Abstract
Acknowledgment
1 Introductory Information
2 Structure of Programs
2.1 The REDUCE Standard Character Set
2.2 Numbers
2.3 Identifiers
2.4 Variables
2.5 Strings
2.6 Comments
2.7 Operators
3 Expressions
3.1 Scalar Expressions
3.2 Integer Expressions
3.3 Boolean Expressions
3.4 Equations
3.5 Proper Statements as Expressions
4 Lists
4.1 Operations on Lists
5 Statements
5.1 Assignment Statements
5.2 Group Statements
5.3 Conditional Statements
5.4 FOR Statements
5.5 WHILE … DO
5.6 REPEAT … UNTIL
5.7 Compound Statements
6 Commands and Declarations
6.1 Array Declarations
6.2 Mode Handling Declarations
6.3 END
6.4 BYE Command
6.5 Timing Facilities
6.6 DEFINE Command
6.7 RESETREDUCE Command
7 Built-in Prefix Operators
7.1 Numerical Operators
7.2 Mathematical Functions
7.3 Combinatorial Numbers
7.4 Bernoulli, Euler and Fibonacci Numbers
7.5 CHANGEVAR Operator
7.6 CONTINUED_FRACTION Operator
7.7 DF Operator
7.8 INT Operator
7.9 LENGTH Operator
7.10 LIMIT Operator
7.11 MAP Operator
7.12 MKID Operator
7.13 The Pochhammer Notation
7.14 PF Operator
7.15 RESIDUE and POLEORDER Operators
7.16 SELECT Operator
7.17 SOLVE Operator
7.18 Support for Solving Inequalities
7.19 Finding Rational or Integer Zeros
7.20 Modular Solve and Roots
7.21 Even and Odd Operators
7.22 Linear Operators
7.23 Non-Commuting Operators
7.24 Symmetric and Antisymmetric Operators
7.25 Declaring New Prefix Operators
7.26 Declaring New Infix Operators
7.27 Creating / Removing Variable Dependency
8 Display and Structuring of Expressions
8.1 Kernels
8.2 The Expression Workspace
8.3 Output of Expressions
8.4 Changing the Internal Order of Variables
8.5 Obtaining Parts of Algebraic Expressions
8.6 COMPACT Operator
8.7 TRIGSIMP package
9 Polynomials and Rationals
9.1 Controlling the Expansion of Expressions
9.2 Factorization of Polynomials
9.3 Cancellation of Common Factors
9.4 Working with Least Common Multiples
9.5 Controlling Use of Common Denominators
9.6 Euclidean Division
9.7 Polynomial Pseudo-Division
9.8 RESULTANT Operator
9.9 DECOMPOSE Operator
9.10 INTERPOL Operator
9.11 Obtaining Parts of Polynomials and Rationals
9.12 Polynomial Coefficient Arithmetic
9.13 Finding Roots
10 Assigning and Testing Algebraic Properties
10.1 REALVALUED Declaration and Check
10.2 SELFCONJUGATE Declaration
10.3 Declaring Complex Conjugates
10.4 Declaring Expressions Positive or Negative
11 Substitution Commands
11.1 SUB Operator
11.2 LET Rules
11.3 Rule Lists
11.4 Asymptotic Commands
12 File Handling Commands
12.1 IN Command
12.2 IN_TEX Command
12.3 OUT Command
12.4 SHUT Command
12.5 Using Variables as Filenames
12.6 REDUCE Startup File
13 Commands for Interactive Use
13.1 Error Handling: errcont, retry
13.2 Referencing Previous Results: input, ws, display
13.3 Interactive Editing: ed, editdef
13.4 Interactive File Control: int, pause, cont
14 Matrix Calculations
14.1 MAT Operator
14.2 Matrix Variables
14.3 Matrix Expressions
14.4 Operators with Matrix Arguments
14.5 Matrix Assignments
14.6 Evaluating Matrix Elements
15 Procedures
15.1 Procedure Heading
15.2 Procedure Body
15.3 Matrix- and List-valued Procedures
15.4 Using LET Inside Procedures
15.5 LET Rules as Procedures
15.6 REMEMBER Statement
16 Series Expansion
16.1 Taylor Expansion
16.2 TPS: Extendible Power Series
16.3 FPS: Automatic Calculation of Formal Power Series
17 Solving Numerical Problems
17.1 Syntax
17.2 Minima
17.3 Roots of Functions / Solutions of Equations
17.4 Integrals
17.5 Ordinary Differential Equations
17.6 Bounds of a Function
17.7 Chebyshev Curve Fitting
17.8 General Curve Fitting
18 Graphical Display
18.1 GNUPLOT: Display of Functions and Surfaces
18.2 Turtle Graphics
18.3 Logo Turtle Graphics
19 Tracing in REDUCE
19.1 Introduction
19.2 RTrace versus RDebug
19.3 Procedure Tracing: RTR, UNRTR
19.4 Assignment Tracing: RTRST, UNRTRST
19.5 Tracing Active Rules: TRRL, UNTRRL
19.6 Tracing Inactive Rules: TRRLID, UNTRRLID
19.7 Output Control: RTROUT
20 User Contributed Packages
20.1 APPLYSYM: Infinitesimal Symmetries of Differential Equations
20.2 ASSIST: Useful Utilities for Various Applications
20.3 ATENSOR: A REDUCE Program for Tensor Simplification
20.4 AVECTOR: A Vector Algebra and Calculus Package
20.5 BIBASIS: A Package for Calculating Boolean Involutive Bases
20.6 BOOLEAN: A Package for Boolean Algebra
20.7 CALI: A Package for Computational Commutative Algebra
20.8 CAMAL: Calculations in Celestial Mechanics
20.9 CANTENS: A Package for Manipulations and Simplifications of Indexed Objects
20.10 CDE: A Package for Integrability of PDEs
