[____] [____] [_____] [____] [__] [Index] [Root]
Index F
WeberF(s) : FldPrElt -> FldPrElt
f(X) : Sch, MapSch -> Sch
Image(f) : MapSch -> Sch
f(p) : MapSch,Pt -> Pt
f(K) : MapSch,Rng -> Map
F<char>
f<char>
WeberF2(s) : FldPrElt -> FldPrElt
WeberF2(g) : RngSerElt -> RngSerElt
GrpFP_1_F27 (Example H22E18)
GrpFP_1_F276 (Example H22E55)
GrpFP_1_F29 (Example H22E57)
GrpCox_F4 (Example H36E12)
FaceFunction(F) : NwtnPgon,Tup -> RngElt
IsFace(N, F) : NwtnPgon,Tup -> BoolElt
FaceFunction(F) : NwtnPgon,Tup -> RngElt
AllFaces(N) : NwtnPgon -> SeqEnum
Faces(N) : NwtnPgon -> SeqEnum
FacesContaining(N,p) : NwtnPgon,Tup -> SeqEnum
InnerFaces(N) : NwtnPgon -> SeqEnum
LowerFaces(N) : NwtnPgon -> SeqEnum
OuterFaces(N) : NwtnPgon -> SeqEnum
Newton_faces-ex (Example H58E2)
FacesContaining(N,p) : NwtnPgon,Tup -> SeqEnum
FactorizationToInteger(f) : RngIntEltFact -> RngIntElt
Facint(f) : RngIntEltFact -> RngIntElt
FactorizationToInteger(s) : [ <RngIntElt, RngIntElt> ] -> RngIntElt
SequenceToFactorization(s) : SeqEnum -> RngIntEltFact
SeqFact(s) : SeqEnum -> RngIntEltFact
Factorization (LOCAL RINGS AND FIELDS)
Factorization (p-ADIC RINGS AND FIELDS)
ClassGroupCyclicFactorGenerators(O) : RngOrd -> ModHomElt
EulerFactor(J) : JacHyp -> RngUPolElt
EulerFactor(J, K) : JacHyp, FldFin -> RngUPolElt
EulerFactorModChar(J) : JacHyp -> RngUPolElt
FactorBasis(K, B) : FldNum, RngIntElt -> [ RngOrdIdl ]
FactorBasis(O) : RngOrd -> [ RngOrdIdl ], Integer
SocleFactor(G) : GrpPerm -> GrpPerm
Factorization (RING OF INTEGERS)
FactorBasis(K, B) : FldNum, RngIntElt -> [ RngOrdIdl ]
FactorBasis(O) : RngOrd -> [ RngOrdIdl ], Integer
FactoredCarmichaelLambda(n) : RngIntElt -> RngIntEltFact
FactoredCharacteristicPolynomial(A: parameters) : Mtrx -> [ <RngUPolElt, RngIntElt>]
FactoredEulerPhi(n) : RngIntElt -> RngIntEltFact
FactoredIndex(G, H) : GrpAb, GrpAb -> [<RngIntElt, RngIntElt>]
FactoredIndex(G, H) : GrpFin, GrpFin -> [ <RngIntElt, RngIntElt> ]
FactoredIndex(G, H) : GrpGPC, GrpGPC -> [<RngIntElt, RngIntElt>]
FactoredIndex(G, H) : GrpMat, GrpMat -> [ <RngIntElt, RngIntElt> ]
FactoredIndex(G, H) : GrpPC, GrpPC -> [<RngIntElt, RngIntElt>]
FactoredIndex(G, H) : GrpPerm, GrpPerm -> [ <RngIntElt, RngIntElt> ]
FactoredMinimalAndCharacteristicPolynomials(A: parameters) : Mtrx -> [<RngUPolElt, RngIntElt>], [<RngUPolElt, RngIntElt>]
FactoredMinimalPolynomial(A: parameter) : Mtrx -> [ <RngUPolElt, RngIntElt>]
FactoredModulus(R) : RngIntRes -> RngIntEltFact
FactoredOrder(A) : AlgMatElt -> [ <RngIntElt, RngIntElt> ]
FactoredOrder(a) : AlgMatElt -> [ <RngIntElt, RngIntElt> ]
FactoredOrder(a) : FldFinElt -> RngIntElt
FactoredOrder(G) : GrpAb -> [<RngIntElt, RngIntElt>]
FactoredOrder(A) : GrpAuto -> [ <RngIntElt, RngIntElt> ]
FactoredOrder(G) : GrpFin -> [ <RngIntElt, RngIntElt> ]
FactoredOrder(G) : GrpGPC -> [<RngIntElt, RngIntElt>]
FactoredOrder(G) : GrpMat -> [ <RngIntElt, RngIntElt> ]
FactoredOrder(g) : GrpMatElt -> [ <RngIntElt, RngIntElt> ]
FactoredOrder(G) : GrpPC -> [<RngIntElt, RngIntElt>]
FactoredOrder(G) : GrpPerm -> [ <RngIntElt, RngIntElt> ]
FactoredOrder(J) : JacHyp -> [ <RngIntElt, RngIntElt> ]
FactoredOrder(P) : Process(pQuot) -> [ <RngIntElt, RngIntElt> ]
FactoredOrder(P) : PtEll -> RngIntElt
FactoredOrder(G) : SchGrpEll -> RngIntElt
FactoredOrder(H) : SetPtEll -> RngIntElt
FactoredProjectiveOrder(a) : AlgMatElt -> [ <RngIntElt, RngIntElt> ]
FactoredProjectiveOrder(A) : AlgMatElt -> [ <RngIntElt, RngIntElt> ], RngElt
Index(G, H: parameters) : GrpFP, GrpFP -> RngIntElt
IsogenyFromKernelFactored(E, psi) : CrvEllSubgroup -> CrvEll, Map
IsogenyFromKernelFactored(G) : CrvEllSubgroup -> CrvEll, Map
Order(G: parameters) : GrpFP -> RngIntElt
FactoredCarmichaelLambda(n) : RngIntElt -> RngIntEltFact
FactoredCharacteristicPolynomial(A: parameters) : Mtrx -> [ <RngUPolElt, RngIntElt>]
FactoredEulerPhi(n) : RngIntElt -> RngIntEltFact
FactoredIndex(G, H) : GrpAb, GrpAb -> [<RngIntElt, RngIntElt>]
FactoredIndex(G, H) : GrpFin, GrpFin -> [ <RngIntElt, RngIntElt> ]
FactoredIndex(G, H) : GrpGPC, GrpGPC -> [<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
FactoredMCPolynomials(A: parameters) : Mtrx -> [<RngUPolElt, RngIntElt>], [<RngUPolElt, RngIntElt>]
FactoredMinimalAndCharacteristicPolynomials(A: parameters) : Mtrx -> [<RngUPolElt, RngIntElt>], [<RngUPolElt, RngIntElt>]
FactoredMCPolynomials(A: parameters) : Mtrx -> [<RngUPolElt, RngIntElt>], [<RngUPolElt, RngIntElt>]
FactoredMinimalAndCharacteristicPolynomials(A: parameters) : Mtrx -> [<RngUPolElt, RngIntElt>], [<RngUPolElt, RngIntElt>]
FactoredMinimalPolynomial(A: parameter) : Mtrx -> [ <RngUPolElt, RngIntElt>]
FactoredModulus(R) : RngIntRes -> RngIntEltFact
FactoredOrder(A) : AlgMatElt -> [ <RngIntElt, RngIntElt> ]
FactoredOrder(a) : AlgMatElt -> [ <RngIntElt, RngIntElt> ]
FactoredOrder(a) : FldFinElt -> RngIntElt
FactoredOrder(G) : GrpAb -> [<RngIntElt, RngIntElt>]
FactoredOrder(A) : GrpAuto -> [ <RngIntElt, RngIntElt> ]
FactoredOrder(G) : GrpFin -> [ <RngIntElt, RngIntElt> ]
FactoredOrder(G) : GrpGPC -> [<RngIntElt, RngIntElt>]
FactoredOrder(G) : GrpMat -> [ <RngIntElt, RngIntElt> ]
FactoredOrder(g) : GrpMatElt -> [ <RngIntElt, RngIntElt> ]
FactoredOrder(G) : GrpPC -> [<RngIntElt, RngIntElt>]
FactoredOrder(G) : GrpPerm -> [ <RngIntElt, RngIntElt> ]
FactoredOrder(J) : JacHyp -> [ <RngIntElt, RngIntElt> ]
FactoredOrder(P) : Process(pQuot) -> [ <RngIntElt, RngIntElt> ]
FactoredOrder(P) : PtEll -> RngIntElt
FactoredOrder(G) : SchGrpEll -> RngIntElt
FactoredOrder(H) : SetPtEll -> RngIntElt
Order(G: parameters) : GrpFP -> RngIntElt
FactoredProjectiveOrder(a) : AlgMatElt -> [ <RngIntElt, RngIntElt> ]
FactoredProjectiveOrder(A) : AlgMatElt -> [ <RngIntElt, RngIntElt> ], RngElt
