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Computer • algebra
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Introduction
Creation Functions
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 (H44E1)
Structure Operations
Related Structures
IntegerRing(F) : FldFunRat -> RngPol
BaseRing(F) : FldFunRat -> Rng
Rank(F) : FldFunRat -> RngIntElt
ValuationRing(F) : FldFunRat -> RngVal
ValuationRing(F, f) : FldFunRat, RngUPolElt -> RngVal
Invariants
Ring Predicates and Booleans
Homomorphisms
hom< P -> S | f, y
1
, ..., y
n
> : FldFunRat, Rng -> Map
Example
FldFunRat_Homomorphism (H44E2)
Element Operations
Arithmetic
Equality and Membership
Numerator, Denominator and Degree
Numerator(f) : FldFunRatElt -> RngElt
Denominator(f) : FldFunRatElt -> RngElt
Degree(f) : FldFunRatElt -> RngIntElt
TotalDegree(f) : FldFunRatElt -> RngIntElt
WeightedDegree(f) : FldFunRatElt -> RngIntElt
Numerator(f, R) : FldFunRatElt -> RngElt
Predicates on Ring Elements
Evaluation
Evaluate(f, r) : FldFunRatUElt, RngElt -> FldFunRatUElt
Evaluate(f, v, r) : FldFunRatMElt, RngIntElt, RngElt -> FldFunRatMElt
Evaluate(f, S) : FldFunRatMElt, [RngElt] -> RngElt
Decomposition
Decomposition(f) : FldFunRatUElt -> [[FldFunRatUElt]]
Example
FldFunRat_decomp-ex (H44E3)
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 (H44E4)
Padé-Hermite Approximants
Introduction
Ordering of Sequences
MaximumDegree(f) : SeqEnum -> RngIntElt
Example
FldFunRat_degree-of-sequence (H44E5)
TypeOfSequence(f) : SeqEnum -> RngIntElt, RngIntElt
Example
FldFunRat_type-of-sequence (H44E6)
MinimalVectorSequence(f,n) : SeqEnum, RngIntElt -> SeqEnum
Example
FldFunRat_minimal-vector-sequence (H44E7)
Example
FldFunRat_the-next_example (H44E8)
Example
FldFunRat_another-example (H44E9)
Example
FldFunRat_one-more (H44E10)
Approximants
PadeHermiteApproximant(f,d) : SeqEnum, SeqEnum -> ModTupRngElt, SeqEnum, RngIntElt
Example
FldFunRat_pade-hermite-approximants (H44E11)
Example
FldFunRat_last-example (H44E12)
Example
FldFunRat_ (H44E13)
PadeHermiteApproximant(f,m) : SeqEnum, RngIntElt -> ModTupRngElt, SeqEnum
Example
FldFunRat_pade-hermite-approximants-vectors (H44E14)
Example
FldFunRat_ (H44E15)
Bibliography
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V2.28, 13 July 2023