, 6, 1, 5, 2, 3, 7, 8, 9, 11, 12, 13]
+ 4 X[11, 13, 4, 5, 2, 6, 1, 3, 7, 8, 9, 10, 12]
+ X[10, 14, 4, 5, 1, 7, 2, 3, 6, 8, 9, 11, 12, 13]
+ 3 X[10, 13, 6, 7, 1, 2, 3, 4, 5, 8, 9, 11, 12]
+ X[10, 14, 1, 8, 2, 6, 3, 4, 5, 7, 9, 11, 12, 13]
+ 3 X[10, 12, 5, 6, 1, 7, 2, 3, 4, 8, 9, 11]
+ 6 X[10, 12, 5, 6, 2, 4, 1, 3, 7, 8, 9, 11]
+ 12 X[11, 13, 3, 6, 2, 5, 1, 4, 7, 8, 9, 10, 12]
+ 6 X[10, 14, 3, 6, 2, 5, 1, 4, 7, 8, 9, 11, 12, 13]
+ 12 X[11, 12, 4, 6, 2, 5, 1, 3, 7, 8, 9, 10]
+ 3 X[11, 12, 4, 7, 2, 3, 1, 5, 6, 8, 9, 10]
+ 3 X[11, 12, 5, 6, 1, 4, 2, 3, 7, 8, 9, 10]
+ 9 X[11, 12, 5, 6, 2, 3, 1, 4, 7, 8, 9, 10]
+ 6 X[11, 12, 5, 7, 1, 3, 2, 4, 6, 8, 9, 10]
+ 4 X[11, 13, 1, 8, 3, 5, 2, 4, 6, 7, 9, 10, 12]
+ 8 X[11, 13, 2, 7, 3, 5, 1, 4, 6, 8, 9, 10, 12]
+ 2 X[11, 13, 2, 8, 3, 4, 1, 5, 6, 7, 9, 10, 12]
+ 8 X[11, 13, 3, 7, 1, 5, 2, 4, 6, 8, 9, 10, 12]
+ 4 X[11, 13, 3, 7, 2, 4, 1, 5, 6, 8, 9, 10, 12]
+ 4 X[11, 13, 4, 6, 1, 5, 2, 3, 7, 8, 9, 10, 12]
+ 6 X[11, 12, 4, 6, 1, 7, 2, 3, 5, 8, 9, 10]
+ 3 X[11, 12, 6, 7, 1, 2, 3, 4, 5, 8, 9, 10]
+ 2 X[11, 13, 1, 8, 2, 6, 3, 4, 5, 7, 9, 10, 12]
+ 4 X[11, 13, 2, 7, 1, 6, 3, 4, 5, 8, 9, 10, 12]
+ 6 X[11, 13, 3, 6, 1, 7, 2, 4, 5, 8, 9, 10, 12]
+ 6 X[10, 13, 4, 6, 1, 7, 2, 3, 5, 8, 9, 11, 12]
+ 12 X[10, 13, 4, 6, 2, 5, 1, 3, 7, 8, 9, 11, 12]
+ 3 X[10, 13, 4, 7, 2, 3, 1, 5, 6, 8, 9, 11, 12]
+ 3 X[10, 13, 5, 6, 1, 4, 2, 3, 7, 8, 9, 11, 12]
+ 9 X[10, 13, 5, 6, 2, 3, 1, 4, 7, 8, 9, 11, 12]
+ 6 X[10, 13, 5, 7, 1, 3, 2, 4, 6, 8, 9, 11, 12]
+ 2 X[10, 14, 1, 8, 3, 5, 2, 4, 6, 7, 9, 11, 12, 13]
+ 4 X[10, 14, 2, 7, 3, 5, 1, 4, 6, 8, 9, 11, 12, 13]
+ X[10, 14, 2, 8, 3, 4, 1, 5, 6, 7, 9, 11, 12, 13]
+ 4 X[10, 14, 3, 7, 1, 5, 2, 4, 6, 8, 9, 11, 12, 13]
+ 2 X[10, 14, 3, 7, 2, 4, 1, 5, 6, 8, 9, 11, 12, 13]
+ 3 X[10, 13, 2, 9, 3, 4, 1, 5, 6, 7, 8, 11, 12]
+ 6 X[10, 13, 3, 8, 2, 4, 1, 5, 6, 7, 9, 11, 12]
+ 2 X[10, 11, 5, 7, 1, 6, 2, 3, 4, 8, 9]
+ 4 X[10, 11, 5, 7, 2, 4, 1, 3, 6, 8, 9]
+ 3 X[10, 11, 6, 7, 1, 4, 2, 3, 5, 8, 9]
+ 3 X[10, 11, 6, 7, 2, 3, 1, 4, 5, 8, 9]
+ 12 X[10, 13, 4, 7, 1, 5, 2, 3, 6, 8, 9, 11, 12]
+ 3 X[11, 12, 2, 9, 3, 4, 1, 5, 6, 7, 8, 10]
+ 6 X[11, 12, 3, 8, 2, 4, 1, 5, 6, 7, 9, 10]
+ 12 X[11, 12, 4, 7, 1, 5, 2, 3, 6, 8, 9, 10]
+ X[10, 11, 7, 8, 1, 2, 3, 4, 5, 6, 9]
+ 2 X[10, 12, 2, 11, 3, 4, 1, 5, 6, 7, 8, 9]
+ 6 X[10, 12, 4, 8, 2, 3, 1, 5, 6, 7, 9, 11]
+ 6 X[10, 12, 3, 9, 2, 4, 1, 5, 6, 7, 8, 11]
+ 9 X[10, 12, 5, 7, 1, 4, 2, 3, 6, 8, 9, 11]
+ X[10, 11, 2, 13, 3, 4, 1, 5, 6, 7, 8, 9, 12]
+ 2 X[10, 11, 3, 12, 2, 4, 1, 5, 6, 7, 8, 9]
+ 12 X[10, 12, 3, 9, 1, 5, 2, 4, 6, 7, 8, 11]
+ 3 X[10, 11, 4, 9, 2, 3, 1, 5, 6, 7, 8]
+ 5 X[10, 11, 5, 8, 1, 4, 2, 3, 6, 7, 9]
+ 2 X[11, 13, 4, 5, 1, 7, 2, 3, 6, 8, 9, 10, 12]
+ 2 X[10, 14, 2, 7, 1, 6, 3, 4, 5, 8, 9, 11, 12, 13]
+ 3 X[10, 14, 3, 6, 1, 7, 2, 4, 5, 8, 9, 11, 12, 13]
+ 2 X[10, 14, 4, 5, 2, 6, 1, 3, 7, 8, 9, 11, 12, 13]
+ X[10, 11, 1, 13, 2, 6, 3, 4, 5, 7, 8, 9, 12]
--------------------------------------------------------------------------------
#
# Symmetric group character table...(service 1)
#
--------------------------------------------------------------------------------
> bg1:=HubBackground([1], [[20]]): print(");
&
1
> HubBackgroundDone(bg1): print(");
table([
1 = false
])
> `SG/Chi`([32,10,3,3,2], [28,3$4, 1$10]): print(");
*
1701
--------------------------------------------------------------------------------
#
# Tableaux and skew tableaux...(services 16, 17)
#
--------------------------------------------------------------------------------
> l:=ListTab([7,4,2,2], [1,3,1,2,2,1,3,2]): nops(l);
*
1005
> ls:=`TAB/ListSkewTab`([[5,3,3,1], [2,1,1]],\
[1,4,2,1]); ls;
*
[[[4], [3, 3], [2, 2], [1, 2, 2]], [[3], [3, 4], [2, 2], [1, 2, 2]],
[[2], [3, 4], [2, 3], [1, 2, 2]], [[2], [3, 4], [2, 2], [1, 2, 3]],
[[2], [3, 3], [2, 2], [1, 2, 4]], [[3], [2, 4], [1, 3], [2, 2, 2]],
[[2], [3, 4], [1, 3], [2, 2, 2]], [[1], [3, 4], [2, 3], [2, 2, 2]],
[[2], [2, 4], [1, 3], [2, 2, 3]]]
--------------------------------------------------------------------------------
#
# Kostka matrix...(service 13)
#
--------------------------------------------------------------------------------
> km:=`SYMF/KostkaMat`(7): print(km);
*
[ 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ]
[ ]
[ 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 ]
[ ]
[ 1 1 1 0 0 0 0 0 0 0 0 0 0 0 0 ]
[ ]
[ 1 2 1 1 0 0 0 0 0 0 0 0 0 0 0 ]
[ ]
[ 1 1 1 0 1 0 0 0 0 0 0 0 0 0 0 ]
[ ]
[ 1 2 2 1 1 1 0 0 0 0 0 0 0 0 0 ]
[ ]
[ 1 3 3 3 1 2 1 0 0 0 0 0 0 0 0 ]
[ ]
[ 1 2 2 1 2 1 0 1 0 0 0 0 0 0 0 ]
[ ]
[ 1 2 3 1 2 2 0 1 1 0 0 0 0 0 0 ]
[ ]
[ 1 3 4 3 3 4 1 2 1 1 0 0 0 0 0 ]
[ ]
[ 1 4 6 6 4 8 4 3 2 3 1 0 0 0 0 ]
[ ]
[ 1 3 5 3 4 6 1 3 3 2 0 1 0 0 0 ]
[ ]
[ 1 4 7 6 6 11 4 6 5 6 1 2 1 0 0 ]
[ ]
[ 1 5 10 10 9 20 10 11 10 15 5 5 4 1 0 ]
[ ]
[ 1 6 14 15 14 35 20 21 21 35 15 14 14 6 1 ]
--------------------------------------------------------------------------------
#
# Ribbon tableaux and spin polynomials in parallel...(service 1000)
#
--------------------------------------------------------------------------------
> bg3:=HubBackground([1000], [[[12$8], [4$6]]]):
&
--------------------------------------------------------------------------------
#
# Littlewood-Richardson rule...(services 10, 11, 12)
#
--------------------------------------------------------------------------------
> HubDisable(SYMF):
> lrr:=Tos(s[3,2,1]*s[4,3,2,1]);
lrr := s[7, 5, 2, 1, 1] + s[7, 4, 4, 1] + s[7, 5, 2, 2] + 2 s[7, 4, 3, 2]
+ s[7, 5, 3, 1] + 3 s[5, 5, 3, 1, 1, 1] + 2 s[5, 5, 2, 2, 2]
+ 3 s[5, 4, 4, 3] + 3 s[5, 3, 3, 3, 1, 1] + s[7, 4, 2, 1, 1, 1]
+ s[6, 4, 2, 1, 1, 1, 1] + s[6, 3, 3, 1, 1, 1, 1] + s[6, 3, 2, 2, 1, 1, 1]
+ 4 s[5, 4, 2, 2, 2, 1] + 6 s[5, 4, 4, 2, 1] + 3 s[5, 4, 4, 1, 1, 1]
+ 6 s[5, 4, 3, 2, 2] + 8 s[5, 4, 3, 2, 1, 1] + 3 s[5, 3, 3, 3, 2]
+ 4 s[5, 3, 3, 2, 2, 1] + 6 s[5, 4, 3, 3, 1] + 3 s[5, 5, 2, 2, 1, 1]
+ 2 s[6, 3, 2, 2, 2, 1] + s[5, 5, 5, 1] + 3 s[5, 5, 4, 2]
+ 3 s[5, 5, 4, 1, 1] + 6 s[5, 5, 3, 2, 1] + 2 s[5, 5, 3, 3]
+ 4 s[6, 4, 3, 1, 1, 1] + 2 s[7, 4, 2, 2, 1] + 2 s[7, 3, 3, 2, 1]
+ s[7, 3, 3, 1, 1, 1] + s[7, 3, 2, 2, 2] + s[7, 3, 2, 2, 1, 1]
+ s[6, 6, 3, 1] + s[6, 6, 2, 2] + s[6, 6, 2, 1, 1] + 2 s[6, 5, 4, 1]
+ 4 s[6, 5, 3, 2] + 4 s[6, 5, 3, 1, 1] + 4 s[6, 5, 2, 2, 1]
+ 3 s[6, 4, 4, 2] + 3 s[6, 4, 4, 1, 1] + 8 s[6, 4, 3, 2, 1]
+ 2 s[6, 5, 2, 1, 1, 1] + 3 s[6, 4, 3, 3] + 3 s[6, 4, 2, 2, 2]
