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

Synopsis

• Usage:
M = deRham f, Mi = deRham(i,f)
• Inputs:
• Optional inputs:
• Strategy => ..., default value Schreyer,
• Outputs:
• Mi, , the i-th deRham cohomology group of the complement of the hypersurface {f = 0}
• M, , 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

• deRhamAll -- deRham complex for the complement of a hypersurface
• Dlocalize -- localization of a D-module
• Dintegration -- integration modules of a D-module

Ways to use deRham :

• "deRham(RingElement)"
• "deRham(ZZ,RingElement)"
• deRham(Ideal) (missing documentation)
• deRham(ZZ,Ideal) (missing documentation)

For the programmer

The object deRham is .