Unterschiede
Hier werden die Unterschiede zwischen zwei Versionen angezeigt.
Nächste Überarbeitung | Vorhergehende Überarbeitung | ||
cpm:mumath [2010/08/03 18:02] – angelegt volkerp | cpm:mumath [2020/11/24 14:35] (aktuell) – [muMATH] volkerp | ||
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====== muMATH ====== | ====== muMATH ====== | ||
- | Algebra-Software für CP/M | + | David R. Stoutemyer, 28.1.2012: |
+ | |||
+ | <wrap hi>//I am delighted that someone is keeping alive the memory of muMath!\\ | ||
+ | best regards, david// | ||
+ | </ | ||
+ | |||
+ | **Computer-Algebra-System für CP/M** | ||
+ | |||
+ | muMATH (manchmal auch myMATH geschrieben) war seinerzeit ein beeindruckendes Stück | ||
+ | Und das alles mit den beschränkten Speicher- und Rechenkapazitäten von CP/M! | ||
+ | |||
+ | muMATH ist fähig, | ||
+ | auch für sich selbst stehen. | ||
+ | |||
+ | muMATH wurde in den 70er Jahren von von Albert D. Rich und David Ross Stoutemyer entwickelt. Beide gründeten 1979 das Unternehmen The Soft Warehouse. | ||
+ | |||
+ | {{ : | ||
+ | |||
+ | Zur Computeralgebrageschichte und zu Implementationsdetails hat D. Stoutemyer 2008 einen Vortrag gehalten: http:// | ||
+ | |||
+ | muMATH ist in einem LISP-Derivat namens muSIMP geschrieben. muMATH war das erste Computeralgebrasystem (CAS), das auf " | ||
+ | |||
+ | muMATH-79 erschien 1979 und lief auf 8080- und Z80-Computern mit weniger als 48Kbyte RAM unter CP/M, und auf dem Radio Shack TRS-80 unter TRS-DOS. muMATH-80 erschien 1980 und lief zusätzlich auf 6502 based Apple II Computern. muMATH-83 erschien 1983 und lief auf 8088 based IBM PC und XT Computern mit weniger als 300Kbytes RAM. | ||
+ | |||
+ | {{: | ||
+ | //September 1, 1982: Microsoft announces the availability of its symbolic mathematic package muMATH/ | ||
+ | the Apple II, TRS-80, and CP/M-80 computer systems.// | ||
+ | |||
+ | DERIVE, der Nachfolger von muMATH, erschien 1988 und war unter DOS und später Windows lange Zeit gerade in der schulischen und studentischen Ausbildung verbreitet. | ||
+ | |||
+ | von http:// | ||
+ | |||
+ | //muMATH was written in a surface language for LISP that we named muSIMP. muSIMP stands for micro Symbolic IMPlementation language. While semantically equivalent to LISP, muSIMP provides a more conventional syntax than LISP (e.g. infix notation for math operators instead of LISP's Cambridge prefix notation, etc.). muSIMP starts out as muLISP, and then the first thing that is loaded is a parser (written in muLISP) that replaces the LISP parser with the more sophisticated muSIMP parser.// | ||
+ | |||
+ | ===== Dokumentation ===== | ||
+ | |||
+ | {{: | ||
+ | |||
+ | Zu Mumath gibt es ein Handbuch (auch in deutscher Sprache von der TUK); Lehrprogramme und außerdem Newsletter. | ||
+ | Diese Newsletter erschienen von Nov. 1979 bis Nov. 1988 in ingesamt 18 Ausgaben und einem Reprint der Ausgaben 1-16. | ||
+ | |||
+ | Vom Autor von Musimp, Albert Rich, habe ich die Newsletter als Original-Wordstar-Texte erhalten. Diese wurden mit [[cpm: | ||
+ | |||
+ | <WRAP clear></ | ||
===== Downloads ===== | ===== Downloads ===== | ||
- | * {{: | + | * {{: |
+ | * {{: | ||