+ 4 s[6, 4, 2, 2, 1, 1] + 3 s[6, 3, 3, 3, 1] + 3 s[6, 3, 3, 2, 2]
+ 4 s[6, 3, 3, 2, 1, 1] + 2 s[7, 4, 3, 1, 1] + s[7, 3, 3, 3]
+ s[4, 4, 4, 1, 1, 1, 1] + 2 s[4, 4, 3, 2, 1, 1, 1] + s[4, 4, 2, 2, 2, 2]
+ s[4, 4, 2, 2, 2, 1, 1] + s[4, 3, 3, 3, 3] + 2 s[4, 3, 3, 3, 2, 1]
+ s[4, 3, 3, 3, 1, 1, 1] + s[4, 3, 3, 2, 2, 2] + s[4, 3, 3, 2, 2, 1, 1]
+ 3 s[4, 4, 3, 3, 1, 1] + s[5, 3, 2, 2, 2, 2] + s[5, 3, 2, 2, 2, 1, 1]
+ s[4, 4, 4, 4] + 3 s[4, 4, 4, 3, 1] + 2 s[4, 4, 4, 2, 2]
+ 3 s[4, 4, 4, 2, 1, 1] + 3 s[4, 4, 3, 3, 2] + 4 s[4, 4, 3, 2, 2, 1]
+ 2 s[5, 4, 2, 2, 1, 1, 1] + s[5, 5, 2, 1, 1, 1, 1]
+ 2 s[5, 4, 3, 1, 1, 1, 1] + 2 s[5, 3, 3, 2, 1, 1, 1]
> HubEnable(SYMF):
> CLG_n(5):
> lrr:=Tos_n(s[6,5,3,1,1]^2): lrr;
*
s[12, 7, 5, 4, 4] + s[12, 6, 6, 5, 3] + s[12, 6, 6, 4, 4] + s[11, 11, 6, 2, 2]
+ s[11, 11, 5, 3, 2] + s[12, 6, 6, 6, 2] + 5 s[10, 8, 5, 5, 4]
+ 3 s[10, 7, 7, 6, 2] + 7 s[10, 7, 7, 5, 3] + 4 s[10, 7, 7, 4, 4]
+ 6 s[10, 7, 6, 6, 3] + 8 s[10, 7, 6, 5, 4] + s[10, 7, 5, 5, 5]
+ 3 s[10, 6, 6, 6, 4] + s[10, 6, 6, 5, 5] + s[9, 9, 9, 3, 2]
+ 3 s[9, 9, 8, 4, 2] + 2 s[9, 9, 8, 3, 3] + 4 s[9, 9, 7, 5, 2]
+ 6 s[9, 9, 7, 4, 3] + 2 s[9, 9, 6, 6, 2] + 6 s[9, 9, 6, 5, 3]
+ 5 s[9, 9, 6, 4, 4] + 3 s[9, 9, 5, 5, 4] + 3 s[9, 8, 8, 5, 2]
+ 4 s[9, 8, 8, 4, 3] + 4 s[9, 8, 7, 6, 2] + 10 s[9, 8, 7, 5, 3]
+ 6 s[9, 8, 7, 4, 4] + 6 s[9, 8, 6, 6, 3] + 10 s[9, 8, 6, 5, 4]
+ 2 s[9, 8, 5, 5, 5] + s[9, 7, 7, 7, 2] + 6 s[9, 7, 7, 6, 3]
+ 7 s[9, 7, 7, 5, 4] + 7 s[9, 7, 6, 6, 4] + 4 s[9, 7, 6, 5, 5]
+ 2 s[9, 6, 6, 6, 5] + s[8, 8, 8, 6, 2] + 2 s[8, 8, 8, 5, 3]
+ 4 s[11, 8, 7, 3, 3] + 6 s[11, 8, 6, 5, 2] + 8 s[11, 8, 6, 4, 3]
+ 4 s[11, 8, 5, 5, 3] + 4 s[11, 8, 5, 4, 4] + s[8, 8, 8, 4, 4]
+ 4 s[8, 8, 7, 6, 3] + 5 s[8, 8, 7, 5, 4] + 4 s[8, 8, 6, 6, 4]
+ 3 s[8, 8, 6, 5, 5] + 2 s[8, 7, 7, 7, 3] + 5 s[8, 7, 7, 6, 4]
+ 3 s[8, 7, 7, 5, 5] + 4 s[8, 7, 6, 6, 5] + s[8, 6, 6, 6, 6]
+ s[7, 7, 7, 7, 4] + 2 s[7, 7, 7, 6, 5] + s[7, 7, 6, 6, 6]
+ s[8, 8, 7, 7, 2] + s[11, 11, 4, 4, 2] + 2 s[11, 10, 7, 2, 2]
+ 4 s[11, 10, 6, 3, 2] + 4 s[11, 10, 5, 4, 2] + 2 s[11, 10, 5, 3, 3]
+ 2 s[11, 10, 4, 4, 3] + 2 s[11, 9, 8, 2, 2] + 5 s[11, 9, 7, 3, 2]
+ 3 s[11, 7, 7, 5, 2] + 4 s[11, 7, 7, 4, 3] + 3 s[11, 7, 6, 6, 2]
+ 6 s[11, 7, 6, 5, 3] + 4 s[11, 7, 6, 4, 4] + 2 s[11, 7, 5, 5, 4]
+ 2 s[11, 6, 6, 6, 3] + 2 s[11, 6, 6, 5, 4] + s[10, 10, 8, 2, 2]
+ 3 s[10, 10, 7, 3, 2] + 4 s[10, 10, 6, 4, 2] + 2 s[12, 7, 6, 5, 2]
+ 2 s[12, 7, 6, 4, 3] + s[12, 7, 5, 5, 3] + s[12, 8, 6, 3, 3]
+ s[12, 8, 5, 5, 2] + 2 s[12, 8, 5, 4, 3] + s[12, 8, 4, 4, 4]
+ 7 s[11, 9, 6, 4, 2] + 4 s[11, 9, 6, 3, 3] + 3 s[11, 9, 5, 5, 2]
+ 6 s[11, 9, 5, 4, 3] + 2 s[11, 9, 4, 4, 4] + 3 s[11, 8, 8, 3, 2]
+ 6 s[11, 8, 7, 4, 2] + 2 s[12, 8, 7, 3, 2] + 3 s[12, 8, 6, 4, 2]
+ s[12, 7, 7, 4, 2] + s[12, 7, 7, 3, 3] + s[12, 9, 7, 2, 2]
+ 2 s[12, 9, 5, 4, 2] + s[12, 9, 5, 3, 3] + s[12, 9, 4, 4, 3]
+ s[12, 8, 8, 2, 2] + 2 s[12, 9, 6, 3, 2] + s[12, 10, 5, 3, 2]
+ s[12, 10, 4, 4, 2] + s[12, 10, 6, 2, 2] + 3 s[10, 10, 6, 3, 3]
+ 2 s[10, 10, 5, 5, 2] + 4 s[10, 10, 5, 4, 3] + s[10, 10, 4, 4, 4]
+ s[10, 9, 9, 2, 2] + 4 s[10, 9, 8, 3, 2] + 7 s[10, 9, 7, 4, 2]
+ 5 s[10, 9, 7, 3, 3] + 6 s[10, 9, 6, 5, 2] + 10 s[10, 9, 6, 4, 3]
+ 5 s[10, 9, 5, 5, 3] + 5 s[10, 9, 5, 4, 4] + 4 s[10, 8, 8, 4, 2]
+ 3 s[10, 8, 8, 3, 3] + 7 s[10, 8, 7, 5, 2] + 10 s[10, 8, 7, 4, 3]
+ 4 s[10, 8, 6, 6, 2] + 11 s[10, 8, 6, 5, 3] + 8 s[10, 8, 6, 4, 4]
--------------------------------------------------------------------------------
#
# Changes of basis...
#
--------------------------------------------------------------------------------
> expr1:=Tos(m[3,2,1,1] + m[3,1]*s[3,3,1]): expr1;
*
- 12 s[1, 1, 1, 1, 1, 1, 1] + 6 s[2, 1, 1, 1, 1, 1] - 3 s[3, 1, 1, 1, 1]
+ s[2, 2, 1, 1, 1] + s[3, 2, 1, 1] - 2 s[2, 2, 2, 1]
+ 2 s[3, 3, 1, 1, 1, 1, 1] - 2 s[3, 3, 2, 2, 1] + s[4, 3, 1, 1, 1, 1]
+ s[3, 3, 2, 1, 1, 1] + s[6, 3, 1, 1] + s[6, 3, 2] - s[5, 4, 1, 1]
- s[5, 5, 1] - s[5, 4, 2] + s[6, 4, 1] - s[4, 3, 2, 2]
> expr2:=Tos(p1^3*p2*p4); expr2;
*
s[1, 1, 1, 1, 1, 1, 1, 1, 1] + 2 s[2, 1, 1, 1, 1, 1, 1, 1]
+ s[2, 2, 1, 1, 1, 1, 1] - 2 s[4, 1, 1, 1, 1, 1] - s[3, 2, 1, 1, 1, 1]
- 2 s[5, 1, 1, 1, 1] + s[4, 2, 1, 1, 1] - 2 s[6, 1, 1, 1] + s[5, 2, 1, 1]
+ 2 s[4, 3, 1, 1] + 2 s[4, 2, 2, 1] - 2 s[3, 3, 2, 1] - s[6, 2, 1]
+ 2 s[8, 1] - 2 s[4, 3, 2] + s[7, 2] - 2 s[3, 3, 3] + s[9]
--------------------------------------------------------------------------------
#
# Some plethysms of symmetric functions (services 2, 3, 4, 7, 8, 9)
#
--------------------------------------------------------------------------------
> pl1:=SfPlethysm(s[3,1]+s[2,2], s[2,1,1], 's', 's', 's'):\
pl1;
**
2 s[7, 5, 2, 1, 1] + 3 s[7, 4, 4, 1] + s[7, 5, 2, 2] + 5 s[7, 4, 3, 2]
+ 2 s[7, 5, 3, 1] + 18 s[5, 5, 3, 1, 1, 1] + 10 s[5, 5, 2, 2, 2]
+ 9 s[5, 4, 4, 3] + 35 s[5, 3, 3, 3, 1, 1] + 7 s[7, 4, 2, 1, 1, 1]
+ 25 s[6, 4, 2, 1, 1, 1, 1] + 22 s[6, 3, 3, 1, 1, 1, 1]
+ 40 s[6, 3, 2, 2, 1, 1, 1] + 47 s[5, 4, 2, 2, 2, 1] + 29 s[5, 4, 4, 2, 1]
+ 19 s[5, 4, 4, 1, 1, 1] + 40 s[5, 4, 3, 2, 2] + 77 s[5, 4, 3, 2, 1, 1]
+ 23 s[5, 3, 3, 3, 2] + 60 s[5, 3, 3, 2, 2, 1] + 33 s[5, 4, 3, 3, 1]
+ 23 s[5, 5, 2, 2, 1, 1] + 32 s[6, 3, 2, 2, 2, 1] + 2 s[5, 5, 5, 1]
+ 7 s[5, 5, 4, 2] + 10 s[5, 5, 4, 1, 1] + 25 s[5, 5, 3, 2, 1]
+ 7 s[5, 5, 3, 3] + 28 s[6, 4, 3, 1, 1, 1] + 7 s[7, 4, 2, 2, 1]
+ 10 s[7, 3, 3, 2, 1] + 9 s[7, 3, 3, 1, 1, 1] + 6 s[7, 3, 2, 2, 2]
+ 13 s[7, 3, 2, 2, 1, 1] + s[6, 6, 3, 1] + s[6, 6, 2, 2] + s[6, 6, 2, 1, 1]
+ 5 s[6, 5, 4, 1] + 8 s[6, 5, 3, 2] + 12 s[6, 5, 3, 1, 1]
+ 10 s[6, 5, 2, 2, 1] + 10 s[6, 4, 4, 2] + 10 s[6, 4, 4, 1, 1]
+ 35 s[6, 4, 3, 2, 1] + 10 s[6, 5, 2, 1, 1, 1] + 7 s[6, 4, 3, 3]
+ 18 s[6, 4, 2, 2, 2] + 32 s[6, 4, 2, 2, 1, 1] + 16 s[6, 3, 3, 3, 1]
+ 18 s[6, 3, 3, 2, 2] + 41 s[6, 3, 3, 2, 1, 1] + 8 s[7, 4, 3, 1, 1]
+ 2 s[7, 3, 3, 3] + 15 s[4, 4, 4, 1, 1, 1, 1] + 60 s[4, 4, 3, 2, 1, 1, 1]
+ 22 s[4, 4, 2, 2, 2, 2] + 41 s[4, 4, 2, 2, 2, 1, 1] + 9 s[4, 3, 3, 3, 3]
+ 40 s[4, 3, 3, 3, 2, 1] + 34 s[4, 3, 3, 3, 1, 1, 1]
+ 28 s[4, 3, 3, 2, 2, 2] + 66 s[4, 3, 3, 2, 2, 1, 1]
+ 37 s[4, 4, 3, 3, 1, 1] + 26 s[5, 3, 2, 2, 2, 2]
+ 60 s[5, 3, 2, 2, 2, 1, 1] + 2 s[4, 4, 4, 4] + 15 s[4, 4, 4, 3, 1]
+ 17 s[4, 4, 4, 2, 2] + 25 s[4, 4, 4, 2, 1, 1] + 21 s[4, 4, 3, 3, 2]
+ 55 s[4, 4, 3, 2, 2, 1] + 58 s[5, 4, 2, 2, 1, 1, 1]
+ 15 s[5, 5, 2, 1, 1, 1, 1] + 42 s[5, 4, 3, 1, 1, 1, 1]
+ 67 s[5, 3, 3, 2, 1, 1, 1] + 5 s[5, 5, 1, 1, 1, 1, 1, 1]
