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Dmodules :: deRhamAll(RingElement)

deRhamAll(RingElement) -- deRham complex for the complement of a hypersurface

Synopsis

Description

The routine deRhamAll can be used to compute cup product structures as in the paper 'The cup product structure for complements of affine varieties' by Walther(2000).

For a more basic functionality see deRham.

i1 : R = QQ[x,y]

o1 = R

o1 : PolynomialRing
i2 : f = x^2-y^3 

        3    2
o2 = - y  + x

o2 : R
i3 : deRhamAll f

                                        2      1
o3 = HashTable{BFunction => (s - 1)(s - -)(s - -)                                                            }
                                        3      3
                                                    1
               CohomologyGroups => HashTable{0 => QQ }
                                                    1
                                             1 => QQ
                                             2 => 0
               LocalizeMap => | -x_2^3+x_1^2 |
                                               1                         2                         1
               OmegaRes => (QQ[x ..x , D ..D ])  <-- (QQ[x ..x , D ..D ])  <-- (QQ[x ..x , D ..D ])  <-- 0
                                1   2   1   2             1   2   1   2             1   2   1   2         
                                                                                                         3
                           0                         1                         2
               PreCycles => HashTable{0 => | 0 |}
                                           | 1 |
                                      1 => | 0 |
                                           | 1 |
                                           | 0 |
                                      2 => 0
               TransferCycles => HashTable{0 => | 3x_2^3-3x_1^2 |}
                                           1 => | 2x_1   |
                                                | 3x_2^2 |
                                           2 => 0
                                                  1                         3                         2
               VResolution => (QQ[x ..x , D ..D ])  <-- (QQ[x ..x , D ..D ])  <-- (QQ[x ..x , D ..D ])  <-- 0
                                   1   2   1   2             1   2   1   2             1   2   1   2         
                                                                                                            3
                              0                         1                         2

o3 : HashTable

See also