[____] [____] [_____] [____] [__] [Index] [Root]

Index E


E

d . eefpg : RngIntElt, RngIntElt, RngIntElt -> FldReElt

e

Quitting (OVERVIEW)

d . eefpg : RngIntElt, RngIntElt, RngIntElt -> FldReElt

E-key

E

e-key

e

EARNS

EARNS(G) : GrpPerm -> GrpPerm

EAS

GrpPC_EAS (Example H19E5)

EasyIdeal

EasyIdeal(I) : RngMPol -> RngMPol

ec_ff_structure_ops

Structure operations for Elliptic Curves over Finite Fields (ELLIPTIC CURVES)

EchelonForm

EchelonForm(a) : AlgMatElt -> AlgMatElt, AlgMatElt

EchelonForm(a) : ModMatElt -> ModMatElt, ModMatElt

EchelonForm(X) : ModMatRngElt -> ModMatRngElt, ModMatRngElt

AlgMat_EchelonForm (Example H51E6)

EcheloniseWord

EcheloniseWord(~P, ~r) : Process(pQuot) -> RngIntElt

ECM

ECM(n) : RngIntElt -> RngIntEltFact, [ RngIntElt ]

edge

The Vertex-Set and Edge-Set of a Graph (GRAPHS)

EdgeGroup

EdgeGroup(G) : Grph -> GrpPerm, GSet

EdgeLabel

EdgeLabel(G, i, j) : Grph, RngIntElt, RngIntElt -> .

EdgeLabels

EdgeLabels(G, S) : Grph, SeqEnum -> SeqEnum

Edges

Edges(G) : Grph -> {@ GrphEdge @}

EdgeSet

EdgeSet(G) : Grph -> GrphEdgeSet

EdgeSets

Graph_EdgeSets (Example H55E6)

EdgeUnion

EdgeUnion(G, H) : GrphDir, GrphDir -> GrphDir

editor

The Magma Line Editor (ENVIRONMENT AND OPTIONS)

EgyptianFractions

Seq_EgyptianFractions (Example H8E4)

Eigenspace

Eigenspace(a, e) : AlgMatElt, FldElt -> ModTup

Eigenspace(g, a) : GrpMatElt, FldElt -> Mod

Eigenvalues

Eigenvalues(a) : AlgMatElt -> { <FldElt, RngIntElt> }

Eigenvalues(g) : GrpMatElt -> { <RngElt, RngIntElt> }

EisensteinSeries

EisensteinSeries(n, q) : RngIntElt, FldPowElt -> FldPowElt

el

Elementary Operations (FINITE PLANES)

el-creation

AlgGrp_el-creation (Example H50E2)

el-ops

Elementary Operations (FINITE PLANES)

Element

PMod_Element (Example H44E2)

element

Accessing and Modifying a Matrix (MATRIX ALGEBRAS)

Accessing and Modifying a Matrix (THE MODULES Hom_(R)(M, N) AND End(M))

Arithmetic (FUNCTION FIELDS AND THEIR ORDERS)

Arithmetic (NUMBER FIELDS AND THEIR ORDERS)

Boolean Operators (STATEMENTS AND EXPRESSIONS)

Construction of a Group Algebra Element (GROUP ALGEBRAS)

Construction of a Matrix (MATRIX ALGEBRAS)

Construction of a Matrix (MATRIX GROUPS)

Construction of a Matrix (THE MODULES Hom_(R)(M, N) AND End(M))

Construction of a Permutation (PERMUTATION GROUPS)

Construction of a Vector (VECTOR SPACES)

Construction of an Element (ABELIAN GROUPS)

Construction of an Element (BLACKBOX GROUPS)

Construction of an Element (GROUPS)

Construction of Direct Sums and Tensor Products of Elements (MATRIX ALGEBRAS)

Coset Spaces: Selection of Cosets (FINITELY PRESENTED GROUPS)

Creation of Coproduct Elements (COPRODUCTS)

Creation of Elements (CYCLOTOMIC FIELDS)

Creation of Elements (FUNCTION FIELDS AND THEIR ORDERS)

Creation of Elements (INTRODUCTION [RINGS AND FIELDS])

Creation of Elements (LOCAL FIELDS)

Creation of Elements (NUMBER FIELDS AND THEIR ORDERS)

Creation of Elements (POWER SERIES AND LAURENT SERIES)

Creation of Elements (QUADRATIC FIELDS)

Creation of Elements (RATIONAL FIELD)

Creation of Elements (RATIONAL FUNCTION FIELDS)

Creation of Elements (REAL AND COMPLEX FIELDS)

Creation of Elements (RESIDUE CLASS RINGS)

Creation of Elements (RING OF INTEGERS)

Creation of Elements (UNIVARIATE POLYNOMIAL RINGS)

Creation of Elements (VALUATION RINGS)

Creation of Module Elements (MODULES OVER AFFINE ALGEBRAS)

Creation of Polynomials (MULTIVARIATE POLYNOMIAL RINGS)

Definition of Soluble Groups using Power-conjugate Presentations (SOLUBLE GROUPS)

Element Constructors (FINITELY PRESENTED SEMIGROUPS)

Element Constructors and Selectors (LOCAL FIELDS)

Element Creation (CHARACTERS OF FINITE GROUPS)

Element Operations (CHARACTERS OF FINITE GROUPS)

Element Operations (CYCLOTOMIC FIELDS)

Element Operations (FINITE FIELDS)

Element Operations (FUNCTION FIELDS AND THEIR ORDERS)

Element Operations (MULTIVARIATE POLYNOMIAL RINGS)

Element Operations (NUMBER FIELDS AND THEIR ORDERS)

Element Operations (POWER SERIES AND LAURENT SERIES)

Element Operations (QUADRATIC FIELDS)

Element Operations (RATIONAL FIELD)

Element Operations (RATIONAL FUNCTION FIELDS)

Element Operations (REAL AND COMPLEX FIELDS)

Element Operations (RING OF INTEGERS)

Element Operations (SOLUBLE GROUPS)

Element Operations (THE MODULES Hom_(R)(M, N) AND End(M))

Element Operations (UNIVARIATE POLYNOMIAL RINGS)

Element Operations (VALUATION RINGS)

Elementary Functions for Words (FINITELY PRESENTED GROUPS)

Elementary Operations on Elements (MATRIX ALGEBRAS)

Elementary Operators for Words (FINITELY PRESENTED GROUPS)

Elements Construction and Operations (GENERAL MODULES)

Elements of M_n as Homomorphisms (MATRIX ALGEBRAS)

Elements Operations (RESIDUE CLASS RINGS)

Generic Element Functions (INTRODUCTION [RINGS AND FIELDS])

Lattice Elements (LATTICES)

Matrix Operations (MATRIX GROUPS)

Module Element Access and Operations (MODULES OVER AFFINE ALGEBRAS)

Operations on Codewords (ERROR-CORRECTING CODES)

Operations on Elements (ABELIAN GROUPS)

Operations on Elements (BLACKBOX GROUPS)

Operations on Elements of Ideals (MULTIVARIATE POLYNOMIAL RINGS)

Operations on Lattice Elements (GENERAL MODULES)

Operations on p-adic Elements (LOCAL FIELDS)

Operations on Poset Elements (GROUPS)

Operations on the Set of Elements (GROUPS)

Operations on the Set of Elements (MATRIX GROUPS)

Operations on the Set of Elements (PERMUTATION GROUPS)

Predicates on Ring Elements (CYCLOTOMIC FIELDS)

Predicates on Ring Elements (FINITE FIELDS)

Predicates on Ring Elements (INTRODUCTION [RINGS AND FIELDS])

Predicates on Ring Elements (MULTIVARIATE POLYNOMIAL RINGS)

Predicates on Ring Elements (POWER SERIES AND LAURENT SERIES)

Predicates on Ring Elements (RATIONAL FIELD)

Predicates on Ring Elements (RATIONAL FUNCTION FIELDS)

Predicates on Ring Elements (RESIDUE CLASS RINGS)

Predicates on Ring Elements (RING OF INTEGERS)

Predicates on Ring Elements (UNIVARIATE POLYNOMIAL RINGS)

Selecting Elements of Sets (SETS)

Selection Operators on Enumerated Sequences (SEQUENCES)

Specialised Operations on Words (FINITELY PRESENTED GROUPS)

Specification of a Word (FINITELY PRESENTED ALGEBRAS)

String Operations on Words (FINITELY PRESENTED SEMIGROUPS)

element-access

Module Element Access and Operations (MODULES OVER AFFINE ALGEBRAS)

element-access-modification

Accessing and Modifying a Matrix (THE MODULES Hom_(R)(M, N) AND End(M))

element-Boolean

Predicates on Ring Elements (CYCLOTOMIC FIELDS)

Predicates on Ring Elements (FINITE FIELDS)

Predicates on Ring Elements (INTRODUCTION [RINGS AND FIELDS])

Predicates on Ring Elements (MULTIVARIATE POLYNOMIAL RINGS)

Predicates on Ring Elements (POWER SERIES AND LAURENT SERIES)

Predicates on Ring Elements (RATIONAL FIELD)

Predicates on Ring Elements (RATIONAL FUNCTION FIELDS)

Predicates on Ring Elements (RESIDUE CLASS RINGS)

Predicates on Ring Elements (RING OF INTEGERS)

Predicates on Ring Elements (UNIVARIATE POLYNOMIAL RINGS)

ElementaryAbelianSeries

ElementaryAbelianSeries(G) : GrpAb -> [GrpAb]

ElementaryAbelianSeries(G) : GrpPC -> [GrpPC]

ElementaryAbelianSeries(G) : GrpPerm -> [ GrpPerm ]

ElementaryAbelianSubgroups

ElementaryAbelianSubgroups(G: parameters) : GrpFin -> [ rec< Grp, RngIntElt, RngIntElt, GrpFP> ]

ElementaryDivisors

ElementaryDivisors(a) : AlgMatElt -> [RngElt]

ElementaryDivisors(X) : ModMatRngElt -> [RngElt]

AlgMat_ElementaryDivisors (Example H51E7)

ElementarySymmetricPolynomial

ElementarySymmetricPolynomial(P, k) : RngMPol, RngIntElt -> RngMPolElt

ElementOperations

RngMPol_ElementOperations (Example H29E15)

Elements

FldFunG_Elements (Example H32E3)

FldNum_Elements (Example H36E7)

RMod_Elements (Example H42E14)

elements

Construction of an Element of a General Algebra (ALGEBRAS)

Construction of Elements of a Structure Constant Algebra (STRUCTURE CONSTANT ALGEBRAS)

ElementSet

ElementSet(G, H) : GrpPerm, GrpPerm -> { GrpPermElt }

ElementToSequence

Coefficients(a) : FldLocElt -> [ RngResElt ]

Coefficients(f) : RngPowSerElt -> [ RngElt ]

Coefficients(p) : RngUPolElt -> [ RngElt ]

ElementToSequence(a) : AlgGenElt -> SeqEnum

ElementToSequence(a) : AlgGrpElt -> SeqEnum

ElementToSequence(a) : AlgMatElt -> [ RngElt ]

ElementToSequence(P): CurveEllPt -> [ RngElt ]

ElementToSequence(a) : FldFinElt -> [ FldFinElt ]

ElementToSequence(a) : FldNumElt -> [ FldRatElt ]

ElementToSequence(x) : GrpAbElt -> [RngIntElt]

ElementToSequence(u) : GrpFPElt -> [ RngIntElt ]

ElementToSequence(g) : GrpMatElt -> [ RngElt ]

ElementToSequence(x) : GrpPCElt -> [RngIntElt]

ElementToSequence(x) : GrpPCElt -> [RngIntElt]

ElementToSequence(g) : GrpPermElt -> [ Elt ]

ElementToSequence(v) : LatElt -> [ RngElt ]

ElementToSequence(a) : ModMatRngElt -> [ RngElt ]

ElementToSequence(u) : ModTupFldElt -> [RngElt]