+ 52 s[4, 3, 3, 2, 1, 1, 1, 1] + 21 s[4, 3, 3, 1, 1, 1, 1, 1, 1]
+ 38 s[4, 3, 2, 2, 2, 2, 1] + 50 s[4, 3, 2, 2, 2, 1, 1, 1]
+ 35 s[4, 3, 2, 2, 1, 1, 1, 1, 1] + 15 s[4, 3, 2, 1, 1, 1, 1, 1, 1, 1]
+ 3 s[4, 3, 1, 1, 1, 1, 1, 1, 1, 1, 1] + 9 s[4, 2, 2, 2, 2, 2, 2]
+ 15 s[4, 2, 2, 2, 2, 2, 1, 1] + 18 s[4, 2, 2, 2, 2, 1, 1, 1, 1]
+ 9 s[4, 2, 2, 2, 1, 1, 1, 1, 1, 1] + 13 s[3, 3, 3, 3, 1, 1, 1, 1]
+ 20 s[3, 3, 3, 2, 2, 2, 1] + 31 s[5, 3, 3, 1, 1, 1, 1, 1]
+ 53 s[5, 3, 2, 2, 1, 1, 1, 1] + 28 s[5, 3, 2, 1, 1, 1, 1, 1, 1]
+ 7 s[5, 3, 1, 1, 1, 1, 1, 1, 1, 1] + 17 s[5, 2, 2, 2, 2, 2, 1]
+ 23 s[5, 2, 2, 2, 2, 1, 1, 1] + 17 s[5, 2, 2, 2, 1, 1, 1, 1, 1]
+ 8 s[5, 2, 2, 1, 1, 1, 1, 1, 1, 1] + 2 s[5, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1]
+ 25 s[4, 4, 3, 1, 1, 1, 1, 1] + 40 s[4, 4, 2, 2, 1, 1, 1, 1]
+ 18 s[4, 4, 2, 1, 1, 1, 1, 1, 1] + 5 s[4, 4, 1, 1, 1, 1, 1, 1, 1, 1]
+ 34 s[5, 4, 2, 1, 1, 1, 1, 1] + 9 s[5, 4, 1, 1, 1, 1, 1, 1, 1]
+ 7 s[6, 4, 1, 1, 1, 1, 1, 1] + 9 s[6, 3, 1, 1, 1, 1, 1, 1, 1]
+ 9 s[6, 2, 2, 2, 2, 2] + 15 s[6, 2, 2, 2, 2, 1, 1]
+ 18 s[6, 2, 2, 2, 1, 1, 1, 1] + 9 s[6, 2, 2, 1, 1, 1, 1, 1, 1]
+ 4 s[6, 2, 1, 1, 1, 1, 1, 1, 1, 1] + 25 s[6, 3, 2, 1, 1, 1, 1, 1]
+ 3 s[6, 5, 1, 1, 1, 1, 1] + 11 s[7, 3, 2, 1, 1, 1, 1]
+ 4 s[7, 3, 1, 1, 1, 1, 1, 1] + 6 s[7, 2, 2, 2, 2, 1]
+ 8 s[7, 2, 2, 2, 1, 1, 1] + 6 s[7, 2, 2, 1, 1, 1, 1, 1]
+ 3 s[7, 2, 1, 1, 1, 1, 1, 1, 1] + s[7, 1, 1, 1, 1, 1, 1, 1, 1, 1]
+ s[8, 4, 3, 1] + 2 s[8, 3, 3, 1, 1] + s[8, 3, 2, 2, 1]
+ 2 s[8, 3, 2, 1, 1, 1] + s[8, 2, 2, 2, 1, 1] + 2 s[8, 2, 2, 1, 1, 1, 1]
+ s[8, 2, 1, 1, 1, 1, 1, 1] + s[7, 5, 4] + 2 s[7, 4, 1, 1, 1, 1, 1]
+ 3 s[3, 2, 2, 2, 1, 1, 1, 1, 1, 1, 1] + s[2, 2, 2, 2, 2, 2, 2, 1, 1]
+ 2 s[2, 2, 2, 2, 2, 2, 1, 1, 1, 1] + s[2, 2, 2, 2, 2, 1, 1, 1, 1, 1, 1]
+ s[3, 2, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1] + 25 s[3, 3, 3, 2, 2, 1, 1, 1]
+ 16 s[3, 3, 3, 2, 1, 1, 1, 1, 1] + 5 s[3, 3, 3, 1, 1, 1, 1, 1, 1, 1]
+ 6 s[3, 3, 2, 2, 2, 2, 2] + 19 s[3, 3, 2, 2, 2, 2, 1, 1]
+ 17 s[3, 3, 2, 2, 2, 1, 1, 1, 1] + 11 s[3, 3, 2, 2, 1, 1, 1, 1, 1, 1]
+ 3 s[3, 3, 2, 1, 1, 1, 1, 1, 1, 1, 1] + 6 s[3, 2, 2, 2, 2, 2, 2, 1]
+ 8 s[3, 2, 2, 2, 2, 2, 1, 1, 1] + 6 s[3, 2, 2, 2, 2, 1, 1, 1, 1, 1]
+ 4 s[4, 2, 2, 1, 1, 1, 1, 1, 1, 1, 1] + 11 s[3, 3, 3, 3, 2, 2]
+ 20 s[3, 3, 3, 3, 2, 1, 1] + 6 s[3, 3, 3, 3, 3, 1]
+ s[2, 2, 2, 2, 2, 2, 2, 2] + s[3, 3, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1]
+ s[6, 6, 4] + s[6, 6, 1, 1, 1, 1] + s[8, 4, 2, 2] + s[8, 2, 2, 2, 2]
> pl2:=SfPlethysm(s[4], s[8], 's', 's', 's'): pl2;
*
s[19, 6, 5, 2] + 3 s[14, 12, 4, 2] + 2 s[15, 11, 4, 2] + 4 s[16, 10, 4, 2]
+ s[8, 8, 8, 8] + s[12, 9, 8, 3] + s[13, 8, 8, 3] + s[12, 10, 7, 3]
+ 2 s[13, 9, 7, 3] + s[14, 8, 7, 3] + s[12, 11, 6, 3] + 2 s[13, 10, 6, 3]
+ 2 s[14, 9, 6, 3] + s[13, 12, 5, 2] + 2 s[14, 11, 5, 2]
+ 3 s[15, 10, 5, 2] + 2 s[16, 9, 5, 2] + 3 s[17, 8, 5, 2] + s[18, 7, 5, 2]
+ s[12, 12, 4, 4] + 2 s[14, 10, 4, 4] + 2 s[16, 8, 4, 4] + s[17, 7, 4, 4]
+ s[18, 6, 4, 4] + s[20, 4, 4, 4] + s[11, 10, 8, 3] + 2 s[12, 12, 6, 2]
+ 4 s[14, 10, 6, 2] + 3 s[15, 9, 6, 2] + 4 s[16, 8, 6, 2] + s[17, 7, 6, 2]
+ 2 s[18, 6, 6, 2] + s[13, 11, 6, 2] + 2 s[12, 10, 8, 2] + 3 s[14, 8, 8, 2]
+ s[12, 11, 7, 2] + 2 s[13, 10, 7, 2] + s[14, 9, 7, 2] + 2 s[15, 8, 7, 2]
+ s[13, 9, 8, 2] + s[17, 8, 4, 3] + s[18, 7, 4, 3] + s[19, 6, 4, 3]
+ s[13, 13, 3, 3] + s[15, 11, 3, 3] + s[17, 9, 3, 3] + s[10, 10, 10, 2]
+ s[17, 7, 5, 3] + s[13, 12, 4, 3] + s[14, 11, 4, 3] + 2 s[15, 10, 4, 3]
+ 2 s[16, 9, 4, 3] + 2 s[15, 8, 6, 3] + s[16, 7, 6, 3] + s[17, 6, 6, 3]
+ 2 s[13, 11, 5, 3] + s[14, 10, 5, 3] + 2 s[15, 9, 5, 3] + s[16, 8, 5, 3]
+ s[15, 7, 6, 4] + s[16, 6, 6, 4] + s[13, 10, 5, 4] + s[14, 9, 5, 4]
+ s[15, 8, 5, 4] + s[13, 8, 7, 4] + 2 s[12, 10, 6, 4] + s[13, 9, 6, 4]
+ 2 s[14, 8, 6, 4] + s[12, 9, 6, 5] + s[13, 8, 6, 5] + s[11, 11, 5, 5]
+ s[10, 10, 8, 4] + 2 s[12, 8, 8, 4] + s[11, 10, 7, 4] + 3 s[17, 13, 2]
+ 6 s[18, 12, 2] + 5 s[19, 11, 2] + 7 s[20, 10, 2] + 5 s[21, 9, 2]
+ 5 s[21, 8, 3] + 3 s[22, 7, 3] + 3 s[23, 6, 3] + s[24, 5, 3] + s[25, 4, 3]
+ 4 s[16, 14, 2] + 2 s[15, 14, 3] + 3 s[16, 13, 3] + 5 s[17, 12, 3]
+ 5 s[18, 11, 3] + 6 s[19, 10, 3] + 5 s[20, 9, 3] + 8 s[18, 10, 4]
+ 7 s[20, 8, 4] + 4 s[21, 7, 4] + 4 s[22, 6, 4] + s[23, 5, 4]
+ 2 s[24, 4, 4] + 6 s[19, 9, 4] + 2 s[21, 6, 5] + 2 s[14, 14, 4]
+ 2 s[15, 13, 4] + 7 s[16, 12, 4] + 5 s[17, 11, 4] + s[24, 5, 2, 1]
+ s[15, 15, 1, 1] + 2 s[17, 13, 1, 1] + 2 s[19, 11, 1, 1] + s[20, 10, 1, 1]
+ s[25, 4, 2, 1] + 7 s[16, 10, 6] + 5 s[17, 9, 6] + 6 s[18, 8, 6]
+ 3 s[19, 7, 6] + 3 s[20, 6, 6] + 2 s[14, 13, 5] + 4 s[15, 10, 7]
+ 3 s[16, 9, 7] + 3 s[17, 8, 7] + 4 s[14, 12, 6] + 4 s[15, 11, 6]
+ s[13, 11, 8] + 4 s[14, 10, 8] + 2 s[15, 9, 8] + 4 s[16, 8, 8]
+ 2 s[13, 12, 7] + 2 s[14, 11, 7] + s[21, 9, 1, 1] + s[23, 7, 1, 1]
+ s[12, 10, 10] + s[13, 10, 9] + 2 s[12, 12, 8] + 2 s[20, 8, 3, 1]
+ s[22, 6, 3, 1] + s[23, 5, 3, 1] + s[15, 14, 2, 1] + 2 s[16, 13, 2, 1]
+ 2 s[21, 7, 3, 1] + 3 s[17, 12, 2, 1] + 3 s[19, 10, 2, 1]
+ 3 s[20, 9, 2, 1] + 3 s[21, 8, 2, 1] + 2 s[22, 7, 2, 1] + s[23, 6, 2, 1]
+ 3 s[18, 11, 2, 1] + 3 s[17, 9, 4, 2] + 2 s[19, 7, 4, 2]
+ 2 s[20, 6, 4, 2] + s[21, 5, 4, 2] + s[22, 4, 4, 2] + 4 s[18, 8, 4, 2]
+ 2 s[21, 6, 4, 1] + s[23, 4, 4, 1] + 3 s[15, 13, 3, 1] + 2 s[16, 12, 3, 1]
+ 4 s[17, 11, 3, 1] + 3 s[18, 10, 3, 1] + 4 s[19, 9, 3, 1] + s[22, 5, 4, 1]
+ 4 s[16, 11, 4, 1] + 5 s[17, 10, 4, 1] + 4 s[18, 9, 4, 1]
+ 4 s[19, 8, 4, 1] + 3 s[20, 7, 4, 1] + 4 s[16, 10, 5, 1]
+ 3 s[18, 8, 5, 1] + 2 s[19, 7, 5, 1] + s[20, 6, 5, 1] + 2 s[14, 13, 4, 1]
+ 3 s[15, 12, 4, 1] + 4 s[17, 9, 5, 1] + 4 s[15, 10, 6, 1]
+ 4 s[17, 8, 6, 1] + 2 s[18, 7, 6, 1] + s[19, 6, 6, 1] + s[13, 13, 5, 1]
+ 2 s[14, 12, 5, 1] + 4 s[15, 11, 5, 1] + 4 s[16, 9, 6, 1]
+ 2 s[14, 9, 8, 1] + 2 s[13, 11, 7, 1] + 3 s[14, 10, 7, 1]
+ 3 s[15, 9, 7, 1] + 2 s[16, 8, 7, 1] + s[17, 7, 7, 1] + 2 s[13, 12, 6, 1]
+ 3 s[14, 11, 6, 1] + 2 s[15, 8, 8, 1] + s[21, 7, 2, 2] + s[23, 5, 2, 2]
+ s[24, 4, 2, 2] + s[26, 2, 2, 2] + s[12, 10, 9, 1] + s[12, 11, 8, 1]
+ 2 s[13, 10, 8, 1] + 2 s[22, 6, 2, 2] + s[20, 7, 3, 2] + 2 s[14, 14, 2, 2]
+ 2 s[16, 12, 2, 2] + s[17, 11, 2, 2] + 3 s[18, 10, 2, 2] + s[19, 9, 2, 2]
+ 3 s[20, 8, 2, 2] + s[21, 6, 3, 2] + 2 s[15, 12, 3, 2] + 2 s[16, 11, 3, 2]
+ 2 s[17, 10, 3, 2] + 2 s[18, 9, 3, 2] + 2 s[19, 8, 3, 2] + s[10, 8, 8, 6]
+ s[12, 8, 6, 6] + s[14, 6, 6, 6] + s[11, 8, 8, 5] + s[11, 9, 7, 5]
