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

• 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

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