ElementToSequence(u) : ModTupRngElt -> [RngElt]

ElementToSequence(p) : PlanePt -> [ FldFinElt ]

ElementToSequence(a) : RngFunOrdElt -> [ RngElt ]

ElementToSequence(u) : SgpFPElt -> [ SgpFPElt ]

Eltseq(a) : FldCycElt -> [ FldRatElt ]

Eltseq(a) : FldQuadElt -> [ FldRatElt ]

Eltseq(f) : RngIntEltFact -> SeqEnum

aInvariants(E) : CurveEll -> [ RngElt ]

EliasAsymptoticBound

EliasAsymptoticBound(K, delta) : FldFin, FldPrElt -> FldPrElt

EliasBound

EliasBound(K, n, d) : FldFin, RngIntElt, RngIntElt -> RngIntElt

elif

The if statement (OVERVIEW)

elim

Elimination (k): elim (MULTIVARIATE POLYNOMIAL RINGS)

Elimination List: elim (MULTIVARIATE POLYNOMIAL RINGS)

elim-k

Elimination (k): elim (MULTIVARIATE POLYNOMIAL RINGS)

elim-list

Elimination List: elim (MULTIVARIATE POLYNOMIAL RINGS)

Eliminate

Eliminate(u, x, v) : GrpFPElt, GrpFPElt, GrpFPElt -> GrpFPElt

Eliminate(u, x, v) : SgpFPElt, SgpFPElt, SgpFPElt -> SgpFPElt

EliminateGenerators

EliminateGenerators(~P: parameters) : Process(Tietze) ->

EliminateRedundancy

EliminateRedundancy(~P) : Process(pQuot) ->

elimination

Construction of Elimination Ideals (MULTIVARIATE POLYNOMIAL RINGS)

Elimination (MULTIVARIATE POLYNOMIAL RINGS)

Univariate Elimination Ideal Generators (MULTIVARIATE POLYNOMIAL RINGS)

elimination-ideal

Construction of Elimination Ideals (MULTIVARIATE POLYNOMIAL RINGS)

EliminationIdeal

EliminationIdeal(I, k) : RngMPol, RngIntElt -> RngMPol

RngMPol_EliminationIdeal (Example H29E17)

elliptic

Combinatorial and Geometrical Structures (OVERVIEW)

Elliptic and Modular functions (POWER SERIES AND LAURENT SERIES)

Elliptic and Modular Functions (REAL AND COMPLEX FIELDS)

ELLIPTIC CURVES

elliptic-curve

ELLIPTIC CURVES

elliptic-modular

Elliptic and Modular functions (POWER SERIES AND LAURENT SERIES)

Elliptic and Modular Functions (REAL AND COMPLEX FIELDS)

EllipticCurve

EllipticCurve(R, j) : Rng, RngElt -> CurveEll

EllipticCurve([a, b]) : [ RngElt ] -> CurveEll

else

The case statement (OVERVIEW)

The if statement (OVERVIEW)

The select expression (OVERVIEW)

elt

Constructor (OVERVIEW)

Operations on Elements (GROUP ALGEBRAS)

Other Point and Line Functions (FINITE PLANES)

C ! [a_1, ..., a_n] : Code, [ FldFinElt ] -> ModTupFldElt

E ! [x, y, z] : CurveEll, [RngElt] -> CurveEllPt

K ! [a_0, ..., a_m - 1] : FldCyc, [FldCycElt] -> FldCycElt

K ! a : FldFun, RngElt -> FldFunElt

F ! [a, b] : FldFun, RngPolElt, RngPolElt -> FldFunElt

K ! a : FldNum, RngIntElt -> FldNumElt

F ! [a_0, a_1] : FldQuad, [FldRatElt] -> FldQuadElt

Q ! [a, b] : FldRat, RngIntElt, RngIntElt -> FldRatElt

L ! Q : Lat, [ RngElt ] -> LatElt

P ! s : RngUPol, RngElt -> RngPolElt

elt< A | r_1, r_2, ..., r_n > : AlgGen, RngElt, RngElt, ..., RngElt -> AlgGenElt

elt< A | r, g > : AlgGrp, RngElt, GrpElt -> AlgGrpElt

elt< R | L > : AlgMat, RngElt -> AlgMatElt

elt<F | a> : FldFin, RngElt -> FldFinElt

elt<R | a> : FldLoc, RngElt -> FldLocElt

elt<R | m, n> : FldRe, FldReElt, RngIntElt -> FldReElt

elt< G | L > : Grp, List(Elt) -> GrpElt

elt< G | L > : GrpMat, List(RngElt) -> GrpMatElt

elt< G | L > : GrpPerm, List(Elt) -> GrpPermElt

elt< B | a, b, c> : MagForm, RngIntElt, RngIntElt, RngIntElt -> MagFormElt

elt<V | L> : ModTupFld, List -> ModTupFldElt

elt< M | a_1, ..., a_n > : ModTupRng, List -> ModTupRngElt

elt< R | a_1, ..., a_k :parameters> : AlgChtr, FldCycElt, ..., FldCycElt -> AlgChtrElt

elt< Z | a_1a_2...a_r > : RngInt, RngIntElt -> RngIntElt

elt< R | v, [ a_1, ..., a_d], p > : RngIntElt, SeqEnum, RngIntElt -> RngPowSerElt

elt< R | k > : RngIntRes, RngIntElt -> RngIntResElt

elt< R | a > : RngMPol, RngElt -> RngMPolElt

elt< P | a_0, ..., a_d > : RngUPol, RngElt, ..., RngElt -> RngUPolElt

elt< C | a_1, a_2, ..., a_k > : SetCart, Elt, ..., Elt -> Tup

elt-ops

Operations on Elements (GROUP ALGEBRAS)

elt-other

Other Point and Line Functions (FINITE PLANES)

Plane_elt-other (Example H57E9)

Eltseq

Coefficients(a) : FldLocElt -> [ RngResElt ]

Coefficients(f) : RngPowSerElt -> [ RngElt ]

Coefficients(p) : RngUPolElt -> [ RngElt ]

ElementToSequence(a) : AlgGenElt -> SeqEnum

ElementToSequence(a) : AlgGrpElt -> SeqEnum

ElementToSequence(a) : AlgMatElt -> [ RngElt ]

ElementToSequence(a) : FldFinElt -> [ FldFinElt ]

ElementToSequence(a) : FldNumElt -> [ FldRatElt ]

ElementToSequence(x) : GrpAbElt -> [RngIntElt]

ElementToSequence(u) : GrpFPElt -> [ RngIntElt ]

ElementToSequence(g) : GrpMatElt -> [ RngElt ]

ElementToSequence(x) : GrpPCElt -> [RngIntElt]

ElementToSequence(x) : GrpPCElt -> [RngIntElt]

ElementToSequence(g) : GrpPermElt -> [ Elt ]

ElementToSequence(v) : LatElt -> [ RngElt ]

ElementToSequence(a) : ModMatRngElt -> [ RngElt ]

ElementToSequence(u) : ModTupFldElt -> [RngElt]

ElementToSequence(u) : ModTupRngElt -> [RngElt]

ElementToSequence(p) : PlanePt -> [ FldFinElt ]

ElementToSequence(a) : RngFunOrdElt -> [ RngElt ]

ElementToSequence(u) : SgpFPElt -> [ SgpFPElt ]

Eltseq(a) : FldCycElt -> [ FldRatElt ]

Eltseq(a) : FldQuadElt -> [ FldRatElt ]

Eltseq(f) : ModMPolElt -> [ RngMPolElt ]

Eltseq(f) : RngIntEltFact -> SeqEnum

Eltseq(R) : SeqEnum -> SeqEnum

aInvariants(E) : CurveEll -> [ RngElt ]

Emacs

Key Bindings (Emacs and VI mode) (ENVIRONMENT AND OPTIONS)

Key Bindings in Emacs mode only (ENVIRONMENT AND OPTIONS)

email

Magma Updates (OVERVIEW)

Embed

Embed(E, F) : FldFin, FldFin ->

embedding

Creating Relations (FINITE FIELDS)

Plane_embedding (Example H57E7)

empty

Sequences (OVERVIEW)

Sets (OVERVIEW)

EmptyDigraph

EmptyDigraph(p) : RngIntElt -> GrphDir

EmptyGraph

EmptyGraph(p) : RngIntElt -> GrphUnd

end

Control-C key (OVERVIEW)

Quitting (OVERVIEW)

endo

Endomorphisms (LATTICES)

endo-hom

Endomorphisms (LATTICES)

endomorphism_ring

The endomorphism ring (ELLIPTIC CURVES)

EndomorphismAlgebra

EndomorphismAlgebra(M) : ModRng -> AlgMat

EndomorphismAlgebra(M) : ModTupRng -> AlgMat

EndomorphismRing

EndomorphismRing(G) : GrpMat -> AlgMat

Endomorphisms

Endomorphisms(G, n) : GrpMat, RngIntElt -> [ AlgMatElt ]

EndoRing

RMod_EndoRing (Example H42E20)

EndVertices

EndVertices(e) : GrphEdge -> [GrphVert]

EndVertices(e) : GrphEdge -> { GrphVert }

enum

ENUMERATIVE COMBINATORICS

enum-comb

ENUMERATIVE COMBINATORICS

enumerated

Enumerated Sequences (SEQUENCES)

Enumerated Sets (SETS)

Sequences (OVERVIEW)

Sets (OVERVIEW)

The Enumerated Sequence Constructor (SEQUENCES)

The Enumerated Set Constructor (SETS)

enumeration

Minimum and Enumeration of Lattice Elements (LATTICES)

Vector Enumeration (FINITELY PRESENTED ALGEBRAS)

Vector Enumeration (FINITELY PRESENTED ALGEBRAS)

enumerator

The Weight Enumerator (ERROR-CORRECTING CODES)

environment

ENVIRONMENT AND OPTIONS

Environment Variables (ENVIRONMENT AND OPTIONS)

environment-options

ENVIRONMENT AND OPTIONS

environment-variable

Environment Variables (ENVIRONMENT AND OPTIONS)

eq

Comparison (OVERVIEW)

u eq v : AlgFPElt, AlgFPElt -> BoolElt

A eq B : AlgGen, AlgGen -> BoolElt

a eq b : AlgGenElt, AlgGenElt -> BoolElt

R eq T : AlgMat, AlgMat -> BoolElt

a eq b : AlgMatElt, AlgMatElt -> BoolElt

C eq D : Code, Code -> BoolElt

E eq F : CurveEll, CurveEll -> BoolElt

P eq Q : CurveEllPt, CurveEllPt -> BoolElt

C_1 eq C_2 : Elt, Elt -> BoolElt

x eq y : Elt, Elt -> BoolElt

x eq y : Elt, Elt -> BoolElt

[Future release] C_1 eq C_2 : Elt, Elt -> BoolElt

G eq H : GrpAb, GrpAb -> BoolElt

u eq v : GrpAbElt, GrpAbElt -> BoolElt

u eq v : GrpBBElt, GrpBBElt -> BoolElt

g eq h : GrpElt, GrpElt -> BoolElt

H eq G : GrpFin, GrpFin -> BoolElt

H eq K : GrpFP, GrpFP -> BoolElt

C1 eq C2 : GrpFPCosElt, GrpFPCosElt -> BoolElt

u eq v : GrpFPElt, GrpFPElt -> BoolElt

G eq H : GrphDir, GrphDir -> BoolElt

s eq t : GrphVert, GrphVert -> BoolElt

H eq G : GrpMat, GrpMat -> BoolElt

g eq h : GrpMatElt, GrpMatElt -> BoolElt

G eq H : GrpPC, GrpPC -> BoolElt

g eq h : GrpPCElt, GrpPCElt -> BoolElt

H eq G : GrpPerm, GrpPerm -> BoolElt

g eq h : GrpPermElt, GrpPermElt -> BoolElt

D eq E : Inc, Inc -> BoolElt

h eq k : KodSym, KodSym -> BoolElt

v eq w : LatElt, LatElt -> BoolElt

M eq N : ModMPol, ModMPol -> BoolElt

f eq g : ModMPolElt, ModMPolElt -> BoolElt

U eq V : ModTupFld, ModTupFld -> BoolElt

N eq M : ModTupRng, ModTupRng -> BoolElt

s eq t : MonStgElt, MonStgElt -> BoolElt

P eq Q : Plane, Plane -> BoolElt

l eq m : PlaneLn, PlaneLn -> BoolElt

p eq q : PlanePt, PlanePt -> BoolElt

R eq S : Rng, Rng -> BoolElt

R eq S : Rng, Rng -> Rng

a eq b : RngElt, RngElt -> BoolElt

I eq J : RngIdl, RngIdl -> BoolElt

I eq J : RngMPol, RngMPol -> BoolElt

I eq J : RngMPolRes, RngMPolRes -> BoolElt

N eq O : RngOrg, RngOrd -> Boolelt

S eq T : SeqEnum, SeqEnum -> BoolElt

R eq S : Set, Set -> BoolElt

u eq v : SgpFPElt, SgpFPElt -> BoolElt

e eq f : SubGrpLatElt, SubGrpLatElt -> SubGrpLatElt

e eq f : SubModLatElt, SubModLatElt -> SubModLatElt

T eq U : Tup, Tup -> BoolElt

equal

Comparison (OVERVIEW)

