|\^/| 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. `############################################################` `# 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 #` `#######################` [2] a*b*R2+a^2*R3 [3] 2*a*b^2*R2+a^2*R2+3*a^2*b*R3+a^3*R4 [4] 6*a*b^3*R2+7*a^2*b*R2+11*a^2*b^2*R3+5*a^3*R3+a^3*b*(6*R4+R2^2)+a^4*R5 [5] 24*a*b^4*R2+46*a^2*b^2*R2+50*a^2*b^3*R3+8*a^3*R2+55*a^3*b*R3+a^3*b^2*(35*R4+10* R2^2)+a^4*(15*R4+5*R2^2)+a^4*b*(10*R5+5*R3*R2)+a^5*R6 [6] 120*a*b^5*R2+326*a^2*b^3*R2+274*a^2*b^4*R3+144*a^3*b*R2+505*a^3*b^2*R3+a^3*b^3* (225*R4+84*R2^2)+84*a^4*R3+a^4*b*(238*R4+96*R2^2)+a^4*b^2*(85*R5+73*R3*R2)+a^5* (35*R5+35*R3*R2)+a^5*b*(15*R6+9*R4*R2+6*R3^2+R2^3)+a^6*R7 [7] 720*a*b^6*R2+2556*a^2*b^4*R2+1764*a^2*b^5*R3+1958*a^3*b^2*R2+4662*a^3*b^3*R3+a^ 3*b^4*(1624*R4+714*R2^2)+180*a^4*R2+1995*a^4*b*R3+a^4*b^2*(2912*R4+1337*R2^2)+a ^4*b^3*(735*R5+826*R3*R2)+a^5*(469*R4+224*R2^2)+a^5*b*(756*R5+917*R3*R2)+a^5*b^ 2*(175*R6+182*R4*R2+119*R3^2+28*R2^3)+a^6*(70*R6+84*R4*R2+56*R3^2+14*R2^3)+a^6* b*(21*R7+14*R5*R2+21*R4*R3+7*R3*R2^2)+a^7*R8 [8] 5040*a*b^7*R2+22212*a^2*b^5*R2+13068*a^2*b^6*R3+25034*a^3*b^3*R2+45462*a^3*b^4* R3+a^3*b^5*(13132*R4+6450*R2^2)+6068*a^4*b*R2+34019*a^4*b^2*R3+a^4*b^3*(34014* R4+17149*R2^2)+a^4*b^4*(6769*R5+8968*R3*R2)+3044*a^5*R3+a^5*b*(14214*R4+7349*R2 ^2)+a^5*b^2*(11892*R5+16444*R3*R2)+a^5*b^3*(1960*R6+2688*R4*R2+1728*R3^2+504*R2 ^3)+a^6*(1869*R5+2688*R3*R2)+a^6*b*(1974*R6+2910*R4*R2+1887*R3^2+572*R2^3)+a^6* b^2*(322*R7+376*R5*R2+548*R4*R3+258*R3*R2^2)+a^7*(126*R7+168*R5*R2+252*R4*R3+ 126*R3*R2^2)+a^7*b*(28*R8+20*R6*R2+32*R5*R3+18*R4^2+12*R4*R2^2+16*R3^2*R2+R2^4) +a^8*R9 [9] 125016*a^5*b*R3+109584*a^2*b^7*R3+322288*a^3*b^4*R2+475572*a^3*b^5*R3+139276*a^ 4*b^2*R2+526506*a^4*b^3*R3+40320*a*b^8*R2+212976*a^2*b^6*R2+a^3*b^6*(118124*R4+ 62856*R2^2)+a^4*b^4*(404706*R4+218970*R2^2)+a^4*b^5*(67284*R5+99666*R3*R2)+a^5* b^2*(297431*R4+163638*R2^2)+a^5*b^3*(171606*R5+260841*R3*R2)+a^5*b^4*(22449*R6+ 36534*R4*R2+23142*R3^2+7834*R2^3)+a^6*b*(70398*R5+109719*R3*R2)+a^6*b^2*(38820* R6+65811*R4*R2+41853*R3^2+14533*R2^3)+a^8*b*(36*R9+27*R7*R2+45*R6*R3+54*R5*R4+ 18*R5*R2^2+54*R4*R3*R2+12*R3^3+9*R3*R2^3)+a^6*b^3*(4536*R7+7047*R5*R2+10017*R4* R3+5850*R3*R2^2)+a^7*b*(4494*R7+7470*R5*R2+10755*R4*R3+6525*R3*R2^2)+a^7*b^2*( 546*R8+690*R6*R2+1068*R5*R3+594*R4^2+567*R4*R2^2+747*R3^2*R2+60*R2^4)+a^6*( 26060*R4+14580*R2^2)+a^8*(210*R8+300*R6*R2+480*R5*R3+270*R4^2+270*R4*R2^2+360* R3^2*R2+30*R2^4)+a^9*R10+a^7*(5985*R6+10548*R4*R2+6714*R3^2+2400*R2^3)+8064*a^5 *R2 [10] a^10*R11+a^8*b*(9240*R8+16690*R6*R2+25475*R5*R3+14100*R4^2+17460*R4*R2^2+22855* R3^2*R2+2240*R2^4)+a^8*b^2*(870*R9+1165*R7*R2+1875*R6*R3+2210*R5*R4+1065*R5*R2^ 