+ s[10, 10, 6, 6] + 4 s[24, 8] + 2 s[25, 7] + 3 s[26, 6] + 2 s[23, 9]
+ 4 s[20, 12] + 2 s[21, 11] + 4 s[22, 10] + s[19, 13] + 4 s[15, 12, 5]
+ 6 s[17, 10, 5] + 5 s[18, 9, 5] + 5 s[19, 8, 5] + 2 s[20, 7, 5]
+ 4 s[16, 11, 5] + 3 s[18, 13, 1] + 4 s[19, 12, 1] + 3 s[20, 11, 1]
+ 4 s[21, 10, 1] + 4 s[22, 9, 1] + 3 s[23, 8, 1] + 2 s[24, 7, 1]
+ 2 s[25, 6, 1] + 6 s[22, 8, 2] + 4 s[24, 6, 2] + 2 s[25, 5, 2]
+ 2 s[26, 4, 2] + s[27, 3, 2] + s[28, 2, 2] + s[16, 15, 1] + 2 s[17, 14, 1]
+ 4 s[23, 7, 2] + s[26, 5, 1] + 2 s[16, 16] + 3 s[18, 14] + s[27, 4, 1]
+ s[32] + s[27, 5] + 2 s[28, 4] + s[29, 3] + s[30, 2]
> HubParallel([3,4], [[s[6],s[10],4], [s[5],s[10],20]]): print(");
#
[
853 s[23, 15, 12, 10] + 361 s[27, 13, 10, 10] + 259 s[28, 12, 10, 10]
+ 125 s[29, 11, 10, 10] + 60 s[30, 10, 10, 10] + 14 s[17, 17, 17, 9]
+ 106 s[18, 17, 16, 9] + 134 s[19, 16, 16, 9] + 122 s[18, 18, 15, 9]
+ 323 s[19, 17, 15, 9] + 387 s[20, 16, 15, 9] + 270 s[21, 15, 15, 9]
+ 382 s[19, 18, 14, 9] + 661 s[20, 17, 14, 9] + 774 s[21, 16, 14, 9]
+ 665 s[22, 15, 14, 9] + 404 s[23, 14, 14, 9] + 83 s[20, 14, 14, 12]
+ 80 s[18, 17, 13, 12] + 141 s[19, 16, 13, 12] + 7 s[16, 16, 14, 14]
+ 5 s[17, 15, 14, 14] + 426 s[20, 20, 12, 8] + 1111 s[21, 19, 12, 8]
+ 1730 s[22, 18, 12, 8] + 2003 s[23, 17, 12, 8] + 2108 s[24, 16, 12, 8]
+ 1858 s[25, 15, 12, 8] + 1512 s[26, 14, 12, 8] + 960 s[27, 13, 12, 8]
+ 487 s[28, 12, 12, 8] + 775 s[21, 20, 11, 8] + 1443 s[22, 19, 11, 8]
+ 1937 s[23, 18, 11, 8] + 2177 s[24, 17, 11, 8] + 2202 s[25, 16, 11, 8]
+ 1971 s[26, 15, 11, 8] + 1625 s[27, 14, 11, 8] + 1137 s[28, 13, 11, 8]
+ 146 s[22, 14, 12, 12] + 929 s[23, 15, 14, 8] + 32 s[18, 15, 14, 13]
+ 24 s[19, 14, 14, 13] + 11 s[18, 14, 14, 14] + 42 s[18, 17, 17, 8]
+ 110 s[18, 18, 16, 8] + 226 s[19, 17, 16, 8] + 243 s[20, 16, 16, 8]
+ 347 s[19, 18, 15, 8] + 563 s[20, 17, 15, 8] + 608 s[21, 16, 15, 8]
+ 374 s[22, 15, 15, 8] + 256 s[19, 19, 14, 8] + 783 s[20, 18, 14, 8]
+ 93 s[18, 16, 15, 11] + 137 s[18, 17, 14, 11] + 227 s[19, 16, 14, 11]
+ 226 s[20, 15, 14, 11] + 151 s[21, 14, 14, 11] + 85 s[18, 18, 13, 11]
+ 260 s[19, 17, 13, 11] + 343 s[20, 16, 13, 11] + 353 s[21, 15, 13, 11]
+ 83 s[19, 15, 15, 11] + 477 s[28, 12, 11, 9] + 179 s[29, 11, 11, 9]
+ 440 s[21, 20, 10, 9] + 828 s[22, 19, 10, 9] + 1111 s[23, 18, 10, 9]
+ 1259 s[24, 17, 10, 9] + 1287 s[25, 16, 10, 9] + 1177 s[26, 15, 10, 9]
+ 990 s[27, 14, 10, 9] + 739 s[28, 13, 10, 9] + 494 s[29, 12, 10, 9]
+ 256 s[30, 11, 10, 9] + 106 s[31, 10, 10, 9] + 136 s[21, 21, 9, 9]
+ 320 s[22, 20, 9, 9] + 538 s[23, 19, 9, 9] + 629 s[24, 18, 9, 9]
+ 714 s[25, 17, 9, 9] + 677 s[26, 16, 9, 9] + 635 s[27, 15, 9, 9]
+ 507 s[28, 14, 9, 9] + 393 s[29, 13, 9, 9] + 254 s[30, 12, 9, 9]
+ 146 s[31, 11, 9, 9] + 62 s[32, 10, 9, 9] + 13 s[33, 9, 9, 9]
+ 4 s[16, 16, 15, 13] + 11 s[17, 15, 15, 13] + 24 s[17, 16, 14, 13]
+ 1091 s[25, 14, 12, 9] + 711 s[26, 13, 12, 9] + 348 s[27, 12, 12, 9]
+ 264 s[20, 20, 11, 9] + 800 s[21, 19, 11, 9] + 1177 s[22, 18, 11, 9]
+ 1433 s[23, 17, 11, 9] + 1475 s[24, 16, 11, 9] + 1372 s[25, 15, 11, 9]
+ 1125 s[26, 14, 11, 9] + 806 s[27, 13, 11, 9] + 17 s[17, 17, 13, 13]
+ 40 s[19, 15, 13, 13] + 26 s[20, 14, 13, 13] + 25 s[18, 16, 13, 13]
+ 264 s[19, 19, 13, 9] + 707 s[20, 18, 13, 9] + 1025 s[21, 17, 13, 9]
+ 1139 s[22, 16, 13, 9] + 1038 s[23, 15, 13, 9] + 769 s[24, 14, 13, 9]
+ 378 s[25, 13, 13, 9] + 570 s[20, 19, 12, 9] + 1348 s[22, 17, 12, 9]
+ 1457 s[23, 16, 12, 9] + 1345 s[24, 15, 12, 9] + 1047 s[21, 18, 12, 9]
+ 28 s[17, 17, 14, 12] + 100 s[18, 16, 14, 12] + 99 s[19, 15, 14, 12]
+ s[15, 15, 15, 15] + s[16, 15, 15, 14] + 94 s[19, 17, 12, 12]
+ 150 s[21, 15, 12, 12] + 84 s[23, 13, 12, 12] + 51 s[24, 12, 12, 12]
+ 23 s[17, 16, 16, 11] + 42 s[17, 17, 15, 11] + 161 s[20, 16, 12, 12]
+ 111 s[25, 12, 12, 11] + 78 s[19, 19, 11, 11] + 167 s[20, 18, 11, 11]
+ 276 s[21, 17, 11, 11] + 291 s[22, 16, 11, 11] + 301 s[23, 15, 11, 11]
+ 238 s[24, 14, 11, 11] + 174 s[25, 13, 11, 11] + 423 s[22, 15, 12, 11]
+ 89 s[26, 12, 11, 11] + 28 s[27, 11, 11, 11] + 27 s[17, 17, 16, 10]
+ 76 s[18, 16, 16, 10] + 137 s[18, 17, 15, 10] + 218 s[19, 16, 15, 10]
+ 152 s[20, 15, 15, 10] + 13 s[21, 13, 13, 13] + 10 s[16, 16, 16, 12]
+ 32 s[17, 16, 15, 12] + 29 s[18, 15, 15, 12] + 146 s[20, 15, 13, 12]
+ 122 s[21, 14, 13, 12] + 51 s[22, 13, 13, 12] + 52 s[18, 18, 12, 12]
+ 426 s[34, 16, 5, 5] + 376 s[35, 15, 5, 5] + 293 s[36, 14, 5, 5]
+ 234 s[37, 13, 5, 5] + 162 s[38, 12, 5, 5] + 117 s[39, 11, 5, 5]
+ 69 s[40, 10, 5, 5] + 42 s[41, 9, 5, 5] + 20 s[42, 8, 5, 5]
+ 9 s[43, 7, 5, 5] + 2 s[44, 6, 5, 5] + 42 s[19, 19, 18, 4]
+ 108 s[20, 18, 18, 4] + 217 s[20, 19, 17, 4] + 342 s[21, 18, 17, 4]
+ 258 s[22, 17, 17, 4] + 232 s[20, 20, 16, 4] + 564 s[21, 19, 16, 4]
+ 808 s[22, 18, 16, 4] + 752 s[23, 17, 16, 4] + 527 s[24, 16, 16, 4]
+ 602 s[21, 20, 15, 4] + 1080 s[22, 19, 15, 4] + 1366 s[23, 18, 15, 4]
+ 1351 s[24, 17, 15, 4] + 1123 s[25, 16, 15, 4] + 596 s[26, 15, 15, 4]
+ 303 s[38, 11, 6, 5] + 198 s[39, 10, 6, 5] + 115 s[40, 9, 6, 5]
+ 64 s[41, 8, 6, 5] + 27 s[42, 7, 6, 5] + 11 s[43, 6, 6, 5]
+ 84 s[25, 25, 5, 5] + 188 s[26, 24, 5, 5] + 339 s[27, 23, 5, 5]
+ 407 s[28, 22, 5, 5] + 506 s[29, 21, 5, 5] + 523 s[30, 20, 5, 5]
+ 558 s[31, 19, 5, 5] + 520 s[32, 18, 5, 5] + 502 s[33, 17, 5, 5]
+ 638 s[26, 23, 6, 5] + 1102 s[28, 21, 6, 5] + 1234 s[29, 20, 6, 5]
+ 1289 s[30, 19, 6, 5] + 1278 s[31, 18, 6, 5] + 1201 s[32, 17, 6, 5]
+ 1082 s[33, 16, 6, 5] + 926 s[34, 15, 6, 5] + 762 s[35, 14, 6, 5]
+ 591 s[36, 13, 6, 5] + 440 s[37, 12, 6, 5] + 901 s[27, 22, 6, 5]
+ 147 s[39, 9, 7, 5] + 251 s[24, 24, 7, 5] + 1220 s[26, 22, 7, 5]
+ 1610 s[27, 21, 7, 5] + 1834 s[28, 20, 7, 5] + 1988 s[29, 19, 7, 5]
+ 1974 s[30, 18, 7, 5] + 1895 s[31, 17, 7, 5] + 1696 s[32, 16, 7, 5]
+ 1468 s[33, 15, 7, 5] + 1188 s[34, 14, 7, 5] + 923 s[35, 13, 7, 5]
+ 663 s[36, 12, 7, 5] + 448 s[37, 11, 7, 5] + 274 s[38, 10, 7, 5]
+ 68 s[40, 8, 7, 5] + 19 s[41, 7, 7, 5] + 331 s[25, 24, 6, 5]
+ 794 s[25, 23, 7, 5] + 173 s[38, 9, 8, 5] + 2001 s[26, 21, 8, 5]
+ 2423 s[27, 20, 8, 5] + 2663 s[28, 19, 8, 5] + 2732 s[29, 18, 8, 5]
+ 2629 s[30, 17, 8, 5] + 2402 s[31, 16, 8, 5] + 2066 s[32, 15, 8, 5]
+ 1695 s[33, 14, 8, 5] + 1293 s[34, 13, 8, 5] + 933 s[35, 12, 8, 5]
+ 606 s[36, 11, 8, 5] + 362 s[37, 10, 8, 5] + 69 s[39, 8, 8, 5]
+ 2140 s[25, 21, 9, 5] + 3111 s[27, 19, 9, 5] + 3239 s[28, 18, 9, 5]