Equality

State_Equality (Example H1E7)

equality

Comparison (OVERVIEW)

Equality (LOCAL FIELDS)

Equality (POWER SERIES AND LAURENT SERIES)

Equality and Membership (CYCLOTOMIC FIELDS)

Equality and Membership (FUNCTION FIELDS AND THEIR ORDERS)

Equality and Membership (MULTIVARIATE POLYNOMIAL RINGS)

Equality and Membership (NUMBER FIELDS AND THEIR ORDERS)

Equality and Membership (POWER SERIES AND LAURENT SERIES)

Equality and Membership (QUADRATIC FIELDS)

Equality and Membership (RATIONAL FUNCTION FIELDS)

Equality and Membership (UNIVARIATE POLYNOMIAL RINGS)

Equality and Membership (VALUATION RINGS)

Equality Operators (STATEMENTS AND EXPRESSIONS)

Identity and Isomorphism (FINITE PLANES)

Identity and Isomorphism (INCIDENCE STRUCTURES AND DESIGNS)

equality-membership

Equality and Membership (CYCLOTOMIC FIELDS)

Equality and Membership (FUNCTION FIELDS AND THEIR ORDERS)

Equality and Membership (MULTIVARIATE POLYNOMIAL RINGS)

Equality and Membership (NUMBER FIELDS AND THEIR ORDERS)

Equality and Membership (POWER SERIES AND LAURENT SERIES)

Equality and Membership (QUADRATIC FIELDS)

Equality and Membership (RATIONAL FUNCTION FIELDS)

Equality and Membership (UNIVARIATE POLYNOMIAL RINGS)

Equality and Membership (VALUATION RINGS)

equality-operators

Equality Operators (STATEMENTS AND EXPRESSIONS)

equals

Comparison (OVERVIEW)

equation

Solution of a System of Linear Equations (VECTOR SPACES)

Solutions of Systems of Linear Equations (MATRIX ALGEBRAS)

Solutions of Systems of Linear Equations (THE MODULES Hom_(R)(M, N) AND End(M))

Solving equations (NUMBER FIELDS AND THEIR ORDERS)

Solving Linear Equations in Z/mZ (RESIDUE CLASS RINGS)

The Solution of Modular Equations (RING OF INTEGERS)

EquationOrder

EquationOrder(F) : FldQuad -> RngQuad

EquationOrder(f) : RngUPolElt -> RngOrd

EquationOrderFinite

EquationOrderFinite(F) : FldFun -> RngFunOrd

EquationOrderInfinite

EquationOrderInfinite(F) : FldFun -> RngFunOrd

EquitablePartition

EquitablePartition(P, G) : { { GrphVert } }, GrphUnd -> { { GrphVert } }

equivalent

Writing Representations over Smaller Fields (MATRIX GROUPS)

equivalent-rep

Writing Representations over Smaller Fields (MATRIX GROUPS)

Erf

ErrorFunction(r) : FldReElt -> FldReElt

Erfc

ComplementaryErrorFunction(r) : FldReElt -> FldReElt

error

Combinatorial and Geometrical Structures (OVERVIEW)

error statement (OVERVIEW)

ERROR-CORRECTING CODES

Possibility of Errors in Database of Groups of Order Dividing 256 (OVERVIEW)

Possibility of Errors in Database of Groups of Order Dividing 729 (OVERVIEW)

error expression, ..., expression;

error-correcting-linear-code

ERROR-CORRECTING CODES

error-if

error if boolexpr, expression, ..., expression;

ErrorFunction

ErrorFunction(r) : FldReElt -> FldReElt

errors

Error Checking and Assertions (STATEMENTS AND EXPRESSIONS)

escape

Performing shell commands from Magma (OVERVIEW)

Eta

Eta(A) : AlgGrp -> AlgGrpElt

Euclidean

Canonical Forms for Matrices over Euclidean Domains (MATRIX ALGEBRAS)

Euclidean-domain

Canonical Forms for Matrices over Euclidean Domains (MATRIX ALGEBRAS)

EuclideanNorm

EuclideanNorm(n) : RngIntElt -> RngIntElt

EuclideanNorm(p) : RngUPol -> RngIntElt

EuclideanNorm(v) : RngValElt -> RngIntElt

EulerGamma

EulerGamma(R) : FldPr -> FldPrElt

EulerianCircuit

[Future release] EulerianCircuit(G) : GrphUnd -> [GrphVert]

EulerianNumber

EulerianNumber(n, r) : RngIntElt, RngIntElt -> RngIntElt

EulerPhi

EulerPhi(n) : RngIntElt -> RngIntElt

Evaluate

Evaluate(f, r) : FldFunUElt, RngElt -> FldFunUElt

Evaluate(f, s) : RngMPolElt, [ RngElt ] -> RngElt

Evaluate(f, s) : RngSerElt, RngElt -> RngElt

Evaluate(p, r) : RngUPolElt, RngElt -> RngElt

evaluate

Evaluation (RATIONAL FUNCTION FIELDS)

Expression (OVERVIEW)

evaluation

Evaluation and Derivative (POWER SERIES AND LAURENT SERIES)

Evaluation in Magma (MAGMA SEMANTICS)

Evaluation, Interpolation (MULTIVARIATE POLYNOMIAL RINGS)

Evaluation, Interpolation (UNIVARIATE POLYNOMIAL RINGS)

Expression (OVERVIEW)

The Evaluation Process Revisited (MAGMA SEMANTICS)

evaluation-derivative

Evaluation and Derivative (POWER SERIES AND LAURENT SERIES)

evaluation-interpolation

Evaluation, Interpolation (MULTIVARIATE POLYNOMIAL RINGS)

EvenWeightCode

EvenWeightCode(n) : RngIntElt -> Code

ExactQuotient

ExactQuotient(n, d) : RngIntElt, RngIntElt -> RngIntElt

ExactQuotient(f, g) : RngUPolElt, RngUPolElt -> RngUPolElt

f div g : RngMPolElt, RngMPolElt -> RngMPolElt

example

Example (OVERVIEW)

Example for Database of Groups of Order Dividing 256 (OVERVIEW)

Example for Database of Groups of Order Dividing 729 (OVERVIEW)

AlgAss_liealg (Example H48E1)

AlgCon_cayley (Example H47E2)

AlgCon_jordan (Example H47E1)

AlgFP_Abstract (Example H52E2)

AlgFP_FreeAlgebra (Example H52E1)

AlgFP_PermutationActionD8 (Example H52E3)

AlgFP_Quotient (Example H52E4)

AlgGen_quaternions (Example H46E1)

AlgGrp_average (Example H50E6)

AlgGrp_creation (Example H50E1)

AlgGrp_el-creation (Example H50E2)

AlgGrp_jacobson (Example H50E4)

AlgGrp_powering (Example H50E5)

AlgGrp_wedderburn (Example H50E3)

AlgLie_CartanSubalgebra (Example H49E4)

AlgLie_DirectSumDecomposition (Example H49E6)

AlgLie_LieAlgebra (Example H49E11)

AlgLie_NonNilpotentElement (Example H49E10)

AlgLie_Operations (Example H49E3)

AlgLie_Other (Example H49E9)

AlgLie_Predicates (Example H49E7)

AlgLie_RootSystem (Example H49E2)

AlgLie_SemiSimpleType (Example H49E8)

AlgLie_Series (Example H49E5)

AlgLie_SimpleLieAlgebra (Example H49E1)

AlgMat_Cambridge (Example H51E2)

AlgMat_CanonicalForms (Example H51E8)

AlgMat_Creation (Example H51E1)

AlgMat_EchelonForm (Example H51E6)

AlgMat_ElementaryDivisors (Example H51E7)

AlgMat_Invariants (Example H51E3)

AlgMat_Products (Example H51E5)

AlgMat_SubAlgebra (Example H51E4)

Chtr_A5 (Example H22E1)

Code_AlternantCode (Example H58E7)

Code_AutomorphismGroup (Example H58E20)

Code_BCHCode (Example H58E8)

Code_CodeFromMatrix (Example H58E2)

Code_CosetLeaders (Example H58E13)

Code_CyclicCode (Example H58E6)

Code_Decode (Example H58E18)

Code_Distance (Example H58E12)

Code_GRSCode (Example H58E10)

Code_GoppaCode (Example H58E9)

Code_HammingCode (Example H58E4)

Code_MattsonSolomonTransform (Example H58E19)

Code_PermutationCode (Example H58E3)

Code_QuadraticResidueCode (Example H58E11)

Code_ReedMullerCode (Example H58E5)

Code_StandardForm (Example H58E14)

Code_TernaryGolayCode (Example H58E1)

Code_WeightDistribution (Example H58E16)

Code_WeightEnumerator (Example H58E17)

Code_Words (Example H58E15)

Coproduct_cop (Example H11E1)

Design_Constructors (Example H56E1)

Design_DevelopDifferenceSet (Example H56E6)

Design_auto (Example H56E10)

Design_automorphism (Example H56E11)

Design_conv (Example H56E9)

Design_design-invar (Example H56E7)

Design_graphs (Example H56E12)

Design_hadamard (Example H56E5)

Design_points-blocks (Example H56E2)

Design_pts-blks-ops (Example H56E8)

Design_related (Example H56E3)

Design_wittex (Example H56E4)

Elcu_BaseExtend (Example H53E3)

Elcu_Creation (Example H53E1)

Elcu_DivisionPolynomial (Example H53E5)

Elcu_DualIsogeny (Example H53E18)

Elcu_Frobenius (Example H53E17)

Elcu_FunctionField (Example H53E2)

Elcu_GenericPoint (Example H53E9)

Elcu_Invariants (Example H53E6)

Elcu_Isogeny (Example H53E14)

Elcu_Isomorphism (Example H53E15)

Elcu_IsomorphismClasses (Example H53E8)

Elcu_Kodaira (Example H53E12)

Elcu_Map (Example H53E16)

Elcu_Models (Example H53E4)

Elcu_MordellWeil (Example H53E7)

Elcu_Order (Example H53E10)

Elcu_PlayWithPoints (Example H53E11)

Elcu_Trace (Example H53E13)

EnumComb_OddGraph (Example H54E1)

EnumComb_Partitions (Example H54E2)

EnumComb_RestrictedPartitions (Example H54E3)

Env_Startup (Example H4E1)

FldCyc_GaussianPeriods (Example H35E1)

FldFin_Extensions (Example H27E1)

FldFin_Functions (Example H27E3)

FldFin_VectorSpace (Example H27E2)

FldFunG_Creation (Example H32E1)

