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OIGroebnerBases : Index
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- VectorInWidth
-- multiply an element of a free OI-module by -1
ColDownRowDown
-- column down row down variable order
ColDownRowUp
-- column down row up variable order
ColUpRowDown
-- column up row down variable order
ColUpRowUp
-- column up row up variable order
degree(VectorInWidth)
-- get the degree of an element of a free OI-module
DegreeShifts
-- grading shifts for free OI-modules
describe(FreeOIModuleMap)
-- display a free OI-module map
describe(OIResolution)
-- describe an OI-resolution
describeFull
-- describe an OI-resolution and the maps
describeFull(OIResolution)
-- describe an OI-resolution and the maps
FreeOIModule
-- the class of all free OI-modules over a polynomial OI-algebra
FreeOIModule _ ZZ
-- get the width n component of a free OI-module
FreeOIModuleMap
-- the class of all maps between free OI-modules
FreeOIModuleMap VectorInWidth
-- apply a free OI-module map to an element
getBasisElements
-- get the basis elements of a free OI-module
getBasisElements(FreeOIModule)
-- get the basis elements of a free OI-module
getFreeOIModule
-- get the free OI-module of an element
getFreeOIModule(VectorInWidth)
-- get the free OI-module of an element
getRank
-- get the rank of a free OI-module
getRank(FreeOIModule)
-- get the rank of a free OI-module
getSchreyerMap
-- get the Schreyer map of a free OI-module if it exists
getSchreyerMap(FreeOIModule)
-- get the Schreyer map of a free OI-module if it exists
getWidth
-- get the width of an element of a free OI-module
getWidth(VectorInWidth)
-- get the width of an element of a free OI-module
image(FreeOIModuleMap)
-- get the basis element images of a free OI-module map
installGeneratorsInWidth
-- install the generators for a component of a free OI-module in a specified width
installGeneratorsInWidth(FreeOIModule,ZZ)
-- install the generators for a component of a free OI-module in a specified width
isComplex
-- verify that an OI-resolution is a complex
isComplex(...,Verbose=>...)
-- verify that an OI-resolution is a complex
isComplex(OIResolution)
-- verify that an OI-resolution is a complex
isHomogeneous(FreeOIModuleMap)
-- checks if a free OI-module map is homogeneous
isHomogeneous(VectorInWidth)
-- check if an element of a free OI-module is homogeneous
isOIGB
-- check if a list of elements of a free OI-module forms a Gröbner basis
isOIGB(...,Verbose=>...)
-- check if a list of elements of a free OI-module forms a Gröbner basis
isOIGB(List)
-- check if a list of elements of a free OI-module forms a Gröbner basis
isZero
-- check if a free OI-module is zero
isZero(FreeOIModule)
-- check if a free OI-module is zero
isZero(FreeOIModuleMap)
-- check if a free OI-module map is zero
isZero(VectorInWidth)
-- check if an element of a free OI-module is zero
leadCoefficient(VectorInWidth)
-- get the lead coefficient of an element of a free OI-module
leadMonomial(VectorInWidth)
-- get the lead monomial of an element of a free OI-module
leadTerm(VectorInWidth)
-- get the lead term of an element of a free OI-module
makeFreeOIModule
-- make a FreeOIModule object
makeFreeOIModule(...,DegreeShifts=>...)
-- make a FreeOIModule object
makeFreeOIModule(...,OIMonomialOrder=>...)
-- make a FreeOIModule object
makeFreeOIModule(Symbol,List,PolynomialOIAlgebra)
-- make a FreeOIModule object
makePolynomialOIAlgebra
-- make a PolynomialOIAlgebra object
makePolynomialOIAlgebra(...,VariableOrder=>...)
-- make a PolynomialOIAlgebra object
makePolynomialOIAlgebra(ZZ,Symbol,Ring)
-- make a PolynomialOIAlgebra object
minimizeOIGB
-- minimize an OI-Gröbner basis
minimizeOIGB(...,Verbose=>...)