+ | * http:// | ||
+ | * {{: | ||
+ | * {{: | ||
+ | * {{: | ||
+ | * {{ : | ||
+ | * {{ : | ||
+ | * http:// | ||
+ | |||
+ | ===== Links ===== | ||
+ | |||
+ | * http:// | ||
+ | * [[http:// | ||
+ | * [[http:// | ||
+ | |||
+ | ===== Schnellstart ===== | ||
+ | |||
+ | Zum Kennenlernen von Musimp (Version 2.14): | ||
+ | |||
+ | - Starte Musimp am CP/M prompt: **MUSIMP ALL** | ||
+ | - Setze " | ||
+ | - Starte die Demo durch folgende Eingabe am "?" | ||
+ | - Beende Musimp | ||
+ | |||
+ | <file - demo.prn> | ||
+ | %*** INTEGER ARITHMETIC EXAMPLES | ||
+ | |||
+ | % INTEGER ADDITION & SUBTRACTION % | ||
+ | |||
+ | 32 + 15 - 24; | ||
+ | @: 23 | ||
+ | |||
+ | |||
+ | ? % MULTIPLICATION & UNARY MINUS % | ||
+ | |||
+ | 5 * -12; | ||
+ | @: -60 | ||
+ | |||
+ | |||
+ | ? % USE OF PARENTHESIS % | ||
+ | |||
+ | 436 * (123 - 57); | ||
+ | @: 28776 | ||
+ | |||
+ | |||
+ | ? % RAISING TO A POWER % | ||
+ | |||
+ | 100^3; | ||
+ | @: 1000000 | ||
+ | |||
+ | |||
+ | ? % ASSIGNMENTS TO A VARIABLE % | ||
+ | |||
+ | FOO: (3*8 - 16)^2; | ||
+ | @: 64 | ||
+ | |||
+ | |||
+ | ? % USE OF ASSIGNED VARIABLE % | ||
+ | |||
+ | 3*FOO^5; | ||
+ | @: 3221225472 | ||
+ | |||
+ | |||
+ | ? % SAVE INTERMEDIATE RESULTS % | ||
+ | |||
+ | SEC#PER#YR: 365*24*3600; | ||
+ | @: 31536000 | ||
+ | |||
+ | |||
+ | ? IN#PER#MI: 5280*12; | ||
+ | @: 63360 | ||
+ | |||
+ | |||
+ | ? % USE OF INTERMEDIATE RESULTS % | ||
+ | % TO FIND INCHES TO ALHPA CENTAURI % | ||
+ | |||
+ | 4 * 186000 * SEC#PER#YR * IN# | ||
+ | @: 1486601994240000000 | ||
+ | |||
+ | |||
+ | ? % EXACT, INFINITE PRECISION % | ||
+ | |||
+ | 99^99; | ||
+ | @: | ||
+ | 3697296376497267726571879056288054405956687642817411 | ||
+ | 0243025997242355257045527752342141065001012823272794 | ||
+ | 0978889548326540119429996769494359451621570193644014 | ||
+ | 418071060667659301384999779999159200499899 | ||
+ | |||
+ | |||
+ | ? | ||
+ | %*** RATIONAL ARITHMETIC EXAMPLES | ||
+ | |||
+ | % REDUCE FRACTIONS TO LOWEST TERMS % | ||
+ | |||
+ | 56/77; | ||
+ | @: 8 / 11 | ||
+ | |||
+ | |||
+ | ? % FIND COMMON DENOMINATOR % | ||
+ | |||
+ | 5/6 - 3/4; | ||
+ | @: 1 / 12 | ||
+ | |||
+ | |||
+ | ? % RATIONAL SIMPLIFICATION % | ||
+ | |||
+ | 3 * (1/2 + 1/6); | ||
+ | @: 2 | ||
+ | |||
+ | |||
+ | ? % FLOATING POINT NOTATION % | ||
+ | |||
+ | POINT: 10$ | ||
+ | |||
+ | ? 1/3; | ||
+ | @: 0.3333333333 | ||
+ | |||
+ | |||
+ | ? | ||
+ | %*** VARIABLE RADIX BASE ***% | ||
+ | |||
+ | % SET FOR HEXADECIMAL ARITHMETIC % | ||
+ | |||
+ | RADIX (16); | ||
+ | @: 0A | ||
+ | |||
+ | |||
+ | ? % USE AS A HEX CALCULATOR % | ||
+ | |||
+ | 7C80 - 2*12EF + 0A3C; | ||
+ | @: 60DE | ||
+ | |||
+ | |||
+ | ? % ASSIGNMENT TO A VARIABLE % | ||
+ | |||
+ | EG: 10000; | ||
+ | @: 10000 | ||
+ | |||
+ | |||
+ | ? % RETURN TO BASE TEN ARITHMETIC % | ||
+ | |||
+ | RADIX (0A); | ||
+ | @: 16 | ||
+ | |||
+ | |||
+ | ? % FIND EG IN BASE TEN % | ||
+ | |||
+ | EG; | ||
+ | @: 65536 | ||
+ | |||
+ | |||
+ | ? % BASE TWO ARITHMETIC % | ||
+ | |||
+ | RADIX (2); | ||
+ | @: 1010 | ||
+ | |||
+ | |||
+ | ? % BINARY ARITHMETIC CALCULATOR % | ||
+ | |||
+ | 101101110 * EG; | ||
