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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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