|\^/| Maple 7 (IBM INTEL LINUX) ._|\| |/|_. Copyright (c) 2001 by Waterloo Maple Inc. \ MAPLE / All rights reserved. Maple is a registered trademark of <____ ____> Waterloo Maple Inc. | Type ? for help. Warning, the protected names norm and trace have been redefined and unprotected bytes used=1642440, alloc=1310480, time=0.01 `############################################################` `# Algebraic Combinatorics Environment, 3.0, June 2, 1998 #` `############################################################` `# Alain Lascoux, Sebastien Veigneau & Co #` `# Institut Gaspard Monge, Universite de Marne-la-Vallee, #` `# Cite Descartes, 5 Boulevard Descartes, Champs-sur-Marne, #` `# 77454, Marne-la-Vallee, Cedex 2, FRANCE. #` `# Email: ACE@univ-mlv.fr #` `# URL: http://phalanstere.univ-mlv.fr/~ace #` `####################################################` `# ACE Algebraic Combinatorics Environment #` `# #` `# SFA Symmetric Functions on different Alphabets #` `# FM Free Module over symmetric polynomials #` `# NCSF NonCommutative Symmetric Functions #` `# CLG Characters of Linear Groups #` `# SP Schubert Polynomials #` `# SYMF SYMmetric Functions # __/__/ __/_/_/ __/_/__/` `# TAB TABleaux # __/ __/ __/ __/` `# FREE FREE algebra # __/_/__/ __/ __/_/` `# BNA hyperoctahedral Algebras # __/ __/ __/ __/` `# SGA Symmetric Group Algebra # __/ __/ __/_/_/ __/_/__/` `# NCA NilCoxeter Algebra #` `# IDCA IDCoxeter Algebra # _/_/_/ _/_/_/` `# HEKA HEcKe Algebra # _/_/ _/ _/` `# # _/_/_/ _/ _/_/_/` `# BN hyperoctahedral groups #` `# SG Symmetric Groups #` `# CG Classical Groups #` `# #` `# PART PARTitions #` `# COMP COMPositions #` `# #` `# ERR ERRors #` `# TEX TEX output #` `# TYP TYPe checking #` `#######################` [1, 1, 1] 2/3*q*z+2/3/q*z+1/3*q^2-1/6/q^2*z-4/3/q-z-1/6*q^2*z-4/3*q+1/3/q^2+2 [2, 1] -1/3/q^2-2/3*q+1/6/q^2*z+1/3*q^2-1/3/q*z+1/3*q*z-1/6*q^2*z+2/3/q [3] -1/3*q+1/3*q^2+1/6/q*z+1/6*q*z-1/6/q^2*z-1/3/q+1/3/q^2-1/6*q^2*z [1, 1, 1, 1] -5/6*z^2-3+37/16*q-3/16*q^3*z+5/8/q*z^2+37/16/q+1/24/q^3*z^2-1/4/q^2*z^2+5/8*q* z^2-37/16*q*z+1/q^2*z-37/16/q*z+q^2*z+1/24*q^3*z^2-3/16/q^3*z+3/16/q^3-1/q^2-q^ 2+3/16*q^3+3*z-1/4*q^2*z^2 [3, 1] 1/2/q^2*z-1/8/q^2*z^2-1/12*z^2-1/2/q^2+1/8/q*z^2+5/16/q+5/16*q+1/8*q*z^2-1/2*q^ 