Exploring Abstract Algebra with Mathematica

Al Hibbard - Central College - e-mail homepage

Ken Levasseur - UMass-Lowell - e-mail homepage



Partial listing of functions, options, and option values in AbstractAlgebra

AbelianQ, Adjoin, Alternating, Annihilator, Associates, AssociativeQ, Automorphism, BooleanRing, CartesianProduct, CayleyTable, Centralizer, Characteristic, ClosedQ, Closure, Commutators, CommutatorSubgroup, ConjugacyClass, Cosets, Cyclic, CyclicGenerators, CyclicQ, DiagonalMatrices, Dihedral, DirectProduct, DisjointCyclesQ, ElementQ, Elements, ElementToPower, EvenPermutationQ, ExtensionDegree, FieldQ, FormGroupoid, FormGroupoidByTable, FormGroupoidFromCycles, FormMorphoid, FormRingoid, FormRingoidByTable, FromCycles, GaussianIntegerQ, GeneralLinear, GenerateGroupoid, GF, GroupCenter, GroupExponent, GroupIdentity, HasIdentityQ, HasInversesQ, HasZeroQ, HermitianQ, HomomorphismQ, IdealQ, Idempotents, InducedIsomorphism, InjectiveQ, InnerAutomorphism, InnerAutomorphismGroup, Inverses, IsomorphismQ, Kernel, Klein4, LeftIdentity, LeftInverse, ModpIrreducibilityQ, MorphismQ, Morphoid, MorphoidComposition, MultiplicativeGroupoid, MultiplyCycles, MultiplyPermutations, NegationOf, NilpotentQ, Nilpotents, NonAssociatingTriples, NonCommutingPairs, Normalizer, NormalQ, Orbit, OrderOfElement, Orders, Parity, PermutationInverse, Poly, PolynomialEvaluation, PolynomialsUpToDegreeN, PrimeIdealQ, PrimitivePolynomials, PrincipalIdeal, ProperSubsetQ, QuaternionGroup, QuotientGroup, QuotientRing, RandomElement, RandomElements, RandomMatrix, RandomPermutation, RightCoset, RightCosets, RootsOfUnity, SemiGroupQ, SkewSymmetricQ, SpecialLinear, Stabilizer, SubgroupGenerated, SubgroupQ, SubringQ, SubsetQ, SurjectiveQ, Symmetric, TableOfPowers, ToCycles, ToOrdinaryPolynomial, ToTranspositions, TwistedZ, U, UnitQ, Units, Visual2, VisualizeMorphoid, WithUnityQ, Z, ZdNorm, ZeroDivisorQ, ZeroDivisors, Zeros

In addition, the following standard functions (including others) have been extended for working with matrices and polynomials over general rings:

Det, Dot, MatrixPower, PolynomialDivision, PolynomialGCD, PolynomialLCM, PolynomialQuotient, PolynomialRemainder, Solve


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