Factorial(n) : RngIntElt -> RngIntElt
Factorial(n) : RngIntElt -> RngIntElt
Factorisation(I) : RngFunOrdIdl -> [<RngFunOrdIdl, RngIntElt>]
Factorization(I) : RngFunOrdIdl -> [ <RngFunOrdIdl, RngIntElt> ]
Factorization(n) : RngIntElt -> RngIntEltFact, RngIntElt, SeqEnum
Factorization(I) : RngOrdFracIdl -> [<RngOrdIdl, RngIntElt>]
Factorization(n) : RngQuadElt -> SeqEnum, Tup
FactorizationOverSplittingField(f) : RngPolElt(FldFin) -> [<RngPolElt, RngIntElt>], FldFin
FactorizationToInteger(s) : [ <RngIntElt, RngIntElt> ] -> RngIntElt
FactorisationOverSplittingField(f) : RngPolElt(FldFin) -> [<RngPolElt, RngIntElt>], FldFin
FactorizationOverSplittingField(f) : RngPolElt(FldFin) -> [<RngPolElt, RngIntElt>], FldFin
FactorisationToInteger(s) : [ <RngIntElt, RngIntElt> ] -> RngIntElt
Facint(s) : [ <RngIntElt, RngIntElt> ] -> RngIntElt
FactorizationToInteger(s) : [ <RngIntElt, RngIntElt> ] -> RngIntElt
DistinctDegreeFactorization(f) : RngUPolElt -> [ <RngIntElt, RngUPolElt> ]
EqualDegreeFactorization(f, d, g) : RngUPolElt, RngIntElt, RngUPolElt -> [ RngUPolElt ]
Facint(f) : RngIntEltFact -> RngIntElt
Factorization(I) : RngFunOrdIdl -> [ <RngFunOrdIdl, RngIntElt> ]
Factorization(n) : RngIntElt -> RngIntEltFact, RngIntElt, SeqEnum
Factorization(f) : RngMPolElt -> [ < RngMPolElt, RngIntElt >], RngElt
Factorization(I) : RngOrdFracIdl -> [<RngOrdIdl, RngIntElt>]
Factorization(n) : RngQuadElt -> SeqEnum, Tup
Factorization(g) : RngUPolElt -> [ < RngUPolElt, RngIntElt > ]
Factorization(g) : RngUPolElt -> [ < RngUPolElt, RngIntElt > ]
Factorization(f) : RngUPolElt -> [ < RngUPolElt, RngIntElt >], RngElt
FactorizationOverSplittingField(f) : RngPolElt(FldFin) -> [<RngPolElt, RngIntElt>], FldFin
FactorizationToInteger(s) : [ <RngIntElt, RngIntElt> ] -> RngIntElt
HasPolynomialFactorization(R) : Rng -> BoolElt
IsUFD(R) : Rng -> BoolElt
PartialFactorization(S) : [ RngIntElt ] -> [ RngIntEltFact ]
SeqFact(s) : SeqEnum -> RngIntEltFact
SquareFreeFactorization(g) : RngUPolElt -> [ < RngUPolElt, RngIntElt > ]
SquareFreeFactorization(g) : RngUPolElt -> [ < RngUPolElt, RngIntElt > ]
SquarefreeFactorization(n) : RngIntElt -> RngIntElt, RngIntElt
SquarefreeFactorization(f) : RngMPolElt -> [ <RngMPolElt, RngIntElt> ]
SquarefreeFactorization(f) : RngUPolElt -> [ <RngUPolElt, RngIntElt> ]
AlgAff_Factorization (Example H51E4)
Factorization (QUADRATIC FIELDS)
Factorization (UNIVARIATE POLYNOMIAL RINGS)
Factorization and Irreducibility (MULTIVARIATE POLYNOMIAL RINGS)
Factorization and Irreducibility (UNIVARIATE POLYNOMIAL RINGS)
Factorization and Primes (ORDERS AND ALGEBRAIC FIELDS)
Factorization Related Functions (RING OF INTEGERS)
Factorization Sequences (RING OF INTEGERS)
General Factorization (RING OF INTEGERS)
Specific Factorization Algorithms (RING OF INTEGERS)
Factorisation(n) : RngIntElt -> RngIntEltFact, RngIntElt, SeqEnum
General Factorization (RING OF INTEGERS)
Factorization and Irreducibility (MULTIVARIATE POLYNOMIAL RINGS)
Factorization and Irreducibility (UNIVARIATE POLYNOMIAL RINGS)
Factorization Related Functions (RING OF INTEGERS)
Factorization Sequences (RING OF INTEGERS)
Specific Factorization Algorithms (RING OF INTEGERS)
FactorisationOverSplittingField(f) : RngPolElt(FldFin) -> [<RngPolElt, RngIntElt>], FldFin
FactorizationOverSplittingField(f) : RngPolElt(FldFin) -> [<RngPolElt, RngIntElt>], FldFin
FactorizationToInteger(f) : RngIntEltFact -> RngIntElt
Facint(f) : RngIntEltFact -> RngIntElt
FactorizationToInteger(s) : [ <RngIntElt, RngIntElt> ] -> RngIntElt
ChiefFactors(G) : GrpPerm -> [ <RngIntElt, RngIntElt, RngIntElt, RngIntElt> ]
CompositionFactors(G) : : GrpFin -> [ <RngIntElt, RngIntElt, RngIntElt> ]
CompositionFactors(G) : : GrpMat -> [ <RngIntElt, RngIntElt, RngIntElt> ]
CompositionFactors(G) : GrpPC -> SeqEnum
CompositionFactors(G) : GrpPerm -> [ <RngIntElt, RngIntElt, RngIntElt> ]
CompositionFactors(M) : ModRng -> [ ModRng ]
InvariantFactors(a) : AlgMatElt -> [ AlgPolElt ]
InvariantFactors(A) : Mtrx -> [ RngUPolElt ]
PrimaryInvariantFactors(a) : AlgMatElt -> [ <RngUPolElt, RngIntElt ]
PrimaryInvariantFactors(A) : Mtrx -> [ <RngUPolElt, RngIntElt> ]
SocleFactors(G) : GrpPerm -> [ GrpPerm ]
SocleFactors(M) : ModRng -> [ ModRng ]
TensorFactors(G) : GrpMat -> GrpMat, GrpMat
Z4CyclotomicFactors(n) : RngIntElt -> [RngUPolElt]
RngLoc_Factors (Example H59E20)
RngPad_Factors (Example H42E18)
Composition Factors (MATRIX GROUPS)
RngLoc_factors-infinite (Example H59E18)
RngPad_factors-infinite (Example H42E16)
RngLoc_factors-precision (Example H59E19)
RngPad_factors-precision (Example H42E17)
IsFaithful(G, Y) : : GrpPerm, GSet -> BoolElt
IsFaithful(x) : AlgChtrElt -> BoolElt
Booleans (OVERVIEW)
true
Families of Linear Codes (LINEAR CODES OVER FINITE FIELDS)
Families of Linear Codes (LINEAR CODES OVER FINITE RINGS)
Special Families of Polynomials (UNIVARIATE POLYNOMIAL RINGS)
Special Families of Polynomials (UNIVARIATE POLYNOMIAL RINGS)
GrpFP_1_Family (Example H22E33)
Farey Symbols and Fundamental domains (SUBGROUPS OF PSL_2(R))
DisplayFareySymbolDomain(FS,filename) : SymFry, MonStgElt -> SeqEnum
FareySymbol(G) : GrpPSL2 -> SymFry
Seq_Farey (Example H8E3)
Farey Symbols and Fundamental domains (SUBGROUPS OF PSL_2(R))
FareySymbol(G) : GrpPSL2 -> SymFry
Magma Updates (OVERVIEW)
UnitalFeet(P, U, p) : Plane, { PlanePt }, PlanePt -> { PlanePt }
Differential Space (PLANE ALGEBRAIC CURVES)
Differentials (PLANE ALGEBRAIC CURVES)
Function Fields (PLANE ALGEBRAIC CURVES)
Operations on Differentials (PLANE ALGEBRAIC CURVES)
Places (PLANE ALGEBRAIC CURVES)
Places (PLANE ALGEBRAIC CURVES)
Sets of Places (PLANE ALGEBRAIC CURVES)
Crv_ff-creation-example (Example H82E10)
Differentials (PLANE ALGEBRAIC CURVES)