FldFunG_Elements (Example H32E3)

FldFunG_Ideals (Example H32E4)

FldFunG_Orders (Example H32E2)

FldFun_FunctionField (Example H31E2)

FldFun_Homomorphism (Example H31E1)

FldFun_PartialFractionDecomposition (Example H31E3)

FldLoc_Creation (Example H39E1)

FldNum_Bases (Example H36E9)

FldNum_BetterPoly (Example H36E4)

FldNum_Compositum (Example H36E3)

FldNum_Creation (Example H36E2)

FldNum_Discriminant (Example H36E12)

FldNum_Elements (Example H36E7)

FldNum_Homomorphisms (Example H36E1)

FldNum_IdealFactorization (Example H36E14)

FldNum_Ideals (Example H36E8)

FldNum_MultiplicationTable (Example H36E10)

FldNum_NormsEtc (Example H36E13)

FldNum_Orders (Example H36E5)

FldNum_Round2 (Example H36E6)

FldNum_UnitGroup (Example H36E11)

FldQuad_Forms (Example H34E4)

FldQuad_Represent (Example H34E5)

FldQuad_creation (Example H34E2)

FldQuad_hom (Example H34E1)

FldQuad_norm-equation (Example H34E3)

FldRat_Coercion (Example H26E1)

FldRat_homomorphism (Example H26E2)

FldRat_numerator (Example H26E3)

FldRe_CreateComplexField (Example H37E3)

FldRe_CreateElements (Example H37E4)

FldRe_FixedPrecision (Example H37E1)

FldRe_Homomorphisms (Example H37E2)

FldRe_Integral (Example H37E7)

FldRe_Roots (Example H37E5)

FldRe_RootsNonExact (Example H37E6)

Func_InteractiveUserAttributes (Example H2E11)

Func_InteractiveUserAttributes (Example H2E12)

Func_Parameters (Example H2E2)

Func_Procedures (Example H2E3)

Func_Recursion (Example H2E1)

Func_SystemAttributes (Example H2E10)

Func_forward (Example H2E4)

Func_import (Example H2E6)

Func_intrinsic (Example H2E5)

Func_require (Example H2E7)

Func_spec (Example H2E8)

Func_startup-spec (Example H2E9)

Graph_AutomorphismAction (Example H55E13)

Graph_AutomorphismGroup (Example H55E14)

Graph_CayleyGraph (Example H55E8)

Graph_ChromaticNumber (Example H55E12)

Graph_Constructors (Example H55E1)

Graph_Constructors (Example H55E3)

Graph_Constructors (Example H55E4)

Graph_Constructors (Example H55E5)

Graph_EdgeSets (Example H55E6)

Graph_Grotzch (Example H55E11)

Graph_Labels (Example H55E7)

Graph_Labels (Example H55E9)

Graph_Quotient (Example H55E10)

Graph_TutteCage (Example H55E2)

GrpAb_AbelianGroup (Example H18E3)

GrpAb_FreeAbelianGroup (Example H18E1)

GrpAb_Relations (Example H18E2)

GrpBB_BlackboxGroup (Example H17E1)

GrpBB_ConstructingHomomorphisms (Example H17E2)

GrpBB_HomomorphismSpeed (Example H17E3)

GrpFP_BuildSubgroups (Example H16E20)

GrpFP_Co1 (Example H16E24)

GrpFP_ControlExtn (Example H16E11)

GrpFP_Coxeter (Example H16E8)

GrpFP_DerSub (Example H16E22)

GrpFP_DirectProduct (Example H16E12)

GrpFP_ExcludedConjugates (Example H16E23)

GrpFP_F27 (Example H16E26)

GrpFP_F276 (Example H16E36)

GrpFP_F29 (Example H16E37)

GrpFP_Family (Example H16E18)

GrpFP_Free (Example H16E1)

GrpFP_G23 (Example H16E25)

GrpFP_G8723 (Example H16E16)

GrpFP_HN (Example H16E17)

GrpFP_Lix1 (Example H16E38)

GrpFP_Lix2 (Example H16E39)

GrpFP_Lix3 (Example H16E40)

GrpFP_Lix4 (Example H16E41)

GrpFP_Modular (Example H16E7)

GrpFP_Relations (Example H16E2)

GrpFP_Replace (Example H16E9)

GrpFP_Rewrite (Example H16E35)

GrpFP_SubgroupOps (Example H16E19)

GrpFP_Subgroups1 (Example H16E14)

GrpFP_Subgroups2 (Example H16E15)

GrpFP_Sym8 (Example H16E10)

GrpFP_Symmetric1 (Example H16E3)

GrpFP_Symmetric2 (Example H16E4)

GrpFP_Tetrahedral (Example H16E5)

GrpFP_ThreeInvols (Example H16E6)

GrpFP_ToddCoxeter (Example H16E21)

GrpFP_WordOps (Example H16E13)

GrpFP_pQuotient1 (Example H16E27)

GrpFP_pQuotient2 (Example H16E28)

GrpFP_pQuotient3 (Example H16E29)

GrpFP_pQuotient4 (Example H16E30)

GrpFP_pQuotient5 (Example H16E31)

GrpFP_pQuotient6 (Example H16E32)

GrpFP_pQuotient7 (Example H16E33)

GrpFP_pQuotient8 (Example H16E34)

GrpMat_Actions (Example H21E15)

GrpMat_Arithmetic (Example H21E3)

GrpMat_Constructions (Example H21E11)

GrpMat_Constructor (Example H21E5)

GrpMat_CosetAction (Example H21E16)

GrpMat_Create (Example H21E1)

GrpMat_Decompose (Example H21E21)

GrpMat_ExtraSpecial (Example H21E22)

GrpMat_GLSylow (Example H21E6)

GrpMat_Invariants (Example H21E4)

GrpMat_IsOverSmallerField (Example H21E24)

GrpMat_IsPrimitive (Example H21E18)

GrpMat_Matrices (Example H21E2)

GrpMat_Orbits (Example H21E14)

GrpMat_Order (Example H21E12)

GrpMat_Quotient (Example H21E8)

GrpMat_Random (Example H21E13)

GrpMat_Semilinearity (Example H21E19)

GrpMat_Series (Example H21E17)

GrpMat_Subgroups (Example H21E7)

GrpMat_Suzuki (Example H21E10)

GrpMat_SymmetricTensor (Example H21E23)

GrpMat_Symplectic (Example H21E9)

GrpMat_Tensor (Example H21E20)

GrpMat_WriteOverSmallerField (Example H21E25)

GrpPC_CompactPresentation (Example H19E13)

GrpPC_DefiningAutomorphisms (Example H19E9)

GrpPC_EAS (Example H19E5)

GrpPC_GeneratepGroups (Example H19E10)

GrpPC_Hall (Example H19E4)

GrpPC_Interactive (Example H19E7)

GrpPC_IsGood (Example H19E11)

GrpPC_PolycyclicGroup (Example H19E1)

GrpPC_PowerGroup (Example H19E8)

GrpPC_PowerGroupTwo (Example H19E12)

GrpPC_Set (Example H19E3)

GrpPC_Standard (Example H19E2)

GrpPC_StandardPresentation (Example H19E6)

GrpPerm_Actions (Example H20E13)

GrpPerm_Arithmetic (Example H20E3)

GrpPerm_BSGS (Example H20E23)

GrpPerm_BasicAccess (Example H20E9)

GrpPerm_BlocksActions (Example H20E15)

GrpPerm_Classes (Example H20E20)

GrpPerm_CompFactors (Example H20E19)

GrpPerm_Constructors (Example H20E5)

GrpPerm_Extensions (Example H20E8)

GrpPerm_Hessian (Example H20E4)

GrpPerm_OrbitActions (Example H20E14)

GrpPerm_Order (Example H20E10)

GrpPerm_Permutations (Example H20E2)

GrpPerm_PrimitiveStructure (Example H20E18)

GrpPerm_Quotient (Example H20E6)

GrpPerm_RandomSchreier (Example H20E24)

GrpPerm_Series (Example H20E17)

GrpPerm_SetOperations (Example H20E11)

GrpPerm_Stabilizers (Example H20E12)

GrpPerm_StandardGroups (Example H20E7)

GrpPerm_SubgroupConstructions (Example H20E16)

GrpPerm_Sym (Example H20E1)

GrpPerm_Transitive (Example H20E21)

GrpPerm_TransitiveProcess (Example H20E22)

Grp_Arithmetic (Example H15E2)

Grp_Classes (Example H15E13)

Grp_CosetAction (Example H15E8)

Grp_CreateSubgroupPoset (Example H15E15)

Grp_Extensions (Example H15E7)

Grp_FPGroup (Example H15E9)

Grp_Generators (Example H15E10)

Grp_GroupConstructors (Example H15E3)

Grp_Homomorphisms (Example H15E1)

Grp_LatticeOperations (Example H15E16)

Grp_Modules (Example H15E17)

Grp_Order (Example H15E11)

Grp_Quotient (Example H15E5)

Grp_SetOperations (Example H15E12)

Grp_StandardGroups (Example H15E6)

Grp_Subgroup (Example H15E4)

Grp_Subgroups (Example H15E14)

HMod_Create (Example H43E1)

HMod_CreateHom (Example H43E2)

HMod_CreateHomGHom (Example H43E3)

HMod_Forms1 (Example H43E10)

HMod_Forms2 (Example H43E11)

HMod_Indexing (Example H43E8)

HMod_Matrix (Example H43E6)

HMod_Operations (Example H43E7)

HMod_Reduce (Example H43E4)

HMod_ReduceHom (Example H43E5)

HMod_RowOps (Example H43E9)

IO_GetTime (Example H3E10)

IO_LineCount (Example H3E9)

IO_Read (Example H3E11)

IO_Regexp (Example H3E3)

IO_Split (Example H3E2)

IO_Sprintf (Example H3E8)

IO_Strings (Example H3E1)

IO_auto-print (Example H3E7)

IO_printf (Example H3E4)

IO_printf (Example H3E6)

IO_printf2 (Example H3E5)

KMod_Arithmetic (Example H41E5)

KMod_Basis (Example H41E12)

KMod_CreateK35 (Example H41E2)

KMod_CreateQ6 (Example H41E1)

KMod_Indexing (Example H41E6)

KMod_LinearTrans (Example H41E13)

KMod_Matrices (Example H41E4)

KMod_Quotients1 (Example H41E9)

KMod_Quotients2 (Example H41E10)

KMod_Quotients3 (Example H41E11)

KMod_Rowops (Example H41E14)

KMod_Subspace1 (Example H41E7)

KMod_Subspace2 (Example H41E8)

KMod_Vectors (Example H41E3)

Lat_AutoAction (Example H45E16)

Lat_AutoDepth (Example H45E18)

Lat_AutoStabilizers (Example H45E17)

Lat_Closest (Example H45E8)

Lat_Code (Example H45E2)

Lat_Isom (Example H45E19)

Lat_Knapsack (Example H45E9)

Lat_LLLXGCD (Example H45E13)

Lat_LatticeCreate (Example H45E1)

Lat_LatticeFunctions (Example H45E4)

Lat_Leech (Example H45E7)

Lat_Neighbour (Example H45E20)

Lat_Neighbour (Example H45E6)

Lat_OrderLattice (Example H45E3)

Lat_Orthogonalize (Example H45E15)

Lat_PositiveDefiniteForm (Example H45E21)

Lat_Seysen (Example H45E14)

Lat_SingularElements (Example H45E10)

Lat_SubSuperQuo (Example H45E5)

Lat_Sublattices (Example H45E22)

Lat_ThetaSeries (Example H45E11)

Lat_Voronoi (Example H45E12)

PMod_Create (Example H44E1)

PMod_Element (Example H44E2)

PMod_FreeResolution (Example H44E6)

PMod_Hilbert (Example H44E4)

PMod_Hilbert (Example H44E5)

PMod_SubQuo (Example H44E3)

Plane_Collineation (Example H57E13)

