Documentation

symp-and-orthog
- Chtr_symp-and-orthog (Example H98E7)
Symplectic
- ASigmaSp(arguments)
- AffineSigmaSymplecticGroup(arguments)
- AffineSymplecticGroup(arguments)
- ConformalSymplecticGroup(n, q) : RngIntElt, RngIntElt -> GrpMat
- ExtendedSymplecticGroup(n,q,m) : RngIntElt, RngIntElt, RngIntElt -> GrpMat
- IsOrthogonal(L) : LSer -> BoolElt
- IsOrthogonalCharacter(chi) : AlgChtrElt -> BoolElt
- IsPseudoSymplecticSpace(W) : ModTupFld -> BoolElt
- IsSymplecticGroup(G) : GrpMat -> BoolElt
- IsSymplecticMatrix(A) : Mtrx -> BoolElt
- IsSymplecticSelfDual(C) : CodeAdd -> BoolElt
- IsSymplecticSelfOrthogonal(C) : CodeAdd -> BoolElt
- IsSymplecticSpace(W) : ModTupFld -> BoolElt
- OrthogonalSymmetrization(L, p) : LSer, SeqEnum -> LSer
- ProjectiveSigmaSymplecticGroup(arguments)
- ProjectiveSymplecticGroup(arguments)
- RandomSymplecticMatrix(g, m) : RngIntElt, RngIntElt -> Mtrx
- SymplecticBasis(V,U,W) : ModTupFld, ModTupFld, ModTupFld -> [ModTupFldElt]
- SymplecticDual(C) : CodeAdd -> CodeAdd
- SymplecticForm(G: parameters) : GrpMat -> BoolElt, AlgMatElt [,SeqEnum]
- SymplecticGroup(n, q) : RngIntElt, RngIntElt -> GrpMat
- SymplecticInnerProduct(v1, v2) : ModTupFldElt, ModTupFldElt -> FldFinElt
- SymplecticMatrixGroupDatabase() : -> DB
- SymplecticSpace(J) : AlgMatElt -> ModTupRng
- SymplecticSymmetrization(chi, p) : AlgChtrElt, [ RngIntElt ] -> AlgChtrElt
- SymplecticTransvection(a, alpha) : ModTupRngElt, FldElt -> AlgMatElt
- GrpASim_Symplectic (Example H71E1)
- GrpData_Symplectic (Example H72E19)
symplectic
- RecognizeSp4(G, q) : Grp, RngIntElt, RngIntElt -> BoolElt, Map, Map, Map, Map, SeqEnum, SeqEnum
- Constructive Recognition of Symplectic Groups (ALMOST SIMPLE GROUPS)
- Symplectic Groups (ALMOST SIMPLE GROUPS)
symplectic-symm
- Lseries_symplectic-symm (Example H136E36)
SymplecticBasis
- SymplecticBasis(V,U,W) : ModTupFld, ModTupFld, ModTupFld -> [ModTupFldElt]
SymplecticDual
- SymplecticDual(C) : CodeAdd -> CodeAdd
SymplecticEg
- QECC_SymplecticEg (Example H167E17)
SymplecticForm
- SymplecticForm(G: parameters) : GrpMat -> BoolElt, AlgMatElt [,SeqEnum]
- Multilinear_SymplecticForm (Example H62E9)
SymplecticGroup
- Sp(n, q) : RngIntElt, RngIntElt -> GrpMat
- SymplecticGroup(n, q) : RngIntElt, RngIntElt -> GrpMat
SymplecticInnerProduct
- SymplecticInnerProduct(v1, v2) : ModTupFldElt, ModTupFldElt -> FldFinElt
SymplecticMatrixGroupDatabase
- SymplecticMatrixGroupDatabase() : -> DB
symplecticselforthog
- QECC_symplecticselforthog (Example H167E18)
SymplecticSpace
- SymplecticSpace(J) : AlgMatElt -> ModTupRng
SymplecticSymmetrization
- SymplecticSymmetrization(L, p) : LSer, SeqEnum -> LSer
- OrthogonalSymmetrization(L, p) : LSer, SeqEnum -> LSer
- SymplecticSymmetrization(chi, p) : AlgChtrElt, [ RngIntElt ] -> AlgChtrElt
SymplecticTransvection
- SymplecticTransvection(a, alpha) : ModTupRngElt, FldElt -> AlgMatElt
symplgps
- Database of Finite Symplectic Matrix Groups (DATABASES OF GROUPS)
sympow
- Symmetric Powers (L-FUNCTIONS)
sympow-ec
- Lseries_sympow-ec (Example H136E32)
sympow-ec2
- Lseries_sympow-ec2 (Example H136E33)
sympow-gross
- Lseries_sympow-gross (Example H136E31)
sympspace
- Symplectic Spaces (POLAR SPACES)
Syn_Decode
- CodeFld_Syn_Decode (Example H161E44)
Syndrome
- Syndrome(w, C) : ModTupFldElt, Code -> ModTupFldElt
- Syndrome(u, C) : ModTupFldElt, CodeLinRng -> ModTupRngElt
- SyndromeDecode(C, u) : CodeLinRng, ModTupFldElt -> BoolElt, ModTupRngElt, ModTupFldElt
- SyndromeDecode(C, Q) : CodeLinRng, [ModTupFldElt] -> SeqEnum, SeqEnum, SeqEnum
- SyndromeDecoding(C, v) : CodeLinFld, ModTupRngElt -> BoolElt, ModTupRngElt
- SyndromeDecoding(C, Q) : CodeLinFld, [ ModTupRngElt ] -> [ BoolElt ], [ ModTupRngElt ]