Operations on Differentials (PLANE ALGEBRAIC CURVES)
Differential Space (PLANE ALGEBRAIC CURVES)
Crv_ff-elements-example (Example H82E11)
Function Fields (PLANE ALGEBRAIC CURVES)
Places (PLANE ALGEBRAIC CURVES)
Places (PLANE ALGEBRAIC CURVES)
Sets of Places (PLANE ALGEBRAIC CURVES)
Curves over Finite Fields (ELLIPTIC CURVES)
Enumeration of Points (ELLIPTIC CURVES)
Point Counting (ELLIPTIC CURVES)
Predicates for Supersingularity (ELLIPTIC CURVES)
Point Counting (ELLIPTIC CURVES)
Enumeration of Points (ELLIPTIC CURVES)
Predicates for Supersingularity (ELLIPTIC CURVES)
Fibonacci(n) : RngIntElt -> RngIntElt
Fibonacci(n) : RngIntElt -> RngIntElt
GeneralizedFibonacciNumber(g0, g1, n) : RngIntElt, RngIntElt, RngIntElt -> RngIntElt
GeneralizedFibonacciNumber(g0, g1, n) : RngIntElt, RngIntElt, RngIntElt -> RngIntElt
HasIrregularFibres(s) : GrphSpl -> BoolElt
AbsoluteField(F) : FldAlg -> FldAlg
Alphabet(C) : Code -> Rng
BaseField(A) : AlgQuat -> Fld
BaseField(Q) : FldRat -> FldRat
BaseField(J) : JacHyp -> Fld
BaseField(C) : Sch -> Fld
BaseField(K) : SrfKum -> Fld
BaseRing(F) : Fld -> Rng
CoefficientRing(F) : FldFun -> Rng
BaseRing(C) : Sch -> Rng
CoefficientField(x) : AlgChtrElt -> Rng
CoefficientField(V) : ModTupFld -> Fld
CoefficientRing(R) : RngInvar -> Grp
CoefficientRing(X) : Sch -> Fld
CoefficientField(X) : Sch -> Fld
ComplexField() : Null -> FldPr
ComplexField(p) : RngIntElt -> FldCom
ConstantField(F) : FldFun -> Rng
CyclotomicField(m) : RngIntElt -> FldCyc
DecompositionField(p) : RngOrdIdl -> FldNum, Map
DegreeOfFieldExtension(G) : GrpMat -> RngIntElt
DimensionOfExactConstantField(F) : FldFun -> RngIntElt
ExactConstantField(F) : FldFunG -> Rng, Map
ExtendField(C, L) : Code, FldFin -> Code, Map
ExtendField(G, L) : GrpMat, FldFin -> GrpMat, Map
ExtendField(V, L) : ModTupFld, Fld -> ModTupFld, MapHom
ExtensionField<F, x | P> : FldFin, RngIntElt -> FldFin, Map
FactorizationOverSplittingField(f) : RngPolElt(FldFin) -> [<RngPolElt, RngIntElt>], FldFin
Field(P) : Plane -> FldFin
FieldOfFractions(F) : FldFun -> FldFun
FieldOfFractions(Q) : FldRat -> FldRat
FieldOfFractions(O) : RngFunOrd -> FldFun
FieldOfFractions(Z) : RngInt -> FldRat
FieldOfFractions(L) : RngLoc -> FldLoc
FieldOfFractions(P) : RngLoc -> FldLoc
FieldOfFractions(O) : RngOrd -> FldOrd
FieldOfFractions(P) : RngPol -> FldFunRat
FieldOfFractions(V) : RngVal -> Rng
FiniteField(q) : RngIntElt -> FldFin
GF(q) : RngIntElt -> FldFin
FiniteField(p, n) : RngIntElt, RngIntElt -> FldFin
GF(p, n) : RngIntElt, RngIntElt -> FldFin
FixedField(K, U) : FldAlg, GrpPerm -> FldNum, Map
FunctionField(A) : Aff -> FldFunRat
FunctionField(C) : Crv -> FldFun
FunctionField(E) : CrvEll -> FldFun
FunctionField(X) : CrvMod -> FldFun
FunctionField(D) : DiffFun -> FldFun
FunctionField(S) : DiffFun -> FldFun
FunctionField(a) : DiffFunElt -> FldFun
FunctionField(d) : DiffFunElt -> FldFun
FunctionField(G) : DivFun -> FldFun
FunctionField(D) : DivFunElt -> FldFun
FunctionField(f : parameters) : RngMPolElt -> FldFun
FunctionField(S) : PlcFun -> FldFun
FunctionField(P) : PlcFunElt -> FldFun
FunctionField(R) : Rng -> FldFunRat
FunctionField(R, r) : Rng, RngIntElt -> FldFunRat
FunctionField(A) : Sch -> FldFunG
FunctionField(C) : Sch -> FldFunG
FunctionFieldDivisor(D) : DivCrvElt -> DivFunElt
FunctionFieldPlace(P) : PlcCrvElt -> PlcFunElt
GHomOverCentralizingField(M, N) : ModGrp, ModGrp -> ModMatGrp
GetDefaultRealField() : Null -> FldPr
GroundField(F) : FldAlg -> Fld
CoefficientField(F) : FldAlg -> Fld
GroundField(F) : FldFin -> FldFin
HeckeEigenvalueField(M) : ModSym -> Fld, Map
HermitianFunctionField(p, d) : RngIntElt, RngIntElt -> FldFun
InertiaField(L) : FldLoc -> FldLoc
InertiaField(p) : RngOrdIdl -> FldNum, Map
IsAbsoluteField(K) : FldAlg -> BoolElt
IsField(R) : Rng -> BoolElt
IsOverSmallerField(G) : GrpMat -> BoolElt, GrpMat
IsOverSmallerField(G, d) : GrpMat, RngIntElt -> BoolElt, GrpMat
IsolGroupOfDegreeFieldSatisfying(d,{p, f}) : RngIntElt, RngIntElt, Predicate -> GrpMat
IsolGroupsOfDegreeFieldSatisfying(d,{p, f}) : RngIntElt, RngIntElt, Predicate -> SeqEnum
IsolNumberOfDegreeField(n, p) : RngIntElt, RngIntElt -> RngIntElt
IsolProcessOfDegreeField(d, p) : ., . -> Process
IsolProcessOfField(p) : . -> Process
LocalRing(p, f, n) : RngIntElt, RngIntElt, RngIntElt -> RngLoc
LocalRing(p, f, g, n) : RngIntElt, RngIntElt, RngUPolElt, RngIntElt -> RngLoc
LocalRing(p, g, n) : RngIntElt, RngUPolElt, RngIntElt -> RngLoc
LocalRing(L, f, n) : RngLoc, RngIntElt -> RngLoc
LocalRing(L, g, n) : RngLoc, RngUPolElt, RngIntElt -> RngLoc
MinimalField(a) : FldCycElt -> FldCyc
MinimalField(q) : FldRatElt -> FldRat
MinimalField(G) : GrpMat -> FldFin
MinimalField(M) : ModRng -> FldFin
MinimalField(S) : SetEnum -> FldRat
MinimalField(S) : [ FldCycElt ] -> FldCyc
NumberField(F) : FldOrd -> FldNum
NumberField(s) : [ RngUPolElt ] -> FldNum
NumberField(O) : RngOrd -> FldNum
NumberField(O) : RngQuad -> FldQuad
NumberField(f) : RngUPolElt -> FldNum
NumberField(e) : SubFldLatElt -> FldNum
PrimeField(F) : Fld -> Fld
PrimeField(F) : FldFin -> FldFin
PrimeRing(F) : FldFun -> Rng
PrimeRing(L) : RngLoc -> RngLoc
pAdicRing(L) : RngLoc -> RngLoc
QuadraticField(m) : RngIntElt -> FldQuad
RamificationField(p) : RngOrdIdl -> FldNum, Map
RamificationField(p, i) : RngOrdIdl -> FldNum, Map
Rationals() : Null -> FldRat
RayClassField(m) : Map -> FldAb
RealField() : Null -> FldPr
RealField(p) : RngIntElt -> FldRe
RelativeField(F, L) : FldAlg, FldAlg -> FldAlg
ResidueClassField(P) : PlcFunElt -> Rng
ResidueClassField(R, I) : Rng, Rng -> Fld, Map
ResidueClassField(I) : RngFunOrdIdl -> Rng, Map
ResidueClassField(L) : RngLoc -> FldFin, Map
ResidueClassField(P) : RngLoc -> FldFin, Map