+ 3175 s[29, 17, 9, 5] + 2905 s[30, 16, 9, 5] + 2513 s[31, 15, 9, 5]
+ 2035 s[32, 14, 9, 5] + 1534 s[33, 13, 9, 5] + 1065 s[34, 12, 9, 5]
+ 652 s[35, 11, 9, 5] + 344 s[36, 10, 9, 5] + 115 s[37, 9, 9, 5]
+ 745 s[24, 23, 8, 5] + 1431 s[25, 22, 8, 5] + 2715 s[26, 20, 9, 5]
+ 3306 s[28, 16, 11, 5] + 2229 s[30, 14, 11, 5] + 1556 s[31, 13, 11, 5]
+ 935 s[32, 12, 11, 5] + 380 s[33, 11, 11, 5] + 1067 s[23, 22, 10, 5]
+ 2028 s[24, 21, 10, 5] + 2811 s[25, 20, 10, 5] + 3337 s[26, 19, 10, 5]
+ 3591 s[27, 18, 10, 5] + 3557 s[28, 17, 10, 5] + 3304 s[29, 16, 10, 5]
+ 2843 s[30, 15, 10, 5] + 2300 s[31, 14, 10, 5] + 1688 s[32, 13, 10, 5]
+ 1134 s[33, 12, 10, 5] + 626 s[34, 11, 10, 5] + 268 s[35, 10, 10, 5]
+ 477 s[23, 23, 9, 5] + 1346 s[24, 22, 9, 5] + 2830 s[29, 15, 11, 5]
+ 2038 s[24, 17, 14, 5] + 482 s[23, 16, 16, 5] + 305 s[20, 20, 15, 5]
+ 854 s[21, 19, 15, 5] + 1213 s[22, 18, 15, 5] + 1302 s[23, 17, 15, 5]
+ 1109 s[24, 16, 15, 5] + 631 s[25, 15, 15, 5] + 811 s[21, 20, 14, 5]
+ 1487 s[22, 19, 14, 5] + 1922 s[23, 18, 14, 5] + 1861 s[25, 16, 14, 5]
+ 1379 s[26, 15, 14, 5] + 750 s[27, 14, 14, 5] + 498 s[21, 21, 13, 5]
+ 1420 s[22, 20, 13, 5] + 2160 s[23, 19, 13, 5] + 2602 s[24, 18, 13, 5]
+ 2718 s[25, 17, 13, 5] + 2522 s[26, 16, 13, 5] + 2038 s[27, 15, 13, 5]
+ 1406 s[28, 14, 13, 5] + 665 s[29, 13, 13, 5] + 1093 s[22, 21, 12, 5]
+ 2061 s[23, 20, 12, 5] + 2788 s[24, 19, 12, 5] + 3215 s[25, 18, 12, 5]
+ 3293 s[26, 17, 12, 5] + 3083 s[27, 16, 12, 5] + 2590 s[28, 15, 12, 5]
+ 1971 s[29, 14, 12, 5] + 1245 s[30, 13, 12, 5] + 592 s[31, 12, 12, 5]
+ 559 s[22, 22, 11, 5] + 1642 s[23, 21, 11, 5] + 2529 s[24, 20, 11, 5]
+ 3190 s[25, 19, 11, 5] + 3523 s[26, 18, 11, 5] + 3558 s[27, 17, 11, 5]
+ 1370 s[31, 16, 7, 6] + 973 s[33, 14, 7, 6] + 747 s[34, 13, 7, 6]
+ 548 s[35, 12, 7, 6] + 359 s[36, 11, 7, 6] + 226 s[37, 10, 7, 6]
+ 114 s[38, 9, 7, 6] + 54 s[39, 8, 7, 6] + 12 s[40, 7, 7, 6]
+ 126 s[24, 24, 6, 6] + 285 s[25, 23, 6, 6] + 502 s[26, 22, 6, 6]
+ 609 s[27, 21, 6, 6] + 746 s[28, 20, 6, 6] + 764 s[29, 19, 6, 6]
+ 808 s[30, 18, 6, 6] + 742 s[31, 17, 6, 6] + 703 s[32, 16, 6, 6]
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+ 62 s[19, 16, 12, 3] + 4 s[16, 15, 8, 7, 4] + 20 s[20, 20, 6, 4]
+ 13 s[17, 16, 14, 3] + 4 s[17, 15, 15, 3] + 19 s[18, 15, 14, 3]
+ 11 s[17, 17, 13, 3] + 31 s[18, 16, 13, 3] + 17 s[19, 14, 14, 3]
+ 4 s[20, 10, 9, 7, 4] + 3 s[16, 16, 15, 3] + 7 s[19, 11, 9, 7, 4]
+ 92 s[20, 17, 9, 4] + 75 s[20, 18, 8, 4] + 41 s[20, 19, 7, 4]
+ 21 s[19, 19, 8, 4] + 29 s[18, 18, 10, 4] + 68 s[19, 17, 10, 4]
+ 114 s[20, 16, 10, 4] + 50 s[19, 18, 9, 4] + 9 s[18, 12, 9, 7, 4]
+ 35 s[19, 14, 13, 4] + 49 s[18, 16, 12, 4] + 13 s[17, 17, 12, 4]
+ 61 s[19, 15, 12, 4] + 39 s[18, 17, 11, 4] + 75 s[19, 16, 11, 4]
+ 91 s[20, 15, 11, 4] + 74 s[20, 14, 12, 4] + 10 s[17, 13, 9, 7, 4]
+ 18 s[20, 13, 13, 4] + 6 s[16, 14, 9, 7, 4] + 12 s[17, 15, 14, 4]
+ 3 s[15, 15, 9, 7, 4] + s[16, 15, 15, 4] + 17 s[18, 14, 14, 4]
+ 20 s[17, 16, 13, 4] + 29 s[18, 15, 13, 4] + 8 s[16, 16, 14, 4]
+ 6 s[19, 10, 10, 7, 4] + 22 s[20, 19, 6, 5] + 3 s[20, 20, 5, 5]
+ 8 s[18, 11, 10, 7, 4] + 11 s[17, 12, 10, 7, 4] + 10 s[16, 13, 10, 7, 4]
+ 40 s[19, 18, 8, 5] + 75 s[20, 17, 8, 5] + 18 s[19, 19, 7, 5]
+ 43 s[20, 18, 7, 5] + 6 s[15, 14, 10, 7, 4] + 3 s[17, 11, 11, 7, 4]
+ 2 s[18, 14, 7, 7, 4] + 3 s[17, 15, 7, 7, 4] + 7 s[20, 11, 8, 7, 4]
+ 30 s[20, 18, 12] + 20 s[20, 19, 11] + 17 s[20, 20, 10] + 20 s[20, 16, 14]
+ 13 s[19, 18, 13] + 20 s[20, 17, 13] + 6 s[19, 19, 12] + 3 s[20, 15, 15]
+ 10 s[19, 17, 14] + 7 s[18, 18, 14] + 3 s[18, 17, 15] + 7 s[19, 16, 15]
+ 50 s[20, 18, 11, 1] + 41 s[20, 19, 10, 1] + 20 s[20, 20, 9, 1]
+ 4 s[18, 16, 16] + 41 s[20, 16, 13, 1] + 28 s[19, 18, 12, 1]
+ 51 s[20, 17, 12, 1] + 19 s[19, 19, 11, 1] + 22 s[20, 15, 14, 1]
+ 10 s[18, 18, 13, 1] + 28 s[19, 17, 13, 1] + 9 s[19, 12, 8, 7, 4]
+ 9 s[18, 13, 8, 7, 4] + 3 s[17, 17, 15, 1] + 7 s[19, 15, 15, 1]
+ 12 s[18, 17, 14, 1] + 22 s[19, 16, 14, 1] + 8 s[18, 16, 15, 1]
+ 30 s[20, 20, 8, 2] + 2 s[17, 16, 16, 1] + 9 s[20, 11, 9, 6, 4]
+ 14 s[19, 12, 9, 6, 4] + 13 s[18, 13, 9, 6, 4] + 12 s[17, 14, 9, 6, 4]
+ 7 s[16, 15, 9, 6, 4] + 8 s[20, 10, 10, 6, 4] + 9 s[19, 11, 10, 6, 4]
+ 16 s[18, 12, 10, 6, 4] + 12 s[17, 13, 10, 6, 4] + 12 s[16, 14, 10, 6, 4]
+ 2 s[15, 15, 10, 6, 4] + 2 s[18, 11, 11, 6, 4] + 8 s[17, 12, 11, 6, 4]
+ 6 s[16, 13, 11, 6, 4] + 5 s[15, 14, 11, 6, 4] + 6 s[16, 12, 12, 6, 4]
+ 3 s[15, 13, 12, 6, 4] + 3 s[14, 14, 12, 6, 4] + 2 s[20, 12, 7, 7, 4]
+ 4 s[19, 13, 7, 7, 4] + 7 s[16, 14, 11, 5, 4] + 3 s[15, 15, 11, 5, 4]
+ 4 s[17, 12, 12, 5, 4] + 4 s[16, 13, 12, 5, 4] + 3 s[15, 14, 12, 5, 4]
+ s[15, 13, 13, 5, 4] + s[14, 14, 13, 5, 4] + 8 s[20, 14, 6, 6, 4]
+ 5 s[19, 15, 6, 6, 4] + 5 s[18, 16, 6, 6, 4] + 9 s[20, 13, 7, 6, 4]
+ 9 s[19, 14, 7, 6, 4] + 7 s[18, 15, 7, 6, 4] + 4 s[17, 16, 7, 6, 4]
+ 16 s[20, 12, 8, 6, 4] + 14 s[19, 13, 8, 6, 4] + 15 s[18, 14, 8, 6, 4]
+ 8 s[17, 15, 8, 6, 4] + 5 s[16, 16, 8, 6, 4] + 5 s[18, 16, 7, 5, 4]
+ 3 s[17, 17, 7, 5, 4] + 14 s[20, 13, 8, 5, 4] + 14 s[19, 14, 8, 5, 4]
+ 11 s[18, 15, 8, 5, 4] + 6 s[17, 16, 8, 5, 4] + 12 s[20, 12, 9, 5, 4]
+ 13 s[19, 13, 9, 5, 4] + 13 s[18, 14, 9, 5, 4] + 9 s[17, 15, 9, 5, 4]
+ 2 s[16, 16, 9, 5, 4] + 9 s[20, 11, 10, 5, 4] + 13 s[19, 12, 10, 5, 4]
+ 13 s[18, 13, 10, 5, 4] + 12 s[17, 14, 10, 5, 4] + 6 s[16, 15, 10, 5, 4]
+ 4 s[19, 11, 11, 5, 4] + 7 s[18, 12, 11, 5, 4] + 8 s[17, 13, 11, 5, 4]
+ 5 s[17, 16, 9, 4, 4] + 12 s[20, 12, 10, 4, 4] + 9 s[19, 13, 10, 4, 4]
+ 12 s[18, 14, 10, 4, 4] + 5 s[17, 15, 10, 4, 4] + 5 s[16, 16, 10, 4, 4]
+ s[20, 11, 11, 4, 4] + 5 s[19, 12, 11, 4, 4] + 5 s[18, 13, 11, 4, 4]
+ 6 s[17, 14, 11, 4, 4] + 2 s[16, 15, 11, 4, 4] + 5 s[18, 12, 12, 4, 4]
+ 3 s[17, 13, 12, 4, 4] + 5 s[16, 14, 12, 4, 4] + s[15, 14, 13, 4, 4]
+ s[14, 14, 14, 4, 4] + s[20, 16, 5, 5, 4] + 2 s[19, 17, 5, 5, 4]
+ 7 s[20, 15, 6, 5, 4] + 5 s[19, 16, 6, 5, 4] + 3 s[18, 17, 6, 5, 4]
+ 10 s[20, 14, 7, 5, 4] + 9 s[19, 15, 7, 5, 4] + 8 s[20, 16, 6, 4, 4]
+ 3 s[19, 17, 6, 4, 4] + 3 s[18, 18, 6, 4, 4] + 8 s[20, 15, 7, 4, 4]
+ 7 s[19, 16, 7, 4, 4] + 3 s[18, 17, 7, 4, 4] + 14 s[20, 14, 8, 4, 4]
+ 8 s[19, 15, 8, 4, 4] + 9 s[18, 16, 8, 4, 4] + s[17, 17, 8, 4, 4]
+ 10 s[20, 13, 9, 4, 4] + 11 s[19, 14, 9, 4, 4] + 7 s[18, 15, 9, 4, 4]
+ 7 s[15, 14, 10, 8, 3] + 3 s[17, 11, 11, 8, 3] + 7 s[16, 12, 11, 8, 3]
+ 5 s[15, 13, 11, 8, 3] + 4 s[15, 12, 12, 8, 3] + 2 s[14, 13, 12, 8, 3]
