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REDUCE includes considerable documentation, not only for the core system, but also for the many application packages included in the release. (The documentation for REDUCE 3.8 , the last commercial version of REDUCE released in 2004, is also still available.)
For all users:
the REDUCE User's Manual [ HTML | PDF ] provides a comprehensive guide to the REDUCE language and the supported packages.
For advanced users:
the Symbolic Mode Primer [ HTML | PDF ] describes the REDUCE implementation language, RLISP, which is Standard Lisp with REDUCE (essentially ALGOL 60) syntax;
the Standard Lisp Report [ HTML | PDF ] defines Standard Lisp;
the PSL Users Manual [ HTML | PDF ] documents Portable Standard Lisp, the original implementation of Standard Lisp, and the CSL Reference documents Codemist Standard Lisp, a later implementation of Standard Lisp.
The following PDF documents for the user-contributed packages are extracts from the full REDUCE User's Manual.
ALGINT : Integration of square roots
APPLYSYM : Infinitesimal symmetries of differential equations
ARNUM : An algebraic number package
ASSERT : Dynamic Verification of Assertions on Function Types
ASSIST : Useful utilities for various applications
AVECTOR : A vector algebra and calculus package
BIBASIS : A Package for Calculating Boolean Involutive Bases
BOOLEAN : A package for boolean algebra
CALI : A package for computational commutative algebra
CAMAL : Calculations in celestial mechanics
CANTENS : A Package for Manipulations and Simplifications of Indexed Objects
CDE : A package for integrability of PDEs
CDIFF : A package for computations in geometry of Differential Equations
CGB : Computing Comprehensive Gröbner Bases
COMPACT : Package for compacting expressions
CRACK : Solving overdetermined systems of PDEs or ODEs
CVIT : Fast calculation of Dirac gamma matrix traces
DEFINT : A definite integration interface
DESIR : Differential linear homogeneous equation solutions in the neighborhood of irregular and regular singular points
DFPART : Derivatives of generic functions
DUMMY : Canonical form of expressions with dummy variables
EXCALC : A differential geometry package
FIDE : Finite difference method for partial differential equations
FPS : Automatic calculation of formal power series
GCREF : A Graph Cross Referencer
GENTRAN : A code generation package
GNUPLOT : Display of functions and surfaces
GROEBNER : A Gröbner basis package
GUARDIAN : Guarded Expressions in Practice
IDEALS : Arithmetic for polynomial ideals
INEQ : Support for solving inequalities
INVBASE : A package for computing involutive bases
LALR : A parser generator
LAPLACE : Laplace transforms
LIE : Functions for the classification of real n -dimensional Lie algebras
LIMITS : A package for finding limits
LINALG : Linear algebra package
LISTVECOPS : Vector operations on lists
LPDO : Linear Partial Differential Operators
MODSR : Modular solve and roots
NCPOLY : Non-commutative polynomial ideals
NORMFORM : Computation of matrix normal forms
NUMERIC : Solving numerical problems
ODESOLVE : Ordinary differential equations solver
ORTHOVEC : Manipulation of scalars and vectors
PHYSOP : Operator calculus in quantum theory
PM : A REDUCE pattern matcher
POLYDIV : Enhanced Polynomial Division
QSUM : Indefinite and Definite Summation of q -hypergeometric Terms
RANDPOLY : A random polynomial generator
RATAPRX : Rational Approximations Package for REDUCE
REACTEQN : Support for chemical reaction equation systems
REDLOG : Extend REDUCE to a computer logic system
RESET : Code to reset REDUCE to its initial state
RESIDUE : A residue package
RLFI : REDUCE L^{a} T_{e} X formula interface
ROOTS : A REDUCE root finding package
RSOLVE : Rational/integer polynomial solvers
RTRACE : Tracing in REDUCE
SCOPE : REDUCE source code optimization package
SETS : A basic set theory package
SPARSE : Sparse Matrix Calculations
SPDE : Finding symmetry groups of PDEs
SPECFN : Package for special functions
SPECFN2 : Package for special special functions
SSTOOLS : Computations with supersymmetric algebraic and differential expressions
SUM : A package for series summation
SYMMETRY : Operations on symmetric matrices
TAYLOR : Manipulation of Taylor series
TPS : A truncated power series package
TRI : T_{e} X REDUCE interface
TRIGSIMP : Simplification and factorization of trigonometric and hyperbolic functions
TURTLE : Turtle Graphics Interface for REDUCE
WU : Wu algorithm for polynomial systems
XCOLOR : Color factor in some field theories
XIDEAL : Gröbner Bases for exterior algebra
ZEILBERG : Indefinite and definite summation
ZTRANS : Z -transform package