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EliminationMatrices
::
maxCol(...,Strategy=>...)
maxCol(...,Strategy=>...) -- choose between Exact and Numeric algorithms
Synopsis
Usage:
maxCol(M, Strategy => s)
Inputs:
m
,
a
matrix
, a matrix (usually with coefficients in a polynomial ring)
s
,
a
symbol
, either
Exact
or
Numeric
Consequences:
If
s
is
Exact
, then the
rank
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
Exact
is the default Strategy.
Further information
Default value:
null
Function:
maxCol
-- Returns a submatrix form by a maximal set of linear independent columns.
Option key:
Strategy
-- an optional argument
See also
maxMinor
-- Returns a maximal minor of the matrix of full rank.
Functions with optional argument named
Strategy
:
"addHook(...,Strategy=>...)"
-- see
addHook
-- add a hook function to an object for later processing
"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
"mingens(...,Strategy=>...)"
-- see
Complement
-- a Strategy option value
"trim(...,Strategy=>...)"
-- see
Complement
-- a Strategy option value
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
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)
"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
"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=>...)
"primaryDecomposition(...,Strategy=>...)"
-- see
strategies for computing primary decomposition
"syz(...,Strategy=>...)"
-- see
syz(Matrix)
-- compute the syzygy matrix
"tangentCone(...,Strategy=>...)"
-- see
tangentCone(Ideal)