Contents

• Contents
• Introduction
  • What is $\Sigma{}^{{\rm it}}$?
  • How do I get and install $\Sigma{}^{{\rm it}}$?
  • How do I use $\Sigma{}^{{\rm it}}$ in my programs?
• User's Guide
  • Basic algebraic categories
  • Arithmetic
  • Data structures
  • Input/Output
  • Linear algebra
  • Univariate polynomials and series
  • Skew polynomials and linear operators
  • Solutions of differential and difference equations
  • Compatibility with C types
  • Profiling and debugging
• Reference Manual
• Basic Categories
  • AbelianGroup
  • AbelianMonoid
  • Algebra
  • CharacteristicZero
  • CommutativeRing
  • DecomposableRing
  • DifferentialExtension
  • DifferentialRing
  • EuclideanDomain
  • Field
  • FiniteField
  • FiniteCharacteristic
  • FiniteSet
  • GcdDomain
  • Group
  • IntegerCategory
  • IntegralDomain
  • LinearArithmeticType
  • LinearCombinationType
  • Module
  • Monoid
  • NonCommutativeIntegralDomain
  • Parsable
  • QRing
  • Ring
  • Specializable
  • SumitType
• Commutative Algebra
  • Automorphism
  • ChineseRemaindering
  • Derivation
  • Fraction
  • FractionalRoot
  • FractionBy
  • FractionByCategory
  • FractionByCategory0
  • FractionCategory
  • FractionFieldCategory
  • FractionFieldCategory0
  • LinearCombinationFraction
  • Product
  • ReducibleModulusException
  • ReducibleModulusExceptionType
  • SimpleAlgebraicExtension
  • SimpleAlgebraicExtensionCategory
  • UnivariatePolynomialMod
  • UnivariatePolynomialQuotient
• Finite Fields
  • SmallPrimes
  • LazyHalfWordSizePrimes
  • HalfWordSizePrimes
  • WordSizePrimes
  • PrimeCollection
  • PrimeFieldCategory
  • PrimeFieldCategory0
  • PrimitiveRoots
  • PthPowering
  • SmallPrimeField
  • SmallPrimeField0
  • SmallPrimeFieldCategory
  • SmallPrimeFieldCategory0
  • ZechPrimeField
• Linear Algebra
  • Backsolve
  • DenseMatrix
  • DivisionFreeGaussElimination
  • FractionFreeGaussElimination
  • HermiteGaussElimination
  • LinearAlgebra
  • LinearAlgebraRing
  • LinearEliminationCategory
  • MatrixCategory
  • MatrixCategoryOverFraction
  • ModulopGaussElimination
  • OrdinaryGaussElimination
  • OverdeterminedLinearSystemSolver
  • SpecializationLinearAlgebra
  • TwoStepFractionFreeGaussElimination
  • UnivariatePolynomialCRTLinearAlgebra
  • UnivariatePolynomialPopovLinearAlgebra
  • Vector
  • VectorOverFraction
• Univariate Polynomials and Series
  • DenseUnivariatePolynomial
  • DenseUnivariateTaylorSeries
  • FactorizationRing
  • FFTRing
  • HeuristicGcd
  • ModularUnivariateGcd
  • ModulopUnivariateGcd
  • PrimeFieldUnivariateFactorizer
  • RationalRootRing
  • Resultant
  • SparseUnivariatePolynomial
  • UnivariateFactorialPolynomial
  • UnivariateFreeAlgebra
  • UnivariateFreeFiniteAlgebra
  • UnivariateFreeFiniteAlgebra2
  • UnivariateFreeFiniteAlgebraOverFraction
  • UnivariateGcdRing
  • UnivariateIntegralFactorizer
  • UnivariateMonomial
  • UnivariatePolynomialAlgebra
  • UnivariatePolynomialCategory
  • UnivariatePolynomialKaratsuba
  • UnivariatePolynomialSquareFree
  • UnivariateTaylorSeriesCategory
• Multivariate Polynomials
  • DenseFreeModule
  • DenseHomogeneousExteriorPower
  • DenseHomogeneousExteriorProduct
  • DenseHomogeneousPolynomial
  • DenseHomogeneousPowerProduct
  • FiniteFreeModule
• Univariate Skew Polynomials and Linear Operators
  • ExteriorPower
  • FractionFreeCyclicVector
  • LinearOrdinaryDifferenceOperator
  • LinearOrdinaryDifferenceOperatorCategory
  • LinearOrdinaryDifferentialOperator
  • LinearOrdinaryDifferentialOperatorCategory
  • LinearOrdinaryQDifferenceOperator
  • LinearOrdinaryQDifferenceOperatorQ
  • LinearOrdinaryRecurrence
  • LinearOrdinaryRecurrenceQ
  • LinearOrdinaryRecurrenceCategory
  • OptimizeSymmetricPower
  • SecondOrderSymmetricPower
  • SymmetricPower
  • UnivariateSkewPolynomial
  • UnivariateSkewPolynomialCategory
  • UnivariateSkewPolynomialCategoryTools
• Solutions of Differential and Difference Equations
  • LinearOrdinaryDifferentialOperatorSeriesSolutions
  • LinearOrdinaryDifferentialSystemSeriesSolutions
  • LinearOrdinaryFirstOrderSystem
  • LinearOrdinaryFirstOrderSystemPolynomialSolutions
  • LinearOrdinaryOperatorPolynomialSolutions
  • LinearOrdinaryOperatorToRecurrence
  • LinearOrdinaryRecurrenceHypergeometricSolutions
  • LinearOrdinaryRecurrenceRationalSolutions
  • LinearOrdinaryRecurrenceSystemRationalSolutions
  • LinearOrdinaryRecurrenceSystemTools
  • LinearOrdinaryRecurrenceTools
• Conditions
  • Case
  • Condition
  • EqualityCondition
  • If
  • UnivariateAlgebraicCondition
• Expression Trees
  • ExpressionTree
  • ExpressionTreeAnd
  • ExpressionTreeAssign
  • ExpressionTreeBigO
  • ExpressionTreeCase
  • ExpressionTreeEqual
  • ExpressionTreeExpt
  • ExpressionTreeGeneralizedPochammer
  • ExpressionTreeGreaterEqual
  • ExpressionTreeGreaterThan
  • ExpressionTreeIf
  • ExpressionTreeLeaf
  • ExpressionTreeLessEqual
  • ExpressionTreeLessThan
  • ExpressionTreeLispList
  • ExpressionTreeList
  • ExpressionTreeMatrix
  • ExpressionTreeMinus
  • ExpressionTreeNotEqual
  • ExpressionTreeOperator
  • ExpressionTreeOperatorTools
  • ExpressionTreePlus
  • ExpressionTreePrefix
  • ExpressionTreeQuotient
  • ExpressionTreeSubscript
  • ExpressionTreeTimes
  • ExpressionTreeVector
• Shells
  • Evaluator
  • InfixExpressionParser
  • LispExpressionParser
  • MakePartialRing
  • Maple
  • Parser
  • ParserReader
  • ParsingTools
  • PartialRing
  • Scanner
  • Shell
  • SymbolTable
  • Token
• Utilities
  • Bits
  • IndexedVariable
  • PartialFunction
  • Permutation
  • Sequence
  • Symbol
• Index
• About this document ...