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# SPDX-License-Identifier: GPL-2.0-or-later
# LocalizeRingForHomalg: A Package for Localization of Polynomial Rings
#
# Declarations
#
## Declarations of procedures for "fake" localized rings.
#! @Chapter Fake localize ring
####################################
#
#! @Section Attributes:
#
####################################
#! @Description
#! Generators of prime ideal at which the base of the fake local ring is localized at
#! @Returns a &homalg; matrix
DeclareAttribute( "GeneratorsOfPrimeIdeal",
IsHomalgRing );
####################################
#
# global functions and operations:
#
####################################
#! @Section constructor methods:
################################################################################
## The ring of the type k(X)[Y] is used mainly in Quillen-Suslin (esp. proc Horrocks)
## These rings will not be used for computaions like Groebner Basis and related.
## Such ring is called "fake" local ring.
################################################################################
# Here we want to localize at a prime ideal p in k[X]
# The expected ring in the algorithm is k[X]_p[Y]
#! @Description
#! Constructor for the fake ring localized at prime ideal
#! second line of documentation
#! @Returns
DeclareOperation( "LocalizeBaseRingAtPrime",
[ IsHomalgRing, IsList, IsList ] );
#! @Description
#! Constructor for the fake ring localized at prime ideal
#! @Returns
DeclareOperation( "LocalizeBaseRingAtPrime",
[ IsHomalgRing, IsList ] );
#! @Description
#! Constructor for elements of fake local ring localized at prime ideal
#! @Returns
DeclareGlobalFunction( "ElementOfHomalgFakeLocalRing" );
#! @Description
#!
#! @Returns
DeclareOperation( "BlindlyCopyMatrixPropertiesToFakeLocalMatrix",
[ IsHomalgMatrix, IsHomalgMatrix ] );
#! @Description
#! Constructor for matrices over fake local ring localized at prime ideal
#! @Returns
DeclareOperation( "MatrixOverHomalgFakeLocalRing",
[ IsHomalgMatrix, IsHomalgRing ] );
#! @Description
#! Returns globalR modulo the prime ideal
#! @Returns
DeclareOperation( "AssociatedResidueClassRing",
[ IsHomalgRing ] );
#! @Description
#! Returns globalR modulo the prime ideal
#! @Returns
DeclareOperation( "AssociatedResidueClassRing",
[ IsHomalgRingElement ] );
#! @Description
#! Returns globalR modulo the prime ideal
#! @Returns
DeclareOperation( "AssociatedResidueClassRing",
[ IsHomalgMatrix ] );
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