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# listDetComplex(...,Strategy=>...) -- choose between Exact and Numeric algorithms

- Usage:
    `listDetComplex(d,v,C, Strategy => s)`
- Inputs:
  - d, an integer, integer corresponding to the degree of the strand of the chain complex.
  - v, a list, list of variables of the polynomial ring R to take into account for elimination
  - C, a complex, a chain complex of free modules over a polynomial ring
  - s, a symbol, either Exact or Numeric
- Consequences:
  - If s is Exact, then therank algorithms is used computing minors; if s is Numeric, then numerical rank computation is used, this is, all coefficients are evaluated in the ground field before computing ranks.

## Description

Exactis the default Strategy.

## See also

- detComplex -- This function calculates the determinant of a graded Complex with respect to a subset of the variables of the polynomial ring in a fixed degree.
- minorsComplex -- calculate some minors of the maps of a graded Complex in a subset of variables and fixed degree

## Functions with optional argument named Strategy:

- `addHook(...,Strategy=>...)` -- see addHook -- add a hook function to an object for later processing
- annihilator(...,Strategy=>...) (missing documentation)
- `basis(...,Strategy=>...)` -- see basis -- basis or generating set of all or part of a ring, ideal or module
- `mingens(...,Strategy=>...)` -- see Complement -- a Strategy option value
- `trim(...,Strategy=>...)` -- see Complement -- a Strategy option value
- `compose(Module,Module,Module,Strategy=>...)` -- see compose -- composition as a pairing on Hom-modules
- decompose(Ideal,Strategy=>...) (missing documentation)
- detComplex(...,Strategy=>...) -- choose between Exact and Numeric algorithms
- determinant(...,Strategy=>...) -- choose between Bareiss, Cofactor and Dynamic algorithms
- `dual(MonomialIdeal,List,Strategy=>...)` -- see dual(MonomialIdeal,Strategy=>...)
- `dual(MonomialIdeal,RingElement,Strategy=>...)` -- see dual(MonomialIdeal,Strategy=>...)
- dual(MonomialIdeal,Strategy=>...)
- `eliminationMatrix(...,Strategy=>...)` -- see eliminationMatrix -- returns a matrix that represents the image of the map
- `End(...,Strategy=>...)` -- see End -- module of endomorphisms
- epicResolutionMap(...,Strategy=>...) (missing documentation)
- exteriorPower(...,Strategy=>...) -- choose between Bareiss, Cofactor and Dynamic algorithms
- `gb(...,Strategy=>...)` -- see gb -- compute a Gröbner basis
- `GF(...,Strategy=>...)` -- see GF -- make a finite field
- `groebnerBasis(...,Strategy=>...)` -- see groebnerBasis -- Gröbner basis, as a matrix
- `Hom(...,Strategy=>...)` -- see Hom -- module of homomorphisms
- `homomorphism'(...,Strategy=>...)` -- see homomorphism' -- get the element of Hom from a homomorphism
- `hooks(...,Strategy=>...)` -- see hooks -- list hooks attached to a key
- `intersect(Ideal,Ideal,Strategy=>...)` -- see intersect(Ideal,Ideal) -- compute an intersection of a sequence of ideals or modules
- `intersect(Module,Module,Strategy=>...)` -- see intersect(Ideal,Ideal) -- compute an intersection of a sequence of ideals or modules
- isPrime(Ideal,Strategy=>...) (missing documentation)
- listDetComplex(...,Strategy=>...) -- choose between Exact and Numeric algorithms
- `match(...,Strategy=>...)` -- see match -- regular expression matching
- maxCol(...,Strategy=>...) -- choose between Exact and Numeric algorithms
- maxMinor(...,Strategy=>...) -- choose between Exact and Numeric algorithms
- minors(...,Strategy=>...) -- choose between Bareiss, Cofactor and Dynamic algorithms
- minorsComplex(...,Strategy=>...) -- choose between Exact and Numeric algorithms
- normalCone(Ideal,RingElement,Strategy=>...) (missing documentation)
- normalCone(Ideal,Strategy=>...) (missing documentation)
- `parallelApply(...,Strategy=>...)` -- see parallelApply -- apply a function to each element in parallel
- `pushForward(...,Strategy=>...)` -- see pushForward(RingMap,Module) -- compute the pushforward of a module along a ring map
- quotient'(...,Strategy=>...) (missing documentation)
- quotient(...,Strategy=>...) (missing documentation)
- `resolutionMap(...,Strategy=>...)` -- see resolutionMap -- map from a free resolution to the given complex
- saturate(...,Strategy=>...) (missing documentation)
- `freeResolution(...,Strategy=>...)` -- see Strategies for free resolutions -- overview of the different algorithms for computing free resolutions
- `syz(...,Strategy=>...)` -- see syz(Matrix) -- compute the syzygy matrix

## Further information

- Default value: null
- Function: listDetComplex -- This function calculates the list with the determinants of some minors of the maps of a graded Complex with respect to a subset of the variables of the polynomial ring in a fixed degree.
- Option key: Strategy -- an optional argument

The source of this document is in /build/macaulay2-88fgJW/macaulay2-1.25.11+ds/M2/Macaulay2/packages/EliminationMatrices.m2:1091:0.