+ s[19, 10, 9, 9, 3] + 2 s[18, 11, 9, 9, 3] + 3 s[17, 12, 9, 9, 3]
+ 3 s[16, 13, 9, 9, 3] + s[15, 14, 9, 9, 3] + 3 s[18, 10, 10, 9, 3]
+ 5 s[17, 11, 10, 9, 3] + 6 s[16, 12, 10, 9, 3] + 5 s[15, 13, 10, 9, 3]
+ s[14, 14, 10, 9, 3] + s[16, 11, 11, 9, 3] + 3 s[15, 12, 11, 9, 3]
+ 2 s[14, 13, 11, 9, 3] + 2 s[14, 12, 12, 9, 3] + 3 s[17, 10, 10, 10, 3]
+ 3 s[16, 11, 10, 10, 3] + 3 s[15, 12, 10, 10, 3] + 2 s[14, 13, 10, 10, 3]
+ s[14, 12, 11, 10, 3] + s[13, 12, 12, 10, 3] + 2 s[20, 18, 4, 4, 4]
+ 3 s[20, 17, 5, 4, 4] + s[19, 18, 5, 4, 4] + 2 s[14, 14, 12, 7, 3]
+ s[14, 13, 13, 7, 3] + 8 s[20, 11, 8, 8, 3] + 10 s[19, 12, 8, 8, 3]
+ 9 s[18, 13, 8, 8, 3] + 8 s[17, 14, 8, 8, 3] + 4 s[16, 15, 8, 8, 3]
+ 5 s[20, 10, 9, 8, 3] + 8 s[19, 11, 9, 8, 3] + 10 s[17, 13, 9, 8, 3]
+ 8 s[16, 14, 9, 8, 3] + 3 s[15, 15, 9, 8, 3] + 7 s[19, 10, 10, 8, 3]
+ 10 s[18, 11, 10, 8, 3] + 11 s[16, 13, 10, 8, 3] + 12 s[16, 15, 10, 6, 3]
+ 6 s[19, 11, 11, 6, 3] + 14 s[18, 12, 11, 6, 3] + 14 s[17, 13, 11, 6, 3]
+ 12 s[16, 14, 11, 6, 3] + 4 s[15, 15, 11, 6, 3] + 8 s[17, 12, 12, 6, 3]
+ 8 s[16, 13, 12, 6, 3] + 6 s[15, 14, 12, 6, 3] + s[15, 13, 13, 6, 3]
+ s[14, 14, 13, 6, 3] + 7 s[20, 13, 7, 7, 3] + 6 s[19, 14, 7, 7, 3]
+ 5 s[18, 15, 7, 7, 3] + 3 s[17, 16, 7, 7, 3] + 14 s[20, 12, 8, 7, 3]
+ 16 s[19, 13, 8, 7, 3] + 14 s[18, 14, 8, 7, 3] + 10 s[17, 15, 8, 7, 3]
+ 3 s[16, 16, 8, 7, 3] + 12 s[20, 11, 9, 7, 3] + 16 s[19, 12, 9, 7, 3]
+ 17 s[18, 13, 9, 7, 3] + 14 s[17, 14, 9, 7, 3] + 8 s[16, 15, 9, 7, 3]
+ 7 s[20, 10, 10, 7, 3] + 13 s[19, 11, 10, 7, 3] + 17 s[18, 12, 10, 7, 3]
+ 18 s[17, 13, 10, 7, 3] + 12 s[16, 14, 10, 7, 3] + 5 s[15, 15, 10, 7, 3]
+ 5 s[18, 11, 11, 7, 3] + 10 s[17, 12, 11, 7, 3] + 10 s[16, 13, 11, 7, 3]
+ 6 s[15, 14, 11, 7, 3] + 5 s[15, 13, 12, 7, 3] + 3 s[17, 17, 7, 6, 3]
+ 25 s[19, 14, 8, 6, 3] + 19 s[18, 15, 8, 6, 3] + 11 s[17, 16, 8, 6, 3]
+ 24 s[20, 12, 9, 6, 3] + 25 s[19, 13, 9, 6, 3] + 23 s[18, 14, 9, 6, 3]
+ 16 s[17, 15, 9, 6, 3] + 6 s[16, 16, 9, 6, 3] + 16 s[20, 11, 10, 6, 3]
+ 24 s[19, 12, 10, 6, 3] + 24 s[18, 13, 10, 6, 3] + 21 s[17, 14, 10, 6, 3]
+ 16 s[17, 14, 11, 5, 3] + 9 s[16, 15, 11, 5, 3] + 7 s[18, 12, 12, 5, 3]
+ 10 s[17, 13, 12, 5, 3] + 8 s[16, 14, 12, 5, 3] + 4 s[15, 15, 12, 5, 3]
+ 3 s[16, 13, 13, 5, 3] + 3 s[15, 14, 13, 5, 3] + 10 s[20, 15, 6, 6, 3]
+ 4 s[18, 17, 6, 6, 3] + 17 s[20, 14, 7, 6, 3] + 15 s[19, 15, 7, 6, 3]
+ 27 s[19, 13, 10, 5, 3] + 23 s[18, 14, 10, 5, 3] + 19 s[17, 15, 10, 5, 3]
+ 5 s[16, 16, 10, 5, 3] + 8 s[20, 11, 11, 5, 3] + 18 s[18, 13, 11, 5, 3]
+ 28 s[20, 13, 9, 5, 3] + 27 s[19, 14, 9, 5, 3] + 22 s[18, 15, 9, 5, 3]
+ 12 s[17, 16, 9, 5, 3] + 22 s[20, 12, 10, 5, 3] + 15 s[18, 16, 8, 5, 3]
+ 7 s[17, 17, 8, 5, 3] + 2 s[18, 18, 6, 5, 3] + 20 s[20, 15, 7, 5, 3]
+ 15 s[19, 16, 7, 5, 3] + 9 s[18, 17, 7, 5, 3] + 27 s[20, 14, 8, 5, 3]
+ 25 s[19, 15, 8, 5, 3] + 4 s[20, 17, 5, 5, 3] + 2 s[19, 18, 5, 5, 3]
+ 9 s[19, 17, 6, 5, 3] + 3 s[17, 13, 13, 4, 3] + 4 s[16, 14, 13, 4, 3]
+ s[15, 15, 13, 4, 3] + s[15, 14, 14, 4, 3] + 17 s[18, 14, 11, 4, 3]
+ 12 s[17, 15, 11, 4, 3] + 5 s[16, 16, 11, 4, 3] + 8 s[19, 12, 12, 4, 3]
+ 10 s[18, 13, 12, 4, 3] + 11 s[17, 14, 12, 4, 3] + 6 s[16, 15, 12, 4, 3]
+ 12 s[17, 16, 10, 4, 3] + 14 s[20, 12, 11, 4, 3] + 17 s[19, 13, 11, 4, 3]
+ 6 s[17, 17, 9, 4, 3] + 26 s[20, 13, 10, 4, 3] + 26 s[19, 14, 10, 4, 3]
+ 20 s[18, 15, 10, 4, 3]
]
> pl3:=`SYMF/Pletss/elem/l`(s[3,2], s[3,2,1], 5): print(pl3);
*
5 s[15, 8, 5, 2] + s[15, 7, 7, 1] + 28 s[13, 10, 6, 1] + 12 s[14, 9, 6, 1]
+ 2 s[15, 8, 6, 1] + 5 s[12, 12, 5, 1] + 9 s[13, 11, 5, 1]
+ 5 s[14, 10, 5, 1] + s[15, 9, 5, 1] + 29 s[12, 11, 6, 1] + s[13, 12, 4, 1]
+ s[14, 11, 4, 1] + s[10, 10, 10] + 6 s[11, 10, 9] + 4 s[12, 9, 9]
+ 4 s[11, 11, 8] + 8 s[12, 10, 8] + 5 s[13, 9, 8] + s[14, 8, 8]
+ 5 s[12, 11, 7] + 5 s[13, 10, 7] + 2 s[14, 9, 7] + s[15, 8, 7]
+ s[12, 12, 6] + 137 s[13, 9, 6, 2] + 42 s[14, 8, 6, 2] + 5 s[15, 7, 6, 2]
+ 66 s[12, 11, 5, 2] + 67 s[13, 10, 5, 2] + 28 s[14, 9, 5, 2]
+ 132 s[10, 9, 9, 2] + 328 s[11, 9, 8, 2] + 310 s[11, 10, 7, 2]
+ 307 s[12, 9, 7, 2] + 131 s[13, 8, 7, 2] + 22 s[14, 7, 7, 2]
+ 108 s[11, 11, 6, 2] + 208 s[12, 10, 6, 2] + 157 s[12, 8, 8, 2]
+ 5 s[14, 10, 3, 3] + 29 s[14, 9, 4, 3] + 5 s[15, 8, 4, 3]
+ 4 s[12, 12, 3, 3] + 8 s[13, 11, 3, 3] + s[15, 9, 3, 3]
+ 188 s[10, 10, 8, 2] + 66 s[12, 11, 4, 3] + 10001 s[11, 6, 5, 5, 3]
+ 1753 s[12, 5, 5, 5, 3] + 15475 s[8, 8, 7, 4, 3] + 157 s[11, 11, 5, 3]
+ 150 s[14, 5, 5, 3, 3] + 3379 s[12, 8, 4, 3, 3] + 1287 s[13, 7, 4, 3, 3]
+ 2271 s[10, 10, 4, 3, 3] + 18532 s[10, 8, 6, 3, 3] + 162 s[14, 5, 4, 4, 3]
+ 11955 s[11, 7, 6, 3, 3] + 11507 s[11, 8, 5, 3, 3]
+ 5861 s[12, 7, 5, 3, 3] + 1491 s[13, 6, 5, 3, 3] + 3204 s[12, 6, 6, 3, 3]
+ 2850 s[8, 8, 8, 3, 3] + 13529 s[9, 8, 7, 3, 3] + 10135 s[10, 7, 7, 3, 3]
+ 9648 s[9, 9, 6, 3, 3] + 14538 s[9, 9, 5, 4, 3] + 1284 s[13, 6, 4, 4, 3]
+ 6 s[15, 4, 4, 4, 3] + 6886 s[12, 6, 5, 4, 3] + 28754 s[10, 8, 5, 4, 3]
+ 14342 s[8, 7, 6, 6, 3] + 20126 s[11, 7, 5, 4, 3] + 8050 s[10, 9, 4, 4, 3]
+ 8833 s[11, 8, 4, 4, 3] + 4654 s[12, 7, 4, 4, 3] + 981 s[13, 5, 5, 4, 3]
+ 21814 s[9, 7, 7, 4, 3] + 35766 s[9, 8, 6, 4, 3] + 33846 s[10, 7, 6, 4, 3]
+ 11957 s[11, 6, 6, 4, 3] + 17561 s[8, 7, 7, 5, 3] + 21387 s[8, 8, 6, 5, 3]
+ 17196 s[10, 6, 6, 5, 3] + 22554 s[9, 8, 5, 5, 3]
+ 22799 s[10, 7, 5, 5, 3] + 36975 s[9, 7, 6, 5, 3] + 4543 s[7, 7, 7, 6, 3]
+ 23 s[14, 4, 4, 4, 4] + 6862 s[8, 7, 5, 5, 5] + 1670 s[10, 5, 5, 5, 5]
+ 5877 s[9, 6, 5, 5, 5] + 354 s[13, 5, 4, 4, 4] + 9138 s[9, 6, 6, 6, 3]
+ 5191 s[11, 7, 4, 4, 4] + 1938 s[12, 6, 4, 4, 4] + 12354 s[10, 6, 5, 5, 4]
+ 2784 s[11, 5, 5, 5, 4] + 10825 s[8, 7, 7, 4, 4] + 13946 s[8, 8, 6, 4, 4]
+ 8474 s[11, 6, 5, 4, 4] + 3556 s[9, 9, 4, 4, 4] + 7140 s[10, 8, 4, 4, 4]
+ 1601 s[12, 5, 5, 4, 4] + 24402 s[9, 7, 6, 4, 4] + 18221 s[9, 8, 5, 4, 4]
+ 18686 s[10, 7, 5, 4, 4] + 11703 s[10, 6, 6, 4, 4] + 6251 s[7, 7, 7, 5, 4]
+ 16876 s[9, 6, 6, 5, 4] + 11248 s[8, 8, 5, 5, 4] + 20841 s[9, 7, 5, 5, 4]
+ 24603 s[8, 7, 6, 5, 4] + 5963 s[7, 7, 6, 6, 4] + 7275 s[8, 6, 6, 6, 4]
+ 2430 s[7, 6, 6, 6, 5] + 5014 s[7, 7, 6, 5, 5] + 6474 s[8, 6, 6, 5, 5]
+ 205 s[6, 6, 6, 6, 6] + 352 s[14, 7, 4, 3, 2] + 1405 s[13, 8, 4, 3, 2]
+ 34 s[15, 6, 4, 3, 2] + 245 s[11, 11, 3, 3, 2] + 481 s[12, 10, 3, 3, 2]
+ 6436 s[12, 7, 6, 3, 2] + 6438 s[12, 8, 5, 3, 2] + 397 s[14, 6, 5, 3, 2]
+ 21 s[15, 5, 5, 3, 2] + 2780 s[12, 9, 4, 3, 2] + 2334 s[13, 7, 5, 3, 2]