20.11 CDIFF: A Package for Computations in Geometry of Differential Equations
20.12 CGB: Computing Comprehensive Gröbner Bases
20.13 COEFF2: A Variant of the coeff Operator
20.14 CONLAW: Find Conservation Laws for Differential Equations
20.15 CRACK: Solving Overdetermined Systems of PDEs or ODEs
20.16 DESIR: Differential Linear Homogeneous Equation Solutions in the Neighborhood of Irregular and Regular Singular Points
20.17 DFPART: Derivatives of Generic Functions
20.18 DUMMY: Canonical Form of Expressions with Dummy Variables
20.19 EDS: A Package for Exterior Differential Systems
20.20 ELLIPFN: A Package for Elliptic Functions and Integrals
20.21 EXCALC: A Differential Geometry Package
20.22 FIDE: Finite Difference Method for Partial Differential Equations
20.23 GCREF: A Graph Cross Referencer
20.24 GENTRAN: A Code Generation Package
20.25 GRINDER: Calculation of three-loop diagrams in Heavy Quark Effective Theory
20.26 GROEBNER: A Gröbner Basis Package
20.27 GUARDIAN: Guarded Expressions in Practice
20.28 IDEALS: Arithmetic for Polynomial Ideals
20.29 INVBASE: A Package for Computing Involutive Bases
20.30 LALR: A Parser Generator
20.31 LAPLACE: Laplace Transforms
20.32 LIE: Functions for the Classification of Real n-Dimensional Lie Algebras
20.33 LINALG: Linear Algebra Package
20.34 LISTVECOPS: Vector Operations on Lists
20.35 LPDO: Linear Partial Differential Operators
20.36 MATHML: REDUCE-MathML Interface
20.37 MATHMLOM: REDUCE OpenMath/MathML Interface
20.38 MRVLIMIT: A New Exp-Log Limits Package
20.39 NCPOLY: Non-commutative Polynomial Ideals
20.40 NORMFORM: Computation of Matrix Normal Forms
20.41 ODESOLVE: Ordinary Differential Equation Solver
20.42 ORTHOVEC: Manipulation of Scalars and Vectors
20.43 PHYSOP: Operator Calculus in Quantum Theory
20.44 PM: A REDUCE Pattern Matcher
20.45 QHULL: Compute the Complex Hull
20.46 QSUM: Indefinite and Definite Summation of q-Hypergeometric Terms
20.47 RANDPOLY: A Random Polynomial Generator
20.48 RATAPRX: Rational Approximations Package for REDUCE
20.49 RATINT: Integrate Rational Functions using the Minimal Algebraic Extension to the Constant Field
20.50 REACTEQN: Support for Chemical Reaction Equation Systems
20.51 REDLOG: Extend REDUCE to a Computer Logic System
20.52 RLFI: REDUCE LaTeX Formula Interface
20.53 SCOPE: REDUCE Source Code Optimization Package
20.54 SETS: A Basic Set Theory Package
20.55 SPARSE: Sparse Matrix Calculations
20.56 SPDE: Finding Symmetry Groups of PDEs
20.57 SPECFN: Package for Special Functions
20.58 SPECFN2: Package for Special Special Functions
20.59 SSTOOLS: Computations with Supersymmetric Algebraic and Differential Expressions
20.60 SUM: A Package for Series Summation
20.61 SUSY2: Supersymmetric Functions and Algebra of Supersymmetric Operators
20.62 SYMMETRY: Operations on Symmetric Matrices
20.63 TRI: TeX REDUCE Interface
20.64 TRIGD: Trigonometrical Functions with Degree Arguments
20.65 TRIGINT: Weierstraß Substitution in REDUCE
20.66 V3TOOLS: Computations with Polynomials of Scalar Vector Products
20.67 WITH: Local Switch Settings
20.68 WU: Wu Algorithm for Polynomial Systems
20.69 XCOLOR: Color Factor in some Field Theories
20.70 XIDEAL: Gröbner Bases for Exterior Algebra
20.71 ZEILBERG: Indefinite and Definite Summation
20.72 ZTRANS: Z-Transform Package
21 Symbolic Mode
21.1 Symbolic Infix Operators
21.2 Symbolic Expressions
21.3 Quoted Expressions
21.4 Lambda Expressions
21.5 Symbolic Assignment Statements
21.6 FOR EACH Statement
21.7 Symbolic Procedures
21.8 Standard Lisp Equivalent of REDUCE Input
21.9 Communicating with Algebraic Mode
21.10 Rlisp ’88
21.11 References
22 Calculations in High Energy Physics
22.1 High Energy Physics Operators
22.2 Vector Variables
22.3 Additional Expression Types
22.4 Trace Calculations
22.5 Mass Declarations
22.6 Example
22.7 Extensions to More Than Four Dimensions
22.8 The CVIT algorithm
23 REDUCE and Rlisp Utilities
23.1 The Standard Lisp Compiler
23.2 Fast Loading Code Generation Program
23.3 The Standard Lisp Cross Reference Program
23.4 Prettyprinting REDUCE Expressions
23.5 Prettyprinting Standard Lisp S-Expressions
24 Maintaining REDUCE
A Reserved Identifiers
A.1 Commands
A.2 Boolean Operators
A.3 Infix Operators
A.4 Numerical Operators
A.5 Prefix Operators
A.6 Reserved Variables
A.7 Switches
A.8 Other Reserved Ids
B Bibliography
C Changes since Version 3.8
D Description of Algorithms
D.1 Definite Integration
D.2 The CVIT package
Index
Symbols
A
B
C
D
E
F
G
H
I
J
K
L
M
N
O
P
Q
R
S
T
U
V
W
X
Y
Z