- SyndromeSpace(C) : Code -> ModTupFld
- SyndromeSpace(C) : CodeLinRng -> ModTupRng, ModTupFld
syndrome
- The Syndrome Space (LINEAR CODES OVER FINITE FIELDS)
syndrome-space
- The Syndrome Space (LINEAR CODES OVER FINITE FIELDS)
syndrome_decoding
- Syndrome Decoding (LINEAR CODES OVER THE INTEGER RESIDUE RING Z₄)
syndrome_space_coset_leaders
- Syndrome Space and Coset Leaders (LINEAR CODES OVER THE INTEGER RESIDUE RING Z₄)
SyndromeDecode
- SyndromeDecode(C, u) : CodeLinRng, ModTupFldElt -> BoolElt, ModTupRngElt, ModTupFldElt
- SyndromeDecode(C, Q) : CodeLinRng, [ModTupFldElt] -> SeqEnum, SeqEnum, SeqEnum
SyndromeDecoding
- SyndromeDecoding(C, v) : CodeLinFld, ModTupRngElt -> BoolElt, ModTupRngElt
- SyndromeDecoding(C, Q) : CodeLinFld, [ ModTupRngElt ] -> [ BoolElt ], [ ModTupRngElt ]
SyndromeSpace
- SyndromeSpace(C) : Code -> ModTupFld
- SyndromeSpace(C) : CodeLinRng -> ModTupRng, ModTupFld
sys
- Operators on Root Systems (ROOT SYSTEMS)
System
- AdjointLinearSystemForNodalCurve(C, d) : Crv, RngIntElt -> LinearSys
- AdjointIdealForNodalCurve(C) : Crv -> RngMPol
- AdjointLinearSystemFromIdeal(I, d) : RngMPol, RngIntElt -> LinearSys
- AsMatrices(T, s, t) : TenSpcElt, RngIntElt, RngIntElt -> SeqEnum
- CanonicalLinearSystem(C) : Crv -> LinearSys
- CanonicalLinearSystemFromIdeal(I, d) : RngMPol, RngIntElt -> LinearSys
- GetHelpExternalSystem() : -> MonStgElt
- ImageSystem(f,S,d) : MapSch,Sch,RngIntElt -> LinearSys
- IrreducibleRootSystem(X, n) : MonStgElt, RngIntElt -> RootSys
- IsLinearSystemNonEmpty(D) : DivSchElt -> BoolElt, DivSchElt
- LinearSystem(L, p) : LinearSys, Point -> LinearSys
- LinearSystem(L, p, m) : LinearSys, Point, RngIntElt -> LinearSys
- LinearSystem(L, p, m, t) : LinearSys, Point, SeqEnum, SeqEnum[SeqEnum]) -> LinearSys
- LinearSystem(L, P, M, T) : LinearSys, Points, SeqEnum[SeqEnum], SeqEnum[SeqEnum[SeqEnum]]) -> LinearSys
- LinearSystem(L, P) : LinearSys, SeqEnum[Point) -> LinearSys
- LinearSystem(L,V) : LinearSys,ModTupFld -> LinearSys
- LinearSystem(L,F) : LinearSys,SeqEnum -> LinearSys
- LinearSystem(L, X : parameters) : LinearSys, Sch -> LinearSys
- LinearSystem(P, d) : Sch, [RngIntElt] -> LinearSys
- LinearSystem(P, d) : Sch,RngIntElt -> LinearSys
- LinearSystem(P, F) : Sch,SeqEnum[RngMPolElt] -> LinearSys
- LinearSystemDivisorRestriction(S,B,ms) : Srfc, SeqEnum[RngMPolElt], SeqEnum[SeqEnum] -> SeqEnum
- LinearSystemTrace(L, X) : LinearSys, Sch -> LinearSys
- MinRankSystem(K, n, k, r) : FldFin, RngIntElt, RngIntElt, RngIntElt -> [ RngMPolBool ]
- ResidueSystem(R) : RngPad -> [RngPadElt]
- ResolveLinearSystem(D) : DivTorElt -> TorVar
- RootSystem(L) : AlgLie -> [ ModTupRngElt ], [ AlgLieElt ], [ ModTupRngElt ], AlgMatElt
- RootSystem(C) : AlgMatElt -> RootSys
- RootSystem(M) : AlgMatElt -> RootSys
- RootSystem(M) : AlgMatElt -> RootSys
- RootSystem(D) : GrphDir -> RootSys
- RootSystem(W) : GrpMat -> RootDtm
- RootSystem(W) : GrpPermCox -> RootDtm
- RootSystem(N) : MonStgElt -> RootSys
- RootSystem(A, B) : Mtrx, Mtrx -> RootSys
- RootSystem(R) : RootDtm -> RootSys
- SchreierSystem(G, H) : GrpFP, GrpFP -> {@ GrpFPElt @}, Map
- SetHelpExternalSystem(s) : MonStgElt ->
- SetHelpUseExternalSystem(b) : BoolElt ->
- StandardRootSystem(X, n) : MonStgElt, RngIntElt -> RootSys
- SylowSystem(G : parameters) : GrpMat[FldFin] -> []
- System(C) : MonStgElt -> RngIntElt
- SystemNormalizer(G) : GrpPC -> GrpPC
- SystemOfEigenvalues(M, prec) : ModSym, RngIntElt -> SeqEnum
- TeichmuellerSystem(R) : Any -> [RngLocElt]
- ToralRootSystem(n) : RngIntElt -> RootSys
- TrivialRootSystem() : -> RootSys

V2.28, 13 July 2023

Magma is maintained and distributed by the Computational Algebra Group, School of Mathematics and Statistics, University of Sydney.