2+3/16*q^3-5/16*q*z-1/8*q^2*z^2-3/16*q^3*z+1/2*q^2*z-3/16/q^3*z+3/16/q^3+1/24*q ^3*z^2+1/24/q^3*z^2-5/16/q*z [2, 2] 1/24*q^3*z^2-3/16/q^3*z+1/3*q^2*z+7/48/q+1/3/q^2*z+3/16/q^3-1/12*q^2*z^2+1/24/q ^3*z^2-1/3/q^2-3/16*q^3*z+7/48*q-1/12/q^2*z^2-1/24*q*z^2-7/48*q*z-7/48/q*z+3/16 *q^3-1/24/q*z^2-1/3*q^2+1/6*z^2 [4] -3/16*q^3*z-1/3*q^2+3/16*q^3-5/48*q*z+1/12/q^2*z^2-5/48/q-1/3/q^2*z+3/16/q^3*z-\ 1/24/q*z^2-3/16/q^3+5/48*q+1/3/q^2-1/12*q^2*z^2+1/24*q*z^2+5/48/q*z-1/24/q^3*z^ 2+1/3*q^2*z+1/24*q^3*z^2 [2, 1, 1] 3/16*q^3+2/3*q^2*z-5/24/q*z^2-37/48/q+2/3/q^2-3/16/q^3-3/16*q^3*z+37/48/q*z+37/ 48*q+3/16/q^3*z-1/6*q^2*z^2-2/3/q^2*z-2/3*q^2-1/24/q^3*z^2-37/48*q*z+1/24*q^3*z ^2+5/24*q*z^2+1/6/q^2*z^2 [4, 1] -4/45/q^4-7/90*q+19/180/q*z^2-11/180/q^4*z^2-1/30/q*z^3+1/120/q^4*z^3+7/60*q*z+ 14/45*q^2-7/15*q^2*z+7/90/q-7/60/q*z+7/15/q^2*z-14/45/q^2-1/30/q^3*z^3-19/180*q *z^2+23/90*q^2*z^2-3/10*q^3+9/20*q^3*z-13/60*q^3*z^2-23/90/q^2*z^2+3/10/q^3+13/ 60/q^3*z^2+1/20/q^2*z^3-9/20/q^3*z+2/15/q^4*z+1/30*q*z^3-1/20*q^2*z^3+1/30*q^3* z^3+4/45*q^4-1/120*q^4*z^3-2/15*q^4*z+11/180*q^4*z^2 [1, 1, 1, 1, 1] 4/45/q^4-149/45*q-6*z-233/90/q*z^2+11/180/q^4*z^2+7/15/q*z^3-1/120/q^4*z^3+19/6 *z^2+149/30*q*z+82/45*q^2-41/15*q^2*z-149/45/q+149/30/q*z-41/15/q^2*z+82/45/q^2 +1/15/q^3*z^3-7/12*z^3-233/90*q*z^2+62/45*q^2*z^2-3/5*q^3+9/10*q^3*z-13/30*q^3* z^2+62/45/q^2*z^2-3/5/q^3-13/30/q^3*z^2-7/30/q^2*z^3+9/10/q^3*z-2/15/q^4*z+7/15 *q*z^3-7/30*q^2*z^3+1/15*q^3*z^3+4/45*q^4-1/120*q^4*z^3-2/15*q^4*z+11/180*q^4*z ^2+4 [2, 2, 1] 4/45/q^4-13/90*q-1/180/q*z^2+11/180/q^4*z^2-1/30/q*z^3-1/120/q^4*z^3-1/6*z^2+13 /60*q*z+16/45*q^2-8/15*q^2*z-13/90/q+13/60/q*z-8/15/q^2*z+16/45/q^2+1/30/q^3*z^ 3+1/12*z^3-1/180*q*z^2+11/45*q^2*z^2-3/10*q^3+9/20*q^3*z-13/60*q^3*z^2+11/45/q^ 2*z^2-3/10/q^3-13/60/q^3*z^2-1/30/q^2*z^3+9/20/q^3*z-2/15/q^4*z-1/30*q*z^3-1/30 *q^2*z^3+1/30*q^3*z^3+4/45*q^4-1/120*q^4*z^3-2/15*q^4*z+11/180*q^4*z^2 [2, 1, 1, 1] -4/45/q^4-149/180*q+233/360/q*z^2-11/180/q^4*z^2-7/60/q*z^3+1/120/q^4*z^3+149/ 120*q*z+41/45*q^2-41/30*q^2*z+149/180/q-149/120/q*z+41/30/q^2*z-41/45/q^2-1/20/ q^3*z^3-233/360*q*z^2+31/45*q^2*z^2-9/20*q^3+27/40*q^3*z-13/40*q^3*z^2-31/45/q^ 2*z^2+9/20/q^3+13/40/q^3*z^2+7/60/q^2*z^3-27/40/q^3*z+2/15/q^4*z+7/60*q*z^3-7/ 