Documentation

euclidean
- Canonical Forms over Euclidean Domains (MATRICES)
- Division Algorithm (QUADRATIC FIELDS)
- Euclidean Algorithm (SERIES RINGS OVER p-ADIC RINGS)
- Euclidean Algorithms, GCDs and LCMs (DIFFERENTIAL RINGS)
- Euclidean Right and Left Division (DIFFERENTIAL RINGS)
- Euclidean Weight (LINEAR CODES OVER THE INTEGER RESIDUE RING Z₄)
- Gröbner Bases over Euclidean Rings (GRÖBNER BASES)
- Least Common Left Multiples (DIFFERENTIAL RINGS)
euclidean-algorithm
- Euclidean Algorithm (SERIES RINGS OVER p-ADIC RINGS)
euclidean-algorithms
- Euclidean Algorithms, GCDs and LCMs (DIFFERENTIAL RINGS)
euclidean-basics
- RngSlope_euclidean-basics (Example H57E2)
euclidean-dist
- CodeZ4_euclidean-dist (Example H169E18)
euclidean-division
- Euclidean Right and Left Division (DIFFERENTIAL RINGS)
- Least Common Left Multiples (DIFFERENTIAL RINGS)
Euclidean-domain
- Canonical Forms for Matrices over Euclidean Domains (MATRIX ALGEBRAS)
EuclideanDecoding
- EuclideanDecoding(C, v) : CodeLinFld, ModTupRngElt -> BoolElt, ModTupRngElt
- EuclideanDecoding(C, Q) : CodeLinFld, [ ModTupRngElt ] -> [ BoolElt ], [ ModTupRngElt ]
EuclideanDistance
- EuclideanDistance(u, v) : ModTupRngElt, ModTupRngElt -> RngIntElt
EuclideanLeftDivision
- EuclideanLeftDivision(D, N) : RngDiffOpElt, RngDiffOpElt -> RngDiffOpElt,RngDiffOpElt
EuclideanNorm
- EuclideanNorm(n) : RngIntElt -> RngIntElt
- EuclideanNorm(a) : RngOrdResElt -> RngIntElt
- EuclideanNorm(x) : RngPadResElt -> RngIntElt
- EuclideanNorm(p) : RngUPol -> RngIntElt
- EuclideanNorm(v) : RngValElt -> RngIntElt
EuclideanRightDivision
- EuclideanRightDivision(N, D) : RngDiffOpElt, RngDiffOpElt -> RngDiffOpElt,RngDiffOpElt
EuclideanWeight
- EuclideanWeight(v) : ModTupRngElt -> RngIntElt
- EuclideanWeight(a) : RngIntRes -> RngIntElt
EuclideanWeightDistribution
- EuclideanWeightDistribution(C) : Code -> SeqEnum
EuclideanWeightEnumerator
- EuclideanWeightEnumerator(C): Code -> RngMPolElt
Euler
- ChangeEulerFactor(L,p,f) : LSer, RngIntElt, RngUPolElt -> LSer
- EulerCharacteristic(s) : GrphSpl -> RngIntElt
- EulerCharacteristic(X) : SmpCpx -> RngIntElt
- EulerFactor(A, p) : ArtRep, RngIntElt -> RngUPolElt
- EulerFactor(C, p) : CrvHyp[FldNum], RngIntElt -> RngUPolElt
- EulerFactor(C, p) : CrvHyp[FldRat], RngIntElt -> RngUPolElt
- EulerFactor(A) : GalRep -> RngUPolElt
- EulerFactor(H, t, p) : HypGeomData, RngQZElt, RngIntElt -> RngUPolElt
- EulerFactor(J) : JacHyp -> RngUPolElt
- EulerFactor(J, K) : JacHyp, FldFin -> RngUPolElt
- EulerFactor(J, p) : JacketMot, RngIntElt -> RngUPolElt
- EulerFactor(L, p) : LSer, RngIntElt -> RngElt
- EulerFactorModChar(J) : JacHyp -> RngUPolElt
- EulerGamma(R) : FldRe -> FldReElt
- EulerPhi(n) : RngIntElt -> RngIntElt
- EulerPhiInverse(m) : RngIntElt -> RngIntElt
- EulerProduct(O, B) : RngOrd, RngIntElt -> FldReElt
- FactoredEulerPhi(n) : RngIntElt -> RngIntEltFact
- FactoredEulerPhiInverse(n) : RngIntElt -> RngIntEltFact
- JacobianOrdersByDeformation(Q, Y) : RngMPolElt, SeqEnum -> SeqEnum
EulerCharacteristic
- EulerCharacteristic(s) : GrphSpl -> RngIntElt
- EulerCharacteristic(X) : SmpCpx -> RngIntElt
EulerFactor
- EulerFactor(A, p) : ArtRep, RngIntElt -> RngUPolElt
- EulerFactor(C, p) : CrvHyp[FldNum], RngIntElt -> RngUPolElt
- EulerFactor(C, p) : CrvHyp[FldRat], RngIntElt -> RngUPolElt
- EulerFactor(A) : GalRep -> RngUPolElt
- EulerFactor(H, t, p) : HypGeomData, RngQZElt, RngIntElt -> RngUPolElt
- EulerFactor(J) : JacHyp -> RngUPolElt
- EulerFactor(J, K) : JacHyp, FldFin -> RngUPolElt
- EulerFactor(J, p) : JacketMot, RngIntElt -> RngUPolElt
- EulerFactor(L, p) : LSer, RngIntElt -> RngElt
EulerFactorModChar
- EulerFactorModChar(J) : JacHyp -> RngUPolElt
EulerFactorsByDeformation
- EulerFactorsByDeformation(Q, Y) : RngMPolElt, SeqEnum -> SeqEnum
- ZetaFunctionsByDeformation(Q, Y) : RngMPolElt, SeqEnum -> SeqEnum
- JacobianOrdersByDeformation(Q, Y) : RngMPolElt, SeqEnum -> SeqEnum
EulerGamma
- EulerGamma(R) : FldRe -> FldReElt
Eulerian
- EulerianGraphDatabase(n : parameters) : RngIntElt -> DB
- EulerianNumber(n, r) : RngIntElt, RngIntElt -> RngIntElt
- IsEulerian(G) : Grph -> BoolElt
EulerianGraphDatabase
- EulerianGraphDatabase(n : parameters) : RngIntElt -> DB
EulerianNumber
- EulerianNumber(n, r) : RngIntElt, RngIntElt -> RngIntElt
EulerPhi
- EulerPhi(n) : RngIntElt -> RngIntElt
EulerPhiInverse
- EulerPhiInverse(m) : RngIntElt -> RngIntElt
EulerProduct
- EulerProduct(O, B) : RngOrd, RngIntElt -> FldReElt
Eval
- RawEval(I, GR) : RngOrdFracIdl, GrossenChar -> FldNumElt, FldCycElt, FldCycElt
- Grossencharacter(psi, chi, T) : GrpHeckeElt, GrpDrchNFElt, SeqEnum -> GrossenChar
eval
- Runtime Evaluation: the eval Expression (STATEMENTS AND EXPRESSIONS)
- eval expression
- RngLaz_eval (Example H52E9)

V2.29, 21 October 2025

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