2+3135*R4*R3*R2+690*R3^3+670*R3*R2^3)+a^7*b*(274263*R6+527440*R4*R2+330495*R3^2 +129620*R2^3)+a^7*b^2*(108042*R7+208612*R5*R2+291877*R4*R3+203015*R3*R2^2)+a^7* b^3*(9450*R8+16025*R6*R2+24100*R5*R3+13275*R4^2+15930*R4*R2^2+20720*R3^2*R2+ 1980*R2^4)+a^6*b^4*(63273*R7+117533*R5*R2+163483*R4*R3+110890*R3*R2^2)+a^6*b*( 1282380*R4+750380*R2^2)+a^6*b^2*(1774805*R5+2945715*R3*R2)+a^9*(330*R9+495*R7* R2+825*R6*R3+990*R5*R4+495*R5*R2^2+1485*R4*R3*R2+330*R3^3+330*R3*R2^3)+a^6*b^3* (678546*R6+1272880*R4*R2+797395*R3^2+306630*R2^3)+a^9*b*(45*R10+35*R8*R2+60*R7* R3+75*R6*R4+25*R6*R2^2+40*R5^2+80*R5*R3*R2+45*R4^2*R2+60*R4*R3^2+15*R4*R2^3+30* R3^2*R2^2+R2^5)+3399796*a^5*b^2*R3+435168*a^5*b*R2+7994890*a^4*b^4*R3+2788716*a ^4*b^3*R2+5357508*a^3*b^6*R3+4294128*a^3*b^5*R2+1026576*a^2*b^8*R3+2239344*a^2* b^7*R2+362880*a*b^9*R2+a^3*b^7*(1172700*R4+663000*R2^2)+a^4*b^5*(5028870*R4+ 2874910*R2^2)+a^4*b^6*(723680*R5+1162050*R3*R2)+a^5*b^3*(5489865*R4+3174640*R2^ 2)+a^5*b^4*(2449800*R5+3999055*R3*R2)+a^5*b^5*(269325*R6+492800*R4*R2+308170*R3 ^2+116460*R2^3)+a^7*(152900*R5+258060*R3*R2)+a^8*(16401*R7+32901*R5*R2+46101*R4 *R3+33000*R3*R2^2)+193248*a^6*R3 [11] a^3*b^8*(12753576*R4+7560960*R2^2)+a^4*b^6*(65925420*R4+39386248*R2^2)+a^4*b^7* (8409500*R5+14353812*R3*R2)+a^5*b^4*(97285342*R4+58595152*R2^2)+a^5*b^5*( 35718474*R5+61639842*R3*R2)+a^5*b^6*(3416930*R6+6810122*R4*R2+4211152*R3^2+ 1732434*R2^3)+a^6*b^2*(40836103*R4+24806078*R2^2)+a^6*b^3*(38551997*R5+67292225 *R3*R2)+a^6*b^4*(11455125*R6+23200199*R4*R2+14356166*R3^2+5978995*R2^3)+a^6*b^5 *(902055*R7+1896136*R5*R2+2588234*R4*R3+1961146*R3*R2^2)+a^10*b*(55*R11+44*R9* R2+77*R8*R3+99*R7*R4+33*R7*R2^2+110*R6*R5+110*R6*R3*R2+132*R5*R4*R2+88*R5*R3^2+ 22*R5*R2^3+99*R4^2*R3+99*R4*R3*R2^2+44*R3^3*R2+11*R3*R2^4)+a^9*b^2*(1320*R10+ 1848*R8*R2+3058*R7*R3+3740*R6*R4+1815*R6*R2^2+1980*R5^2+5676*R5*R3*R2+3168*R4^2 *R2+4191*R4*R3^2+1364*R4*R2^3+2706*R3^2*R2^2+110*R2^5)+12144264*a^6*b*R3+ 78976150*a^5*b^3*R3+15041628*a^5*b^2*R2+123179848*a^4*b^5*R3+53133096*a^4*b^4* R2+64957992*a^3*b^7*R3+59925072*a^3*b^6*R2+10628640*a^2*b^9*R3+25659360*a^2*b^8 *R2+3628800*a*b^10*R2+a^9*b*(17556*R9+33726*R7*R2+53493*R6*R3+62568*R5*R4+39314 *R5*R2^2+114576*R4*R3*R2+25080*R3^3+29843*R3*R2^3)+a^8*b^2*(266640*R8+564883*R6 *R2+834306*R5*R3+456720*R4^2+658559*R4*R2^2+849057*R3^2*R2+93918*R2^4)+a^8*b^3* (18150*R9+32868*R7*R2+51315*R6*R3+59565*R5*R4+36454*R5*R2^2+105204*R4*R3*R2+ 22902*R3^3+26686*R3*R2^3)+a^7*b*(8885954*R5+15694261*R3*R2)+a^7*b^2*(8202359*R6 +16890148*R4*R2+10450407*R3^2+4413222*R2^3)+a^7*b^3*(2250138*R7+4844224*R5*R2+ 