ResidueClassField(O, I) : RngOrd, RngOrdIdl -> FldFin, Map
ResidueField(R) : RngGal -> RngIntElt
RestrictField(G, S) : GrpMat, FldFin -> GrpMat, Map
RestrictField(V, L) : ModTupFld, Fld -> ModTupFld, MapHom
RootsInSplittingField(f) : RngPolElt(FldFin) -> [<RngPolElt, RngIntElt>], FldFin
SetDefaultRealField(R) : FldRe ->
SplittingField(F) : FldAlg -> FldAlg, SeqEnum
SplittingField(S) : RngPolElt(FldFin) -> FldFin
SplittingField(P) : RngPolElt(FldFin) -> FldFin
SubfieldSubcode(C, S) : Code, FldFin -> Code, Map
SupportOverSplittingField(Z) : Clstr -> SetEnum
WriteOverLargerField(G) : GrpMat -> GrpMat, GrpMat, GrpAb, SeqEnum
WriteOverSmallerField(G, F) : GrpMat, FldFin -> GrpMat, Map
ext< K | f > : FldFunRat, RngUPolElt -> FldFun
pAdicRing(p, n) : RngIntElt, RngIntElt -> RngLoc
pAdicRing(p, n) : RngIntElt, RngIntElt -> RngLoc
pAdicRing(p, n) : RngIntElt, RngIntElt -> RngLoc
pAdicRing(p, n) : RngIntElt, RngIntElt -> RngLoc
Affine Algebras which are Fields (AFFINE ALGEBRAS)
ALGEBRAIC FUNCTION FIELDS
Algebraic Function Fields (ALGEBRAIC FUNCTION FIELDS)
ALGEBRAICALLY CLOSED FIELDS
Arithmetic (ORDERS AND ALGEBRAIC FIELDS)
Between Ring and Field (LOCAL RINGS AND FIELDS)
Between Ring and Field (p-ADIC RINGS AND FIELDS)
Canonical Forms for Matrices over a Field (MATRIX ALGEBRAS)
Canonical Forms over Fields (MATRICES)
Changing the Coefficient Field (VECTOR SPACES)
Class Field Theory (ORDERS AND ALGEBRAIC FIELDS)
FINITE FIELDS
ORDERS AND ALGEBRAIC FIELDS
p-adic Fields (p-ADIC RINGS AND FIELDS)
Q as a Number Field (RING OF INTEGERS)
RATIONAL FUNCTION FIELDS
Residue Class Fields (INTRODUCTION [BASIC RINGS])
Rings, Fields, and Algebras (OVERVIEW)
Arithmetic (ORDERS AND ALGEBRAIC FIELDS)
FieldOfFractions(F) : FldFun -> FldFun
FieldOfFractions(Q) : FldRat -> FldRat
FieldOfFractions(O) : RngFunOrd -> FldFun
FieldOfFractions(Z) : RngInt -> FldRat
FieldOfFractions(L) : RngLoc -> FldLoc
FieldOfFractions(P) : RngLoc -> FldLoc
FieldOfFractions(O) : RngOrd -> FldOrd
FieldOfFractions(P) : RngPol -> FldFunRat
FieldOfFractions(V) : RngVal -> Rng
CompositeFields(F, L) : FldAlg, FldAlg -> SeqEnum
MergeFields(F, L) : FldAlg, FldAlg -> SeqEnum
Gröbner Bases over Fields (IDEAL THEORY AND GRÖBNER BASES)
Local Fields (LOCAL RINGS AND FIELDS)
Rings, Fields, and Algebras (OVERVIEW)
The Fields of the Record (DATABASES OF GROUPS)
MAGMA_STARTUP_FILE
HasOutputFile() : -> BoolElt
NFSCycleFile(n, F, tuple) : RngIntElt, RngMPolElt, Tup -> .
OpenGraphFile(s, f, p): MonStgElt, RngIntElt, RngIntElt -> File
PrintFile(F, x) : MonStgElt, Var ->
PrintFile(F, x, L) : MonStgElt, Var, MonStgElt ->
PrintFileMagma(F, x) : MonStgElt, Var ->
SetLogFile(F) : MonStgElt ->
SetLogFile(F) : MonStgElt ->
SetOutputFile(F) : MonStgElt ->
SetOutputFile(F) : MonStgElt ->
UnsetLogFile() : ->
UnsetOutputFile() : ->
External Files (INPUT AND OUTPUT)
Opening Files (INPUT AND OUTPUT)
Printing to a File (INPUT AND OUTPUT)
Reading a Complete File (INPUT AND OUTPUT)
ReverseFilling(P1) : SeqEnum -> Tableau
ReverseFilling(P1, P2) : SeqEnum,SeqEnum -> Tableau
LP_FillingLPObject (Example H100E4)
Finding Legal Keys (DATABASES OF GROUPS)
Finding Irreducibles (CHARACTERS OF FINITE GROUPS)
Finding Irreducibles (CHARACTERS OF FINITE GROUPS)
GB_FindingPrimes (Example H50E5)
Control-C key (OVERVIEW)
Quitting (OVERVIEW)
EquationOrderFinite(F) : FldFun -> RngFunOrd
EquationOrderFinite(F) : FldFun -> RngFunOrd
MaximalOrderFinite(F) : FldFun -> RngFunOrd
FiniteAffinePlane(D) : Inc -> Plane, PlanePtSet, PlaneLnSet
FiniteAffinePlane(W) : ModFld -> PlaneAff
FiniteAffinePlane< v | X : parameters > : RngIntElt, List -> PlaneAff
FiniteAffinePlane(P, l) : PlaneProj, PlaneLn -> PlaneAff, PlanePtSet, PlaneLnSet, Map
FiniteField(q) : RngIntElt -> FldFin
FiniteField(p, n) : RngIntElt, RngIntElt -> FldFin
FiniteProjectivePlane(D) : Inc -> Plane, PlanePtSet, PlaneLnSet
FiniteProjectivePlane(W) : ModTupFld -> PlaneProj
FiniteProjectivePlane< v | X : parameters > : RngIntElt, List -> PlaneProj
HasFiniteOrder(g) : GrpMatElt -> BoolElt, RngIntElt
HasFiniteOrder(A) : Mtrx -> BoolElt
IsFinite(G) : GrpAb -> BoolElt
IsFinite(G) : GrpAtc -> BoolElt, RngIntElt
IsFinite(G) : GrpGPC -> BoolElt
IsFinite(G) : GrpMat -> Bool, RngIntElt
IsFinite(G) : GrpRWS -> BoolElt, RngIntElt
IsFinite(x) : Infty -> BoolElt
IsFinite(M) : MonRWS -> BoolElt, RngIntElt
IsFinite(P) : PlcFunElt -> BoolElt
IsFinite(R) : Rng -> BoolElt
IsFiniteOrder(O) : RngFunOrd -> BoolElt
MaximalOrderFinite(F) : FldFun -> RngFunOrd
Finite Dimensional Affine Algebras (AFFINE ALGEBRAS)
FINITE FIELDS
Rings, Fields, and Algebras (OVERVIEW)
Finite Dimensional Affine Algebras (AFFINE ALGEBRAS)
FINITE FIELDS
FiniteAffinePlane(D) : Inc -> Plane, PlanePtSet, PlaneLnSet
FiniteAffinePlane(W) : ModFld -> PlaneAff
FiniteAffinePlane< v | X : parameters > : RngIntElt, List -> PlaneAff
FiniteAffinePlane(P, l) : PlaneProj, PlaneLn -> PlaneAff, PlanePtSet, PlaneLnSet, Map
GaloisField(q) : RngIntElt -> FldFin
GF(q) : RngIntElt -> FldFin
FiniteField(q) : RngIntElt -> FldFin
FiniteField(p, n) : RngIntElt, RngIntElt -> FldFin
RngMPol_FiniteFieldFactorization (Example H45E10)
Polynomials over finite fields (UNIVARIATE POLYNOMIAL RINGS)
FINITELY PRESENTED ALGEBRAS
Finitely Presented Algebras (FINITELY PRESENTED ALGEBRAS)
FINITELY PRESENTED GROUPS
Finitely Presented Modules (FINITELY PRESENTED ALGEBRAS)
FINITELY PRESENTED SEMIGROUPS
FP GROUPS - ADVANCED FEATURES
Rings, Fields, and Algebras (OVERVIEW)
FINITELY PRESENTED ALGEBRAS
FINITELY PRESENTED GROUPS
FINITELY PRESENTED SEMIGROUPS
FP GROUPS - ADVANCED FEATURES
Finitely Presented Algebras (FINITELY PRESENTED ALGEBRAS)
Finitely Presented Modules (FINITELY PRESENTED ALGEBRAS)
Presentations (MATRIX GROUPS)
