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Index F


F-key

F<char>

f-key

f<char>

F27

GrpFP_F27 (Example H16E26)

F276

GrpFP_F276 (Example H16E36)

F29

GrpFP_F29 (Example H16E37)

Facint

Facint(f) : RngIntEltFact -> RngIntElt

FactorizationToInteger(s) : [ <RngIntElt, RngIntElt> ] -> RngIntElt

factor

Factorization (RING OF INTEGERS)

FactorBasis

FactorBasis(K, B) : FldNum, RngIntElt -> [ RngOrdIdl ]

FactoredCarmichaelLambda

FactoredCarmichaelLambda(n) : RngIntElt -> RngIntEltFact

FactoredEulerPhi

FactoredEulerPhi(n) : RngIntElt -> RngIntEltFact

FactoredIndex

FactoredIndex(G, H) : GrpAb, GrpAb -> [<RngIntElt, RngIntElt>]

FactoredIndex(G, H) : GrpFin, GrpFin -> [ <RngIntElt, RngIntElt> ]

FactoredIndex(G, H) : GrpMat, GrpMat -> [ <RngIntElt, RngIntElt> ]

FactoredIndex(G, H) : GrpPC, GrpPC -> [<RngIntElt, RngIntElt>]

FactoredIndex(G, H) : GrpPerm, GrpPerm -> [ <RngIntElt, RngIntElt> ]

Index(G, H: parameters) : GrpFP, GrpFP -> RngIntElt, Map, RngIntElt, RngIntElt

FactoredModulus

FactoredModulus(R) : RngIntRes -> RngIntEltFact

FactoredOrder

FactoredOrder(a) : AlgMatElt -> [ <RngIntElt, RngIntElt> ]

FactoredOrder(a) : FldFinElt -> RngIntElt

FactoredOrder(G) : GrpAb -> [<RngIntElt, RngIntElt>]

FactoredOrder(G) : GrpFin -> [ <RngIntElt, RngIntElt> ]

FactoredOrder(G) : GrpMat -> [ <RngIntElt, RngIntElt> ]

FactoredOrder(g) : GrpMatElt -> [ <RngIntElt, RngIntElt> ]

FactoredOrder(G) : GrpPC -> [<RngIntElt, RngIntElt>]

FactoredOrder(G) : GrpPerm -> [ <RngIntElt, RngIntElt> ]

FactoredOrder(P) : Process(pQuot) -> [ <RngIntElt, RngIntElt> ]

Order(G: parameters) : GrpFP -> RngIntElt

FactoredProjectiveOrder

FactoredProjectiveOrder(a) : AlgMatElt -> [ <RngIntElt, RngIntElt> ]

Factorial

Factorial(n) : RngIntElt -> RngIntElt

Factorial(n) : RngIntElt -> RngIntElt

Factorisation

Factorization(n) : RngIntElt -> RngIntEltFact, RngIntElt, SeqEnum

FactorisationToInteger

FactorizationToInteger(s) : [ <RngIntElt, RngIntElt> ] -> RngIntElt

Factorization

Factorization(I) : RngFunOrdIdl -> [ <RngFunOrdIdl, RngIntElt> ]

Factorization(n) : RngIntElt -> RngIntEltFact, RngIntElt, SeqEnum

Factorization(f) : RngMPolElt -> [ < RngMPolElt, RngIntElt >], RngElt

Factorization(I) : RngOrdIdl -> [Tup(RngOrdIdl, RngIntElt])

Factorization(p) : RngUPolElt -> [ < RngUPolElt, RngIntElt >], RngElt

factorization

Factorization (MULTIVARIATE POLYNOMIAL RINGS)

Factorization (UNIVARIATE POLYNOMIAL RINGS)

Factorization and Irreducibility (MULTIVARIATE POLYNOMIAL RINGS)

Factorization and Irreducibility (UNIVARIATE POLYNOMIAL RINGS)

Factorization and Primes (NUMBER FIELDS AND THEIR ORDERS)

Factorization Sequences (RING OF INTEGERS)

General Factorization (RING OF INTEGERS)

Ideal Factorization (FUNCTION FIELDS AND THEIR ORDERS)

Related Functions (RING OF INTEGERS)

Specific Factorization Algorithms (RING OF INTEGERS)

factorization-general

General Factorization (RING OF INTEGERS)

factorization-irreducibility

Factorization and Irreducibility (MULTIVARIATE POLYNOMIAL RINGS)

Factorization and Irreducibility (UNIVARIATE POLYNOMIAL RINGS)

factorization-related

Related Functions (RING OF INTEGERS)

factorization-sequence

Factorization Sequences (RING OF INTEGERS)

factorization-specific

Specific Factorization Algorithms (RING OF INTEGERS)

