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DHom.exa.m2
path = join(path, {"../"}) load "Dloadfile.m2" Dtrace 4 ----------------------- EXAMPLES for PolySols, PolyExt ------------------------- -- Example 0: Simple example W = QQ[x,Dx,WeylAlgebra => {x=>Dx}] I = ideal(x*Dx^4) PolySols I PolyExt I -- Example 1: Polynomial solutions of a GKZ I = gkz(matrix{{1,3}}, {9}, Vars => Local) PolySols I PolySols (I, Alg => Duality) PolyExt I -- Example 2: Polynomial solutions of an Appell F1 I = AppellF1({-1,5,4,-2}) PolySols I PolySols (I, Alg => Duality) PolyExt I --------------------- EXAMPLES for RatSols and RatExt ----------------------- -- Example 1: Rational solutions of an Appell F1 I = AppellF1({2,-3,-2,5}) RatSols (I, x, {1,8}) RatlExt (I, x) RatlExt (I, y-1) -- Example 2: W = QQ[x,y,Dx,Dy,WeylAlgebra =>{x=>Dx, y=>Dy}] tx = x*Dx ty = y*Dy I = ideal(tx*(tx+ty)-x*(tx+ty+3)*(tx-1), ty*(tx+ty)-y*(tx+ty+3)*(ty+1)) RatSols(I, y, {10,1}) RatSols(I, y-1, {10,1}) holonomicRank I (mingens singLocus I)_(0,0) == x*y*(x-1)*(y-1)*(x-y) RatSols(I, {x,y,x-1,y-1,x-y}, {10,1}) ------------------------- EXAMPLES for DHom --------------------------- -- Example 1: Simple ODE examples W = QQ[x, dx, WeylAlgebra => {x=>dx}] M = cokernel matrix{{x*(dx-1)^2}} N = cokernel matrix{{x*dx*(dx-1)}} DHom(M,N) DHom(N,M) DExt(M,N) DExt(N,M) -- Example 2: small GKZ A = matrix{{1,2}} I = gkz(A, {2}) J = substitute(gkz(A, {1}), ring I) B = DHom(I,J) (matrix{{B#0_(0,0)}})*(gens I)%(gens J) -- Fool-proof test: nonholomonic! W = QQ[x, dx, y, dy, WeylAlgebra => {x=>dx, y=>dy}] M = cokernel matrix{{dx}} N = cokernel matrix{{dx,dy}} DHom(M,N) DHom(N,M)
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