FiniteProjectivePlane(D) : Inc -> Plane, PlanePtSet, PlaneLnSet
FiniteProjectivePlane(W) : ModTupFld -> PlaneProj
FiniteProjectivePlane< v | X : parameters > : RngIntElt, List -> PlaneProj
FireCode(h, s, n) : RngUPolElt, RngIntElt, RngIntElt -> Code
FireCode(h, s, n) : RngUPolElt, RngIntElt, RngIntElt -> Code
IsFirm(C) : CosetGeom -> BoolElt
IsFirm(D) : IncGeom -> BoolElt
BasisOfHolomorphicDifferentials(F) : FldFunG -> SeqEnum[DiffFunElt]
BasisOfDifferentialsFirstKind(F) : FldFunG -> SeqEnum[DiffFunElt]
BreadthFirstSearchTree(u) : GrphVert -> Grph
ChebyshevFirst(n) : RngIntElt -> RngUPolElt
DepthFirstSearchTree(u) : GrphVert -> Grph
DicksonFirst(n, a) : RngIntElt, RngElt -> RngUPolElt
DicksonFirst(n, a) : RngIntElt, RngElt -> RngUPolElt
FirstColumnEntry(t, j) : Tableau,RngIntElt -> RngIntElt
FirstRowEntry(t, i) : Tableau,RngIntElt -> RngIntElt
SpaceOfDifferentialsFirstKind(C) : Crv -> ModFld, Map
SpaceOfDifferentialsFirstKind(F) : FldFunG -> ModFld, Map
StirlingFirst(m, n) : RngIntElt, RngIntElt -> RngIntElt
StirlingFirst(m, n) : RngIntElt, RngIntElt -> RngIntElt
The `first use' Rule (MAGMA SEMANTICS)
The `first use' Rule (MAGMA SEMANTICS)
FirstColumnEntry(t, j) : Tableau,RngIntElt -> RngIntElt
FirstRowEntry(t, i) : Tableau,RngIntElt -> RngIntElt
FittingLength(G) : GrpGPC -> RngIntElt
FittingSeries(G) : GrpGPC -> [GrpGPC]
FittingSubgroup(G) : GrpGPC -> GrpGPC
FittingSubgroup(G) : GrpAb -> GrpAb
FittingSubgroup(G) : GrpFin -> GrpFin
[Future release] FittingSubgroup(G) : GrpMat -> GrpMat
FittingSubgroup(G) : GrpPC -> GrpPC
FittingSubgroup(G) : GrpPerm -> GrpPerm
FittingGroup(G) : GrpGPC -> GrpGPC
FittingSubgroup(G) : GrpGPC -> GrpGPC
FittingSubgroup(G) : GrpPC -> GrpPC
FittingLength(G) : GrpGPC -> RngIntElt
FittingSeries(G) : GrpGPC -> [GrpGPC]
FittingGroup(G) : GrpGPC -> GrpGPC
FittingSubgroup(G) : GrpGPC -> GrpGPC
FittingSubgroup(G) : GrpAb -> GrpAb
FittingSubgroup(G) : GrpFin -> GrpFin
[Future release] FittingSubgroup(G) : GrpMat -> GrpMat
FittingSubgroup(G) : GrpPC -> GrpPC
FittingSubgroup(G) : GrpPerm -> GrpPerm
GrpGPC_FittingSubgroup (Example H24E15)
REFLECTION GROUPS
Fix(C, G) : Code, GrpPerm -> Code
Fix(G, Y) : GrpPerm, GSet -> { Elt }
Fix(g, Y): GrpPermElt, GSet -> { Elt }
Fix(M): Mod -> Mod
FixedField(K, U) : FldAlg, GrpPerm -> FldNum, Map
FixedGroup(K, L) : FldAlg, FldAlg -> GrpPerm
FixedPoints(g,H) : GrpPSL2Elt, SpcHyp -> SeqEnum
NumberOfFixedSpaces (x, s) : GrpMatElt, RngIntElt -> RngIntElt
Fixed Precision Real Numbers (REAL AND COMPLEX FIELDS)
Free and Fixed Precision (POWER, LAURENT AND PUISEUX SERIES)
The Fixed-point Space of a Module (MODULES OVER A MATRIX ALGEBRA)
The Fixed-point Space of a Module (MODULES OVER A MATRIX ALGEBRA)
Fixed Precision Real Numbers (REAL AND COMPLEX FIELDS)
Free and Fixed Precision (POWER, LAURENT AND PUISEUX SERIES)
FixedField(K, U) : FldAlg, GrpPerm -> FldNum, Map
FixedGroup(K, L) : FldAlg, FldAlg -> GrpPerm
FixedPoints(g,H) : GrpPSL2Elt, SpcHyp -> SeqEnum
FldRe_FixedPrecision (Example H43E1)
Flat(C) : Cop -> Cop
Flat(C) : SetCart -> SetCart
Flat(T) : Tup -> Tup
Flat(e) : FldAlgElt -> [ FldRatElt]
Flattening (COPRODUCTS)
Rings, Fields, and Algebras (OVERVIEW)
Rings, Fields, and Algebras (OVERVIEW)
Rings, Fields, and Algebras (OVERVIEW)
Rings, Fields, and Algebras (OVERVIEW)
Rings, Fields, and Algebras (OVERVIEW)
Rings, Fields, and Algebras (OVERVIEW)
Rings, Fields, and Algebras (OVERVIEW)
Rings, Fields, and Algebras (OVERVIEW)
Rings, Fields, and Algebras (OVERVIEW)
Rings, Fields, and Algebras (OVERVIEW)
ReidNumber(X) : VSrfK3 -> RngIntElt
FletcherNumber(X) : VSrfK3 -> RngIntElt
AltinokNumber(X) : VSrfK3 -> RngIntElt
AFRNumber(X) : VSrfK3 -> RngIntElt
ReidNumber(X) : VSrfK3 -> RngIntElt
FletcherNumber(X) : VSrfK3 -> RngIntElt
AltinokNumber(X) : VSrfK3 -> RngIntElt
AFRNumber(X) : VSrfK3 -> RngIntElt
IsFlex(C,p) : Sch,Pt -> BoolElt,RngIntElt
IsInflectionPoint(p) : Sch,Pt -> BoolElt,RngIntElt
InflectionPoints(C) : Sch -> SeqEnum
Flexes(C) : Sch -> SeqEnum
Translation(A,p) : Sch,Pt -> AutSch
FlipCoordinates(A) : Sch -> AutSch
Automorphism(A,q) : Sch,RngMPolElt -> AutSch
IdentityAutomorphism(A) : Sch -> AutSch
Translation(A,p) : Sch,Pt -> AutSch
FlipCoordinates(A) : Sch -> AutSch
Automorphism(A,q) : Sch,RngMPolElt -> AutSch
IdentityAutomorphism(A) : Sch -> AutSch
Floor(q) : FldRatElt -> RngIntElt
Floor(r) : FldReElt -> RngIntElt
Floor(n) : RngIntElt -> RngIntElt
Flush(F) : File ->
SearchForDecomposition(G, S) : GrpMat, [GrpMatElt] -> BoolElt
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 i := expr_1 to expr_2 do : ->
Definite Iteration (STATEMENTS AND EXPRESSIONS)
forall(t){ e(x) : x in E | P(x) }
forall(t){ e(x_1, ..., x_k): x_1 in E_1,..., x_k in E_k | P(x_1, ..., x_k) }
Forced Coercion (INTRODUCTION [BASIC RINGS])
Magmas (or Structures) (OVERVIEW)
IsForest(G) : GrphUnd -> BoolElt
SpanningForest(G) : Grph -> Grph
DualCoxeterForm( RD ) : RootDtm -> AlgMatElt
CoxeterForm( RD ) : RootDtm -> AlgMatElt
DiagonalForm(f) : RngMPolElt -> RngMPolElt, ModMatRngElt
EchelonForm(a) : AlgMatElt -> AlgMatElt, AlgMatElt
EchelonForm(A) : Mtrx -> Mtrx, AlgMatElt
FormType(G) : GrpMat -> MonStgElt
HermiteForm(X) : AlgMatElt -> AlgMatElt, AlgMatElt
HermiteForm(A) : Mtrx -> Mtrx, ModMatRngElt
HessenbergForm(a) : AlgMatElt -> AlgMatElt
HessenbergForm(A) : Mtrx -> AlgMatElt
HilbertForm(X) : VSrfK3 -> SeqEnum
NoetherForm(X) : VSrfK3 -> SeqEnum
IndexFormEquation(O, k) : RngOrd, RngIntElt -> [ RngOrdElt ]
JordanForm(a) : AlgMatElt -> AlgMatElt, AlgMatElt, [ <RngUPolElt, RngIntElt ]
JordanForm(A) : Mtrx -> Mtrx, AlgMatElt, [ <RngUPolElt, RngIntElt> ]
LegendreEquation(C) : CrvCon -> RngMPolElt, ModMatRngElt
ManhattanForm(M) : Mtrx -> Mtrx, AlgMatElt
