Macaulay2 » Documentation
Packages » EliminationMatrices :: minorsComplex(...,Strategy=>...)

Synopsis

• Usage:

  minorsComplex(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 chain 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.

Further information

• Default value: null
• Function: minorsComplex -- calculate some minors of the maps of a graded ChainComplex in a subset of variables and fixed degree
• Option key: Strategy -- an optional argument

See also

• detComplex -- This function calculates the determinant of a graded ChainComplex with respect to a subset of the variables of the polynomial ring in a fixed degree.
• listDetComplex -- This function calculates the list with the determinants of some minors of the maps of a graded ChainComplex with respect to a subset of the variables of the polynomial ring in a fixed degree.

Functions with optional argument named Strategy :

• addHook(...,Strategy=>...) -- see addHook -- add a hook function to an object for later processing
• adjoint(...,Strategy=>...) (missing documentation)
• annihilator(...,Strategy=>...) -- see annihilator -- the annihilator ideal
• associatedPrimes(...,Strategy=>...) -- see associatedPrimes -- find associated primes
• basis(...,Strategy=>...) -- see basis -- basis or generating set of all or part of a ring, ideal or module
• canonicalBundle(...,Strategy=>...) (missing documentation)
• 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
• cotangentSheaf(...,Strategy=>...) (missing documentation)
• detComplex(...,Strategy=>...) -- choose between Exact and Numeric algorithms
• determinant(...,Strategy=>...) -- choose between Bareiss, Cofactor and Dynamic algorithms
• dual(ChainComplex,Strategy=>...) (missing documentation)
• dual(Matrix,Strategy=>...) (missing documentation)
• dual(MonomialIdeal,List,Strategy=>...) -- see dual(MonomialIdeal,Strategy=>...)
• dual(MonomialIdeal,RingElement,Strategy=>...) -- see dual(MonomialIdeal,Strategy=>...)
• dual(MonomialIdeal,Strategy=>...)
• dual(SheafMap,Strategy=>...) (missing documentation)
• eliminationMatrix(...,Strategy=>...) -- see eliminationMatrix -- returns a matrix that represents the image of the map
• End(...,Strategy=>...) -- see End -- module of endomorphisms
• exteriorPower(...,Strategy=>...) -- choose between Bareiss, Cofactor and Dynamic algorithms
• gb(...,Strategy=>...) -- see gb -- compute a Gröbner basis
• gcdLLL(...,Strategy=>...) (missing documentation)
• GF(...,Strategy=>...) -- see GF -- make a finite field
• groebnerBasis(...,Strategy=>...) -- see groebnerBasis -- Gröbner basis, as a matrix
• hermite(...,Strategy=>...) (missing documentation)
• 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
• idealizer(...,Strategy=>...) -- see idealizer -- compute Hom(I,I) as a quotient ring
• integralClosure(...,Strategy=>...) -- control the algorithm used
• 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
• intersectInP(...,Strategy=>...) -- see intersectInP(...,BasisElementLimit=>...) -- Option for intersectInP
• isPrimary(...,Strategy=>...) -- see isPrimary -- determine whether a submodule is primary
• isPrime(Ideal,Strategy=>...) -- see isPrime(Ideal) -- whether an ideal is prime
• listDetComplex(...,Strategy=>...) -- choose between Exact and Numeric algorithms
• LLL(...,Strategy=>...) -- choose among different algorithms
• localize(...,Strategy=>...) -- see localize -- localize an ideal at a prime ideal
• match(...,Strategy=>...) -- see match -- regular expression matching
• maxCol(...,Strategy=>...) -- choose between Exact and Numeric algorithms
• maxMinor(...,Strategy=>...) -- choose between Exact and Numeric algorithms
• decompose(Ideal,Strategy=>...) -- see minimalPrimes -- minimal primes of an ideal
• minimalPrimes(...,Strategy=>...) -- see minimalPrimes -- minimal primes of an ideal
• minors(...,Strategy=>...) -- choose between Bareiss, Cofactor and Dynamic algorithms
• minorsComplex(...,Strategy=>...) -- choose between Exact and Numeric algorithms
• parallelApply(...,Strategy=>...) -- see parallelApply -- apply a function to each element in parallel
• primaryComponent(...,Strategy=>...) -- see primaryComponent -- find a primary component corresponding to an associated prime
• pushForward(...,Strategy=>...) (missing documentation)
• quotient(...,Strategy=>...)
• radical(...,Strategy=>...) -- see radical -- the radical of an ideal
• radicalContainment(...,Strategy=>...) -- see radicalContainment -- whether an element is contained in the radical of an ideal
• analyticSpread(...,Strategy=>...) -- see reesIdeal(...,Strategy=>...) -- Choose a strategy for the saturation step
• distinguished(...,Strategy=>...) -- see reesIdeal(...,Strategy=>...) -- Choose a strategy for the saturation step
• isLinearType(...,Strategy=>...) -- see reesIdeal(...,Strategy=>...) -- Choose a strategy for the saturation step
• isReduction(...,Strategy=>...) -- see reesIdeal(...,Strategy=>...) -- Choose a strategy for the saturation step
• minimalReduction(...,Strategy=>...) -- see reesIdeal(...,Strategy=>...) -- Choose a strategy for the saturation step
• multiplicity(...,Strategy=>...) -- see reesIdeal(...,Strategy=>...) -- Choose a strategy for the saturation step
• normalCone(...,Strategy=>...) -- see reesIdeal(...,Strategy=>...) -- Choose a strategy for the saturation step
• reesAlgebra(...,Strategy=>...) -- see reesIdeal(...,Strategy=>...) -- Choose a strategy for the saturation step
• reesIdeal(...,Strategy=>...) -- Choose a strategy for the saturation step
• specialFiber(...,Strategy=>...) -- see reesIdeal(...,Strategy=>...) -- Choose a strategy for the saturation step
• specialFiberIdeal(...,Strategy=>...) -- see reesIdeal(...,Strategy=>...) -- Choose a strategy for the saturation step
• regSeqInIdeal(...,Strategy=>...) -- see regSeqInIdeal -- a regular sequence contained in an ideal
• resolution(...,Strategy=>...)
• saturate(...,Strategy=>...)
• sheafHom(...,Strategy=>...) (missing documentation)
• primaryDecomposition(...,Strategy=>...) -- see strategies for computing primary decomposition
• syz(...,Strategy=>...) -- see syz(Matrix) -- compute the syzygy matrix
• tangentCone(...,Strategy=>...) -- see tangentCone(Ideal)
• tangentSheaf(...,Strategy=>...) (missing documentation)