+ 7303 s[11, 7, 7, 3, 2] + 13448 s[10, 9, 6, 3, 2] + 18 s[15, 5, 4, 4, 2]
+ 13935 s[11, 8, 6, 3, 2] + 4486 s[10, 10, 5, 3, 2]
+ 8966 s[11, 9, 5, 3, 2] + 1253 s[13, 6, 6, 3, 2] + 8201 s[9, 9, 7, 3, 2]
+ 14614 s[10, 8, 7, 3, 2] + 28779 s[10, 8, 6, 4, 2]
+ 3918 s[12, 8, 4, 4, 2] + 272 s[14, 6, 4, 4, 2] + 5821 s[9, 8, 8, 3, 2]
+ 1474 s[13, 7, 4, 4, 2] + 2090 s[13, 6, 5, 4, 2] + 16623 s[11, 8, 5, 4, 2]
+ 202 s[14, 5, 5, 4, 2] + 2659 s[10, 10, 4, 4, 2] + 5357 s[11, 9, 4, 4, 2]
+ 8371 s[12, 7, 5, 4, 2] + 15046 s[9, 9, 6, 4, 2] + 4634 s[8, 8, 8, 4, 2]
+ 16111 s[10, 7, 7, 4, 2] + 4839 s[12, 6, 6, 4, 2]
+ 15478 s[10, 9, 5, 4, 2] + 18388 s[11, 7, 6, 4, 2] + 485 s[13, 5, 5, 5, 2]
+ 11349 s[11, 7, 5, 5, 2] + 21682 s[9, 8, 7, 4, 2] + 3725 s[12, 6, 5, 5, 2]
+ 16546 s[10, 8, 5, 5, 2] + 16968 s[9, 7, 7, 5, 2]
+ 24270 s[10, 7, 6, 5, 2] + 26103 s[9, 8, 6, 5, 2] + 8245 s[11, 6, 6, 5, 2]
+ 8437 s[9, 9, 5, 5, 2] + 7766 s[8, 7, 7, 6, 2] + 949 s[7, 7, 7, 7, 2]
+ 4589 s[11, 9, 4, 3, 3] + 7670 s[8, 8, 6, 6, 2] + 12859 s[9, 7, 6, 6, 2]
+ 5493 s[10, 6, 6, 6, 2] + 12210 s[8, 8, 7, 5, 2] + 96 s[14, 7, 3, 3, 3]
+ 371 s[13, 8, 3, 3, 3] + 9 s[15, 6, 3, 3, 3] + 17 s[15, 5, 4, 3, 3]
+ 243 s[14, 6, 4, 3, 3] + 667 s[11, 10, 3, 3, 3] + 726 s[12, 9, 3, 3, 3]
+ 10662 s[10, 9, 5, 3, 3] + 4 s[12, 12, 2, 2, 2] + 4 s[14, 10, 2, 2, 2]
+ s[15, 9, 2, 2, 2] + 1030 s[8, 7, 7, 7, 1] + 7 s[13, 11, 2, 2, 2]
+ 96 s[13, 10, 3, 2, 2] + 331 s[13, 9, 3, 3, 2] + 14 s[15, 7, 3, 3, 2]
+ 109 s[14, 8, 3, 3, 2] + 95 s[12, 11, 3, 2, 2] + 7 s[15, 8, 3, 2, 2]
+ 140 s[14, 8, 4, 2, 2] + 18 s[15, 7, 4, 2, 2] + 322 s[11, 11, 4, 2, 2]
+ 219 s[14, 7, 5, 2, 2] + 917 s[13, 8, 5, 2, 2] + 631 s[12, 10, 4, 2, 2]
+ 431 s[13, 9, 4, 2, 2] + 20 s[15, 6, 5, 2, 2] + 1749 s[11, 10, 5, 2, 2]
+ 1857 s[12, 9, 5, 2, 2] + 1990 s[10, 10, 6, 2, 2] + 2681 s[12, 8, 6, 2, 2]
+ 882 s[13, 7, 6, 2, 2] + 115 s[14, 6, 6, 2, 2] + 3904 s[11, 9, 6, 2, 2]
+ 1592 s[9, 9, 8, 2, 2] + 4031 s[10, 9, 7, 2, 2] + 3833 s[11, 8, 7, 2, 2]
+ 1364 s[12, 7, 7, 2, 2] + 2275 s[10, 8, 8, 2, 2] + 2583 s[11, 10, 4, 3, 2]
+ 5746 s[9, 9, 7, 4, 1] + 5028 s[11, 7, 7, 4, 1] + 9076 s[10, 9, 6, 4, 1]
+ 9343 s[11, 8, 6, 4, 1] + 10185 s[10, 8, 7, 4, 1] + 2511 s[12, 7, 5, 5, 1]
+ 5533 s[9, 8, 6, 6, 1] + 1788 s[12, 6, 6, 5, 1] + 4820 s[10, 9, 5, 5, 1]
+ 5111 s[11, 8, 5, 5, 1] + 6814 s[10, 7, 7, 5, 1] + 2071 s[8, 8, 8, 5, 1]
+ 6005 s[9, 9, 6, 5, 1] + 11378 s[10, 8, 6, 5, 1] + 7109 s[11, 7, 6, 5, 1]
+ 9349 s[9, 8, 7, 5, 1] + 4947 s[10, 7, 6, 6, 1] + 3306 s[8, 8, 7, 6, 1]
+ 1532 s[11, 6, 6, 6, 1] + 4449 s[9, 7, 7, 6, 1] + 40 s[14, 9, 3, 2, 2]
+ 1363 s[12, 8, 7, 2, 1] + 341 s[13, 7, 7, 2, 1] + 1438 s[12, 9, 6, 2, 1]
+ 674 s[13, 8, 6, 2, 1] + 1159 s[10, 10, 7, 2, 1] + 322 s[9, 9, 9, 2, 1]
+ 1551 s[10, 9, 8, 2, 1] + 1151 s[11, 8, 8, 2, 1] + 2191 s[11, 9, 7, 2, 1]
+ 1899 s[12, 7, 7, 3, 1] + 538 s[13, 9, 4, 3, 1] + 174 s[14, 8, 4, 3, 1]
+ 22 s[15, 7, 4, 3, 1] + 96 s[12, 11, 3, 3, 1] + 25 s[15, 6, 5, 3, 1]
+ 401 s[11, 11, 4, 3, 1] + 787 s[12, 10, 4, 3, 1] + 1217 s[13, 8, 5, 3, 1]
+ 289 s[14, 7, 5, 3, 1] + 1205 s[13, 7, 6, 3, 1] + 2340 s[11, 10, 5, 3, 1]
+ 2484 s[12, 9, 5, 3, 1] + 155 s[14, 6, 6, 3, 1] + 5671 s[10, 9, 7, 3, 1]
+ 4257 s[12, 7, 6, 4, 1] + 2261 s[9, 9, 8, 3, 1] + 3222 s[10, 8, 8, 3, 1]
+ 2755 s[10, 10, 6, 3, 1] + 5397 s[11, 9, 6, 3, 1] + 3692 s[12, 8, 6, 3, 1]
+ 5369 s[11, 8, 7, 3, 1] + 682 s[13, 8, 4, 4, 1] + 167 s[14, 7, 4, 4, 1]
+ 16 s[15, 6, 4, 4, 1] + 234 s[14, 6, 5, 4, 1] + 11 s[15, 5, 5, 4, 1]
+ 1267 s[11, 10, 4, 4, 1] + 1358 s[12, 9, 4, 4, 1] + 810 s[13, 6, 6, 4, 1]
+ 595 s[13, 6, 5, 5, 1] + 4136 s[9, 8, 8, 4, 1] + 52 s[14, 5, 5, 5, 1]
+ 2794 s[10, 10, 5, 4, 1] + 3964 s[12, 8, 5, 4, 1] + 1415 s[13, 7, 5, 4, 1]
+ 5565 s[11, 9, 5, 4, 1] + 697 s[12, 10, 5, 2, 1] + 18 s[15, 7, 5, 2, 1]
+ 161 s[12, 11, 4, 2, 1] + 161 s[13, 10, 4, 2, 1] + 149 s[14, 8, 5, 2, 1]
+ 1387 s[11, 10, 6, 2, 1] + 145 s[14, 7, 6, 2, 1] + 10 s[15, 6, 6, 2, 1]
+ 359 s[11, 11, 5, 2, 1] + 469 s[13, 9, 5, 2, 1] + 95 s[13, 10, 3, 3, 1]
+ 6 s[15, 8, 3, 3, 1] + 41 s[14, 9, 3, 3, 1] + 142 s[13, 9, 6, 1, 1]
+ 22 s[14, 7, 7, 1, 1] + 317 s[11, 10, 7, 1, 1] + 133 s[13, 8, 7, 1, 1]
+ 216 s[12, 10, 6, 1, 1] + 43 s[14, 8, 6, 1, 1] + 112 s[11, 11, 6, 1, 1]
+ 192 s[10, 10, 8, 1, 1] + 135 s[10, 9, 9, 1, 1] + s[14, 11, 2, 2, 1]
+ 24 s[13, 11, 3, 2, 1] + 3 s[15, 9, 3, 2, 1] + 14 s[14, 10, 3, 2, 1]
+ s[13, 12, 2, 2, 1] + 161 s[12, 8, 8, 1, 1] + 316 s[12, 9, 7, 1, 1]
+ 336 s[11, 9, 8, 1, 1] + 68 s[14, 9, 4, 2, 1] + 13 s[12, 12, 3, 2, 1]
+ 11 s[15, 8, 4, 2, 1] + 5 s[15, 7, 6, 1, 1] + 68 s[13, 10, 5, 1, 1]
+ 70 s[12, 11, 5, 1, 1] + s[13, 12, 3, 1, 1] + s[14, 11, 3, 1, 1]
+ 9 s[14, 10, 4, 1, 1] + 29 s[14, 9, 5, 1, 1] + 4 s[15, 8, 5, 1, 1]
+ 9 s[12, 12, 4, 1, 1] + 16 s[13, 11, 4, 1, 1] + 2 s[15, 9, 4, 1, 1]
+ 634 s[12, 9, 5, 4] + 328 s[13, 7, 6, 4] + 41 s[14, 6, 6, 4]
+ 598 s[11, 10, 5, 4] + 310 s[13, 8, 5, 4] + 229 s[8, 8, 7, 7]
+ 286 s[8, 8, 8, 6] + 286 s[9, 7, 7, 7] + 1551 s[11, 8, 7, 4]
+ 540 s[12, 7, 7, 4] + 770 s[10, 10, 6, 4] + 1504 s[11, 9, 6, 4]
+ 672 s[9, 9, 8, 4] + 29 s[14, 6, 5, 5] + 952 s[10, 8, 8, 4]
+ 1649 s[10, 9, 7, 4] + s[15, 5, 5, 5] + 540 s[12, 8, 5, 5]
+ 188 s[13, 7, 5, 5] + 733 s[12, 7, 6, 5] + 132 s[13, 6, 6, 5]
+ 390 s[10, 10, 5, 5] + 770 s[11, 9, 5, 5] + 1973 s[10, 8, 7, 5]
+ 952 s[11, 7, 7, 5] + 1622 s[10, 9, 6, 5] + 1649 s[11, 8, 6, 5]
+ 672 s[11, 7, 6, 6] + 1124 s[10, 8, 6, 6] + 834 s[9, 8, 8, 5]
+ 1124 s[9, 9, 7, 5] + 152 s[12, 6, 6, 6] + 1193 s[9, 8, 7, 6]
+ 834 s[10, 7, 7, 6] + 603 s[9, 9, 6, 6] + 1021 s[12, 8, 6, 4]
+ 72 s[14, 7, 5, 4] + 80 s[11, 11, 4, 4] + 157 s[12, 10, 4, 4]
+ 6 s[15, 6, 5, 4] + 540 s[10, 10, 7, 3] + 1021 s[11, 9, 7, 3]
+ 733 s[10, 9, 8, 3] + 540 s[11, 8, 8, 3] + 4 s[15, 7, 4, 4]
+ 152 s[9, 9, 9, 3] + 108 s[13, 9, 4, 4] + 35 s[14, 8, 4, 4]
+ 656 s[12, 9, 6, 3] + 634 s[12, 8, 7, 3] + 157 s[13, 7, 7, 3]
+ 634 s[11, 10, 6, 3] + 307 s[13, 8, 6, 3] + 66 s[14, 7, 6, 3]
+ 4 s[15, 6, 6, 3] + 307 s[12, 10, 5, 3] + 208 s[13, 9, 5, 3]
+ 66 s[14, 8, 5, 3] + 8 s[15, 7, 5, 3] + 66 s[13, 10, 4, 3]
+ 41 s[11, 9, 9, 1] + 72 s[11, 10, 8, 1] + 66 s[12, 9, 8, 1]
+ 22 s[13, 8, 8, 1] + 35 s[11, 11, 7, 1] + 66 s[12, 10, 7, 1]
+ 42 s[13, 9, 7, 1] + 12 s[14, 8, 7, 1] + 8 s[12, 12, 4, 2]
+ 15 s[13, 11, 4, 2] + 9 s[14, 10, 4, 2] + 2 s[15, 9, 4, 2]
+ s[13, 12, 3, 2] + s[14, 11, 3, 2] + s[15, 10, 3, 2] + 29 s[10, 10, 9, 1]
+ 2 s[13, 11, 6] + s[14, 10, 6] + s[13, 12, 5]