ManhattanForm(M) : Mtrx -> Mtrx, AlgMatElt
ModularForm(E) : CrvEll -> ModFrm
ModularForm(E) : CrvEll -> ModFrm
NormalForm(f, M) : ModMPolElt, ModMPol -> ModMPolElt
NormalForm(f, I) : RngMPolElt, RngMPol -> RngMPolElt
NormalForm(f, S) : RngMPolElt, [ RngMPolElt ] -> RngMPolElt
PositiveDefiniteForm(G) : GrpMat -> AlgMatElt
PrimaryRationalForm(a) : AlgMatElt -> AlgMatElt, AlgMatElt, [ <RngUPolElt, RngIntElt ]
PrimaryRationalForm(A) : Mtrx -> AlgMatElt, AlgMatElt, [ <RngUPolElt, RngIntElt ]
PrimeForm(Q, p) : QuadBin, RngIntElt -> QuadBinElt
QuadraticForm(G): GrpMat -> AlgMatElt
QuadraticForm(L) : Lat -> RngMPolElt
QuadraticForm(I) : RngQuadFracIdl -> QuadBinElt
QuadraticForm(S) : { PlanePt } -> RngMPolElt
RationalForm(a) : AlgMatElt -> AlgMatElt, AlgMatElt, [ RngUPolElt ]
RationalForm(A) : Mtrx -> Mtrx, AlgMatElt, [ RngUPolElt ]
ReducedForm(C) : CrvCon -> RngMPolElt, ModMatRngElt
Reduction(f) : QuadBinElt -> QuadBinElt
ScalarsQuadraticForm(G) : GrpMat -> SeqEnum
ScalarsSymmetricBilinearForm(G) : GrpMat -> SeqEnum
ScalarsSymplecticForm(G) : GrpMat -> SeqEnum
ScalarsUnitaryForm(G) : GrpMat -> SeqEnum
SmithForm(a) : AlgMatElt -> AlgMatElt, AlgMatElt, AlgMatElt
SmithForm(A) : ModMatRngElt -> ModMatRngElt, ModMatRngElt, ModMatRngElt
StandardForm(C) : Code -> Code, Map
StandardForm(C) : Code -> Code, Map
SymmetricBilinearForm(G) : GrpMat -> AlgMatElt
SymmetricBilinearForm(f) : RngMPolElt -> ModMatRngElt
SymplecticForm(G) : GrpMat -> AlgMatElt
UnitaryForm(G) : GrpMat -> AlgMatElt
WeierstrassForm(C,p) : Crv, Pt -> CrvEll, MapSch
Canonical Forms (MATRIX ALGEBRAS)
Index Form Equations (ORDERS AND ALGEBRAIC FIELDS)
Matrix Action on Forms (BINARY QUADRATIC FORMS)
Operations on Forms (BINARY QUADRATIC FORMS)
The Standard Form (LINEAR CODES OVER FINITE RINGS)
Matrix Action on Forms (BINARY QUADRATIC FORMS)
Operations on Forms (BINARY QUADRATIC FORMS)
FormalSet(M) : Struct -> SetForm
PowerFormalSet(R) : Struct -> PowSetIndx
Formal Sequences (SEQUENCES)
Formal Sets (SETS)
Sets (OVERVIEW)
The Formal Sequence Constructor (SEQUENCES)
The Formal Set Constructor (SETS)
FormalSet(M) : Struct -> SetForm
Format(r) : Rec -> RecFormat
RECORDS
The Record Format Constructor (RECORDS)
AmbiguousForms(Q) : QuadBin -> SeqEnum
AntisymmetricForms(G) : GrpMat -> [ AlgMatElt ]
AntisymmetricForms(G, n) : GrpMat, RngIntElt -> [ AlgMatElt ]
BinaryQuadraticForms(D) : RngIntElt -> QuadBin
ClassicalForms(G): GrpMat -> BoolElt
DimensionCuspForms(eps, k) : GrpDrchElt, RngIntElt -> RngIntElt
DimensionCuspFormsGamma0(N, k) : RngIntElt, RngIntElt -> RngIntElt
DimensionCuspFormsGamma1(N, k) : RngIntElt, RngIntElt -> RngIntElt
DimensionNewCuspFormsGamma0(N, k) : RngIntElt, RngIntElt -> RngIntElt
DimensionNewCuspFormsGamma1(N, k) : RngIntElt, RngIntElt -> RngIntElt
InvariantForms(G) : GrpMat -> [ AlgMatElt ]
InvariantForms(G, n) : GrpMat, RngIntElt -> [ AlgMatElt ]
IsRingOfAllModularForms(M) : ModFrm -> BoolElt
ModularForms(G) : -> ModFrm
ModularForms(G, k) : -> ModFrm
ModularForms (N) : RngIntElt -> ModFrm
ModularForms(N, k) : RngIntElt, RngIntElt -> ModFrm
ModularForms(chars, k) : [GrpDrchElt], RngIntElt -> ModFrm
NumberOfAntisymmetricForms(G) : GrpMat -> RngIntElt
NumberOfInvariantForms(G) : GrpMat -> RngIntElt, RngIntElt
NumberOfSymmetricForms(G) : GrpMat -> RngIntElt
ReducedForms(Q) : QuadBin -> [ QuadBinElt ]
SymmetricForms(G) : GrpMat -> [ AlgMatElt ]
SymmetricForms(G, n) : GrpMat, RngIntElt -> [ AlgMatElt ]
QuadBin_Forms (Example H67E1)
An Illustrative Overview (MODULAR FORMS)
Invariant Forms (LATTICES)
MODULAR FORMS
Modular Forms (MODULAR FORMS)
Mat_Forms1 (Example H62E10)
FormType(G) : GrpMat -> MonStgElt
Dimension Formulas (MODULAR SYMBOLS)
Dimensions of Spaces (BRANDT MODULES)
Recursion and forward (OVERVIEW)
The forward Declaration (FUNCTIONS, PROCEDURES AND PACKAGES)
forward f; : identifier ->
Func_forward (Example H2E5)
Construction from a Finite Permutation or Matrix Group (FINITELY PRESENTED GROUPS)
Construction of an FP-Group (FINITELY PRESENTED GROUPS)
Construction of the Standard Presentation for a Coxeter Group (FINITELY PRESENTED GROUPS)
Conversion from a Special Form of FP-Group (FINITELY PRESENTED GROUPS)
Generators and Relations (PERMUTATION GROUPS)
Groups (OVERVIEW)
Rings, Fields, and Algebras (OVERVIEW)
The FP-Group Constructor (FINITELY PRESENTED GROUPS)
The Quotient Group Constructor (FINITELY PRESENTED GROUPS)
Generators and Relations (PERMUTATION GROUPS)
Construction of an FP-Group (FINITELY PRESENTED GROUPS)
Construction from a Finite Permutation or Matrix Group (FINITELY PRESENTED GROUPS)
The FP-Group Constructor (FINITELY PRESENTED GROUPS)
Conversion from a Special Form of FP-Group (FINITELY PRESENTED GROUPS)
Construction of the Standard Presentation for a Coxeter Group (FINITELY PRESENTED GROUPS)
The Quotient Group Constructor (FINITELY PRESENTED GROUPS)
GrpCox_FPCoxeterGroups (Example H36E13)
GrpFP_1_FPCoxeterGroups (Example H22E12)
FPGroup(G) : GrpGPC -> GrpFP, Map
FPGroup(G) : GrpPerm -> GrpFP, Hom(Grp)
FPGroup(A) : GrpAb -> GrpFP, Hom(Grp)
FPGroup(A) : GrpAuto -> GrpFP, Map
FPGroup(G) : GrpPC -> GrpFP, Hom(Grp)
FPGroup(G) : GrpPC -> GrpFP, Map
FPGroup(G) : GrpPerm :-> GrpFP, Hom(Grp)
FPGroup(G: parameters) : GrpPerm :-> GrpFP, Hom(Grp)
FPGroupStrong(G) : GrpPerm -> GrpFP, Hom(Grp)
FPGroupStrong(G) : GrpMat :-> GrpFP, Hom(Grp)
FPGroupStrong(G, N) : GrpPerm, GrpPerm -> GrpFP, Hom(Grp)
FPGroupStrong(G: parameters) : GrpPerm :-> GrpFP, Hom(Grp)
OuterFPGroup(A) : GrpAuto -> GrpFP, Map
Grp_FPGroup (Example H19E10)
GrpFP_1_FPGroup1 (Example H22E11)
GrpFP_1_FPGroup2 (Example H22E13)
PGroupStrong(G) : GrpMat -> GrpFP, Hom(Grp)
FPGroupStrong(G) : GrpPerm -> GrpFP, Hom(Grp)
FPGroupStrong(G) : GrpMat :-> GrpFP, Hom(Grp)
