asir-contrib - sm1

sm1_deRham([f,v]|proc=p): :: ask the server to evaluate the dimensions of the de Rham cohomology groups of C^n - (the zero set of f=0).

It returns the dimensions of the de Rham cohomology groups of X = C^n \ V(f). In other words, it returns [dim H^0(X,C), dim H^1(X,C), dim H^2(X,C), ..., dim H^n(X,C)].
v is a list of variables. n = length(v).
sm1_deRham requires huge computer resources. For example, sm1_deRham(0,[x*y*z*(x+y+z-1)*(x-y),[x,y,z]]) is already very hard.
To efficiently analyze the roots of b-function, ox_asir should be used from ox_sm1_forAsir. It is recommended to load the communication module for ox_asir by the command
sm1(0,"[(parse) (oxasir.sm1) pushfile] extension"); This command is automatically executed when ox_sm1_forAsir is started.
If you make an interruption to the function sm1_deRham by ox_reset(Sm1_proc);, the server might get out of the standard mode. So, it is strongly recommended to execute the command ox_shutdown(Sm1_proc); to interrupt and restart the server.

[332] sm1_deRham([x^3-y^2,[x,y]]);
[1,1,0]
[333] sm1_deRham([x*(x-1),[x]]);
[1,2]

Reference: sm1_start, deRham (sm1 command)
Reference paper: Oaku, Takayama, An algorithm for de Rham cohomology groups of the complement of an affine variety via D-module computation, Journal of pure and applied algebra 139 (1999), 201--233.