--------------------------------------------------------------------------------
#
# Stanley polynomials...
#
--------------------------------------------------------------------------------
> ltr:=`SG/Perm2ListRdTab`([3,1,7,2,8,5,4,6]):
*
> ltform:=map(Tab2Part, ltr);
ltform := [[5, 4, 1], [5, 3, 2], [5, 3, 1, 1], [4, 3, 3], [4, 4, 2],
[4, 4, 1, 1], [4, 3, 2, 1]]
> NbTotalRd:=convert(map(SgDimRep, ltform), `+`);
NbTotalRd := 2835
> Perm2ListRd([3,1,7,2,8,5,4,6], 'nb');
2835
> Stanley:=convert(map(form -> s[op(form)],\
ltform), `+`);
Stanley := s[5, 4, 1] + s[5, 3, 2] + s[5, 3, 1, 1] + s[4, 3, 3] + s[4, 4, 2]
+ s[4, 4, 1, 1] + s[4, 3, 2, 1]
--------------------------------------------------------------------------------
#
# More on reduced decompositions: key polynomials...
#
--------------------------------------------------------------------------------
> Rd2K:=proc(ltr) local lkey, l, kpol;\
if (ltr=[[]]) then\
K[0]\
else\
lkey:=map(Word2Key, map(Tab2Word, ltr),\
'left', 'nil');\
l:=map(proc(wrd)\
[op(Part2Conjugate(sort(map(op, wrd),\
proc(x,y) evalb(x>=y) end))), 0]\
end, lkey);\
kpol:=convert(map(proc(wrd) local i;\
K[seq(wrd[i]-wrd[i+1],\
i=1..nops(wrd)-1)]\
end, l), `+`);\
fi\
end:\
\
TableX2K:=proc(n) local perm, t;\
t:=table();\
for perm in ListPerm(n) do\
t[perm]:=Rd2K(`SG/Perm2ListRdTab`(perm))\
od:\
eval(t)\
end:
> tX2K:=TableX2K(4): print(tX2K);
************************
table([
[1, 4, 2, 3] = K[0, 2]
[1, 4, 3, 2] = K[0, 2, 1]
[4, 2, 3, 1] = K[3, 1, 1]
[2, 4, 1, 3] = K[1, 2]
[3, 4, 1, 2] = K[2, 2]
[3, 1, 2, 4] = K[2]
[3, 2, 1, 4] = K[2, 1]
[3, 2, 4, 1] = K[2, 1, 1]
[2, 3, 1, 4] = K[1, 1]
[4, 3, 2, 1] = K[3, 2, 1]
[2, 4, 3, 1] = K[1, 2, 1]
[2, 1, 3, 4] = K[1]
[3, 4, 2, 1] = K[2, 2, 1]
[2, 1, 4, 3] = K[1, 0, 1] + K[2]
[4, 2, 1, 3] = K[3, 1]
[1, 2, 4, 3] = K[0, 0, 1]
[1, 3, 4, 2] = K[0, 1, 1]
[2, 3, 4, 1] = K[1, 1, 1]
[4, 3, 1, 2] = K[3, 2]
[1, 2, 3, 4] = K[0]
[1, 3, 2, 4] = K[0, 1]
[3, 1, 4, 2] = K[2, 0, 1]
[4, 1, 2, 3] = K[3]
[4, 1, 3, 2] = K[3, 0, 1]
])
--------------------------------------------------------------------------------
#
# You can also do it in parallel...(service 30)
#
--------------------------------------------------------------------------------
> TableX2K:=proc(n) local trd,lp,i;\
lp:=ListPerm(n);\
trd:=HubParallel([30$n!], map(p->[p], lp));\
table([seq(lp[i]=Rd2K(trd[i]), i=1..n!)]);\
end:
> tX2K:=TableX2K(4): print(tX2K);
#
table([
[1, 4, 2, 3] = K[0, 2]
[1, 4, 3, 2] = K[0, 2, 1]
[4, 2, 3, 1] = K[3, 1, 1]
[2, 4, 1, 3] = K[1, 2]
[3, 4, 1, 2] = K[2, 2]
[3, 1, 2, 4] = K[2]
[3, 2, 1, 4] = K[2, 1]
[3, 2, 4, 1] = K[2, 1, 1]
[2, 3, 1, 4] = K[1, 1]
[4, 3, 2, 1] = K[3, 2, 1]
[2, 4, 3, 1] = K[1, 2, 1]
[2, 1, 3, 4] = K[1]
[3, 4, 2, 1] = K[2, 2, 1]
[2, 1, 4, 3] = K[1, 0, 1] + K[2]
[4, 2, 1, 3] = K[3, 1]
[1, 2, 4, 3] = K[0, 0, 1]
[1, 3, 4, 2] = K[0, 1, 1]
[2, 3, 4, 1] = K[1, 1, 1]
[4, 3, 1, 2] = K[3, 2]
[1, 2, 3, 4] = K[0]
[1, 3, 2, 4] = K[0, 1]
[3, 1, 4, 2] = K[2, 0, 1]
[4, 1, 2, 3] = K[3]
[4, 1, 3, 2] = K[3, 0, 1]
])
--------------------------------------------------------------------------------
#
# or in background...
#
--------------------------------------------------------------------------------
> RunTableX2K:=proc(n) local lp,i;\
lp:=ListPerm(n);\
HubBackground([30$n!], map(p->[p], lp));\
end:\
\
ReadTableX2K:=proc(n, backnb) local trd, lp, i;\
lp:=ListPerm(n);\
trd:=HubBackgroundRead(backnb);\
table([seq(lp[i]=Rd2K(trd[i]), i=1..n!)]);\
end:
> bg2:=RunTableX2K(4): HubBackgroundDone(bg2): print(");
&
table([
3 = false
])
--------------------------------------------------------------------------------
#
# Hall-Littlewood polynomials...(service 28)
#
--------------------------------------------------------------------------------
> TableHL:=proc(n) local lp, tHL, i;\
lp:=ListPart(n);\
tHL:=HubParallel([28$nops(lp)], map(p->[p], lp));\
table([seq(lp[i]=tHL[i], i=1..nops(lp))]);\
end:
> tHL:=TableHL(6):
#
> print(tHL);
table([
[5, 1] = s[5, 1] + q s[6]
2 3
[4, 1, 1] = s[4, 1, 1] + (q + q ) s[5, 1] + q s[4, 2] + q s[6]
2 3
[3, 1, 1, 1] = s[3, 1, 1, 1] + (q + q + q ) s[4, 1, 1]
2 3 4 5 2 3 4
+ (q + q ) s[3, 2, 1] + (q + q + q ) s[5, 1] + (q + q + q ) s[4, 2]
3 6
+ q s[3, 3] + q s[6]
2 3 4
[2, 1, 1, 1, 1] = s[2, 1, 1, 1, 1] + (q + q + q + q ) s[3, 1, 1, 1]
2 3 3 4 5 6 7
+ (q + q + q ) s[2, 2, 1, 1] + (q + q + 2 q + q + q ) s[4, 1, 1]
2 3 4 5 6
+ (q + 2 q + 2 q + 2 q + q ) s[3, 2, 1]
6 7 8 9 2 4
+ (q + q + q + q ) s[5, 1] + (q + q ) s[2, 2, 2]
4 5 6 7 8 4 5 7
+ (q + q + 2 q + q + q ) s[4, 2] + (q + q + q ) s[3, 3]
10
+ q s[6]
[6] = s[6]
2 3 4
[2, 2, 1, 1] = q s[3, 1, 1, 1] + s[2, 2, 1, 1] + (q + q + q ) s[4, 1, 1]
2 3 4 5 6
+ (q + 2 q + q ) s[3, 2, 1] + (q + q + q ) s[5, 1] + q s[2, 2, 2]
3 4 5 2 4 7
+ (2 q + q + q ) s[4, 2] + (q + q ) s[3, 3] + q s[6]
2
[4, 2] = q s[5, 1] + s[4, 2] + q s[6]
3 2 4 5
[2, 2, 2] = q s[4, 1, 1] + (q + q ) s[3, 2, 1] + (q + q ) s[5, 1]
2 3 4 3 6
+ s[2, 2, 2] + (q + q + q ) s[4, 2] + q s[3, 3] + q s[6]
2 3 2
[3, 2, 1] = q s[4, 1, 1] + s[3, 2, 1] + (q + q ) s[5, 1] + (q + q ) s[4, 2]
4
+ q s[3, 3] + q s[6]
[1, 1, 1, 1, 1, 1] = s[1, 1, 1, 1, 1, 1]
2 3 4 5
+ (q + q + q + q + q ) s[2, 1, 1, 1, 1]
3 4 5 6 7 8 9
+ (q + q + 2 q + 2 q + 2 q + q + q ) s[3, 1, 1, 1]
2 3 4 5 6 7 8
+ (q + q + 2 q + q + 2 q + q + q ) s[2, 2, 1, 1]
6 7 8 9 10 11 12
+ (q + q + 2 q + 2 q + 2 q + q + q ) s[4, 1, 1]
4 5 6 7 8 9 10 11
+ (q + 2 q + 2 q + 3 q + 3 q + 2 q + 2 q + q ) s[3, 2, 1]
10 11 12 13 14
+ (q + q + q + q + q ) s[5, 1]
3 5 6 7 9
+ (q + q + q + q + q ) s[2, 2, 2]
7 8 9 10 11 12 13
+ (q + q + 2 q + q + 2 q + q + q ) s[4, 2]
6 8 9 10 12 15
+ (q + q + q + q + q ) s[3, 3] + q s[6]
2 3
[3, 3] = q s[5, 1] + q s[4, 2] + s[3, 3] + q s[6]
])
--------------------------------------------------------------------------------
#
# What about background processes ???
#
--------------------------------------------------------------------------------
> HubBackgroundDone(bg1, bg2, bg3): print(");
table([
1 = true
2 = true
3 = true
])
> ReadTableX2K(4, bg2): print(");
table([
[1, 4, 2, 3] = K[0, 2]
[1, 4, 3, 2] = K[0, 2, 1]
[4, 2, 3, 1] = K[3, 1, 1]
[2, 4, 1, 3] = K[1, 2]
[3, 4, 1, 2] = K[2, 2]
[3, 1, 2, 4] = K[2]
[3, 2, 1, 4] = K[2, 1]
[3, 2, 4, 1] = K[2, 1, 1]
[2, 3, 1, 4] = K[1, 1]
[4, 3, 2, 1] = K[3, 2, 1]
[2, 4, 3, 1] = K[1, 2, 1]
[2, 1, 3, 4] = K[1]
[3, 4, 2, 1] = K[2, 2, 1]
[2, 1, 4, 3] = K[1, 0, 1] + K[2]
[4, 2, 1, 3] = K[3, 1]
[1, 2, 4, 3] = K[0, 0, 1]
[1, 3, 4, 2] = K[0, 1, 1]
[2, 3, 4, 1] = K[1, 1, 1]
[4, 3, 1, 2] = K[3, 2]
[1, 2, 3, 4] = K[0]
[1, 3, 2, 4] = K[0, 1]
[3, 1, 4, 2] = K[2, 0, 1]
[4, 1, 2, 3] = K[3]
[4, 1, 3, 2] = K[3, 0, 1]
])
> spinpol:=HubBackgroundRead(bg3): print(spinpol);
34 35 36 31 28 29 30
[1855 q + 415 q + 65 q + 50281 q + 466023 q + 243871 q + 116461 q
32 33 17 18 19
+ 19400 q + 6534 q + 2179511 q + 2939387 q + 3605081 q
20 21 22 23 25
+ 4035366 q + 4133796 q + 3884576 q + 3354332 q + 1950475 q
26 27 24 16 15
+ 1315010 q + 816300 q + 2665436 q + 1463645 q + 885445 q
14 13 11 12 10 8
+ 479530 q + 230538 q + 35601 q + 97381 q + 11041 q + 554 q
9 7 6
+ 2805 q + 75 q + 5 q ]
> subs(q=1, spinpol);
[34990795]
--------------------------------------------------------------------------------
That's all for HUB !