FPGroupStrong(G, N) : GrpPerm, GrpPerm -> GrpFP, Hom(Grp)
FPGroupStrong(G: parameters) : GrpPerm :-> GrpFP, Hom(Grp)
FPQuotient(G, N) : GrpPerm, GrpPerm :-> GrpFP, Hom(Grp)
fprintf file, format, expression, ..., expression;
frac< R | a_1, ..., a_r > : Rng, RngElt, ..., RngElt -> Fld, Map
ContinuedFraction(r) : FldPrElt -> [ RngIntElt ]
PartialFractionDecomposition(f) : FldFunRatUElt -> [ <RngUPolElt, RngIntElt, RngUPolElt> ]
SquarefreePartialFractionDecomposition(f) : FldFunRatUElt -> [ <RngUPolElt, RngIntElt, RngUPolElt> ]
Continued Fractions (REAL AND COMPLEX FIELDS)
Partial Fraction Decomposition (RATIONAL FUNCTION FIELDS)
Rings, Fields, and Algebras (OVERVIEW)
FieldOfFractions(F) : FldFun -> FldFun
FieldOfFractions(Q) : FldRat -> FldRat
FieldOfFractions(O) : RngFunOrd -> FldFun
FieldOfFractions(Z) : RngInt -> FldRat
FieldOfFractions(L) : RngLoc -> FldLoc
FieldOfFractions(P) : RngLoc -> FldLoc
FieldOfFractions(O) : RngOrd -> FldOrd
FieldOfFractions(P) : RngPol -> FldFunRat
FieldOfFractions(V) : RngVal -> Rng
RngOrd_fractions (Example H53E5)
FrattiniSubgroup(G) : GrpAb -> GrpAb
FrattiniSubgroup(G) : GrpFin -> GrpFin
FrattiniSubgroup(G) : GrpMat -> GrpMat
FrattiniSubgroup(G) : GrpPC -> GrpPC
FrattiniSubgroup(G) : GrpPerm -> GrpPerm
FrattiniSubgroup(G) : GrpAb -> GrpAb
FrattiniSubgroup(G) : GrpFin -> GrpFin
FrattiniSubgroup(G) : GrpMat -> GrpMat
FrattiniSubgroup(G) : GrpPC -> GrpPC
FrattiniSubgroup(G) : GrpPerm -> GrpPerm
FreeAbelianGroup(GrpGPC, n) : Cat, RngIntElt -> GrpGPC
FreeAbelianGroup(n) : RngIntElt -> GrpAb
FreeAbelianQuotient(G) : GrpAb -> GrpAb, Map
FreeAbelianQuotient(G) : GrpGPC -> GrpAb, Map
FreeAlgebra(R, M) : Rng, MonFP -> AlgFP
FreeGroup(n) : RngIntElt -> GrpFP
FreeMonoid(n) : RngIntElt -> MonFP
FreeNilpotentGroup(r, e) : RngIntElt, RngIntElt -> GrpGPC
FreeProduct(G, H) : GrpFP, GrpFP -> GrpFP
FreeProduct(R, S) : SgpFP, SgpFP -> SgpFP
FreeProduct(Q) : [ GrpFP ] -> GrpFP
FreeResolution(M) : ModMPol -> [ ModMPol ]
FreeResolution(R) : RngInvar -> [ ModMPol ]
FreeSemigroup(n) : RngIntElt -> SgpFP
IsBasePointFree(L) : LinSys -> BoolElt
MinimalFreeResolution(M) : ModMPol -> [ ModMPol ]
MinimalFreeResolution(M) : ModMPol -> [ ModMPol ]
SquareFreeFactorization(g) : RngUPolElt -> [ < RngUPolElt, RngIntElt > ]
SquareFreeFactorization(g) : RngUPolElt -> [ < RngUPolElt, RngIntElt > ]
TorsionFreeRank(A) : GrpAb -> RngIntElt
TorsionFreeRank(G) : GrpFP -> RngIntElt
TorsionFreeSubgroup(A) : GrpAb -> GrpAb
GrpFP_1_Free (Example H22E1)
Construction of a Free Group (FINITELY PRESENTED GROUPS)
Free Modules (FREE MODULES)
Free Real Numbers (REAL AND COMPLEX FIELDS)
Free Resolutions (MODULES OVER AFFINE ALGEBRAS)
Structure Constructors (ABELIAN GROUPS)
Structure Constructors (FINITELY PRESENTED SEMIGROUPS)
Structure Constructors (GROUPS WHOSE ELEMENTS ARE STRAIGHT-LINE PROGRAMS)
Free Modules (FREE MODULES)
Free Resolutions (MODULES OVER AFFINE ALGEBRAS)
FreeAbelianGroup(GrpGPC, n) : Cat, RngIntElt -> GrpGPC
FreeAbelianGroup(n) : RngIntElt -> GrpAb
GrpAb_FreeAbelianGroup (Example H28E1)
FreeAbelianQuotient(G) : GrpAb -> GrpAb, Map
FreeAbelianQuotient(G) : GrpGPC -> GrpAb, Map
FreeAlgebra(R, M) : Rng, MonFP -> AlgFP
AlgFP_FreeAlgebra (Example H74E1)
FreeGroup(n) : RngIntElt -> GrpFP
FreeMonoid(n) : RngIntElt -> MonFP
FreeNilpotentGroup(r, e) : RngIntElt, RngIntElt -> GrpGPC
FreeProduct(G, H) : GrpFP, GrpFP -> GrpFP
FreeProduct(R, S) : SgpFP, SgpFP -> SgpFP
FreeProduct(Q) : [ GrpFP ] -> GrpFP
FreeResolution(M) : ModMPol -> [ ModMPol ]
FreeResolution(R) : RngInvar -> [ ModMPol ]
PMod_FreeResolution (Example H52E6)
FreeSemigroup(n) : RngIntElt -> SgpFP
SgpFP_FreeSemigroup (Example H17E1)
freeze;
Frobenius(P, k) : JacHypPt, FldFin -> JacHypPt
Frobenius(P, F) : PtHyp, FldFin -> PtHyp
FrobeniusAutomorphisms(G) : GrpMat -> SeqEnum
FrobeniusMap(E) : CrvEll -> Map
FrobeniusMap(E, i) : CrvEll, RngIntElt -> Map
IsFrobenius(G) : GrpPerm -> BoolElt
Trace(H): SetPtEll -> RngIntElt
Trace(H, r): SetPtEll, RngIntElt -> RngIntElt
CrvEll_Frobenius (Example H85E37)
Frobenius (HYPERELLIPTIC CURVES)
Frobenius (HYPERELLIPTIC CURVES)
FrobeniusAutomorphisms(G) : GrpMat -> SeqEnum
FrobeniusMap(E) : CrvEll -> Map
FrobeniusMap(E, i) : CrvEll, RngIntElt -> Map
ConvertFromManinSymbol(M, x) : ModSym, Tup -> ModSymElt
GSetFromIndexed(G, Y) : GrpPerm, SetIndx -> GSet
HyperellipticCurveFromIgusa(S) : SeqEnum -> CrvHyp
IsogenyFromKernel(E, psi) : CrvEll, RngUPolElt -> CrvEll, Map
IsogenyFromKernel(G) : CrvEllSubgroup -> CrvEll, Map
IsogenyFromKernelFactored(E, psi) : CrvEllSubgroup -> CrvEll, Map
IsogenyFromKernelFactored(G) : CrvEllSubgroup -> CrvEll, Map
K3SurfaceFromAFR(DB,c,n) : SeqEnum,RngIntElt,RngIntElt -> VSrfK3
K3SurfacesFromBasket(DB,B) : SeqEnum,SeqEnum -> SeqEnum
K3SurfacesFromWeights(DB,W) : SeqEnum,SeqEnum -> SeqEnum
ProjectionFromNonsingularPoint(X,p) : Sch,Pt -> Sch,MapSch,Sch
Creation from Curve Singularities (RESOLUTION GRAPHS AND SPLICE DIAGRAMS)
Creation from Pencils (RESOLUTION GRAPHS AND SPLICE DIAGRAMS)
Transfer from GrpPC (FINITE SOLUBLE GROUPS)
Transfer from GrpPC (FINITE SOLUBLE GROUPS)
IsFTGeometry(C) : CosetGeom -> BoolElt
IsFTGeometry(D) : IncGeom -> BoolElt
pAdicField(p, n) : RngIntElt, RngIntElt -> FldLoc
Creation Functions (p-ADIC RINGS AND FIELDS)
Function Expressions (OVERVIEW)
f := func< x_1, ..., x_n: parameters | expression >;
BesselFunction(n, r) : RngIntElt, FldReElt -> FldReElt
ClassFunctionSpace(G) : Grp -> AlgChtr
ComplementaryErrorFunction(r) : FldReElt -> FldReElt
DivisionFunction(E, n) : Fld, RngIntElt -> RngFunOrdElt
ErrorFunction(r) : FldReElt -> FldReElt
FaceFunction(F) : NwtnPgon,Tup -> RngElt
Function(f) : Map -> UserProgram
FunctionDegree(f) : MapSch -> RngIntElt
