OIGroebnerBases : Table of Contents

• OIGroebnerBases -- OI-modules over Noetherian polynomial OI-algebras

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