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bFunction.ideal.exa.m2
loadPackage ("Dmodules", FileName => "../../Dmodules.m2") -------------------------EXAMPLES for bFunction --Example of non-specializable R = QQ[x,y,Dx,Dy, WeylAlgebra => {x=>Dx, y=>Dy}] I = ideal Dx bFunction(I, {1,1}) --Example 1 (GD_of_HDE Example 5.2.10) R = QQ[x, y, dx, dy, WeylAlgebra => {x=>dx, y=>dy}] I = ideal(x, dy-1) time bFunction(I, {1,0}) --Example 1b (GD_of_HDE Example 5.2.10) R = frac(QQ[p]/ ideal p)[x, y, dx, dy, WeylAlgebra => {x=>dx, y=>dy}] I = ideal(x, dy-1) time bFunction(I, {1,0}) --Example 2 (Algs_for_D_mods Example 5.5) A = matrix{{0,0,1,1},{1,0,1,0},{0,1,0,1}} b = {15,100,40} I = gkz(A,b) transpose gens I w = {1,1,1,0} time(apply(20, i->print bFunction(I, w))) time(apply(20, i->print bFunction(I, w, Homogenization => false))) bf = bFunction(I, w) -- Expected answer bf == (s:=(ring bf)_0; (s-b#1)*(s+b#0-b#1-b#2)) --Example 2a (Algs_for_D_mods Example 5.5) A = matrix{{0,0,1,1},{1,0,1,0},{0,1,0,1}} b = {15,100,40} I = gkz(A,b) transpose gens I w = {1,1,1,1} bf = bFunction(I,w) -- Expected answer bf == (s:=(ring bf)_0; s-b#1-b#2) --Example 3 (Algs_for_D_mods Example 4.7) -- !!! Doesn't finish !!! W = QQ[t_1,t_2,x,y,z, d_1,d_2,dx,dy,dz, WeylAlgebra => {t_1=>d_1, t_2=>d_2, x=>dx, y=>dy, z=>dz}] I = ideal(t_1-x^3+y^2, t_2-y^3+z^2, dx+3*x^2*d_1, dy-2*y*d_1+3*y^2*d_2, dz-2*z*d_2) w = {1,1,0,0,0} bFunction(I, w) -- log canonical threshold restart; loadPackage "Dmodules"; QQ[x_1..x_6]; time lct minors(2, matrix{{x_1, x_2, x_3}, {x_4, x_5, x_6}}) QQ[x_1..x_3]; time lct ideal (x_2^2-x_1*x_3, x_1^3-x_3^2); QQ[x_1..x_3]; time lct ideal (x_1^3-x_2^2, x_2^3-x_3^2); QQ[x_1..x_3]; time lct ideal (x_1^4-x_2^3, x_3^2-x_1*x_2^2); -- does not finish -- rlct restart loadPackage ("Dmodules", FileName => "../../Dmodules.m2") debug Dmodules makeWA QQ[x,y] f = x^2+y^3 sort bFunctionRoots globalBFunction f sort bFunctionRoots localBFunction(f, ideal gens ring f) rlct f QQ[x,y,z] f = (x^2+y^2+z^2)^2+x^6 isFsLocallyIntegrable(f,-17/24) isFsLocallyIntegrable(f,-19/24)