FunctionField(A) : Aff -> FldFunRat
FunctionField(C) : Crv -> FldFun
FunctionField(E) : CrvEll -> FldFun
FunctionField(X) : CrvMod -> FldFun
FunctionField(D) : DiffFun -> FldFun
FunctionField(S) : DiffFun -> FldFun
FunctionField(a) : DiffFunElt -> FldFun
FunctionField(d) : DiffFunElt -> FldFun
FunctionField(G) : DivFun -> FldFun
FunctionField(D) : DivFunElt -> FldFun
FunctionField(f : parameters) : RngMPolElt -> FldFun
FunctionField(S) : PlcFun -> FldFun
FunctionField(P) : PlcFunElt -> FldFun
FunctionField(R) : Rng -> FldFunRat
FunctionField(R, r) : Rng, RngIntElt -> FldFunRat
FunctionField(A) : Sch -> FldFunG
FunctionField(C) : Sch -> FldFunG
FunctionFieldDivisor(D) : DivCrvElt -> DivFunElt
FunctionFieldPlace(P) : PlcCrvElt -> PlcFunElt
GrowthFunction(G) : GrpAtc -> FldFunRatElt
HermitianFunctionField(p, d) : RngIntElt, RngIntElt -> FldFun
ImplicitFunction(f, d, n) : RngUPolElt, RngIntElt, RngIntElt -> RngSerElt
IsAmbientFunction(A,f) : Sch,RngElt -> BoolElt, RngElt
IsAmbientRationalFunction(A,f) : Sch,RngElt -> BoolElt
IsMaximisingFunction(L) : LP -> BoolElt
ObjectiveFunction(L) : LP -> Mtrx
RationalFunction(a) : FldFunGElt -> RngElt
SetMaximiseFunction(L, m) : LP, BoolElt ->
SetObjectiveFunction(L, F) : LP, Mtrx ->
ZetaFunction(E) : CrvEll -> FldFunRatUElt
ZetaFunction(C) : CrvHyp -> FldFunRatUElt
ZetaFunction(C,K) : CrvHyp, FldFin -> FldFunRatUElt
ZetaFunction(F) : FldFun -> FldFunRatUElt
ZetaFunction(F, m) : FldFun, RngIntElt -> FldFunRatUElt
ZetaFunction(s) : FldPrElt -> FldPrElt
ext< K | f > : FldFunRat, RngUPolElt -> FldFun
ALGEBRAIC FUNCTION FIELDS
Algebraic Function Fields (ALGEBRAIC FUNCTION FIELDS)
Arithmetic Functions (RING OF INTEGERS)
Function (MAPPINGS)
Function Application (MAGMA SEMANTICS)
Function Expressions (MAGMA SEMANTICS)
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 (MAGMA SEMANTICS)
Function Expressions (MAGMA SEMANTICS)
ALGEBRAIC FUNCTION FIELDS
Algebraic Function Fields (ALGEBRAIC FUNCTION FIELDS)
Functions and Procedures (FUNCTIONS, PROCEDURES AND PACKAGES)
Functions, Procedures, and Mappings (OVERVIEW)
FUNCTIONS, PROCEDURES AND PACKAGES
Function Values Assigned to Identifiers (MAGMA SEMANTICS)
Function Field (ELLIPTIC CURVES)
Function Field (HYPERELLIPTIC CURVES)
Function Field and Polynomial Ring (ELLIPTIC CURVES)
Function Fields (PLANE ALGEBRAIC CURVES)
Torsion Polynomials (ELLIPTIC CURVES)
DefiningEquation(E) : CrvEll -> RngMPolElt
Function Field and Polynomial Ring (ELLIPTIC CURVES)
Torsion Polynomials (ELLIPTIC CURVES)
Function Field and Polynomial Ring (HYPERELLIPTIC CURVES)
FunctionDegree(f) : MapSch -> RngIntElt
FunctionField(A) : Aff -> FldFunRat
FunctionField(C) : Crv -> FldFun
FunctionField(E) : CrvEll -> FldFun
FunctionField(X) : CrvMod -> FldFun
FunctionField(D) : DiffFun -> FldFun
FunctionField(S) : DiffFun -> FldFun
FunctionField(a) : DiffFunElt -> FldFun
FunctionField(d) : DiffFunElt -> FldFun
FunctionField(G) : DivFun -> FldFun
FunctionField(D) : DivFunElt -> FldFun
FunctionField(f : parameters) : RngMPolElt -> FldFun
FunctionField(S) : PlcFun -> FldFun
FunctionField(P) : PlcFunElt -> FldFun
FunctionField(R) : Rng -> FldFunRat
FunctionField(R, r) : Rng, RngIntElt -> FldFunRat
FunctionField(A) : Sch -> FldFunG
FunctionField(C) : Sch -> FldFunG
ext< K | f > : FldFunRat, RngUPolElt -> FldFun
FldFunRat_FunctionField (Example H46E1)
FunctionFieldDivisor(D) : DivCrvElt -> DivFunElt
FunctionFieldPlace(P) : PlcCrvElt -> PlcFunElt
RationalFunctions(P) : CrvPlcElt -> SeqEnum
FldAC_Functions (Example H56E4)
FldFin_Functions (Example H47E3)
FldFin_Functions (Example H47E4)
Associated Structures (MODULAR CURVES)
Construction Functions (FINITE SOLUBLE GROUPS)
Elementary Functions (MODULES OVER ORDERS)
Function Field and Polynomial Ring (ELLIPTIC CURVES)
Functions and Homogeneity on Ambient Spaces (SCHEMES)
The Functions (FP GROUPS - ADVANCED FEATURES)
Transfer Between Group Categories (FINITE SOLUBLE GROUPS)
FundamentalDiscriminant(D) : RngIntElt -> RngIntElt
FundamentalDomain(G) :GrpPSL2 -> SeqEnum
FundamentalDomain(FS) : SymFry -> SeqEnum
FundamentalGroup( t ) : AlgMatElt -> GrpAb
FundamentalGroup( G ) : GrpLie -> RootDtm
FundamentalGroup( RD ) : RootDtm -> GrpAb
FundamentalInvariants(R) : RngInvar -> [ RngMPolElt ]
FundamentalQuotient(Q) : QuadBin -> Map
FundamentalUnit(K) : FldQuad -> FldQuadElt
FundamentalUnits(O) : RngFunOrd -> SeqEnum[RngFunOrdElt]
FundamentalWeights( W ) : GrpCox -> SeqEnum
FundamentalWeights( G ) : GrpLie -> SeqEnum
FundamentalWeights( RD ) : RootDtm -> Mtrx
IsFundamentalDiscriminant(D) : RngIntElt -> BoolElt
SetOrderUnitsAreFundamental(O) : RngOrd ->
Fundamental Invariants (INVARIANT RINGS OF FINITE GROUPS)
FundamentalCoweights( W ) : GrpCox -> SeqEnum
FundamentalWeights( W ) : GrpCox -> SeqEnum
FundamentalWeights( G ) : GrpLie -> SeqEnum
FundamentalWeights( RD ) : RootDtm -> Mtrx
FundamentalDiscriminant(D) : RngIntElt -> RngIntElt
FundamentalDomain(G) :GrpPSL2 -> SeqEnum
FundamentalDomain(FS) : SymFry -> SeqEnum
FundamentalGroup( t ) : AlgMatElt -> GrpAb
FundamentalGroup( G ) : GrpLie -> RootDtm
FundamentalGroup( RD ) : RootDtm -> GrpAb
FundamentalInvariants(R) : RngInvar -> [ RngMPolElt ]
RngInvar_FundamentalInvariants (Example H78E8)
FundamentalQuotient(Q) : QuadBin -> Map
FundamentalUnit(K) : FldQuad -> FldQuadElt
FundamentalUnits(O) : RngFunOrd -> SeqEnum[RngFunOrdElt]
FundamentalCoweights( W ) : GrpCox -> SeqEnum
FundamentalWeights( W ) : GrpCox -> SeqEnum
FundamentalWeights( G ) : GrpLie -> SeqEnum
FundamentalWeights( RD ) : RootDtm -> Mtrx
CrvEll_FunWithHeights (Example H85E18)
Further Ideal Operations (ALGEBRAIC FUNCTION FIELDS)
[____] [____] [_____] [____] [__] [Index] [Root]