Plane_CollineationGSet (Example H57E12)

Plane_Constructors (Example H57E1)

Plane_arcs (Example H57E10)

Plane_baer (Example H57E14)

Plane_cent-coll (Example H57E15)

Plane_codes (Example H57E18)

Plane_decon (Example H57E8)

Plane_designs (Example H57E17)

Plane_elt-other (Example H57E9)

Plane_embedding (Example H57E7)

Plane_invar (Example H57E6)

Plane_points-lines (Example H57E2)

Plane_sub (Example H57E4)

Plane_sub (Example H57E5)

Plane_supp (Example H57E3)

Plane_trans (Example H57E16)

Plane_unital (Example H57E11)

RMod_Access (Example H42E9)

RMod_CompSeries (Example H42E18)

RMod_Constructions (Example H42E11)

RMod_CreateA4wrC3 (Example H42E7)

RMod_CreateA7 (Example H42E5)

RMod_CreateK6 (Example H42E2)

RMod_CreateL27 (Example H42E3)

RMod_CreateLattice (Example H42E21)

RMod_CreateM11 (Example H42E6)

RMod_CreateM12 (Example H42E4)

RMod_CreateMatrices (Example H42E8)

RMod_CreateZ6 (Example H42E1)

RMod_Dual (Example H42E10)

RMod_Elements (Example H42E14)

RMod_EndoRing (Example H42E20)

RMod_GModules1 (Example H42E12)

RMod_GModules2 (Example H42E13)

RMod_LatticeOps (Example H42E22)

RMod_Meataxe (Example H42E17)

RMod_Minimals (Example H42E19)

RMod_Operations (Example H42E15)

RMod_Submodule (Example H42E16)

Rec_Record (Example H12E2)

Rec_RecordAccess (Example H12E3)

Rec_RecordFormat (Example H12E1)

RngIntRes_Coercion (Example H25E1)

RngInt_Amicable (Example H24E4)

RngInt_Integers (Example H24E2)

RngInt_IsPrime (Example H24E3)

RngInt_Perfect (Example H24E6)

RngInt_RepUnits (Example H24E5)

RngInt_hom (Example H24E1)

RngInt_norm-equation (Example H24E7)

RngInvar_AdemMilgram (Example H30E6)

RngInvar_Attributes (Example H30E15)

RngInvar_Depth (Example H30E11)

RngInvar_FundamentalInvariants (Example H30E8)

RngInvar_GModule (Example H30E2)

RngInvar_GroupActions (Example H30E1)

RngInvar_HomogeneousModuleTest2 (Example H30E14)

RngInvar_InvariantsOfDegree (Example H30E3)

RngInvar_InvariantsOfDegree (Example H30E4)

RngInvar_MinimalAlgebraGenerators (Example H30E13)

RngInvar_Module (Example H30E9)

RngInvar_MolienSeries (Example H30E5)

RngInvar_Relations (Example H30E10)

RngInvar_SecondaryInvariants (Example H30E7)

RngInvar_SteenrodOperation (Example H30E12)

RngMPol_AssignNames (Example H29E2)

RngMPol_ChangeOrder (Example H29E21)

RngMPol_ChangeRing (Example H29E20)

RngMPol_Coefficients (Example H29E4)

RngMPol_Coordinates (Example H29E13)

RngMPol_Cyclic6 (Example H29E10)

RngMPol_ElementOperations (Example H29E15)

RngMPol_EliminationIdeal (Example H29E17)

RngMPol_FiniteFieldFactorization (Example H29E9)

RngMPol_Graded (Example H29E24)

RngMPol_GroebnerWalk (Example H29E12)

RngMPol_Heron (Example H29E8)

RngMPol_Hilbert (Example H29E25)

RngMPol_HilbertGroebner (Example H29E26)

RngMPol_HomogeneousModuleTest1 (Example H29E31)

RngMPol_Homomorphism (Example H29E1)

RngMPol_IdealArithmetic (Example H29E14)

RngMPol_Interpolate (Example H29E5)

RngMPol_IsSymmetric (Example H29E30)

RngMPol_Map1 (Example H29E29)

RngMPol_MinimalPolynomial (Example H29E28)

RngMPol_Order (Example H29E3)

RngMPol_PrimaryDecomposition (Example H29E23)

RngMPol_Radical (Example H29E22)

RngMPol_RelationIdeal (Example H29E19)

RngMPol_RungeKutta2 (Example H29E11)

RngMPol_SyzygyModule (Example H29E27)

RngMPol_Trinomials (Example H29E6)

RngMPol_Vandermonde (Example H29E7)

RngMPol_Variety (Example H29E16)

RngMPol_ZRadical (Example H29E18)

RngPol_ChangeRing (Example H28E3)

RngPol_Hensel (Example H28E4)

RngPol_Homomorphism (Example H28E1)

RngPol_Polynomials (Example H28E2)

Seq_EgyptianFractions (Example H8E4)

Seq_Farey (Example H8E3)

Seq_NestedIteration (Example H8E6)

Seq_PowerSequence (Example H8E2)

Seq_Progression (Example H8E1)

Seq_Self (Example H8E5)

Set_AlmostFermat (Example H7E2)

Set_AlmostFermatIndexed (Example H7E3)

Set_Exists (Example H7E12)

Set_ExtractRep (Example H7E9)

Set_Include (Example H7E10)

Set_Join (Example H7E11)

Set_Miscellaneous (Example H7E7)

Set_Multiset (Example H7E4)

Set_NestedExists (Example H7E13)

Set_PowerSet (Example H7E6)

Set_Progression (Example H7E5)

Set_Random (Example H7E8)

Set_Reduction (Example H7E14)

Set_Universe (Example H7E1)

SgpFP_FreeSemigroup (Example H14E1)

SgpFP_Monoid (Example H14E2)

State_Booleans (Example H1E8)

State_Equality (Example H1E7)

State_GeneratorNaming (Example H1E5)

State_GeneratorNamingSequence (Example H1E4)

State_Identifiers (Example H1E1)

State_InLineConditional (Example H1E11)

State_Indexing (Example H1E3)

State_MultipleReturns (Example H1E2)

State_MutationAssignment (Example H1E6)

State_Time (Example H1E17)

State_Various (Example H1E16)

State_break (Example H1E15)

State_case (Example H1E12)

State_if (Example H1E10)

State_repeat (Example H1E14)

State_where (Example H1E9)

State_while (Example H1E13)

Tup_CartesianProduct (Example H9E1)

Tup_Tuple (Example H9E2)

Tup_TupleAccess (Example H9E3)

Example-A5

Chtr_A5 (Example H22E1)

Example-AbelianGroup

GrpAb_AbelianGroup (Example H18E3)

Example-Abstract

AlgFP_Abstract (Example H52E2)

Example-Access

RMod_Access (Example H42E9)

Example-Actions

GrpMat_Actions (Example H21E15)

GrpPerm_Actions (Example H20E13)

Example-AdemMilgram

RngInvar_AdemMilgram (Example H30E6)

Example-AlmostFermat

Set_AlmostFermat (Example H7E2)

Example-AlmostFermatIndexed

Set_AlmostFermatIndexed (Example H7E3)

Example-AlternantCode

Code_AlternantCode (Example H58E7)

Example-Amicable

RngInt_Amicable (Example H24E4)

Example-arcs

Plane_arcs (Example H57E10)

Example-Arithmetic

GrpMat_Arithmetic (Example H21E3)

GrpPerm_Arithmetic (Example H20E3)

Grp_Arithmetic (Example H15E2)

KMod_Arithmetic (Example H41E5)

Example-AssignNames

RngMPol_AssignNames (Example H29E2)

Example-Attributes

RngInvar_Attributes (Example H30E15)

Example-auto

Design_auto (Example H56E10)

Example-auto-print

IO_auto-print (Example H3E7)

Example-AutoAction

Lat_AutoAction (Example H45E16)

Example-AutoDepth

Lat_AutoDepth (Example H45E18)

Example-automorphism

Design_automorphism (Example H56E11)

Example-AutomorphismAction

Graph_AutomorphismAction (Example H55E13)

Example-AutomorphismGroup

Code_AutomorphismGroup (Example H58E20)

Graph_AutomorphismGroup (Example H55E14)

Example-AutoStabilizers

Lat_AutoStabilizers (Example H45E17)

Example-average

AlgGrp_average (Example H50E6)

Example-baer

Plane_baer (Example H57E14)

Example-BaseExtend

Elcu_BaseExtend (Example H53E3)

Example-Bases

FldNum_Bases (Example H36E9)

Example-BasicAccess

GrpPerm_BasicAccess (Example H20E9)

Example-Basis

KMod_Basis (Example H41E12)

Example-BCHCode

Code_BCHCode (Example H58E8)

Example-BetterPoly

FldNum_BetterPoly (Example H36E4)

Example-BlackboxGroup

GrpBB_BlackboxGroup (Example H17E1)

Example-BlocksActions

GrpPerm_BlocksActions (Example H20E15)

Example-Booleans

State_Booleans (Example H1E8)

Example-break

State_break (Example H1E15)

Example-BSGS

GrpPerm_BSGS (Example H20E23)

Example-BuildSubgroups

GrpFP_BuildSubgroups (Example H16E20)

Example-Cambridge

AlgMat_Cambridge (Example H51E2)

Example-CanonicalForms

AlgMat_CanonicalForms (Example H51E8)

Example-CartanSubalgebra

AlgLie_CartanSubalgebra (Example H49E4)

Example-CartesianProduct

Tup_CartesianProduct (Example H9E1)

Example-case

State_case (Example H1E12)

Example-cayley

AlgCon_cayley (Example H47E2)

Example-CayleyGraph

Graph_CayleyGraph (Example H55E8)

Example-cent-coll

Plane_cent-coll (Example H57E15)

Example-ChangeOrder

RngMPol_ChangeOrder (Example H29E21)

Example-ChangeRing

RngMPol_ChangeRing (Example H29E20)

RngPol_ChangeRing (Example H28E3)

Example-ChromaticNumber

Graph_ChromaticNumber (Example H55E12)

Example-Classes

GrpPerm_Classes (Example H20E20)

Grp_Classes (Example H15E13)

Example-Closest

Lat_Closest (Example H45E8)

Example-Co1

GrpFP_Co1 (Example H16E24)

Example-Code

Lat_Code (Example H45E2)

Example-CodeFromMatrix

Code_CodeFromMatrix (Example H58E2)

Example-codes

Plane_codes (Example H57E18)

Example-Coefficients

RngMPol_Coefficients (Example H29E4)

Example-Coercion

FldRat_Coercion (Example H26E1)

RngIntRes_Coercion (Example H25E1)

Example-Collineation

Plane_Collineation (Example H57E13)

Example-CollineationGSet

Plane_CollineationGSet (Example H57E12)

Example-CompactPresentation

GrpPC_CompactPresentation (Example H19E13)

Example-CompFactors

GrpPerm_CompFactors (Example H20E19)

Example-Compositum

FldNum_Compositum (Example H36E3)

Example-CompSeries

RMod_CompSeries (Example H42E18)

Example-ConstructingHomomorphisms

GrpBB_ConstructingHomomorphisms (Example H17E2)

Example-Constructions

GrpMat_Constructions (Example H21E11)

RMod_Constructions (Example H42E11)

Example-Constructor

GrpMat_Constructor (Example H21E5)

Example-Constructors

Design_Constructors (Example H56E1)

Graph_Constructors (Example H55E1)

Graph_Constructors (Example H55E3)

Graph_Constructors (Example H55E4)

Graph_Constructors (Example H55E5)

GrpPerm_Constructors (Example H20E5)

Plane_Constructors (Example H57E1)

Example-ControlExtn

GrpFP_ControlExtn (Example H16E11)

Example-conv

Design_conv (Example H56E9)

Example-Coordinates

RngMPol_Coordinates (Example H29E13)

Example-cop

Coproduct_cop (Example H11E1)

Example-CosetAction

GrpMat_CosetAction (Example H21E16)

