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Macaulay2 website
EliminationMatrices
::
maxMinor(...,Strategy=>...)
maxMinor(...,Strategy=>...) -- choose between Exact and Numeric algorithms
Synopsis
Usage:
maxMinor(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:
maxMinor
-- Returns a maximal minor of the matrix of full rank.
Option key:
Strategy
-- an optional argument
See also
maxCol
-- Returns a submatrix form by a maximal set of linear independent columns.
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
"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 and Cofactor 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 and Cofactor 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
"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
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 and Cofactor algorithms
minorsComplex(...,Strategy=>...)
-- choose between Exact and Numeric algorithms
pushForward(...,Strategy=>...)
(missing documentation)
quotient(...,Strategy=>...)
resolution(...,Strategy=>...)
saturate(...,Strategy=>...)
"syz(...,Strategy=>...)"
-- see
syz(Matrix)
-- compute the syzygy matrix