deRham -- deRham cohomology groups for the complement of a hypersurface

Synopsis

Usage:

M = deRham f, Mi = deRham(i,f)
Inputs:
- i, an integer
- f, a ring element
Optional inputs:
- Strategy => ..., default value Schreyer,
Outputs:
- Mi, a module, the i-th deRham cohomology group of the complement of the hypersurface {f = 0}
- M, a hash table, containing the entries of the form i=>Mi

Description

The algorithm used appears in the paper 'An algorithm for deRham cohomology groups of the complement of an affine variety via D-module computation' by Oaku-Takayama(1999). The method is to compute the localization of the polynomial ring by f, then compute the derived integration of the localization.

i1 : R = QQ[x,y]

o1 = R

o1 : PolynomialRing

i2 : f = x^2-y^3 

        3    2
o2 = - y  + x

o2 : R

i3 : deRham f

                      1
o3 = HashTable{0 => QQ }
                      1
               1 => QQ
               2 => 0

o3 : HashTable

i4 : deRham(1,f)

       1
o4 = QQ

o4 : QQ-module, free

Ways to use `deRham` :

"deRham(RingElement)"
"deRham(ZZ,RingElement)"

For the programmer

The object deRham is a method function with options.

deRham -- deRham cohomology groups for the complement of a hypersurface

Synopsis

Description

See also

Ways to use deRham :

For the programmer

Ways to use `deRham` :