resolution(Ideal) -- compute a projective resolution of (the quotient ring corresponding to) an ideal

Synopsis

Function: resolution
Usage:

resolution I
Inputs:
- I, an ideal, an ideal in a ring R, say
Optional inputs:
- DegreeLimit => ..., default value null, compute only up to this degree
- FastNonminimal => ..., default value false, compute a non-minimal graded free resolution
- HardDegreeLimit => ..., default value {},
- LengthLimit => ..., default value infinity, stop when the resolution reaches this length
- PairLimit => ..., default value infinity, stop when this number of pairs has been handled
- ParallelizeByDegree (missing documentation) => ..., default value false,
- SortStrategy => ..., default value 0,
- StopBeforeComputation => ..., default value false, whether to stop the computation immediately
- Strategy => ..., default value null,
- SyzygyLimit => ..., default value infinity, stop when this number of syzygies is reached
Outputs:
- a chain complex, a resolution of R/I by projective R-modules

Description

i1 : R = ZZ[a..d]

o1 = R

o1 : PolynomialRing

i2 : I = ideal(a,b,c,d)

o2 = ideal (a, b, c, d)

o2 : Ideal of R

i3 : C = res I

      1      4      6      4      1
o3 = R  <-- R  <-- R  <-- R  <-- R  <-- 0
                                         
     0      1      2      3      4      5

o3 : ChainComplex

i4 : C_2

      6
o4 = R

o4 : R-module, free, degrees {6:2}

i5 : C.dd_2

o5 = {1} | -b 0  -c 0  0  -d |
     {1} | a  -c 0  0  -d 0  |
     {1} | 0  b  a  -d 0  0  |
     {1} | 0  0  0  c  b  a  |

             4      6
o5 : Matrix R  <-- R

Ways to use this method: