[gg vlist weight] wIntegration0 [ igg bb] list of strings gg; list of strings vlist; list weight; integer k1; list of polys igg; list of polys base; gg are input ideal or submodule. igg are relations and bb are bases. They give the integral. This function fails when weight is not generic. cf. intwbf, intwbfRoots, integral-k1. This function is defined in intw.sm1 and requires oxasir.sm1 and ox_asir server. See Grobner Deformations of Hypergeometric Differential Equations, Springer Section 5.5 for the algorithm. Example 1: [ [(Dt - (3 t^2-x)) (Dx + t)] [(t) (x)] [(t) -1 (Dt) 1]] wIntegration0 Example 2: [[(-3 x^2 Dy-2 y Dx) (2 x Dx+3 y Dy+6)] [(x) (y)] [(x) -1 (Dx) 1 (y) -2 (Dy) 2]] wIntegration0 The output [[-x, 1] [x,1]] implies the integral is (K x + K 1)/(K (-x) + K 1) = 0 where K is the base field and x and 1 is the vector space basis. Note that the order of weight and the order of the variables must be the same. Note also that the next of (x) must be (Dx) and so on.

Nobuki Takayama 2020-11-24