-- minimize an OI-Gröbner basis
minimizeOIGB(List)
-- minimize an OI-Gröbner basis
ModuleInWidth
-- the class of all modules that appear as a component of a free OI-module
net(FreeOIModule)
-- display a free OI-module
net(FreeOIModuleMap)
-- display a free OI-module map source and target
net(ModuleInWidth)
-- display a component of a free OI-module in a specified width
net(OIResolution)
-- display an OI-resolution
net(PolynomialOIAlgebra)
-- display a polynomial OI-algebra
net(VectorInWidth)
-- display an element of a free OI-module
Number * VectorInWidth
-- multiply an element of a free OI-module by a number
oiGB
-- compute a Gröbner basis for a submodule of a free OI-module
oiGB(...,Strategy=>...)
-- compute a Gröbner basis for a submodule of a free OI-module
oiGB(...,Verbose=>...)
-- compute a Gröbner basis for a submodule of a free OI-module
oiGB(List)
-- compute a Gröbner basis for a submodule of a free OI-module
OIGroebnerBases
-- OI-modules over Noetherian polynomial OI-algebras
OIMonomialOrder
-- monomial order option for free OI-modules
oiOrbit
-- compute the n-orbit of a list of elements of a free OI-module
oiOrbit(List,ZZ)
-- compute the n-orbit of a list of elements of a free OI-module
oiRes
-- compute an OI-resolution
oiRes(...,Strategy=>...)
-- compute an OI-resolution
oiRes(...,TopNonminimal=>...)
-- compute an OI-resolution
oiRes(...,Verbose=>...)
-- compute an OI-resolution
oiRes(List,ZZ)
-- compute an OI-resolution
OIResolution
-- the class of all resolutions of submodules of free OI-modules
OIResolution _ ZZ
-- get a module of an OI-resolution is specified homological degree
oiSyz
-- compute a Gröbner basis for the syzygy module of a submodule of a free OI-module
oiSyz(...,Strategy=>...)
-- compute a Gröbner basis for the syzygy module of a submodule of a free OI-module
oiSyz(...,Verbose=>...)
-- compute a Gröbner basis for the syzygy module of a submodule of a free OI-module
oiSyz(List,Symbol)
-- compute a Gröbner basis for the syzygy module of a submodule of a free OI-module
PolynomialOIAlgebra
-- the class of all Noetherian polynomial OI-algebras over a field
PolynomialOIAlgebra _ ZZ
-- get the $K$-algebra in a specified width of a polynomial OI-algebra
ranks
-- display the ranks of an OI-resolution
ranks(OIResolution)
-- display the ranks of an OI-resolution
reduceOIGB
-- reduce an OI-Gröbner basis
reduceOIGB(...,Verbose=>...)
-- reduce an OI-Gröbner basis
reduceOIGB(List)
-- reduce an OI-Gröbner basis
restrictedRanks
-- display the ranks of an OI-resolution restricted to a given width
restrictedRanks(OIResolution,ZZ)
-- display the ranks of an OI-resolution restricted to a given width
RingElement * VectorInWidth
-- multiply an element of a free OI-module by a ring element
RowDownColDown
-- row down column down variable order
RowDownColUp
-- row up column up variable order
RowUpColDown
-- row up column down variable order
RowUpColUp
-- row up column up variable order
terms(VectorInWidth)
-- get the terms of an element of a free OI-module
TopNonminimal
-- option for minimizing the top Gröbner basis of an OI-resolution
toString(FreeOIModule)
-- display a free OI-module in condensed form
toString(PolynomialOIAlgebra)
-- display a polynomial OI-algebra in condensed form
use(ModuleInWidth)
-- use a component of a free OI-module
VariableOrder
-- variable ordering for polynomial OI-algebras
VectorInWidth
-- the class of all elements of a free OI-module
VectorInWidth + VectorInWidth
-- add two elements of a free OI-module
VectorInWidth - VectorInWidth
-- subtract an element of a free OI-module from another