Grp_CosetAction (Example H15E8)

Example-CosetLeaders

Code_CosetLeaders (Example H58E13)

Example-Coxeter

GrpFP_Coxeter (Example H16E8)

Example-Create

GrpMat_Create (Example H21E1)

HMod_Create (Example H43E1)

PMod_Create (Example H44E1)

Example-CreateA4wrC3

RMod_CreateA4wrC3 (Example H42E7)

Example-CreateA7

RMod_CreateA7 (Example H42E5)

Example-CreateComplexField

FldRe_CreateComplexField (Example H37E3)

Example-CreateElements

FldRe_CreateElements (Example H37E4)

Example-CreateHom

HMod_CreateHom (Example H43E2)

Example-CreateHomGHom

HMod_CreateHomGHom (Example H43E3)

Example-CreateK35

KMod_CreateK35 (Example H41E2)

Example-CreateK6

RMod_CreateK6 (Example H42E2)

Example-CreateL27

RMod_CreateL27 (Example H42E3)

Example-CreateLattice

RMod_CreateLattice (Example H42E21)

Example-CreateM11

RMod_CreateM11 (Example H42E6)

Example-CreateM12

RMod_CreateM12 (Example H42E4)

Example-CreateMatrices

RMod_CreateMatrices (Example H42E8)

Example-CreateQ6

KMod_CreateQ6 (Example H41E1)

Example-CreateSubgroupPoset

Grp_CreateSubgroupPoset (Example H15E15)

Example-CreateZ6

RMod_CreateZ6 (Example H42E1)

Example-Creation

AlgMat_Creation (Example H51E1)

Elcu_Creation (Example H53E1)

FldFunG_Creation (Example H32E1)

FldLoc_Creation (Example H39E1)

FldNum_Creation (Example H36E2)

Example-creation

AlgGrp_creation (Example H50E1)

FldQuad_creation (Example H34E2)

Example-Cyclic6

RngMPol_Cyclic6 (Example H29E10)

Example-CyclicCode

Code_CyclicCode (Example H58E6)

Example-Decode

Code_Decode (Example H58E18)

Example-Decompose

GrpMat_Decompose (Example H21E21)

Example-decon

Plane_decon (Example H57E8)

Example-DefiningAutomorphisms

GrpPC_DefiningAutomorphisms (Example H19E9)

Example-Depth

RngInvar_Depth (Example H30E11)

Example-DerSub

GrpFP_DerSub (Example H16E22)

Example-design-invar

Design_design-invar (Example H56E7)

Example-designs

Plane_designs (Example H57E17)

Example-DevelopDifferenceSet

Design_DevelopDifferenceSet (Example H56E6)

Example-DirectProduct

GrpFP_DirectProduct (Example H16E12)

Example-DirectSumDecomposition

AlgLie_DirectSumDecomposition (Example H49E6)

Example-Discriminant

FldNum_Discriminant (Example H36E12)

Example-Distance

Code_Distance (Example H58E12)

Example-DivisionPolynomial

Elcu_DivisionPolynomial (Example H53E5)

Example-Dual

RMod_Dual (Example H42E10)

Example-DualIsogeny

Elcu_DualIsogeny (Example H53E18)

Example-EAS

GrpPC_EAS (Example H19E5)

Example-EchelonForm

AlgMat_EchelonForm (Example H51E6)

Example-EdgeSets

Graph_EdgeSets (Example H55E6)

Example-EgyptianFractions

Seq_EgyptianFractions (Example H8E4)

Example-el-creation

AlgGrp_el-creation (Example H50E2)

Example-Element

PMod_Element (Example H44E2)

Example-ElementaryDivisors

AlgMat_ElementaryDivisors (Example H51E7)

Example-ElementOperations

RngMPol_ElementOperations (Example H29E15)

Example-Elements

FldFunG_Elements (Example H32E3)

FldNum_Elements (Example H36E7)

RMod_Elements (Example H42E14)

Example-EliminationIdeal

RngMPol_EliminationIdeal (Example H29E17)

Example-elt-other

Plane_elt-other (Example H57E9)

Example-embedding

Plane_embedding (Example H57E7)

Example-EndoRing

RMod_EndoRing (Example H42E20)

Example-Equality

State_Equality (Example H1E7)

Example-ExcludedConjugates

GrpFP_ExcludedConjugates (Example H16E23)

Example-Exists

Set_Exists (Example H7E12)

Example-Extensions

FldFin_Extensions (Example H27E1)

GrpPerm_Extensions (Example H20E8)

Grp_Extensions (Example H15E7)

Example-ExtractRep

Set_ExtractRep (Example H7E9)

Example-ExtraSpecial

GrpMat_ExtraSpecial (Example H21E22)

Example-F27

GrpFP_F27 (Example H16E26)

Example-F276

GrpFP_F276 (Example H16E36)

Example-F29

GrpFP_F29 (Example H16E37)

Example-Family

GrpFP_Family (Example H16E18)

Example-Farey

Seq_Farey (Example H8E3)

Example-FiniteFieldFactorization

RngMPol_FiniteFieldFactorization (Example H29E9)

Example-FixedPrecision

FldRe_FixedPrecision (Example H37E1)

Example-Forms

FldQuad_Forms (Example H34E4)

Example-Forms1

HMod_Forms1 (Example H43E10)

Example-Forms2

HMod_Forms2 (Example H43E11)

Example-forward

Func_forward (Example H2E4)

Example-FPGroup

Grp_FPGroup (Example H15E9)

Example-Free

GrpFP_Free (Example H16E1)

Example-FreeAbelianGroup

GrpAb_FreeAbelianGroup (Example H18E1)

Example-FreeAlgebra

AlgFP_FreeAlgebra (Example H52E1)

Example-FreeResolution

PMod_FreeResolution (Example H44E6)

Example-FreeSemigroup

SgpFP_FreeSemigroup (Example H14E1)

Example-Frobenius

Elcu_Frobenius (Example H53E17)

Example-FunctionField

Elcu_FunctionField (Example H53E2)

FldFun_FunctionField (Example H31E2)

Example-Functions

FldFin_Functions (Example H27E3)

Example-FundamentalInvariants

RngInvar_FundamentalInvariants (Example H30E8)

Example-G23

GrpFP_G23 (Example H16E25)

Example-G8723

GrpFP_G8723 (Example H16E16)

Example-GaussianPeriods

FldCyc_GaussianPeriods (Example H35E1)

Example-GeneratepGroups

GrpPC_GeneratepGroups (Example H19E10)

Example-GeneratorNaming

State_GeneratorNaming (Example H1E5)

Example-GeneratorNamingSequence

State_GeneratorNamingSequence (Example H1E4)

Example-Generators

Grp_Generators (Example H15E10)

Example-GenericPoint

Elcu_GenericPoint (Example H53E9)

Example-GetTime

IO_GetTime (Example H3E10)

Example-GLSylow

GrpMat_GLSylow (Example H21E6)

Example-GModule

RngInvar_GModule (Example H30E2)

Example-GModules1

RMod_GModules1 (Example H42E12)

Example-GModules2

RMod_GModules2 (Example H42E13)

Example-GoppaCode

Code_GoppaCode (Example H58E9)

Example-Graded

RngMPol_Graded (Example H29E24)

Example-graphs

Design_graphs (Example H56E12)

Example-GroebnerWalk

RngMPol_GroebnerWalk (Example H29E12)

Example-Grotzch

Graph_Grotzch (Example H55E11)

Example-GroupActions

RngInvar_GroupActions (Example H30E1)

Example-GroupConstructors

Grp_GroupConstructors (Example H15E3)

Example-GRSCode

Code_GRSCode (Example H58E10)

Example-hadamard

Design_hadamard (Example H56E5)

Example-Hall

GrpPC_Hall (Example H19E4)

Example-HammingCode

Code_HammingCode (Example H58E4)

Example-Hensel

RngPol_Hensel (Example H28E4)

Example-Heron

RngMPol_Heron (Example H29E8)

Example-Hessian

GrpPerm_Hessian (Example H20E4)

Example-Hilbert

PMod_Hilbert (Example H44E4)

PMod_Hilbert (Example H44E5)

RngMPol_Hilbert (Example H29E25)

Example-HilbertGroebner

RngMPol_HilbertGroebner (Example H29E26)

Example-HN

GrpFP_HN (Example H16E17)

Example-hom

FldQuad_hom (Example H34E1)

RngInt_hom (Example H24E1)

Example-HomogeneousModuleTest1

RngMPol_HomogeneousModuleTest1 (Example H29E31)

Example-HomogeneousModuleTest2

RngInvar_HomogeneousModuleTest2 (Example H30E14)

Example-Homomorphism

FldFun_Homomorphism (Example H31E1)

RngMPol_Homomorphism (Example H29E1)

RngPol_Homomorphism (Example H28E1)

Example-homomorphism

FldRat_homomorphism (Example H26E2)

Example-Homomorphisms

FldNum_Homomorphisms (Example H36E1)

FldRe_Homomorphisms (Example H37E2)

Grp_Homomorphisms (Example H15E1)

Example-HomomorphismSpeed

GrpBB_HomomorphismSpeed (Example H17E3)

Example-IdealArithmetic

RngMPol_IdealArithmetic (Example H29E14)

Example-IdealFactorization

FldNum_IdealFactorization (Example H36E14)

Example-Ideals

FldFunG_Ideals (Example H32E4)

FldNum_Ideals (Example H36E8)

Example-Identifiers

State_Identifiers (Example H1E1)

Example-if

State_if (Example H1E10)

Example-import

Func_import (Example H2E6)

Example-Include

Set_Include (Example H7E10)

Example-Indexing

HMod_Indexing (Example H43E8)

KMod_Indexing (Example H41E6)

State_Indexing (Example H1E3)

Example-InLineConditional

State_InLineConditional (Example H1E11)

Example-Integers

RngInt_Integers (Example H24E2)

Example-Integral

FldRe_Integral (Example H37E7)

Example-Interactive

GrpPC_Interactive (Example H19E7)

Example-InteractiveUserAttributes

Func_InteractiveUserAttributes (Example H2E11)

Func_InteractiveUserAttributes (Example H2E12)

Example-Interpolate

RngMPol_Interpolate (Example H29E5)

Example-intrinsic

Func_intrinsic (Example H2E5)

Example-invar

Plane_invar (Example H57E6)

Example-Invariants

AlgMat_Invariants (Example H51E3)

Elcu_Invariants (Example H53E6)

GrpMat_Invariants (Example H21E4)

Example-InvariantsOfDegree

RngInvar_InvariantsOfDegree (Example H30E3)

RngInvar_InvariantsOfDegree (Example H30E4)

Example-IsGood

GrpPC_IsGood (Example H19E11)

Example-Isogeny

Elcu_Isogeny (Example H53E14)

Example-Isom

Lat_Isom (Example H45E19)

Example-Isomorphism

Elcu_Isomorphism (Example H53E15)

Example-IsomorphismClasses

Elcu_IsomorphismClasses (Example H53E8)

Example-IsOverSmallerField

GrpMat_IsOverSmallerField (Example H21E24)

Example-IsPrime

RngInt_IsPrime (Example H24E3)

Example-IsPrimitive

GrpMat_IsPrimitive (Example H21E18)

Example-IsSymmetric

RngMPol_IsSymmetric (Example H29E30)

Example-jacobson

AlgGrp_jacobson (Example H50E4)

Example-Join

Set_Join (Example H7E11)

Example-jordan

AlgCon_jordan (Example H47E1)

Example-Knapsack

Lat_Knapsack (Example H45E9)

Example-Kodaira

Elcu_Kodaira (Example H53E12)

Example-Labels

Graph_Labels (Example H55E7)

Graph_Labels (Example H55E9)

Example-LatticeCreate

Lat_LatticeCreate (Example H45E1)

Example-LatticeFunctions

Lat_LatticeFunctions (Example H45E4)

