Macaulay 2, version 0.9.2 --Copyright 1993-2001, D. R. Grayson and M. E. Stillman --Singular-Factory 2.0.5, copyright 1993-2001, G.-M. Greuel, et al. --Singular-Libfac 2.0.4, copyright 1996-2001, M. Messollen i1 : load "D-modules.m2" --loaded Dbasic.m2 from /usr/lib/Macaulay2-0.9.2/packages/D-modules/Dbasic.m2 --loaded Gbw.m2 from /usr/lib/Macaulay2-0.9.2/packages/D-modules/Gbw.m2 --loaded Dsystems.m2 from /usr/lib/Macaulay2-0.9.2/packages/D-modules/Dsystems.m2 --loaded switch.m2 from /usr/lib/Macaulay2-0.9.2/packages/D-modules/switch.m2 --loaded newRings.m2 from /usr/lib/Macaulay2-0.9.2/packages/D-modules/newRings.m2 --loaded Dresolution.m2 from /usr/lib/Macaulay2-0.9.2/packages/D-modules/Dresolution.m2 --loaded Drestriction.m2 from /usr/lib/Macaulay2-0.9.2/packages/D-modules/Drestriction.m2 --loaded Sparsemat.m2 from /usr/lib/Macaulay2-0.9.2/packages/D-modules/Sparsemat.m2 --loaded Dlocalize.m2 from /usr/lib/Macaulay2-0.9.2/packages/D-modules/Dlocalize.m2 --loaded WeylClosure.m2 from /usr/lib/Macaulay2-0.9.2/packages/D-modules/WeylClosure.m2 --loaded Ddual.m2 from /usr/lib/Macaulay2-0.9.2/packages/D-modules/Ddual.m2 --loaded DHom.m2 from /usr/lib/Macaulay2-0.9.2/packages/D-modules/DHom.m2 --loaded DeRham.m2 from /usr/lib/Macaulay2-0.9.2/packages/D-modules/DeRham.m2 --loaded DiffOps.m2 from /usr/lib/Macaulay2-0.9.2/packages/D-modules/DiffOps.m2 --loaded bFunction.ideal.m2 from /usr/lib/Macaulay2-0.9.2/packages/D-modules/bFunction.ideal.m2 --loaded globalBFunction.m2 from /usr/lib/Macaulay2-0.9.2/packages/D-modules/globalBFunction.m2 --loaded annFs.m2 from /usr/lib/Macaulay2-0.9.2/packages/D-modules/annFs.m2 --loaded bFunction.module.m2 from /usr/lib/Macaulay2-0.9.2/packages/D-modules/bFunction.module.m2 --loaded localCohom.m2 from /usr/lib/Macaulay2-0.9.2/packages/D-modules/localCohom.m2 --loaded paramBpoly.m2 from /usr/lib/Macaulay2-0.9.2/packages/D-modules/paramBpoly.m2 --loaded makeCyclic.m2 from /usr/lib/Macaulay2-0.9.2/packages/D-modules/makeCyclic.m2 --loaded D-modules/Dloadfile.m2 from /usr/lib/Macaulay2-0.9.2/packages/D-modules/Dloadfile.m2 --loaded D-modules.m2 from /usr/lib/Macaulay2-0.9.2/packages/D-modules.m2 i2 : load "trans.m2" --loaded trans.m2 i3 : makeTauInputTest(0); 3 3 2 4 5 6 5 3 2 x y + x y + x*y + y + x + x y {6} | 18/25y3-23/10xy+43/50y2+3/10x-27/25y 18/25xy2+36/25y3-23/10x2-241/50xy-2/25y2+3/5x-54/25y | {5} | -3/25xy3+23/50x2y-3/25xy2+1/10y3-3/50x2+6/25xy -3/25x2y2-6/25xy3+23/50x3+49/50x2y+4/25xy2+1/5y3-3/25x2+12/25xy | {5} | -3/25y4-1/25x2y+9/25xy2-4/25y3-3/50x2-3/50xy+9/50y2 -3/25xy3-6/25y4-1/25x3+7/25x2y+37/50xy2-1/50y3-3/25x2-3/25xy+9/25y2 | 3 3 3 4 23 2 3 2 1 3 1 2 9 2 4 3 18 3 3 2 6 3 2 3 9 2 23 43 2 3 27 3 2 2 6 3 3 3 6 4 23 3 49 2 4 2 1 3 1 3 7 2 37 2 1 3 18 2 36 3 3 2 12 3 2 3 9 2 23 2 241 