6629777*R4*R3+5110501*R3*R2^2)+a^7*b^4*(157773*R8+322234*R6*R2+472648*R5*R3+ 258214*R4^2+364298*R4*R2^2+468094*R3^2*R2+50864*R2^4)+a^8*b*(898491*R7+1982519* R5*R2+2714547*R4*R3+2133758*R3*R2^2)+a^10*(495*R10+770*R8*R2+1320*R7*R3+1650*R6 *R4+825*R6*R2^2+880*R5^2+2640*R5*R3*R2+1485*R4^2*R2+1980*R4*R3^2+660*R4*R2^3+ 1320*R3^2*R2^2+55*R2^5)+a^9*(39963*R8+87890*R6*R2+130108*R5*R3+71214*R4^2+ 105545*R4*R2^2+136345*R3^2*R2+15400*R2^4)+a^11*R12+604800*a^6*R2+a^7*(2286636* R4+1401444*R2^2)+a^8*(696905*R6+1459700*R4*R2+902440*R3^2+386980*R2^3) [12] a^10*(88803*R9+209352*R7*R2+321750*R6*R3+369798*R5*R4+280995*R5*R2^2+802230*R4* R3*R2+173745*R3^3+240240*R3*R2^3)+a^9*(2641925*R7+6390956*R5*R2+8581144*R4*R3+ 7379372*R3*R2^2)+a^10*b*(31317*R10+63105*R8*R2+102903*R7*R3+124689*R6*R4+79206* R6*R2^2+65802*R5^2+244776*R5*R3*R2+136062*R4^2*R2+179166*R4*R3^2+71702*R4*R2^3+ 141537*R3^2*R2^2+6783*R2^5)+a^10*b^2*(1925*R11+2792*R9*R2+4718*R8*R3+5922*R7*R4 +2889*R7*R2^2+6500*R6*R5+9390*R6*R3*R2+11124*R5*R4*R2+7368*R5*R3^2+2408*R5*R2^3 +8235*R4^2*R3+10692*R4*R3*R2^2+4720*R3^3*R2+1445*R3*R2^4)+a^9*b^3*(32670*R10+ 62286*R8*R2+99936*R7*R3+119970*R6*R4+74520*R6*R2^2+63120*R5^2+227616*R5*R3*R2+ 126036*R4^2*R2+165168*R4*R3^2+64944*R4*R2^3+127584*R3^2*R2^2+6006*R2^5)+a^8*b^4 *(357423*R9+784772*R7*R2+1193214*R6*R3+1367158*R5*R4+993135*R5*R2^2+2813254*R4* R3*R2+605861*R3^3+809636*R3*R2^3)+a^9*b*(2579148*R8+6287718*R6*R2+9061839*R5*R3 +4918470*R4^2+8112078*R4*R2^2+10335171*R3^2*R2+1275234*R2^4)+a^9*b^2*(598884*R9 +1361282*R7*R2+2085408*R6*R3+2397148*R5*R4+1774956*R5*R2^2+5053564*R4*R3*R2+ 1091756*R3^3+1481414*R3*R2^3)+480398884*a^6*b^2*R3+47568960*a^6*b*R2+1717252962 *a^5*b^4*R3+432556644*a^5*b^3*R2+1957043576*a^4*b^6*R3+1002507192*a^4*b^5*R2+ 845642712*a^3*b^8*R3+880322352*a^3*b^7*R2+120543840*a^2*b^10*R3+318540960*a^2*b ^9*R2+39916800*a*b^11*R2+a^6*b^4*(789386117*R5+1435718315*R3*R2)+a^8*b*( 47240193*R6+104003551*R4*R2+63631644*R3^2+28865115*R2^3)+a^8*b^2*(31457504*R7+ 74791181*R5*R2+100528702*R4*R3+85145849*R3*R2^2)+a^8*b^3*(6525090*R8+15526404* R6*R2+22355709*R5*R3+12137441*R4^2+19641618*R4*R2^2+24999891*R3^2*R2+3038878*R2 ^4)+a^7*b^5*(2637558*R8+6133950*R6*R2+8803848*R5*R3+4776093*R4^2+7609620*R4*R2^ 2+9668526*R3^2*R2+1160268*R2^4)+a^7*b^4*(44362383*R7+103742928*R5*R2+139454244* R4*R3+116500692*R3*R2^2)+a^7*b^3*(207244362*R6+450810946*R4*R2+276008505*R3^2+ 123815502*R2^3)+a^6*b^5*(193828653*R6+416825723*R4*R2+255273060*R3^2+113366187* R2^3)+a^6*b^6*(13339535*R7+30711608*R5*R2+41239960*R4*R3+34036736*R3*R2^2)+a^7* b*(165762636*R4+104617700*R2^2)+a^7*b^2*(327806713*R5+601291427*R3*R2)+a^3*b^9* (150917976*R4+92958240*R2^2)+a^4*b^7*(915175740*R4+566826752*R2^2)+a^4*b^8*( 