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# resolution(Matrix) -- given a module map represented by a matrix, produce a comparison map between resolutions of its source and target

## Synopsis

• Function: resolution
• Usage:
resolution f
• Inputs:
• f, , a module homomorphism N <--- M
• 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
• 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 map from a projective resolution of the source of f to a resolution of the target of f

## Description

 i1 : R = ZZ[x,y,z] o1 = R o1 : PolynomialRing i2 : N = R^1/(x,y,z) o2 = cokernel | x y z | 1 o2 : R-module, quotient of R i3 : M = R^1/(x^2,y^2,x*y*z,z^2) o3 = cokernel | x2 y2 xyz z2 | 1 o3 : R-module, quotient of R i4 : f = map(N,M,1) o4 = | 1 | o4 : Matrix i5 : res f 1 1 o5 = 0 : R <--------- R : 0 | 1 | 3 4 1 : R <-------------------- R : 1 {1} | x 0 yz 0 | {1} | 0 y 0 0 | {1} | 0 0 0 z | 3 6 2 : R <---------------------------- R : 2 {2} | xy yz 0 0 0 0 | {2} | 0 0 0 yz 0 0 | {2} | 0 0 0 0 yz xz | 1 3 3 : R <------------------ R : 3 {3} | 0 yz 0 | 4 : 0 <----- 0 : 4 0 o5 : ChainComplexMap