FactorizationToInteger

Facint(f) : RngIntEltFact -> RngIntElt

FactorizationToInteger(s) : [ <RngIntElt, RngIntElt> ] -> RngIntElt

false

Booleans (OVERVIEW)

true

Family

GrpFP_Family (Example H16E18)

Farey

Seq_Farey (Example H8E3)

feature

Magma Updates (OVERVIEW)

ff

Functions for Elliptic Curves over Finite Fields (ELLIPTIC CURVES)

Fibonacci

Fibonacci(n) : RngIntElt -> RngIntElt

Fibonacci(n) : RngIntElt -> RngIntElt

Field

Alphabet(C) : Code -> FldFin

Field(P) : Plane -> FldFin

field

Arithmetic (FUNCTION FIELDS AND THEIR ORDERS)

Arithmetic (NUMBER FIELDS AND THEIR ORDERS)

Canonical Forms for Matrices over a Field (MATRIX ALGEBRAS)

Changing the Coefficient Field (VECTOR SPACES)

FINITE FIELDS

FUNCTION FIELDS AND THEIR ORDERS

NUMBER FIELDS AND THEIR ORDERS

RATIONAL FUNCTION FIELDS

Residue Fields (INTRODUCTION [RINGS AND FIELDS])

Rings, Fields, and Algebras (OVERVIEW)

field-element

Arithmetic (FUNCTION FIELDS AND THEIR ORDERS)

Arithmetic (NUMBER FIELDS AND THEIR ORDERS)

FieldOfFractions

FieldOfFractions(Q) : FldRat -> FldRat

FieldOfFractions(Z) : RngInt -> FldRat

FieldOfFractions(O) : RngOrd -> FldNum

FieldOfFractions(P) : RngPol -> FldFun

FieldOfFractions(O) : RngQuad -> FldQuad

FieldOfFractions(V) : RngVal -> Rng

pAdicField(p) : RngIntElt -> FldAdic

fields

Rings, Fields, and Algebras (OVERVIEW)

file

External Files (INPUT AND OUTPUT)

Opening Files (INPUT AND OUTPUT)

Printing to a File (INPUT AND OUTPUT)

Reading a Complete File (INPUT AND OUTPUT)

finding

Finding Irreducibles (CHARACTERS OF FINITE GROUPS)

finding-irreducibles

Finding Irreducibles (CHARACTERS OF FINITE GROUPS)

finish

Control-C key (OVERVIEW)

Quitting (OVERVIEW)

finite

Finite Dimensional Affine Algebras (MULTIVARIATE POLYNOMIAL RINGS)

FINITE FIELDS

Rings, Fields, and Algebras (OVERVIEW)

finite-dimension-quotient

Finite Dimensional Affine Algebras (MULTIVARIATE POLYNOMIAL RINGS)

finite-Galois-field

FINITE FIELDS

FiniteField

FiniteField(q) : RngIntElt -> FldFin

FiniteFieldFactorization

RngMPol_FiniteFieldFactorization (Example H29E9)

finitely

FINITELY PRESENTED ALGEBRAS

Finitely Presented Algebras (FINITELY PRESENTED ALGEBRAS)

FINITELY PRESENTED GROUPS

Finitely Presented Modules (FINITELY PRESENTED ALGEBRAS)

FINITELY PRESENTED SEMIGROUPS

Rings, Fields, and Algebras (OVERVIEW)

The Finitely Presented Group Associated with a Permutation Group (PERMUTATION GROUPS)

finitely-presented

FINITELY PRESENTED ALGEBRAS

FINITELY PRESENTED GROUPS

FINITELY PRESENTED SEMIGROUPS

finitely-presented-algebra

Finitely Presented Algebras (FINITELY PRESENTED ALGEBRAS)

finitely-presented-group

The Finitely Presented Group Associated with a Permutation Group (PERMUTATION GROUPS)

finitely-presented-module

Finitely Presented Modules (FINITELY PRESENTED ALGEBRAS)

finitely_presented_group

The Finitely Presented Group Associated with a Matrix Group (MATRIX GROUPS)

FireCode

FireCode(h, s, n) : RngUPolElt, RngIntElt, RngIntElt -> Code

first

The `first use' Rule (MAGMA SEMANTICS)

first-use

The `first use' Rule (MAGMA SEMANTICS)

FittingSubgroup

FittingSubgroup(G) : GrpAb -> GrpAb

FittingSubgroup(G) : GrpFin -> GrpFin

[Future release] FittingSubgroup(G) : GrpMat -> GrpMat

FittingSubgroup(G) : GrpPC -> GrpPC

FittingSubgroup(G) : GrpPerm -> GrpPerm

Fix

Fix(C, G) : Code, GrpPerm -> Code

Fix(g, Y): GrpPermElt, GSet -> { Elt }

Fix(M): Mod -> Mod

fixed

Arbitrary versus fixed precision (LOCAL FIELDS)

Fixed Precision Real Numbers (REAL AND COMPLEX FIELDS)

Free and Fixed Precision (POWER SERIES AND LAURENT SERIES)

fixed-precision

Fixed Precision Real Numbers (REAL AND COMPLEX FIELDS)

FixedPrecision

FldRe_FixedPrecision (Example H37E1)

Flat

Flat(C) : Cop -> Cop

Flat(C) : SetCart -> SetCart

flat

Flattening (COPRODUCTS)

FldCom

Rings, Fields, and Algebras (OVERVIEW)

FldCyc

Rings, Fields, and Algebras (OVERVIEW)

FldFin

Rings, Fields, and Algebras (OVERVIEW)

FldFun

Rings, Fields, and Algebras (OVERVIEW)

FldNum

Rings, Fields, and Algebras (OVERVIEW)

FldPad

Rings, Fields, and Algebras (OVERVIEW)

FldPr

Rings, Fields, and Algebras (OVERVIEW)

FldQuad

Rings, Fields, and Algebras (OVERVIEW)

FldRat

Rings, Fields, and Algebras (OVERVIEW)

FldRe

Rings, Fields, and Algebras (OVERVIEW)

Floor

Floor(q) : FldRatElt -> RngIntElt

Floor(r) : FldReElt -> RngIntElt

Floor(n) : RngIntElt -> RngIntElt

Flush

Flush(F) : File ->

for

Definite Iteration (STATEMENTS AND EXPRESSIONS)

The for statement (OVERVIEW)

for x in S do statements; end for;

for i := expr_1 to expr_2 by expr_3 do : ->

for-statement

Definite Iteration (STATEMENTS AND EXPRESSIONS)

forall

forall(t){ e(x) : x in E | P(x) }

Force

[Future release] Force(V, i, j) : GrpFPCos, GrpFPCosElt, GrpFPCosElt -> GrpFPCosElt

forced

Forced Coercion (INTRODUCTION [RINGS AND FIELDS])

Magmas (or Structures) (OVERVIEW)

form

Canonical Forms (MATRIX ALGEBRAS)

Canonical Forms for Elements (THE MODULES Hom_(R)(M, N) AND End(M))

Creation of Forms (QUADRATIC FIELDS)

Functions Relating to Forms (QUADRATIC FIELDS)

Matrix Action on Forms (QUADRATIC FIELDS)

The Standard Form (ERROR-CORRECTING CODES)

form-action-matrix

Matrix Action on Forms (QUADRATIC FIELDS)

formal

Formal Sequences (SEQUENCES)

Formal Sets (SETS)

Sets (OVERVIEW)

The Formal Sequence Constructor (SEQUENCES)

The Formal Set Constructor (SETS)

FormalSet

FormalSet(M) : Struct -> SetForm

Format

Format(r) : Rec -> RecFormat

format

RECORDS

The Record Format Constructor (RECORDS)

Forms

FldQuad_Forms (Example H34E4)

forms

Invariant Forms (LATTICES)

Forms1

HMod_Forms1 (Example H43E10)

Forms2

HMod_Forms2 (Example H43E11)

forward

Recursion and forward (OVERVIEW)

The forward Declaration (FUNCTIONS, PROCEDURES AND PACKAGES)

forward f; : identifier ->

Func_forward (Example H2E4)

fp

Groups (OVERVIEW)

Rings, Fields, and Algebras (OVERVIEW)

FPGroup

FPGroup(A) : GrpAb -> GrpFP, Hom(Grp)

FPGroup(G) : GrpPC -> GrpFP, Map

FPGroup(G: parameters) : GrpMat :-> GrpFP, Hom(Grp)

FPGroup(G: parameters) : GrpPerm :-> GrpFP, Hom(Grp)

FPGroup(G: parameters) : GrpPerm :-> GrpFP, Hom(Grp)

Grp_FPGroup (Example H15E9)

FPQuotient

FPQuotient(G, N) : GrpPerm, GrpPerm :-> GrpFP, Hom(Grp)

fprintf

fprintf file, format, expression, ..., expression;

frac

frac< R | a_1, ..., a_r > : Rng, RngElt, ..., RngElt -> Fld, Map

fraction

Continued Fractions (REAL AND COMPLEX FIELDS)

Partial Fraction Decomposition (RATIONAL FUNCTION FIELDS)

Rings, Fields, and Algebras (OVERVIEW)

FrattiniSubgroup

FrattiniSubgroup(G) : GrpAb -> GrpAb

FrattiniSubgroup(G) : GrpFin -> GrpFin

FrattiniSubgroup(G) : GrpMat -> GrpMat

FrattiniSubgroup(G) : GrpPC -> GrpPC

FrattiniSubgroup(G) : GrpPerm -> GrpPerm

Free

GrpFP_Free (Example H16E1)

free

Construction of a Free Group (FINITELY PRESENTED GROUPS)