Example-LatticeOperations

Grp_LatticeOperations (Example H15E16)

Example-LatticeOps

RMod_LatticeOps (Example H42E22)

Example-Leech

Lat_Leech (Example H45E7)

Example-liealg

AlgAss_liealg (Example H48E1)

Example-LieAlgebra

AlgLie_LieAlgebra (Example H49E11)

Example-LinearTrans

KMod_LinearTrans (Example H41E13)

Example-LineCount

IO_LineCount (Example H3E9)

Example-Lix1

GrpFP_Lix1 (Example H16E38)

Example-Lix2

GrpFP_Lix2 (Example H16E39)

Example-Lix3

GrpFP_Lix3 (Example H16E40)

Example-Lix4

GrpFP_Lix4 (Example H16E41)

Example-LLLXGCD

Lat_LLLXGCD (Example H45E13)

Example-Map

Elcu_Map (Example H53E16)

Example-Map1

RngMPol_Map1 (Example H29E29)

Example-Matrices

GrpMat_Matrices (Example H21E2)

KMod_Matrices (Example H41E4)

Example-Matrix

HMod_Matrix (Example H43E6)

Example-MattsonSolomonTransform

Code_MattsonSolomonTransform (Example H58E19)

Example-Meataxe

RMod_Meataxe (Example H42E17)

Example-MinimalAlgebraGenerators

RngInvar_MinimalAlgebraGenerators (Example H30E13)

Example-MinimalPolynomial

RngMPol_MinimalPolynomial (Example H29E28)

Example-Minimals

RMod_Minimals (Example H42E19)

Example-Miscellaneous

Set_Miscellaneous (Example H7E7)

Example-Models

Elcu_Models (Example H53E4)

Example-Modular

GrpFP_Modular (Example H16E7)

Example-Module

RngInvar_Module (Example H30E9)

Example-Modules

Grp_Modules (Example H15E17)

Example-MolienSeries

RngInvar_MolienSeries (Example H30E5)

Example-Monoid

SgpFP_Monoid (Example H14E2)

Example-MordellWeil

Elcu_MordellWeil (Example H53E7)

Example-MultipleReturns

State_MultipleReturns (Example H1E2)

Example-MultiplicationTable

FldNum_MultiplicationTable (Example H36E10)

Example-Multiset

Set_Multiset (Example H7E4)

Example-MutationAssignment

State_MutationAssignment (Example H1E6)

Example-Neighbour

Lat_Neighbour (Example H45E20)

Lat_Neighbour (Example H45E6)

Example-NestedExists

Set_NestedExists (Example H7E13)

Example-NestedIteration

Seq_NestedIteration (Example H8E6)

Example-NonNilpotentElement

AlgLie_NonNilpotentElement (Example H49E10)

Example-norm-equation

FldQuad_norm-equation (Example H34E3)

RngInt_norm-equation (Example H24E7)

Example-NormsEtc

FldNum_NormsEtc (Example H36E13)

Example-numerator

FldRat_numerator (Example H26E3)

Example-OddGraph

EnumComb_OddGraph (Example H54E1)

Example-Operations

AlgLie_Operations (Example H49E3)

HMod_Operations (Example H43E7)

RMod_Operations (Example H42E15)

Example-OrbitActions

GrpPerm_OrbitActions (Example H20E14)

Example-Orbits

GrpMat_Orbits (Example H21E14)

Example-Order

Elcu_Order (Example H53E10)

GrpMat_Order (Example H21E12)

GrpPerm_Order (Example H20E10)

Grp_Order (Example H15E11)

RngMPol_Order (Example H29E3)

Example-OrderLattice

Lat_OrderLattice (Example H45E3)

Example-Orders

FldFunG_Orders (Example H32E2)

FldNum_Orders (Example H36E5)

Example-Orthogonalize

Lat_Orthogonalize (Example H45E15)

Example-Other

AlgLie_Other (Example H49E9)

Example-Parameters

Func_Parameters (Example H2E2)

Example-PartialFractionDecomposition

FldFun_PartialFractionDecomposition (Example H31E3)

Example-Partitions

EnumComb_Partitions (Example H54E2)

Example-Perfect

RngInt_Perfect (Example H24E6)

Example-PermutationActionD8

AlgFP_PermutationActionD8 (Example H52E3)

Example-PermutationCode

Code_PermutationCode (Example H58E3)

Example-Permutations

GrpPerm_Permutations (Example H20E2)

Example-PlayWithPoints

Elcu_PlayWithPoints (Example H53E11)

Example-points-blocks

Design_points-blocks (Example H56E2)

Example-points-lines

Plane_points-lines (Example H57E2)

Example-PolycyclicGroup

GrpPC_PolycyclicGroup (Example H19E1)

Example-Polynomials

RngPol_Polynomials (Example H28E2)

Example-PositiveDefiniteForm

Lat_PositiveDefiniteForm (Example H45E21)

Example-PowerGroup

GrpPC_PowerGroup (Example H19E8)

Example-PowerGroupTwo

GrpPC_PowerGroupTwo (Example H19E12)

Example-powering

AlgGrp_powering (Example H50E5)

Example-PowerSequence

Seq_PowerSequence (Example H8E2)

Example-PowerSet

Set_PowerSet (Example H7E6)

Example-pQuotient1

GrpFP_pQuotient1 (Example H16E27)

Example-pQuotient2

GrpFP_pQuotient2 (Example H16E28)

Example-pQuotient3

GrpFP_pQuotient3 (Example H16E29)

Example-pQuotient4

GrpFP_pQuotient4 (Example H16E30)

Example-pQuotient5

GrpFP_pQuotient5 (Example H16E31)

Example-pQuotient6

GrpFP_pQuotient6 (Example H16E32)

Example-pQuotient7

GrpFP_pQuotient7 (Example H16E33)

Example-pQuotient8

GrpFP_pQuotient8 (Example H16E34)

Example-Predicates

AlgLie_Predicates (Example H49E7)

Example-PrimaryDecomposition

RngMPol_PrimaryDecomposition (Example H29E23)

Example-PrimitiveStructure

GrpPerm_PrimitiveStructure (Example H20E18)

Example-printf

IO_printf (Example H3E4)

IO_printf (Example H3E6)

Example-printf2

IO_printf2 (Example H3E5)

Example-Procedures

Func_Procedures (Example H2E3)

Example-Products

AlgMat_Products (Example H51E5)

Example-Progression

Seq_Progression (Example H8E1)

Set_Progression (Example H7E5)

Example-pts-blks-ops

Design_pts-blks-ops (Example H56E8)

Example-QuadraticResidueCode

Code_QuadraticResidueCode (Example H58E11)

Example-quaternions

AlgGen_quaternions (Example H46E1)

Example-Quotient

AlgFP_Quotient (Example H52E4)

Graph_Quotient (Example H55E10)

GrpMat_Quotient (Example H21E8)

GrpPerm_Quotient (Example H20E6)

Grp_Quotient (Example H15E5)

Example-Quotients1

KMod_Quotients1 (Example H41E9)

Example-Quotients2

KMod_Quotients2 (Example H41E10)

Example-Quotients3

KMod_Quotients3 (Example H41E11)

Example-Radical

RngMPol_Radical (Example H29E22)

Example-Random

GrpMat_Random (Example H21E13)

Set_Random (Example H7E8)

Example-RandomSchreier

GrpPerm_RandomSchreier (Example H20E24)

Example-Read

IO_Read (Example H3E11)

Example-Record

Rec_Record (Example H12E2)

Example-RecordAccess

Rec_RecordAccess (Example H12E3)

Example-RecordFormat

Rec_RecordFormat (Example H12E1)

Example-Recursion

Func_Recursion (Example H2E1)

Example-Reduce

HMod_Reduce (Example H43E4)

Example-ReduceHom

HMod_ReduceHom (Example H43E5)

Example-Reduction

Set_Reduction (Example H7E14)

Example-ReedMullerCode

Code_ReedMullerCode (Example H58E5)

Example-Regexp

IO_Regexp (Example H3E3)

Example-related

Design_related (Example H56E3)

Example-RelationIdeal

RngMPol_RelationIdeal (Example H29E19)

Example-Relations

GrpAb_Relations (Example H18E2)

GrpFP_Relations (Example H16E2)

RngInvar_Relations (Example H30E10)

Example-repeat

State_repeat (Example H1E14)

Example-Replace

GrpFP_Replace (Example H16E9)

Example-Represent

FldQuad_Represent (Example H34E5)

Example-RepUnits

RngInt_RepUnits (Example H24E5)

Example-require

Func_require (Example H2E7)

Example-RestrictedPartitions

EnumComb_RestrictedPartitions (Example H54E3)

Example-Rewrite

GrpFP_Rewrite (Example H16E35)

Example-Roots

FldRe_Roots (Example H37E5)

Example-RootsNonExact

FldRe_RootsNonExact (Example H37E6)

Example-RootSystem

AlgLie_RootSystem (Example H49E2)

Example-Round2

FldNum_Round2 (Example H36E6)

Example-RowOps

HMod_RowOps (Example H43E9)

Example-Rowops

KMod_Rowops (Example H41E14)

Example-RungeKutta2

RngMPol_RungeKutta2 (Example H29E11)

Example-SecondaryInvariants

RngInvar_SecondaryInvariants (Example H30E7)

Example-Self

Seq_Self (Example H8E5)

Example-Semilinearity

GrpMat_Semilinearity (Example H21E19)

Example-SemiSimpleType

AlgLie_SemiSimpleType (Example H49E8)

Example-Series

AlgLie_Series (Example H49E5)

GrpMat_Series (Example H21E17)

GrpPerm_Series (Example H20E17)

Example-Set

GrpPC_Set (Example H19E3)

Example-SetOperations

GrpPerm_SetOperations (Example H20E11)

Grp_SetOperations (Example H15E12)

Example-Seysen

Lat_Seysen (Example H45E14)

Example-SimpleLieAlgebra

AlgLie_SimpleLieAlgebra (Example H49E1)

Example-SingularElements

Lat_SingularElements (Example H45E10)

Example-spec

Func_spec (Example H2E8)

Example-Split

IO_Split (Example H3E2)

Example-Sprintf

IO_Sprintf (Example H3E8)

Example-Stabilizers

GrpPerm_Stabilizers (Example H20E12)

Example-Standard

GrpPC_Standard (Example H19E2)

Example-StandardForm

Code_StandardForm (Example H58E14)

Example-StandardGroups

GrpPerm_StandardGroups (Example H20E7)

Grp_StandardGroups (Example H15E6)

Example-StandardPresentation

GrpPC_StandardPresentation (Example H19E6)

Example-Startup

Env_Startup (Example H4E1)

Example-startup-spec

Func_startup-spec (Example H2E9)

Example-SteenrodOperation

RngInvar_SteenrodOperation (Example H30E12)

Example-Strings

IO_Strings (Example H3E1)

Example-sub

Plane_sub (Example H57E4)

Plane_sub (Example H57E5)

Example-SubAlgebra

AlgMat_SubAlgebra (Example H51E4)

Example-Subgroup

Grp_Subgroup (Example H15E4)

Example-SubgroupConstructions

GrpPerm_SubgroupConstructions (Example H20E16)

Example-SubgroupOps

GrpFP_SubgroupOps (Example H16E19)

Example-Subgroups

GrpMat_Subgroups (Example H21E7)

Grp_Subgroups (Example H15E14)

Example-Subgroups1

GrpFP_Subgroups1 (Example H16E14)

Example-Subgroups2

GrpFP_Subgroups2 (Example H16E15)

Example-Sublattices

Lat_Sublattices (Example H45E22)

Example-Submodule

RMod_Submodule (Example H42E16)

Example-SubQuo

PMod_SubQuo (Example H44E3)

Example-Subspace1

KMod_Subspace1 (Example H41E7)

Example-Subspace2

KMod_Subspace2 (Example H41E8)

Example-SubSuperQuo

Lat_SubSuperQuo (Example H45E5)