105258076*R5+188462412*R3*R2)+a^5*b^5*(1719763578*R4+1071457928*R2^2)+a^5*b^6*( 539868266*R5+974018526*R3*R2)+a^5*b^7*(45995730*R6+97847214*R4*R2+59913744*R3^2 +26371278*R2^3)+a^6*b^3*(1091093415*R4+684059464*R2^2)+a^11*b*(66*R12+54*R10*R2 +96*R9*R3+126*R8*R4+42*R8*R2^2+144*R7*R5+144*R7*R3*R2+75*R6^2+180*R6*R4*R2+120* R6*R3^2+30*R6*R2^3+96*R5^2*R2+288*R5*R4*R3+144*R5*R3*R2^2+54*R4^3+81*R4^2*R2^2+ 216*R4*R3^2*R2+18*R4*R2^4+24*R3^4+48*R3^2*R2^3+R2^6)+a^8*(18128396*R5+33549516* R3*R2)+19056960*a^7*R3+a^11*(715*R11+1144*R9*R2+2002*R8*R3+2574*R7*R4+1287*R7* R2^2+2860*R6*R5+4290*R6*R3*R2+5148*R5*R4*R2+3432*R5*R3^2+1144*R5*R2^3+3861*R4^2 *R3+5148*R4*R3*R2^2+2288*R3^3*R2+715*R3*R2^4)+a^12*R13 [13] 68428800*a^7*R2+a^8*b*(1502689916*R5+2864648644*R3*R2)+a^8*b^2*(1999648521*R6+ 4589160004*R4*R2+2782906568*R3^2+1323727184*R2^3)+a^8*b^3*(915090930*R7+ 2310162543*R5*R2+3057797470*R4*R3+2752801103*R3*R2^2)+a^7*b^6*(44990231*R8+ 115214112*R6*R2+162260202*R5*R3+87502740*R4^2+153328708*R4*R2^2+192834694*R3^2* R2+25048218*R2^4)+a^8*b^5*(6926634*R9+17416737*R7*R2+25876825*R6*R3+29323541*R5 *R4+24264968*R5*R2^2+67577900*R4*R3*R2+14406912*R3^3+21434582*R3*R2^3)+a^9*b^2* (104517140*R8+276240900*R6*R2+389641629*R5*R3+210093182*R4^2+377473590*R4*R2^2+ 475342023*R3^2*R2+63020906*R2^4)+a^9*b*(206636001*R7+528105734*R5*R2+698355541* R4*R3+635708281*R3*R2^2)+a^8*b^4*(148612737*R8+386391200*R6*R2+544912121*R5*R3+ 293917234*R4^2+520930566*R4*R2^2+655721391*R3^2*R2+85985939*R2^4)+a^11*b*(53053 *R11+111072*R9*R2+185003*R8*R3+229866*R7*R4+147225*R7*R2^2+250978*R6*R5+472446* R6*R3*R2+555984*R5*R4*R2+366808*R5*R3^2+147810*R5*R2^3+408486*R4^2*R3+651027*R4 *R3*R2^2+286156*R3^3*R2+103558*R3*R2^4)+a^9*b^3*(17016714*R9+43737122*R7*R2+ 65216866*R6*R3+73996234*R5*R4+62104484*R5*R2^2+173409548*R4*R3*R2+37034790*R3^3 +55730545*R3*R2^3)+a^9*b^4*(749463*R10+1742832*R8*R2+2721862*R7*R3+3216174*R6* R4+2389140*R6*R2^2+1683344*R5^2+7138820*R5*R3*R2+3924076*R4^2*R2+5093868*R4*R3^ 2+2312986*R4*R2^3+4498728*R3^2*R2^2+237224*R2^5)+a^10*b^2*(1246674*R10+2995850* R8*R2+4715841*R7*R3+5594719*R6*R4+4226859*R6*R2^2+2931812*R5^2+12706304*R5*R3* R2+6997497*R4^2*R2+9110075*R4*R3^2+4191993*R4*R2^3+8176272*R3^2*R2^2+436852*R2^ 5)+a^10*b^3*(55770*R11+110838*R9*R2+181636*R8*R3+223353*R7*R4+140322*R7*R2^2+ 242645*R6*R5+444600*R6*R3*R2+519948*R5*R4*R2+341588*R5*R3^2+135590*R5*R2^3+ 379080*R4^2*R3+592644*R4*R3*R2^2+259402*R3^3*R2+92456*R3*R2^4)+a^11*b^2*(2717* R12+4056*R10*R2+6968*R9*R3+8918*R8*R4+4368*R8*R2^2+10036*R7*R5+14586*R7*R3*R2+ 