Elements and Local Monomial Orders
Local Graded Lexicographical: lglex
Local Graded Reverse Lexicographical: lgrev-lex
Local Polynomial Rings and Ideals
Creation of Local Polynomial Rings and Accessing their Monomial Orders
LocalPolynomialRing(K, n) : Rng, RngIntElt -> RngMPolLoc
LocalPolynomialRing(K, n, order) : Rng, RngIntElt, MonStgElt, ... -> RngMPolLoc
LocalPolynomialRing(K, n, T) : Rng, RngIntElt, Tup -> RngMPolLoc
MonomialOrder(R) : RngMPolLoc -> Tup
MonomialOrderWeightVectors(R) : RngMPol -> [ [ FldRatElt ] ]
Localization(R) : RngMPol -> RngMPolLoc
Example RngMPolLoc_Order (H107E1)
Creation of Ideals and Accessing their Bases
ideal<R | L> : RngMPolLoc, List -> RngMPolLoc
Ideal(B) : [ RngMPolLocElt ] -> RngMPolLoc
Ideal(f) : RngMPolLocElt -> RngMPolLoc
Basis(I) : RngMPolLoc -> [ RngMPolLocElt ]
BasisElement(I, i) : RngMPolLoc, RngIntElt -> RngMPolLocElt
Construction of Standard Bases
StandardBasis(I) : RngMPolLoc -> RngMPolLocElt
StandardBasis(S) : [ RngMPolLocElt ] -> [ RngMPolLocElt ]
Example RngMPolLoc_StandardBasis (H107E2)
Example RngMPolLoc_StandardBasis2 (H107E3)
Basic Operations
I + J : RngMPolLoc, RngMPolLoc -> RngMPolLoc
I * J : RngMPolLoc, RngMPolLoc -> RngMPolLoc
I ^ k : RngMPolLoc, RngIntElt -> RngMPolLoc
QuotientDimension(I) : RngMPol -> RngIntElt
Generic(I) : RngMPolLoc -> RngMPolLoc
LeadingMonomialIdeal(I) : RngMPolLoc -> RngMPolLoc
I meet J : RngMPolLoc, RngMPolLoc -> RngMPolLoc
&meet S : [ RngMPolLoc ] -> RngMPolLoc
Ideal Predicates
I eq J : RngMPolLoc, RngMPolLoc -> BoolElt
I ne J : RngMPolLoc, RngMPolLoc -> BoolElt
I notsubset J : RngMPolLoc, RngMPolLoc -> BoolElt
I subset J : RngMPolLoc, RngMPolLoc -> BoolElt
IsZero(I) : RngMPolLoc -> BoolElt
IsProper(I) : RngMPolLoc -> BoolElt
IsZeroDimensional(I) : RngMPolLoc -> BoolElt
Example RngMPolLoc_IdealArithmetic (H107E4)
Operations on Elements of Ideals
f in I : RngMPolLocElt, RngMPolLoc -> BoolElt
NormalForm(f, I) : RngMPolLocElt, RngMPolLoc -> RngMPolLocElt
f notin I : RngMPolLocElt, RngMPolLoc -> BoolElt
Example RngMPolLoc_ElementOperations (H107E5)
Changing Coefficient Ring
ChangeRing(I, L) : RngMPolLoc, Rng -> RngMPolLoc
Changing Monomial Order
ChangeOrder(I, Q) : RngMPolLoc, RngMPolLoc -> RngMPolLoc, Map
ChangeOrder(I, order) : RngMPolLoc, ..., -> RngMPolLoc, Map
Dimension of Ideals
Dimension(I) : RngMPolLoc -> RngIntElt, [ RngIntElt ]
Bibliography
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Wed Apr 24 15:09:57 EST 2013