Example-supp

Plane_supp (Example H57E3)

Example-Suzuki

GrpMat_Suzuki (Example H21E10)

Example-Sym

GrpPerm_Sym (Example H20E1)

Example-Sym8

GrpFP_Sym8 (Example H16E10)

Example-Symmetric1

GrpFP_Symmetric1 (Example H16E3)

Example-Symmetric2

GrpFP_Symmetric2 (Example H16E4)

Example-SymmetricTensor

GrpMat_SymmetricTensor (Example H21E23)

Example-Symplectic

GrpMat_Symplectic (Example H21E9)

Example-SystemAttributes

Func_SystemAttributes (Example H2E10)

Example-SyzygyModule

RngMPol_SyzygyModule (Example H29E27)

Example-Tensor

GrpMat_Tensor (Example H21E20)

Example-TernaryGolayCode

Code_TernaryGolayCode (Example H58E1)

Example-Tetrahedral

GrpFP_Tetrahedral (Example H16E5)

Example-ThetaSeries

Lat_ThetaSeries (Example H45E11)

Example-ThreeInvols

GrpFP_ThreeInvols (Example H16E6)

Example-Time

State_Time (Example H1E17)

Example-ToddCoxeter

GrpFP_ToddCoxeter (Example H16E21)

Example-Trace

Elcu_Trace (Example H53E13)

Example-trans

Plane_trans (Example H57E16)

Example-Transitive

GrpPerm_Transitive (Example H20E21)

Example-TransitiveProcess

GrpPerm_TransitiveProcess (Example H20E22)

Example-Trinomials

RngMPol_Trinomials (Example H29E6)

Example-Tuple

Tup_Tuple (Example H9E2)

Example-TupleAccess

Tup_TupleAccess (Example H9E3)

Example-TutteCage

Graph_TutteCage (Example H55E2)

Example-unital

Plane_unital (Example H57E11)

Example-UnitGroup

FldNum_UnitGroup (Example H36E11)

Example-Universe

Set_Universe (Example H7E1)

Example-Vandermonde

RngMPol_Vandermonde (Example H29E7)

Example-Variety

RngMPol_Variety (Example H29E16)

Example-Various

State_Various (Example H1E16)

Example-Vectors

KMod_Vectors (Example H41E3)

Example-VectorSpace

FldFin_VectorSpace (Example H27E2)

Example-Voronoi

Lat_Voronoi (Example H45E12)

Example-wedderburn

AlgGrp_wedderburn (Example H50E3)

Example-WeightDistribution

Code_WeightDistribution (Example H58E16)

Example-WeightEnumerator

Code_WeightEnumerator (Example H58E17)

Example-where

State_where (Example H1E9)

Example-while

State_while (Example H1E13)

Example-wittex

Design_wittex (Example H56E4)

Example-WordOps

GrpFP_WordOps (Example H16E13)

Example-Words

Code_Words (Example H58E15)

Example-WriteOverSmallerField

GrpMat_WriteOverSmallerField (Example H21E25)

Example-ZRadical

RngMPol_ZRadical (Example H29E18)

examples

Examples (FUNCTIONS, PROCEDURES AND PACKAGES)

ExceptionalUnitOrbit

ExceptionalUnitOrbit(u) : RngOrdElt -> [ RngOrdElt ]

ExceptionalUnits

ExceptionalUnits(O) : RngOrd -> [ RngOrdElt ]

Exclude

Exclude(~S, x) : SeqEnum, Elt ->

Exclude(~S, x) : SetEnum, Elt ->

ExcludedConjugates

ExcludedConjugates(V) : GrpFPCos -> { GrpFPElt }

GrpFP_ExcludedConjugates (Example H16E23)

Exists

Set_Exists (Example H7E12)

exists

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

ExistsConwayPolynomial

ExistsConwayPolynomial(p, n) : RngIntElt, RngIntElt -> BoolElt, RngUPolElt

exit

Control-C key (OVERVIEW)

Quitting (OVERVIEW)

Exp

Exp(f) : FldLocElt -> RngIntElt

Exp(s) : FldPrElt -> FldPrElt

Exp(f) : RngSerElt -> RngSerElt

ExplicitCoset

ExplicitCoset(V, i) : GrpFPCos, RngIntElt -> GrpFPCosElt

Explode

Explode(R) : SeqEnum -> List

Explode(T) : Tup -> List

Exponent

Exponent(G) : GrpAb -> RngIntElt

Exponent(G) : GrpFin -> RngIntElt

Exponent(G) : GrpMat -> RngIntElt

Exponent(G) : GrpPC -> RngIntElt

Exponent(G) : GrpPerm -> RngIntElt

exponential

Exponential, Logarithmic and Polylogarithmic Functions (REAL AND COMPLEX FIELDS)

ExponentialIntegral

ExponentialIntegral(r) : FldReElt -> FldReElt

exponentiation

Operators (OVERVIEW)

ExponentLaw

ExponentLaw(~P : parameters) : Proc(pQuot) ->

ExponentSum

ExponentSum(u, x) : GrpFPElt, GrpFPElt -> RngIntElt

expression

Expression (OVERVIEW)

Function Expressions (MAGMA SEMANTICS)

Function Expressions (OVERVIEW)

Procedure Expressions (MAGMA SEMANTICS)

Procedure Expressions (OVERVIEW)

The Case Expression (STATEMENTS AND EXPRESSIONS)

The Simple Conditional Expression (STATEMENTS AND EXPRESSIONS)

expressions

STATEMENTS AND EXPRESSIONS

ExpurgateCode

ExpurgateCode(C) : Code -> Code

ext

Constructor (OVERVIEW)

ext<F | n> : FldFin, RngIntElt -> FldFin, Map

ext< Q | f > : FldRat, RngUPolElt -> FldNum

ext< L | S > : Lat, List -> Lat

ext< R | > : Rng -> RngUPol

ext< O | a_1, ..., a_r > : RngOrd, RngOrdElt, ..., RngOrdElt -> RngOrd

ExtendBasis

ExtendBasis(S, A) : AlgGen, AlgGen -> [ AlgElt ]

ExtendBasis(Q, U) : [ModTupFldElt], ModTupFld -> [ModTupFldElt]

ExtendBasis(Q, M) : [ModTupRngElt], ModTupRng -> [ModTupRngElt]

ExtendCode

ExtendCode(C) : Code -> Code

ExtendedGreatestCommonDivisor

ExtendedGreatestCommonDivisor(m, n) : RngIntElt, RngIntElt -> RngIntElt, RngIntElt, RngIntElt

ExtendedGreatestCommonDivisor(f, g) : RngUPolElt, RngUPolElt -> RngUPolElt, RngUPolElt, RngUPolElt

ExtendedGreatestCommonDivisor(v, w) : RngValElt, RngValElt -> RngValElt, RngValElt, RngValElt

ExtendField

ExtendField(C, L) : Code, FldFin -> Code, Map

ExtendField(G, L) : GrpMat, FldFin -> GrpMat, Map

ExtendField(V, L) : ModTupFld, Fld -> ModTupFld, MapHom

ExtendField(V, L) : ModTupFld, Fld -> ModTupFld, MapHom

ExtendPresentation

ExtendPresentation(~P, k): StdPresP, RngIntElt ->

Extension

Extension(G, H, f) : GrpPC, GrpPC, [Map] -> GrpPC

Extension(P, Q) : Process -> GrpFinFP

Extension(P, Q) : Process -> GrpFP

Extension(I, U) : RngMPol, [ RngIntElt ] -> RngMPol, Map

LiftCharacter(x, f, G) : AlgChtrElt, MapHom, Grp -> AlgChtrElt

LiftCharacters(T, f, G) : AlgChtrElt, MapHom, Grp -> AlgChtrElt

extension

Construction of Extensions (FINITELY PRESENTED GROUPS)

Construction of Extensions (GROUPS)

Construction of Extensions (MATRIX GROUPS)

Construction of Extensions (PERMUTATION GROUPS)

Construction of Extensions (SOLUBLE GROUPS)

Constructor (OVERVIEW)

Extension and Contraction of Ideals (MULTIVARIATE POLYNOMIAL RINGS)

Extensions (FINITELY PRESENTED SEMIGROUPS)

Ground Field and Relationships (FINITE FIELDS)

Induction, Restriction, Extension (CHARACTERS OF FINITE GROUPS)

Standard Constructions for General Modules (GENERAL MODULES)

Standard Groups and Extensions (FINITELY PRESENTED GROUPS)

Standard Groups and Extensions (GROUPS)

Standard Groups and Extensions (PERMUTATION GROUPS)

Subgroups, Quotient Groups and Extensions (SOLUBLE GROUPS)

The Construction of Extensions and their Elements (MATRIX ALGEBRAS)

Transcendental Extension (INTRODUCTION [RINGS AND FIELDS])

Variable Extension of Ideals (MULTIVARIATE POLYNOMIAL RINGS)

extension-contraction

Extension and Contraction of Ideals (MULTIVARIATE POLYNOMIAL RINGS)

extension-standard-group

Standard Groups and Extensions (FINITELY PRESENTED GROUPS)

Standard Groups and Extensions (GROUPS)

Standard Groups and Extensions (PERMUTATION GROUPS)

ExtensionField

ExtensionField<F, x | P> : FldFin, RngIntElt -> FldFin, Map

ExtensionProcess

ExtensionProcess(G, M, F) : GrpFin, ModRng, GrpFinFP -> Process

ExtensionProcess(G, M, F) : GrpPerm, ModRng, GrpFP -> Process

Extensions

FldFin_Extensions (Example H27E1)

GrpPerm_Extensions (Example H20E8)

Grp_Extensions (Example H15E7)

Exterior

Exterior(P, C) : Plane, { PlanePt } -> { PlanePt }

ExteriorSquare

ExteriorSquare(a) : AlgMat -> AlgMatElt

ExteriorSquare(L) : Lat -> Lat

ExteriorSquare(M) : ModTupRng -> ModTupRng

ExternalLines

ExternalLines(P, A) : Plane, { PlanePt } -> { PlaneLn }

extra

Addition of extra generators (BLACKBOX GROUPS)

extra-generators

Addition of extra generators (BLACKBOX GROUPS)

ExtractAutomorphisms

ExtractAutomorphisms(P) : Process(pgaProc) -> [Mat]

ExtractAutomorphisms(P) : StdPresP -> [Map]

ExtractBlock

Submatrix(a, i, j, p, q) : AlgMatElt, RngIntElt, RngIntElt, RngIntElt, RngIntElt -> ModMatRngElt

Submatrix(a, i, j, p, q) : ModMatRngElt, RngIntElt, RngIntElt, RngIntElt, RngIntElt -> ModMatRngElt

ExtractGenerators

ExtractGenerators(P) : Process(Lix) -> { GrpFPElt }

ExtractGroup

ExtractGroup(P) : Process(Lix) -> GrpFP

ExtractGroup(P) : Process(pgaProc) -> GrpPC

ExtractGroup(P) : Process(pQuot) -> GrpPC

ExtractGroup(P) : Process(Tietze) -> GrpFP

ExtractGroup(P) : StdPresP -> GrpPC

ExtractMapping

ExtractMapping(P) : StdPresP -> Map

ExtractRep

ExtractRep(~R, ~r) : SetEnum, Elt ->

Set_ExtractRep (Example H7E9)

ExtraSpecial

GrpMat_ExtraSpecial (Example H21E22)

ExtraSpecialGroup

ExtraSpecialGroup(C, p, n) : Cat, RngIntElt, RngIntElt -> GrpFin

ExtraSpecialGroup(GrpPC, p, n) : Cat, RngIntElt, RngIntElt -> GrpPC

ExtraSpecialGroup(GrpPerm, p, n) : Cat, RngIntElt, RngIntElt -> GrpPC

ExtraSpecialGroup (G) : GrpMat -> GrpMat

ExtraSpecialParameters

ExtraSpecialParameters(G) : GrpMat -> [RngIntElt, RngIntElt]


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