Creation of Structures
FunctionField(R) : Rng -> FldFunRat
FunctionField(R, r) : Rng, RngIntElt -> FldFunRat
FieldOfFractions(P) : RngUPol -> FldFunRat
Names
AssignNames(~F, s) : FldFunRat, [ MonStgElt ]) ->
Name(F, i) : FldFunRat, RngIntElt -> FldFunRatElt
Creation of Elements
F ! [a, b] : FldFunRat, RngUPolElt, RngUPolElt -> FldFunRatElt
F ! a : FldFunRat, FldElt -> FldFunRatElt
K . i : FldFunRat, RngIntElt -> FldFunRatElt
Example FldFunRat_FunctionField (H41E1)
Related Structures
IntegerRing(F) : FldFunRat -> RngPol
BaseRing(F) : FldFunRat -> Rng
Rank(F) : FldFunRat -> RngIntElt
ValuationRing(F) : FldFunRat -> RngVal
ValuationRing(F, f) : FldFunRat, RngUPolElt -> RngVal
Homomorphisms
hom< P -> S | f, y1, ..., yn > : FldFunRat, Rng -> Map
Example FldFunRat_Homomorphism (H41E2)
Numerator, Denominator and Degree
Numerator(f) : FldFunRatElt -> RngElt
Denominator(f) : FldFunRatElt -> RngElt
Degree(f) : FldFunRatElt -> RngIntElt
TotalDegree(f) : FldFunRatElt -> RngIntElt
WeightedDegree(f) : FldFunRatElt -> RngIntElt
Evaluation
Evaluate(f, r) : FldFunRatUElt, RngElt -> FldFunRatUElt
Evaluate(f, v, r) : FldFunRatMElt, RngIntElt, RngElt -> FldFunRatMElt
Derivative
Derivative(f) : FldFunRatUElt -> FldFunRatUElt
Derivative(f, k) : FldFunRatUElt, RngIntElt -> FldFunRatUElt
Derivative(f, v) : FldFunRatMElt, RngIntElt -> FldFunRatMElt
Derivative(f, v, k) : FldFunRatMElt, RngIntElt, RngIntElt -> FldFunRatMElt
Partial Fraction Decomposition
PartialFractionDecomposition(f) : FldFunRatUElt -> [ <RngUPolElt, RngIntElt, RngUPolElt> ]
SquarefreePartialFractionDecomposition(f) : FldFunRatUElt -> [ <RngUPolElt, RngIntElt, RngUPolElt> ]
Example FldFunRat_PartialFractionDecomposition (H41E3)
Ordering of Sequences
MaximumDegree(f) : SeqEnum -> RngIntElt
Example FldFunRat_degree-of-sequence (H41E4)
TypeOfSequence(f) : SeqEnum -> RngIntElt, RngIntElt
Example FldFunRat_type-of-sequence (H41E5)
MinimalVectorSequence(f,n) : SeqEnum, RngIntElt -> SeqEnum
Example FldFunRat_minimal-vector-sequence (H41E6)
Example FldFunRat_the-next_example (H41E7)
Example FldFunRat_another-example (H41E8)
Example FldFunRat_one-more (H41E9)
Approximants
PadeHermiteApproximant(f,d) : SeqEnum, SeqEnum -> ModTupRngElt, SeqEnum, RngIntElt
Example FldFunRat_pade-hermite-approximants (H41E10)
Example FldFunRat_last-example (H41E11)
Example FldFunRat_ (H41E12)
PadeHermiteApproximant(f,m) : SeqEnum, RngIntElt -> ModTupRngElt, SeqEnum
Example FldFunRat_pade-hermite-approximants-vectors (H41E13)
Example FldFunRat_ (H41E14)
Bibliography
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Version: V2.19 of
Wed Apr 24 15:09:57 EST 2013