Reduce: Software for Algebraic Computation

ISBN-13: 9780387965987 / Angielski / Miękka / 1987 / 329 str.

Gerhard Rayna; Anthony C. Hearn

Opis

CONTRIBUTED BY DR. ANTHONY C. HEARN THE RAND CORPORATION, SANTA MONICA, CALIFORNIA REDUCE is a computer program for algebraic computation that IS III world-wide use by thousands of scientists, engineers, and mathematicians. Although it traces its beginnings to 1963, until recently it has only been available on main-frame computers because of its relatively large resource requirements. In 1980 I predicted (1) that by the mid-1980's it would be possible to obtain personal computers in the $10,000 $20,000 range capable of running REDUCE. I am therefore delighted to see that machines of the power of the IBM PC can now run this system, even though these computers are more modestly priced than my 1980 vision of the personal algebra machine. In addition to the need for the more widespread access that personal computers can now provide, there has been a longstanding need for a textbook to help the beginning user become better acquainted with the system. I am therefore very glad that Dr. Rayna has undertaken to write such a book, just as the era of the REDUCE personal algebra machine is beginning. In order to understand the nature of REDUCE, a little history is in order. In 1963 I met Dr. John McCarthy, the inventor of LISP.

Spis treści

1.Overview.- 1.1. Variables, values, assignments.- 1.2. The basic operations.- 1.3. Giving commands, getting answers.- 1.4. A first look at CLEAR.- 1.5. WS, SAVEAS, INPUT n.- 1.6. Some built-in functions.- 1.7. NUM and DEN.- 1.8. Differentiation.- 1.8.1. Partial derivatives.- 1.9. Integration.- 1.10. FOR … DO.- 1.11. FOR … SUM.- 1.12. FOR … PRODUCT.- 1.13. WHILE … DO.- 1.14. Boolean expressions.- 1.15. REPEAT … UNTIL.- 2. A Harder Look.- 2.1. The SUBSTITUTION function.- 2.2. ARRAY and OPERATOR.- 2.2.1. Arrays.- 2.2.2. Operators.- 2.3. Matrices.- 2.3.1. MAT.- 2.3.2. Printing matrices.- 2.3.3. Matrix expressions.- 2.3.4. Other matrix operations.- 2.3.5. A matrix example.- 2.4. The COEFF function.- 2.4.1. Multi-dimensional arrays.- 2.4.2. Simple variable destinations.- 2.5. FACTORIZE.- 2.5.1. Simple variable destinations.- 2.6. The SOLVE function.- 2.7. LET and CLEAR.- 2.7.1. A first look at LET.- 2.7.2. LET power =….- 2.7.3. MATCH power =….- 2.7.4. LET product =….- 2.7.5. LET sum =….- 2.7.6. LET operator =….- 2.7.7. CLEAR.- 2.7.8. FOR ALL X LET… =….- 2.7.9. FOR ALL… SUCH THAT … LET …=….- 2.7.10. LET DF(…) =.- 2.7.11. Overlapping rules.- 2.7.12. WEIGHT.- 2.7.13. Complex assignments.- 2.8. WRITE.- 2.9. Grouping.- 2.9.1. Grouped statements.- 2.9.2. Groups as expressions.- 2.10. IF… THEN.- 2.10.1. IF… THEN statements.- 2.10.2. IF… THEN expressions.- 2.11. PART and setting a PART.- 2.11.1. PART.- 2.11.2. Setting a PART.- 3. Setting Modes and Options.- 3.1. EXP.- 3.2. GCD.- 3.3. LCM.- 3.4. MCD.- 3.5. RESUBS.- 3.6. ORDER.- 3.7. FACTOR command.- 3.8. FACTOR switch.- 3.9. DIV.- 3.10. RAT.- 3.11. ALLFAC.- 3.12. LIST.- 3.13. NERO.- 3.14. NAT, FORT.- 3.15. PRI.- 3.16. KORDER.- 3.17. Domain modes.- 3.17.1. FLOAT.- 3.17.2. BIGFLOAT and NUMVAL.- 3.17.3. RATIONAL.- 3.17.4. MODULAR.- 4. Procedures.- 4.1. Procedures without parameters or RETURN.- 4.2. Procedures with RETURN.- 4.3. Returning multiple values.- 4.4. Procedures with one parameter.- 4.5. Procedures with more than one parameter.- 4.6. Procedures with local variables.- 4.7. Interaction of procedures.- 4.8. Linkage questions.- 4.8.1. Formal parameters.- 4.8.1.1. The copy variable.- 4.8.1.2. The LET exception.- 4.8.1.3. CLEAR.- 4.8.1.4. The SUB exception.- 4.8.1.5. Arrays and the like.- 4.8.1.6. Advice.- 4.8.2. Local variables.- 4.8.3. The scopes of variables.- 4.8.4. Exit on error.- 4.9. Procedures with GO TO.- 4.10. LET rules as procedures.- 5. Case Studies.- 5.1. Find the variables.- 5.1.1. Find a given variable.- 5.1.2. Finding all variables.- 5.2. Dividing polynomials.- 5.2.1. Exact division.- 5.2.2. Divisions with remainder.- 5.2.2.1. The linear denominator case.- 5.2.3. A polynomial division procedure.- 5.2.4. The REMAINDER function.- 5.3. LCM, GCD, and the Euclidean Algorithm.- 5.3.1. Least common multiple.- 5.3.2. Greatest common divisor.- 5.3.3. The Euclidean Algorithm.- 5.4. Systems of linear equations.- 5.4.1. A procedure.- 5.5. Series approximations to quotients.- 5.5.1. Maclaurin expansion.- 5.6. Families of polynomials.- 5.6.1. The Tschebycheff polynomials.- 5.6.2. The Newton polynomials.- 5.6.3. Orthogonal polynomials.- 5.7. Rationalizing denominators.- 5.7.1. Automating the process.- 5.7.2. Algebraic numbers as denominators.- 5.8. A bug involving surds.- 5.9. Noncommuting symbols.- 5.9.1. Quaternions.- 5.9.2. Steenrod Squares.- 6. Running REDUCE.- 6.1. The basics.- 6.2. IN from files.- 6.2.1. REDUCE.INI.- 6.2.2. PAUSE, CONT, and DEMO.- 6.3. Making corrections.- 6.3.1. Correcting as you type.- 6.3.2. Correcting the previous statement.- 6.3.3. Editing earlier statements.- 6.3.4. Correcting syntax errors in files.- 6.3.5. Correcting files.- 6.3.6. Correcting procedures.- 6.4. INPUT, RETRY, CMD.- 6.5. OUT, FORT, LINELENGTH.- 6.5.1. OUT to files.- 6.5.2. FORT.- 6.5.3. LINELENGTH and FORTWIDTH!*.- 6.6. COMPILE, FASLOUT, LOAD.- 6.6.1. Fast-loading files/fast-running procedures.- 6.7. TIME, SHOWTIME.- 6.8. DEFINE.- 6.9. Tracing.- 6.10. Expression input.- 6.11. Lost in LISP?.