2 2 3 54 {{- --*x*y dx - --*y dy + --*x y*dx - --*x*y dx + --*y dx - --*x y*dy + --*x*y dy - --*y dy - --*y - --*x dx + --*x*y*dx - --*x dy - --*x*y*dy + --*y dy + --*x*y - --*y - --*x + --*y, - --*x y dx - --*x*y dx - --*x*y dy - --*y dy + --*x dx + --*x y*dx + --*x*y dx + -*y dx - --*x dy + --*x y*dy + --*x*y dy - --*y dy - --*x*y - --*y - --*x dx + --*x*y*dx - --*x dy - --*x*y*dy + --*y dy + --*x + ---*x*y + --*y - -*x + --*y}} 25 25 50 25 10 25 25 25 25 50 25 50 50 50 10 50 10 25 25 25 25 25 50 50 25 5 25 25 50 50 25 25 25 25 25 25 25 10 50 25 5 25 iAllt (integrationAllWithTransfer) in trans.m2 cokernel | -3/25xy3dx-3/25y4dy+23/50x2ydx-3/25xy2dx+1/10y3dx-1/25x2ydy+9/25xy2dy-4/25y3dy-18/25y3-3/50x2dx+6/25xydx-3/50x2dy-3/50xydy+9/50y2dy+23/10xy-43/50y2-3/10x+27/25y -3/25x2y2dx-6/25xy3dx-3/25xy3dy-6/25y4dy+23/50x3dx+49/50x2ydx+4/25xy2dx+1/5y3dx-1/25x3dy+7/25x2ydy+37/50xy2dy-1/50y3dy-18/25xy2-36/25y3-3/25x2dx+12/25xydx-3/25x2dy-3/25xydy+9/25y2dy+23/10x2+241/50xy+2/25y2-3/5x+54/25y | 1 8 19 19 8 1 QQ [x, y, dx, dy, WeylAlgebra => {x => dx, y => dy}] <-- QQ [x, y, dx, dy, WeylAlgebra => {x => dx, y => dy}] <-- QQ [x, y, dx, dy, WeylAlgebra => {x => dx, y => dy}] <-- QQ [x, y, dx, dy, WeylAlgebra => {x => dx, y => dy}] <-- QQ [x, y, dx, dy, WeylAlgebra => {x => dx, y => dy}] <-- QQ [x, y, dx, dy, WeylAlgebra => {x => dx, y => dy}] <-- 0 0 1 2 3 4 5 6 {0, 0, | 0 |} | 0 | | x-5/6 | | 1 | | 0 | | 0 | {0, 0, | -y2dx+x2dy+xydy+y2dy-23/6xdx+1/2ydx+7/3xdy-ydy+x+2y-7/3dx-373/60dy-29/6 |, | x2+xy+y2+7/3x-y-373/60 |} | 1/10xdy-251/60dx-157/60dy | | 1/10x-157/60 | | -x2dy-5/2xydy-5/2ydx-1/12xdy-121/12ydy-5/2x+1205/72dx+805/72dy-121/12 | | -x2-5/2xy-1/12x-121/12y+805/72 | | xdx+ydy-5/6dx+1/3dy+2 | | y+1/3 | | 0 | | 0 | | 0 | | 0 | | -y2-23/6x+1/2y-7/3 | | -251/60 | | -5/2y+1205/72 | | x-5/6 | | 0 | | 0 | {0, 1, | -x3y3dx-x2y4dx-xy5dx-y6dx-x5dx-x3y2dx-3x2y3-2xy4-y5-5x4-3x2y2 |, | x3y3+x2y4+xy5+y6+x5+x3y2 |} | x3y3dy+x2y4dy+xy5dy+y6dy+x5dy+x3y2dy+3x3y2+4x2y3+5xy4+6y5+2x3y | {1, 0, | 2/5x -33/25x-3/280 56/75x-41/30 |} | 6/25x 66/125x+461/700 -112/375x-3/25 | | -x 3y2+3/2y -28/9y2 | | 0 1 0 | | 0 107/28y -y | | 0 0 0 | {1, 0, | 6/25x3y2dx+2/5x2y3dx+6/25x2y3dy+2/5xy4dy+2/25x4dx-8/25x3ydx+2/25x4dy+2/25x3ydy-6/25x2y2dy+36/25x2y2+12/5xy3+2/5x3-36/25x2y -107/28y6dx^2+107/28y6dxdy-107/28xy5dy^2-107/28y6dy^2-107/56y5dx^2-107/28x3y2dy^2-107/28xy4dy^2-107/56y5dy^2-309/125x3y2dx-133/25x2y3dx-6/5xy4dx+535/28y5dx+66233/1008x2y2dx^2-7597/280xy3dx^2+16799/1008y4dx^2-309/125x2y3dy-6281/175xy4dy-2759/70y5dy-6527/336x2y2dxdy+46973/840xy3dxdy-61097/1680y4dxdy-107/84x3ydy^2-535/504x2y2dy^2-321/28xy3dy^2+14659/2520y4dy^2-253/125x4dx+412/125x3ydx-107/28x2y2dx+107/56xy3dx-107/56y4dx-16799/1680x2ydx^2+16799/420xy2dx^2-103/125x4dy-16917/1750x3ydy+309/125x2y2dy-214/7xy