5200*R6^2+17940*R6*R4*R2+11895*R6*R3^2+3900*R6*R2^3+9516*R5^2*R2+28236*R5*R4*R3 +18408*R5*R3*R2^2+5265*R4^3+10296*R4^2*R2^2+27300*R4*R3^2*R2+2795*R4*R2^4+3016* R3^4+7410*R3^2*R2^3+182*R2^6)+a^12*(1001*R12+1638*R10*R2+2912*R9*R3+3822*R8*R4+ 1911*R8*R2^2+4368*R7*R5+6552*R7*R3*R2+2275*R6^2+8190*R6*R4*R2+5460*R6*R3^2+1820 *R6*R2^3+4368*R5^2*R2+13104*R5*R4*R3+8736*R5*R3*R2^2+2457*R4^3+4914*R4^2*R2^2+ 13104*R4*R3^2*R2+1365*R4*R2^4+1456*R3^4+3640*R3^2*R2^3+91*R2^6)+a^13*R14+a^10*( 8691683*R8+23377562*R6*R2+32944938*R5*R3+17749927*R4^2+32392724*R4*R2^2+ 40788384*R3^2*R2+5475652*R2^4)+a^10*b*(6668376*R9+17552041*R7*R2+26211393*R6*R3 +29728257*R5*R4+25409033*R5*R2^2+71040892*R4*R3*R2+15192879*R3^3+23180326*R3*R2 ^3)+a^9*(109425316*R6+253452836*R4*R2+153561772*R3^2+73713276*R2^3)+a^4*b^8*( 13462642752*R4+8592430392*R2^2)+a^4*b^9*(1414014888*R5+2631136560*R3*R2)+a^3*b^ 10*(1931559552*R4+1227788640*R2^2)+a^12*b*(78*R13+65*R11*R2+117*R10*R3+156*R9* R4+52*R9*R2^2+182*R8*R5+182*R8*R3*R2+195*R7*R6+234*R7*R4*R2+156*R7*R3^2+39*R7* R2^3+260*R6*R5*R2+390*R6*R4*R3+195*R6*R3*R2^2+208*R5^2*R3+234*R5*R4^2+234*R5*R4 *R2^2+312*R5*R3^2*R2+26*R5*R2^4+351*R4^2*R3*R2+156*R4*R3^3+156*R4*R3*R2^3+104* R3^3*R2^2+13*R3*R2^5)+a^7*b^4*(4859140481*R6+11054995198*R4*R2+6707980747*R3^2+ 3164293808*R2^3)+a^7*b^3*(9992155355*R5+18922602166*R3*R2)+a^7*b^2*(7451435108* R4+4823623948*R2^2)+a^6*b^5*(15888639390*R5+29901546610*R3*R2)+a^6*b^6*( 3348940036*R6+7557243824*R4*R2+4587226956*R3^2+2147750852*R2^3)+a^6*b^7*( 206070150*R7+508811992*R5*R2+673525606*R4*R3+595055838*R3*R2^2)+a^6*b^4*( 26901192916*R4+17326603866*R2^2)+a^5*b^6*(30923406332*R4+19823493352*R2^2)+a^5* b^7*(8519378036*R5+15939372436*R3*R2)+a^5*b^8*(657206836*R6+1471835352*R4*R2+ 893477052*R3^2+415558416*R2^3)+a^7*b^5*(862673253*R7+2152901634*R5*R2+ 2850644953*R4*R3+2540822063*R3*R2^2)+a^11*(183183*R10+456092*R8*R2+720902*R7*R3 +855400*R6*R4+662025*R6*R2^2+448084*R5^2+1996540*R5*R3*R2+1100190*R4^2*R2+ 1436435*R4*R3^2+672490*R4*R2^3+1314495*R3^2*R2^2+71344*R2^5)+1695897216*a^7*b* R3+36493347748*a^5*b^5*R3+11397538632*a^5*b^4*R2+479001600*a*b^12*R2+4261576320 *a^2*b^10*R2+13636988064*a^3*b^8*R2+1486442880*a^2*b^11*R3+11783981664*a^3*b^9* R3+a^8*(292271616*R4+190217664*R2^2)+32321926104*a^4*b^7*R3+15592925140*a^6*b^3 *R3+19123810464*a^4*b^6*R2+2301753600*a^6*b^2*R2 [14] 89677392288*a^6*b^3*R2+458539997916*a^6*b^4*R3+a^14*R15+a^12*(355355*R11+924742 *R9*R2+1494402*R8*R3+1815177*R7*R4+1424150*R7*R2^2+1957865*R6*R5+4452175*R6*R3* R2+5165615*R5*R4*R2+3384745*R5*R3^2+1603875*R5*R2^3+3741465*R4^2*R3+6951945*R4* R3*R2^2+3030755*R3^3*R2+1248520*R3*R2^4)+a^11*(25537655*R9+74586655*R7*R2+ 