resolution Module -- make a projective resolution

resolution Module -- make a projective resolution

Synopsis:

Usage: C = resolution M

Function: resolution -- make a projective resolution

Input:

M, an instance of class Module: a module

Output:

C, an instance of class ChainComplex: a free resolution of M

Optional arguments :

resolution(..., DegreeLimit => ...) -- compute only up to this degree

resolution(..., HardDegreeLimit => ...) -- compute only up to this degree

resolution(..., LengthLimit => ...) -- stop when the resolution reaches this length

resolution(..., PairLimit => ...) -- stop when this number of pairs are handled

resolution(..., SortStrategy => ...) -- specify a strategy for sorting S-pairs

resolution(..., StopBeforeComputation => ...) -- whether to stop the computation immediately

resolution(..., Strategy => ...) -- specify a computational strategy

resolution(..., SyzygyLimit => ...) -- stop when this number of syzygies are obtained

For an abbreviation, use res.

i1 : R = ZZ/32003[a..d]/(a^2+b^2+c^2+d^2);

i2 : M = coker vars R



o2 = cokernel | a b c d |



                            1

o2 : R-module, quotient of R

i3 : C = resolution(M, LengthLimit=>6)



      1      4      7      8      8      8      8

o3 = R  <-- R  <-- R  <-- R  <-- R  <-- R  <-- R

                                                

     0      1      2      3      4      5      6



o3 : ChainComplex

For an overview of resolutions, in order of increasing detail, see

Hilbert functions and free resolutions

free resolutions of modules

computing resolutions -- most detailed

Some useful related functions

betti ChainComplex -- display of degrees in a chain complex

status Resolution -- status of a resolution computation