3dy-535/28y4dy-3103/420x2ydxdy-11449/560xy2dxdy+16799/560y3dxdy+4387/1680x2ydy^2+4387/1680xy2dy^2-4387/560y3dy^2-1854/125x2y2-13611/175xy3-2927/35y4-535/168x3dx-14659/504x2ydx+2406109/5040xy2dx-1108627/5040y3dx-107/84x3dy-535/63x2ydy-13375/112xy2dy+11877/112y3dy-253/25x3+1854/125x2y-107/2xy2-2033/56y3+4387/1680x2dx-152689/1680xydx+184789/840y2dx+4387/1680x2dy-963/560xydy-8453/105y2dy-2675/168x2-75863/504xy+537461/1260y2+4387/336x-34561/240y y6dx^2-y6dxdy+xy5dy^2+y6dy^2+1/2y5dx^2+x3y2dy^2+xy4dy^2+1/2y5dy^2+3164/1125x3y2dx+3304/675x2y3dx+56/45xy4dx-107/27y5dx-619/36x2y2dx^2+71/10xy3dx^2-157/36y4dx^2+5992/3375x2y3dy+2668/225xy4dy+1378/135y5dy+61/12x2y2dxdy-439/30xy3dxdy+571/60y4dxdy+1/3x3ydy^2+5/18x2y2dy^2+3xy3dy^2-137/90y4dy^2+1288/1125x4dx-3052/1125x3ydx+x2y2dx-1/2xy3dx+1/2y4dx+157/60x2ydx^2-157/15xy2dx^2-112/1125x4dy+3538/1125x3ydy-3164/1125x2y2dy+8xy3dy+5y4dy+29/15x2ydxdy+107/20xy2dxdy-157/20y3dxdy-41/60x2ydy^2-41/60xy2dy^2+41/20y3dy^2+15484/1125x2y2+25124/675xy3+3008/135y4+5/6x3dx+137/18x2ydx-22487/180xy2dx+10361/180y3dx+1/3x3dy+20/9x2ydy+125/4xy2dy-111/4y3dy+1288/225x3-15484/1125x2y+14xy2+19/2y3-41/60x2dx+1427/60xydx-1727/30y2dx-41/60x2dy+9/20xydy+316/15y2dy+25/6x2+709/18xy-5023/45y2-41/12x+2261/60y |, | 6/25x2y3+2/5xy4+2/25x4+2/25x3y-6/25x2y2 107/28y6dx-107/28xy5dy-107/28y6dy-107/28x3y2dy-107/28xy4dy-107/56y5dy-309/125x2y3-11749/700xy4-577/35y5-6527/336x2y2dx+46973/840xy3dx-61097/1680y4dx-107/84x3ydy-535/504x2y2dy-321/28xy3dy+14659/2520y4dy-103/125x4-253/125x3y+309/125x2y2-107/7xy3-535/56y4-3103/420x2ydx-11449/560xy2dx+16799/560y3dx+4387/1680x2ydy+4387/1680xy2dy-4387/560y3dy-535/84x2y-9523/112xy2+59599/720y3-11663/1680xy-19153/336y2 -y6dx+xy5dy+y6dy+x3y2dy+xy4dy+1/2y5dy+5992/3375x2y3+1543/225xy4+568/135y5+61/12x2y2dx-439/30xy3dx+571/60y4dx+1/3x3ydy+5/18x2y2dy+3xy3dy-137/90y4dy-112/1125x4+1288/1125x3y-3164/1125x2y2+4xy3+5/2y4+29/15x2ydx+107/20xy2dx-157/20y3dx-41/60x2ydy-41/60xy2dy+41/20y3dy+5/3x2y+89/4xy2-3899/180y3+109/60xy+179/12y2 |} | 6/25x3y2+2/5x2y3+2/25x4-8/25x3y -107/28y6dx-107/56y5dx-309/125x3y2-133/25x2y3-6/5xy4-107/28y5+66233/1008x2y2dx-7597/280xy3dx+16799/1008y4dx-253/125x4+412/125x3y-107/28x2y2+107/56xy3-107/56y4-16799/1680x2ydx+16799/420xy2dx-535/168x3+2461/252x2y+179653/1008xy2-238717/5040y3+16799/1680x2-16799/560xy+50397/560y2 y6dx+1/2y5dx+3164/1125x3y2+3304/675x2y3+56/45xy4+55/27y5-619/36x2y2dx+71/10xy3dx-157/36y4dx+1288/1125x4-3052/1125x3y+x2y2-1/2xy3+1/2y4+157/60x2ydx-157/15xy2dx+5/6x3-23/9x2y-1679/36xy2+2231/180y3-157/60x2+157/20xy-471/20y2 | {2, 0, | 1 -x y3 -xy3 xy2 x3y y4 |} 1 3 3 1 2 4 1 5 1 6 1 5 1 3 2 -*x y + -*x y + -*x*y + -*y + -*x + -*x y 3 3 3 3 3 3 3 3 2 4 5 6 5 3 2 x y + x y + x*y + y + x + x y i4 : quit; Process M2 finished t.txt is copied to tau.rr. It is set to the variable LL in tau.rr