108780815*R6*R3+121953975*R5*R4+116367160*R5*R2^2+319646600*R4*R3*R2+67649400* R3^3+113233120*R3*R2^3)+a^10*(539651112*R7+1457761032*R5*R2+1900585960*R4*R3+ 1831663288*R3*R2^2)+a^13*(1365*R13+2275*R11*R2+4095*R10*R3+5460*R9*R4+2730*R9* R2^2+6370*R8*R5+9555*R8*R3*R2+6825*R7*R6+12285*R7*R4*R2+8190*R7*R3^2+2730*R7*R2 ^3+13650*R6*R5*R2+20475*R6*R4*R3+13650*R6*R3*R2^2+10920*R5^2*R3+12285*R5*R4^2+ 16380*R5*R4*R2^2+21840*R5*R3^2*R2+2275*R5*R2^4+24570*R4^2*R3*R2+10920*R4*R3^3+ 13650*R4*R3*R2^3+9100*R3^3*R2^2+1365*R3*R2^5)+2699672832*a^8*R3+a^9*b^4*( 443488383*R9+1252285603*R7*R2+1826346790*R6*R3+2050975782*R5*R4+1901322276*R5* R2^2+5221205871*R4*R3*R2+1103810575*R3^3+1806524699*R3*R2^3)+a^9*b^5*(16669653* R10+44623173*R8*R2+68060510*R7*R3+79344720*R6*R4+67609885*R6*R2^2+41348650*R5^2 +198030448*R5*R3*R2+108143301*R4^2*R2+139111371*R4*R3^2+70797804*R4*R2^3+ 136379768*R3^2*R2^2+7873572*R2^5)+a^11*b^3*(91091*R12+187362*R10*R2+312312*R9* R3+391167*R8*R4+247940*R8*R2^2+434532*R7*R5+806400*R7*R3*R2+224175*R6^2+976080* R6*R4*R2+642600*R6*R3^2+256970*R6*R2^3+514976*R5^2*R2+1507632*R5*R4*R3+1189720* R5*R3*R2^2+279342*R4^3+661122*R4^2*R2^2+1739976*R4*R3^2*R2+208299*R4*R2^4+ 190792*R3^4+548016*R3^2*R2^3+15288*R2^6)+a^10*b*(777032828*R8+2219150976*R6*R2+ 3072009199*R5*R3+1646543808*R4^2+3210194260*R4*R2^2+4001287591*R3^2*R2+ 568395996*R2^4)+a^10*b^2*(309703628*R9+888812375*R7*R2+1296958155*R6*R3+ 1455733884*R5*R4+1367540699*R5*R2^2+3757334091*R4*R3*R2+794906420*R3^3+ 1314501552*R3*R2^3)+a^10*b^3*(40708668*R10+111289836*R8*R2+170408987*R7*R3+ 198983330*R6*R4+171756382*R6*R2^2+103737865*R5^2+504623203*R5*R3*R2+275806482* R4^2*R2+355415823*R4*R3^2+182736344*R4*R2^3+352579766*R3^2*R2^2+20556872*R2^5)+ a^10*b^4*(1474473*R11+3593478*R9*R2+5732118*R8*R3+6926143*R7*R4+5235272*R7*R2^2 +7459949*R6*R5+16199645*R6*R3*R2+18723075*R5*R4*R2+12197745*R5*R3^2+5622491*R5* R2^3+13445635*R4^2*R3+24190299*R4*R3*R2^2+10494435*R3^3*R2+4213468*R3*R2^4)+a^9 *(2961802480*R5+5823745200*R3*R2)+a^11*b^2*(2437435*R11+6128528*R9*R2+9855454* R8*R3+11962965*R7*R4+9179331*R7*R2^2+12910870*R6*R5+28591017*R6*R3*R2+33143614* R5*R4*R2+21651168*R5*R3^2+10097444*R5*R2^3+23909319*R4^2*R3+43632687*R4*R3*R2^2 +18978064*R3^3*R2+7707686*R3*R2^4)+a^12*b*(86086*R12+185976*R10*R2+315042*R9*R3 +398958*R8*R4+257152*R8*R2^2+446019*R7*R5+847518*R7*R3*R2+230580*R6^2+1033872* R6*R4*R2+683193*R6*R3^2+276780*R6*R2^3+546868*R5^2*R2+1612044*R5*R4*R3+1293530* R5*R3*R2^2+299628*R4^3+721056*R4^2*R2^2+1904763*R4*R3^2*R2+231042*R4*R2^4+ 209636*R3^4+610113*R3^2*R2^3+17248*R2^6)+a^11*b*(15834819*R10+44308159*R8*R2+ 