REDUCE User's Manual - REDUCE Computer …

1 REDUCE . User's Manual Version Anthony C. Hearn Santa Monica, CA, USA. Email: February 2004. Copyright 2004. c Anthony C. Hearn. All rights reserved. Registered system holders may reproduce all or any part of this publication for internal purposes, provided that the source of the material is clearly acknowledged, and the copyright notice is retained. Contents Abstract 11. 1 Introductory Information 15. 2 Structure of Programs 19. The REDUCE Standard Character Set .. 19. Numbers .. 19. Identifiers .. 21. Variables .. 22. Strings .. 23. Comments .. 23. Operators .. 24.

2 3 Expressions 27. Scalar Expressions .. 27. Integer Expressions .. 28. Boolean Expressions .. 29. Equations .. 30. Proper Statements as Expressions .. 31. 4 Lists 33. Operations on Lists .. 33. LIST .. 34. FIRST .. 34. 1. 2 CONTENTS. SECOND .. 34. THIRD .. 34. REST .. 34.. (Cons) Operator .. 34. APPEND .. 34. REVERSE .. 35. List Arguments of Other Operators .. 35. Caveats and Examples .. 35. 5 Statements 37. Assignment Statements .. 38. Set Statement .. 38. Group Statements .. 39. Conditional Statements .. 39. FOR Statements .. 40. WHILE .. DO .. 42. REPEAT .. UNTIL.

3 43. Compound Statements .. 43. Compound Statements with GO TO .. 45. Labels and GO TO Statements .. 45. RETURN Statements .. 46. 6 Commands and Declarations 49. Array Declarations .. 49. Mode Handling Declarations .. 50. END .. 51. BYE Command .. 51. SHOWTIME Command .. 51. DEFINE Command .. 51. 7 Built-in Prefix Operators 53. Numerical Operators .. 53. CONTENTS 3. ABS .. 53. CEILING .. 54. CONJ .. 54. FACTORIAL .. 54. FIX .. 54. FLOOR .. 55. IMPART .. 55. MAX/MIN .. 55. NEXTPRIME .. 55. RANDOM .. 56. RANDOM NEW SEED .. 56. REPART .. 56. ROUND .. 57. SIGN .. 57. Mathematical Functions.

4 57. DF Operator .. 61. Adding Differentiation Rules .. 61. INT Operator .. 62. Options .. 63. Advanced Use .. 63. References .. 63. LENGTH Operator .. 64. MAP Operator .. 64. MKID Operator .. 65. PF Operator .. 66. SELECT Operator .. 67. SOLVE Operator .. 68. Handling of Undetermined Solutions .. 69. Solutions of Equations Involving Cubics and Quartics .. 71. Other Options .. 73. 4 CONTENTS. Parameters and Variable Dependency .. 74. Even and Odd Operators .. 78. Linear Operators .. 78. Non-Commuting Operators .. 79. Symmetric and Antisymmetric Operators .. 80. Declaring New Prefix Operators.

5 80. Declaring New Infix Operators .. 81. Creating/Removing Variable Dependency .. 82. 8 Display and Structuring of Expressions 83. Kernels .. 83. The Expression Workspace .. 84. Output of Expressions .. 85. LINELENGTH Operator .. 86. Output Declarations .. 86. Output Control Switches .. 87. WRITE Command .. 91. Suppression of Zeros .. 93. FORTRAN Style Output Of Expressions .. 93. Saving Expressions for Later Use as Input .. 96. Displaying Expression Structure .. 96. Changing the Internal Order of Variables .. 99. Obtaining Parts of Algebraic Expressions .. 99. COEFF Operator.

6 99. COEFFN Operator .. 100. PART Operator .. 100. Substituting for Parts of Expressions .. 102. 9 Polynomials and Rationals 103. Controlling the Expansion of Expressions .. 104. Factorization of Polynomials .. 104. CONTENTS 5. Cancellation of Common Factors .. 106. Determining the GCD of Two Polynomials .. 107. Working with Least Common Multiples .. 108. Controlling Use of Common Denominators .. 108. REMAINDER Operator .. 108. RESULTANT Operator .. 109. DECOMPOSE Operator .. 110. INTERPOL operator .. 111. Obtaining Parts of Polynomials and Rationals .. 111. DEG Operator.

7 111. DEN Operator .. 112. LCOF Operator .. 112. LPOWER Operator .. 113. LTERM Operator .. 113. MAINVAR Operator .. 113. NUM Operator .. 114. REDUCT Operator .. 114. Polynomial Coefficient Arithmetic .. 115. Rational Coefficients in Polynomials .. 115. Real Coefficients in Polynomials .. 115. Modular Number Coefficients in Polynomials .. 117. Complex Number Coefficients in Polynomials .. 117. 10 Substitution Commands 119. SUB Operator .. 119. LET Rules .. 120. FOR ALL .. LET .. 122. FOR ALL .. SUCH THAT .. LET .. 123. Removing Assignments and Substitution Rules.

8 124. Overlapping LET Rules .. 124. Substitutions for General Expressions .. 125. 6 CONTENTS. Rule Lists .. 127. Asymptotic Commands .. 133. 11 File Handling Commands 135. IN Command .. 135. OUT Command .. 136. SHUT Command .. 136. 12 Commands for Interactive Use 137. Referencing Previous Results .. 137. Interactive Editing .. 138. Interactive File Control .. 139. 13 Matrix Calculations 141. MAT Operator .. 141. Matrix Variables .. 142. Matrix Expressions .. 142. Operators with Matrix Arguments .. 143. DET Operator .. 143. MATEIGEN Operator .. 144. TP Operator .. 145.

9 Trace Operator .. 145. Matrix Cofactors .. 145. NULLSPACE Operator .. 146. RANK Operator .. 147. Matrix Assignments .. 147. Evaluating Matrix Elements .. 147. 14 Procedures 149. Procedure Heading .. 150. Procedure Body .. 151. Using LET Inside Procedures .. 153. CONTENTS 7. LET Rules as Procedures .. 154. 15 user Contributed Packages 157. ALGINT: Integration of square roots .. 157. APPLYSYM: Infinitesimal symmetries of differential equations . 158. ARNUM: An algebraic number package .. 158. ASSIST: Useful utilities for various applications .. 158. AVECTOR: A vector algebra and calculus package.

10 159. BOOLEAN: A package for boolean algebra .. 159. CALI: A package for computational commutative algebra .. 159. CAMAL: Calculations in celestial mechanics .. 159. CHANGEVR: Change of Independent Variable(s) in DEs .. 160. : Package for compacting expressions .. 160. : Solving overdetermined systems of PDEs or ODEs .. 160. : Fast calculation of Dirac gamma matrix traces .. 161. : A definite integration interface .. 161. : Differential linear homogeneous equation solutions in the neighborhood of irregular and regular singular points .. 161. : Derivatives of generic functions.