60*q^2*z^3+1/20*q^3*z^3+4/45*q^4-1/120*q^4*z^3-2/15*q^4*z+11/180*q^4*z^2 [5] 4/45/q^4-7/360*q-19/720/q*z^2+11/180/q^4*z^2+1/120/q*z^3-1/120/q^4*z^3+7/240*q* z+7/45*q^2-7/30*q^2*z-7/360/q+7/240/q*z-7/30/q^2*z+7/45/q^2+1/40/q^3*z^3-19/720 *q*z^2+23/180*q^2*z^2-9/40*q^3+27/80*q^3*z-13/80*q^3*z^2+23/180/q^2*z^2-9/40/q^ 3-13/80/q^3*z^2-1/40/q^2*z^3+27/80/q^3*z-2/15/q^4*z+1/120*q*z^3-1/40*q^2*z^3+1/ 40*q^3*z^3+4/45*q^4-1/120*q^4*z^3-2/15*q^4*z+11/180*q^4*z^2 [3, 2] -4/45/q^4-13/360*q+1/720/q*z^2-11/180/q^4*z^2+1/120/q*z^3+1/120/q^4*z^3+13/240* q*z+8/45*q^2-4/15*q^2*z+13/360/q-13/240/q*z+4/15/q^2*z-8/45/q^2-1/40/q^3*z^3-1/ 720*q*z^2+11/90*q^2*z^2-9/40*q^3+27/80*q^3*z-13/80*q^3*z^2-11/90/q^2*z^2+9/40/q ^3+13/80/q^3*z^2+1/60/q^2*z^3-27/80/q^3*z+2/15/q^4*z-1/120*q*z^3-1/60*q^2*z^3+1 /40*q^3*z^3+4/45*q^4-1/120*q^4*z^3-2/15*q^4*z+11/180*q^4*z^2 [3, 1, 1] 4/45/q^4-97/360*q-229/720/q*z^2+11/180/q^4*z^2+11/120/q*z^3-1/120/q^4*z^3+1/6*z ^2+97/240*q*z+5/9*q^2-5/6*q^2*z-97/360/q+97/240/q*z-5/6/q^2*z+5/9/q^2+1/24/q^3* z^3-1/12*z^3-229/720*q*z^2+4/9*q^2*z^2-3/8*q^3+9/16*q^3*z-13/48*q^3*z^2+4/9/q^2 *z^2-3/8/q^3-13/48/q^3*z^2-1/12/q^2*z^3+9/16/q^3*z-2/15/q^4*z+11/120*q*z^3-1/12 *q^2*z^3+1/24*q^3*z^3+4/45*q^4-1/120*q^4*z^3-2/15*q^4*z+11/180*q^4*z^2 [2, 2, 2] -1/90/q^2*z^4+7/360/q*z^4+83/1920*q-1/48*t*q*z-1/96*t*q*z^2+1/48*t*q*z^3+1/96*t *q-1/48*t/q*z-1/96*t/q*z^2+1/48*t/q*z^3+1/96*t/q-1/720/q^5*z^4-27/160/q^3+1/90* q^2*z^4-11/90*q^2*z^2+101/2880*q*z^3-7/360*q*z^4+47/5760*q*z^2+1/720*q^5*z^4-25 /1728*q^5*z^3+175/3456*q^5*z^2-125/1728*q^5*z+125/3456*q^5+7/135*q^4*z^3-23/135 *q^4*z^2+32/135*q^4*z-1/180*q^4*z^4-16/135*q^4+9/40*q^3*z^2+1/240*q^3*z^4-27/80 *q^3*z-9/160*q^3*z^3+27/160*q^3-1/90*q^2*z^3-175/3456/q^5*z^2-83/960*q*z-2/15*q ^2+4/15*q^2*z+25/1728/q^5*z^3-83/1920/q+83/960/q*z-125/3456/q^5-1/240/q^3*z^4+1 /90/q^2*z^3+11/90/q^2*z^2-4/15/q^2*z+2/15/q^2+16/135/q^4-47/5760/q*z^2-101/2880 /q*z^3+9/160/q^3*z^3-9/40/q^3*z^2+27/80/q^3*z-32/135/q^4*z+1/180/q^4*z^4-7/135/ q^4*z^3+125/1728/q^5*z+23/135/q^4*z^2 [4, 2] -1/120/q*z^4+91/5760*q-1/144*t*q*z-1/288*t*q*z^2+1/144*t*q*z^3+1/288*t*q+1/144* t/q*z+1/288*t/q*z^2-1/144*t/q*z^3-1/288*t/q+1/720/q^5*z^4+9/64/q^3-5/54*q^2*z^2 +19/2880*q*z^3-1/120*q*z^4+53/5760*q*z^2+1/720*q^5*z^4-25/1728*q^5*z^3+175/3456 *q^5*z^2-125/1728*q^5*z+125/3456*q^5+7/135*q^4*z^3-23/135*q^4*z^2+32/135*q^4*z-\ 1/180*q^4*z^4-16/135*q^4+13/64*q^3*z^2+1/144*q^3*z^4-9/32*q^3*z-1/16*q^3*z^3+9/ 64*q^3+1/54*q^2*z^3+175/3456/q^5*z^2-91/2880*q*z-2/27*q^2+4/27*q^2*z-25/1728/q^ 5*z^3+91/5760/q-91/2880/q*z+125/3456/q^5+1/144/q^3*z^4+1/54/q^2*z^3-5/54/q^2*z^ 2+4/27/q^2*z-2/27/q^2-16/135/q^4+53/5760/q*z^2+19/2880/q*z^3-1/16/q^3*z^3+1/90* z^4+13/64/q^3*z^2-9/32/q^3*z+32/135/q^4*z-1/180/q^4*z^4+7/135/q^4*z^3-125/1728/ q^5*z-23/135/q^4*z^2 [2, 1, 1, 1, 1] 1/15/q^2*z^4-7/120/q*z^4+1631/1920*q+1/144*t*q*z+1/288*t*q*z^2-1/144*t*q*z^3-1/ 288*t*q+1/144*t/q*z+1/288*t/q*z^2-1/144*t/q*z^3-1/288*t/q-1/720/q^5*z^4-27/40/q ^3-1/15*q^2*z^4-427/270*q^2*z^2-421/960*q*z^3+7/120*q*z^4+2473/1920*q*z^2+1/720 *q^5*z^4-25/1728*q^5*z^3+175/3456*q^5*z^2-125/1728*q^5*z+125/3456*q^5+14/135*q^ 4*z^3-46/135*q^4*z^2+64/135*q^4*z-1/90*q^4*z^4-32/135*q^4+159/160*q^3*z^2+3/80* q^3*z^4-27/20*q^3*z-51/160*q^3*z^3+27/40*q^3+143/270*q^2*z^3-175/3456/q^5*z^2-\ 1631/960*q*z-142/135*q^2+284/135*q^2*z+25/1728/q^5*z^3-1631/1920/q+1631/960/q*z -125/3456/q^5-3/80/q^3*z^4-143/270/q^2*z^3+427/270/q^2*z^2-284/135/q^2*z+142/ 135/q^2+32/135/q^4-2473/1920/q*z^2+421/960/q*z^3+51/160/q^3*z^3-159/160/q^3*z^2 +27/20/q^3*z-64/135/q^4*z+1/90/q^4*z^4-14/135/q^4*z^3+125/1728/q^5*z+46/135/q^4 *z^2 [5, 1] -1/72/q^2*z^4+1/144/q*z^4+7/576*q+1/720/q^5*z^4+27/128/q^3-1/72*q^2*z^4-7/36*q^ 2*z^2-7/288*q*z^3+1/144*q*z^4+7/192*q*z^2+1/720*q^5*z^4-25/1728*q^5*z^3+175/ 3456*q^5*z^2-125/1728*q^5*z+125/3456*q^5+7/108*q^4*z^3-23/108*q^4*z^2+8/27*q^4* z-1/144*q^4*z^4-4/27*q^4+41/128*q^3*z^2+1/72*q^3*z^4-27/64*q^3*z-7/64*q^3*z^3+ 27/128*q^3+1/12*q^2*z^3+175/3456/q^5*z^2-7/288*q*z-1/9*q^2+2/9*q^2*z-25/1728/q^ 5*z^3+7/576/q-7/288/q*z+125/3456/q^5+1/72/q^3*z^4+1/12/q^2*z^3-7/36/q^2*z^2+2/9 /q^2*z-1/9/q^2-4/27/q^4+7/192/q*z^2-7/288/q*z^3-7/64/q^3*z^3-1/360*z^4+41/128/q ^3*z^2-27/64/q^3*z+8/27/q^4*z-1/144/q^4*z^4+7/108/q^4*z^3-125/1728/q^5*z-23/108 /q^4*z^2 [6] 1/180/q^2*z^4-1/720/q*z^4+7/2880*q-1/720/q^5*z^4-81/640/q^3-1/180*q^2*z^4-7/90* q^2*z^2-7/1440*q*z^3+1/720*q*z^4+7/960*q*z^2+1/720*q^5*z^4-25/1728*q^5*z^3+175/ 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