67986415*R7*R3+79365062*R6*R4+69694891*R6*R2^2+41361061*R5^2+205089213*R5*R3*R2 +112111923*R4^2*R2+144713478*R4*R3^2+75369420*R4*R2^3+145599286*R3^2*R2^2+ 8588748*R2^5)+a^4*b^9*(209697014688*R4+137280895416*R2^2)+a^3*b^11*(26596717056 *R4+17358253920*R2^2)+a^12*b^2*(3731*R13+5705*R11*R2+9933*R10*R3+12908*R9*R4+ 6342*R9*R2^2+14798*R8*R5+21609*R8*R3*R2+15715*R7*R6+27279*R7*R4*R2+18102*R7*R3^ 2+5950*R7*R2^3+30030*R6*R5*R2+44625*R6*R4*R3+29190*R6*R3*R2^2+23688*R5^2*R3+ 26523*R5*R4^2+34692*R5*R4*R2^2+46032*R5*R3^2*R2+4725*R5*R2^4+51534*R4^2*R3*R2+ 22792*R4*R3^3+28070*R4*R3*R2^3+18620*R3^3*R2^2+2751*R3*R2^5)+a^13*b*(21*R4*R2^5 +112*R3^4*R2+175*R6^2*R2+315*R6*R4^2+35*R6*R2^4+49*R8*R2^3+196*R8*R3^2+224*R9* R5+245*R8*R6+63*R10*R2^2+189*R10*R4+140*R11*R3+77*R12*R2+224*R5*R3^3+189*R4^3* R2+378*R4^2*R3^2+126*R4^2*R2^3+70*R3^2*R2^4+336*R5^2*R4+168*R5^2*R2^2+1008*R5* R4*R3*R2+126*R7^2+91*R14+R2^7+224*R5*R3*R2^3+315*R6*R4*R2^2+504*R4*R3^2*R2^2+ 224*R9*R3*R2+294*R8*R4*R2+336*R7*R5*R2+504*R7*R4*R3+252*R7*R3*R2^2+560*R6*R5*R3 +420*R6*R3^2*R2)+a^7*b^3*(271520867464*R4+179693859688*R2^2)+a^7*b^5*( 110568624971*R6+261123472218*R4*R2+157218893111*R3^2+77383202792*R2^3)+a^6*b^8* (3336118786*R7+8707678336*R5*R2+11382585802*R4*R3+10631306994*R3*R2^2)+a^6*b^6* (321409604754*R5+622521081882*R3*R2)+a^6*b^7*(59667816152*R6+140075346992*R4*R2 +84368639964*R3^2+41290739980*R2^3)+a^6*b^5*(640705256184*R4+422374683094*R2^2) +a^5*b^7*(571567520804*R4+375437315008*R2^2)+a^5*b^8*(140814276932*R5+ 271548766972*R3*R2)+a^5*b^9*(9957703756*R6+23248309224*R4*R2+14005474308*R3^2+ 6819809136*R2^3)+a^4*b^10*(20313753096*R5+39015645648*R3*R2)+a^8*b^5*( 3292560006*R8+9180469396*R6*R2+12722321031*R5*R3+6825587608*R4^2+13023676274*R4 *R2^2+16234840629*R3^2*R2+2265962678*R2^4)+a^8*b^6*(135036473*R9+375741441*R7* R2+547081211*R6*R3+614156527*R5*R4+563286836*R5*R2^2+1544910542*R4*R3*R2+ 326288522*R3^3+529417098*R3*R2^3)+a^7*b^7*(790943153*R8+2182332292*R6*R2+ 3022911374*R5*R3+1621892272*R4^2+3068330692*R4*R2^2+3823420762*R3^2*R2+ 529848732*R2^4)+a^7*b^6*(16906280013*R7+44462928454*R5*R2+58116103997*R4*R3+ 54638008243*R3*R2^2)+a^8*b^3*(69016208044*R6+164044427806*R4*R2+98715246833*R3^ 2+48896327172*R2^3)+a^8*b^4*(24369452975*R7+64622722913*R5*R2+84426694513*R4*R3 +79965371346*R3*R2^2)+a^8*b*(29255995776*R4+19442697568*R2^2)+a^8*b^2*( 76240813068*R5+149110242568*R3*R2)+a^9*b^3*(3469001198*R8+9784465103*R6*R2+ 13556455563*R5*R3+7270503352*R4^2+14012910758*R4*R2^2+17469731503*R3^2*R2+ 2458505420*R2^4)+a^9*b^2*(9951201050*R7+26625397659*R5*R2+34755538832*R4*R3+ 33192355315*R3*R2^2)+a^9*b*(10289403488*R6+24626050960*R4*R2+14808273116*R3^2+ 