[[f1 f2 ...] [t1 t2 ...] [vars params] [k0 k1 limitdeg ]] integration [ 0-th cohomology group, (-1)-th cohomology group, .... ] [[f1 f2 ...] [t1 t2 ...] [vars params] limitdeg] integration This function can be used by loading the experimental package cohom.sm1. Integration of the D-ideal [f1 f2 ...] to t1=0, t2=0, ... is computed. vars is a list of the variables and params is a list of parameters. k0 is the minimum integral root of the b-function and k1 is the maximum integral root of the b-function. If these values are not given and they are small, then they are automatically computed. The program returns 0-th, ..., -limitdeg-th cohomology groups. [vars params] and [k0 k1 deg] are optional arguments. If vars and params are not given, the values of the global variables BFvarlist and BFparlist will be used. The operator restriciton will be used after the laplace transformation. For the algorithm, see math.AG/9805006, http://xxx.langl.gov Example 1: [[(x (x-1)) (x) ] annfs 0 get [(x)] [[(x)] [ ]]] integration :: Example 2: [ [(Dt - (3 t^2-x)) (Dx + t)] [(t)] [[(t) (x)] [ ]] 0] integration :: Example 3: [ [[(Dt - (3 t^2-x)) (0)] [ (Dx + t) (0)]] [(t)] [[(t) (x)] [ ]] 0] integration :: In case of vector input, INTEGRAL VARIABLES MUST APPEAR FIRST in the list of variable. We are using wbfRoots to get the roots of b-functions, so we can use only generic weight vector for now.

Nobuki Takayama 2020-11-24