Construction of a Free Module (GENERAL MODULES)

Free and Fixed Precision (POWER SERIES AND LAURENT SERIES)

Free Modules (GENERAL MODULES)

Free Real Numbers (REAL AND COMPLEX FIELDS)

Free Resolutions (MODULES OVER AFFINE ALGEBRAS)

Structure Constructors (ABELIAN GROUPS)

Structure Constructors (BLACKBOX GROUPS)

Structure Constructors (FINITELY PRESENTED SEMIGROUPS)

free-fixed

Free and Fixed Precision (POWER SERIES AND LAURENT SERIES)

free-module

Construction of a Free Module (GENERAL MODULES)

free-resolution

Free Resolutions (MODULES OVER AFFINE ALGEBRAS)

FreeAbelianGroup

FreeAbelianGroup(n) : RngIntElt -> GrpAb

GrpAb_FreeAbelianGroup (Example H18E1)

FreeAlgebra

FreeAlgebra(R, M) : Rng, MonFP -> AlgFP

AlgFP_FreeAlgebra (Example H52E1)

FreeGroup

FreeGroup(n) : RngIntElt -> GrpFP

FreeMonoid

FreeMonoid(n) : RngIntElt -> MonFP

FreeProduct

FreeProduct(G, H) : GrpFP, GrpFP -> GrpFP

FreeProduct(R, S) : SgpFP, SgpFP -> SgpFP

FreeResolution

FreeResolution(M) : ModMPol -> [ ModMPol ]

FreeResolution(R) : RngInvar -> [ ModMPol ]

PMod_FreeResolution (Example H44E6)

FreeSemigroup

FreeSemigroup(n) : RngIntElt -> SgpFP

SgpFP_FreeSemigroup (Example H14E1)

freeze

freeze;

Frobenius

Elcu_Frobenius (Example H53E17)

FrobeniusAutomorphisms

FrobeniusAutomorphisms (G) : GrpMat -> SeqEnum

FrobeniusMap

FrobeniusMap(E, i) : CurveEll, RngIntElt -> Map

func

Function Expressions (OVERVIEW)

f := func< x_1, ..., x_n: parameters | expression >;

Function

Function(f) : Map -> UserProgram

function

Arithmetic Functions (RING OF INTEGERS)

Function (MAPPINGS)

Function Application (MAGMA SEMANTICS)

Function Expressions (MAGMA SEMANTICS)

FUNCTION FIELDS AND THEIR ORDERS

Function Values Assigned to Identifiers (MAGMA SEMANTICS)

Functions (FUNCTIONS, PROCEDURES AND PACKAGES)

Functions (OVERVIEW)

Functions and Procedures (FUNCTIONS, PROCEDURES AND PACKAGES)

FUNCTIONS, PROCEDURES AND PACKAGES

Functions, Procedures, and Mappings (OVERVIEW)

RATIONAL FUNCTION FIELDS

Rings, Fields, and Algebras (OVERVIEW)

Structure Creation (CHARACTERS OF FINITE GROUPS)

f := function(x_1, ..., x_n: parameters) : ->

function-application

Function Application (MAGMA SEMANTICS)

function-expression

Function Expressions (MAGMA SEMANTICS)

function-field

FUNCTION FIELDS AND THEIR ORDERS

function-procedure

Functions and Procedures (FUNCTIONS, PROCEDURES AND PACKAGES)

function-procedure-mapping

Functions, Procedures, and Mappings (OVERVIEW)

function-procedure-package

FUNCTIONS, PROCEDURES AND PACKAGES

function-value-assignment

Function Values Assigned to Identifiers (MAGMA SEMANTICS)

FunctionField

FunctionField(E) : CurveEll -> FldFun

FunctionField(f : parameters) : RngUPolElt -> FldFun

FunctionField(R) : Rng -> FldFun

FunctionField(O) : RngFunOrd -> RngFunOrd

Elcu_FunctionField (Example H53E2)

FldFun_FunctionField (Example H31E2)

Functions

FldFin_Functions (Example H27E3)

fundamental

Fundamental Invariants (INVARIANT RINGS OF FINITE GROUPS)

FundamentalDiscriminant

FundamentalDiscriminant(d) : RngIntElt -> RngIntElt

FundamentalInvariants

FundamentalInvariants(R) : RngInvar -> [ RngMPolElt ]

RngInvar_FundamentalInvariants (Example H30E8)

FundamentalUnit

FundamentalUnit(K) : FldQuad -> FldQuadElt

FundamentalUnits

FundamentalUnits(O) : RngFunOrd -> SeqEnum


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