7386265096*R2^3)+a^7*b^4*(277568441563*R5+540138260984*R3*R2)+6227020800*a*b^13 *R2+61148511360*a^2*b^11*R2+91755393584*a^7*b^2*R3+7369938432*a^7*b*R2+ 222761182752*a^3*b^9*R2+175201211232*a^3*b^10*R3+19802759040*a^2*b^12*R3+ 557103863832*a^4*b^8*R3+373089740448*a^4*b^7*R2+288381507624*a^5*b^5*R2+ 775663716436*a^5*b^6*R3 [15] 283465647360*a^2*b^13*R3+3833696305728*a^3*b^10*R2+2770340966208*a^3*b^11*R3+ 7492855215840*a^4*b^8*R2+10037999331408*a^4*b^9*R3+7191067238160*a^5*b^6*R2+a^9 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R5^2*R4+13440*R5^2*R2^2+8400*R3^2*R2^4+11200*R3^4*R2+2520*R4*R2^5+12600*R4^2*R2 ^3+30240*R4^2*R3^2+15120*R4^3*R2+17920*R5*R3^3+11760*R8*R3^2)+a^13*b*(134680* R13+298695*R11*R2+513045*R10*R3+659580*R9*R4+427260*R9*R2^2+750540*R8*R5+ 1436820*R8*R3*R2+794010*R7*R6+1797300*R7*R4*R2+1189200*R7*R3^2+483815*R7*R2^3+ 1969260*R6*R5*R2+2909640*R6*R4*R3+2347725*R6*R3*R2^2+1540560*R5^2*R3+1720080*R5 *R4^2+2774550*R5*R4*R2^2+3669600*R5*R3^2*R2+447090*R5*R2^4+4095810*R4^2*R3*R2+ 1805480*R4*R3^3+2638650*R4*R3*R2^3+1744260*R3^3*R2^2+297150*R3*R2^5)+a^14*b*(48 *R3^5+160*R5^3+720*R5*R3^2*R2^2+360*R5*R4*R2^3+60*R9*R2^3+420*R8*R5*R2+360*R9* R4*R2+270*R10*R3*R2+405*R7*R4*R2^2+630*R8*R4*R3+1350*R6*R4*R3*R2+720*R7*R5*R3+ 450*R7*R6*R2+315*R8*R3*R2^2+300*R6*R3*R2^3+450*R6*R5*R2^2+900*R6*R5*R4+540*R7* R3^2*R2+810*R5*R4^2*R2+720*R5^2*R3*R2+1080*R5*R4*R3^2+225*R4*R3*R2^4+720*R4*R3^ 3*R2+810*R4^2*R3*R2^2+15*R3*R2^6+200*R3^3*R2^3+405*R4^3*R3+30*R5*R2^5+315*R8*R7 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12397418329716*R9+42386195499982*R7*R2+58827397570026*R6*R3+64631842526566*R5* R4+74051537556922*R5*R2^2+195613681395623*R4*R3*R2+40349793950587*R3^3+ 79367032070950*R3*R2^3)+a^10*b^6*(930626523288*R10+3239489275917*R8*R2+ 4675386858528*R7*R3+5289549526125*R6*R4+5959220765303*R6*R2^2+2730710319294*R5^ 2+16633034287013*R5*R3*R2+8944406039393*R4^2*R2+11238204120217*R4*R3^2+ 7279898725345*R4*R2^3+13676016772943*R3^2*R2^2+957663685439*R2^5)+a^11*b^5*( 94762622844*R11+328196418288*R9*R2+491838038049*R8*R3+571721991171*R7*R4+ 618648325473*R7*R2^2+604585340826*R6*R5+1807860369642*R6*R3*R2+2032563070044*R5 *R4*R2+1294601603160*R5*R3^2+810325178898*R5*R2^3+1403753613643*R4^2*R3+ 3345538491603*R4*R3*R2^2+1416524412531*R3^3*R2+728806870001*R3*R2^4)+a^12*b^4*( 7082187216*R12+23665340586*R10*R2+36819636048*R9*R3+43987580172*R8*R4+ 44375486138*R8*R2^2+47543810580*R7*R5+135303448273*R7*R3*R2+24309248430*R6^2+ 157660745551*R6*R4*R2+101663501388*R6*R3^2+59874245225*R6*R2^3+82145051314*R5^2 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