+ | @: 1011011100000000000000000 | ||
+ | |||
+ | |||
+ | ? % RETURN TO BASE TEN ARITHMETIC % | ||
+ | |||
+ | RADIX (1010); | ||
+ | @: 2 | ||
+ | |||
+ | |||
+ | ? | ||
+ | %*** EXPONENTIAL SIMPLIFICATIONS | ||
+ | |||
+ | % FRACTIONAL POWERS % | ||
+ | 8 ^ (2/3); | ||
+ | @: 4 | ||
+ | |||
+ | |||
+ | ? 12 ^ (1/2); | ||
+ | @: 2 * 3^0.5 | ||
+ | |||
+ | |||
+ | ? % POWERS OF THE IMAGINARY NUMBER % | ||
+ | |||
+ | #I^2; | ||
+ | @: -1 | ||
+ | |||
+ | |||
+ | ? #I^-7; | ||
+ | @: #I | ||
+ | |||
+ | |||
+ | ? % COMPLEX EXPONENTIALS % | ||
+ | |||
+ | #E ^ (#I*#PI); | ||
+ | @: -1 | ||
+ | |||
+ | |||
+ | ? | ||
+ | %*** | ||
+ | |||
+ | 5!; | ||
+ | @: 120 | ||
+ | |||
+ | |||
+ | ? 50!^2; | ||
+ | @: | ||
+ | 9250170652825079190134707232358836823494868074219019 | ||
+ | 8770613927101881057071736043444238321314044821530214 | ||
+ | 4000000000000000000000000 | ||
+ | |||
+ | |||
+ | ? % BINOMIAL COEFFICIENTS [12:30] % | ||
+ | |||
+ | N: 30; | ||
+ | @: 30 | ||
+ | |||
+ | |||
+ | ? M: 12; | ||
+ | @: 12 | ||
+ | |||
+ | |||
+ | ? N! / ((N-M)!*M!); | ||
+ | @: 86493225 | ||
+ | |||
+ | |||
+ | ? | ||
+ | %*** BASIC ALGEBRA EXAMPLES | ||
+ | |||
+ | % AUTOMATIC ALGEBRAIC SIMPLIFICATION % | ||
+ | |||
+ | % COMBINES SIMILAR TERMS AND FACTORS % | ||
+ | |||
+ | 3*X - X; | ||
+ | @: 2 * X | ||
+ | |||
+ | |||
+ | ? Y^3 * Y^(R+1); | ||
+ | @: Y ^ (4+R) | ||
+ | |||
+ | |||
+ | ? | ||
+ | % EXPLOITS IDENTITIES AND ZEROS % | ||
+ | |||
+ | 0 + X; | ||
+ | @: X | ||
+ | |||
+ | |||
+ | ? 1 * Y; | ||
+ | @: Y | ||
+ | |||
+ | |||
+ | ? Z * 0; | ||
+ | @: 0 | ||
+ | |||
+ | |||
+ | ? X^1; | ||
+ | @: X | ||
+ | |||
+ | |||
+ | ? Y^0; | ||
+ | @: 1 | ||
+ | |||
+ | |||
+ | ? 1^X; | ||
+ | @: 1 | ||
+ | |||
+ | |||
+ | ? % MULTIPLE SIMPLIFICATIONS % | ||
+ | |||
+ | 5*X^1*Y + Y^2*-3*X/Y + W^(Z^2 - Z*Z); | ||
+ | @: 1 + 2*X*Y | ||
+ | |||
+ | |||
+ | ? % POLYNOMIAL MULTIPLICATION % | ||
+ | |||
+ | (3*X - 2*Y) * (Y^2 + 4*X); | ||
+ | @: -8*X*Y + 3*X*Y^2 + 12*X^2 - 2*Y^3 | ||
+ | |||
+ | |||
+ | ? % POLYNOMIAL POWERS % | ||
+ | |||
+ | (X+1)^2; | ||
+ | @: 1 + 2*X + X^2 | ||
+ | |||
+ | |||
+ | ? (X+5) * (X^2-2*X+3)^2; | ||
+ | @: 45 - 51*X + 38*X^2 - 10*X^3 + X^4 + X^5 | ||
+ | |||
+ | |||
+ | ? % CONTENT FACTORIZATION % | ||
+ | |||
+ | FCTR (6*X^3*Y + 15*X^2*Y); | ||
+ | @: 3 * X^2 * Y * (5+2*X) | ||
+ | |||
+ | |||
+ | ? | ||
+ | %*** LOGARITHMIC SIMPLIFICATIONS | ||
+ | |||
+ | % NATURAL LOG OF ONE % | ||
+ | |||
+ | LN (1); | ||
+ | @: 0 | ||
+ | |||
+ | |||
+ | ? % COMMON LOG OF 1000 % | ||
+ | |||
+ | LOG (1000, 10); | ||
+ | @: 3 | ||
+ | |||
+ | |||
+ | ? % EXPAND THE LOG OF A PRODUCT % | ||
+ | |||
+ | LN (X*Y); | ||
+ | @: LN(X) + LN(Y) | ||
+ | |||
+ | |||
+ | ? % EXPAND THE LOG OF A POWER % | ||
+ | |||
+ | LOG (Z^3, 10); | ||
+ | @: 3*LN(Z) / LN(10) | ||
+ | |||
+ | |||
+ | ? % MULTIPLE SIMPLIFICATIONS % | ||
+ | |||
+ | LN(X^2*Y) - 2*LN(X); | ||
+ | @: LN (Y) | ||
+ | |||
+ | |||
+ | ? % INTER-BASE SIMPLIFICATIONS % | ||
+ | |||
+ | LOG(X,10) * LOG(10,# | ||
+ | @: LN (X) | ||
+ | |||
+ | |||
+ | ? % LOGARITHMIC POWERS % | ||
+ | |||
+ | #E ^ LN(X+5); | ||
+ | @: 5 + X | ||
+ | |||
+ | |||
+ | ? | ||
+ | %*** TRIGONOMETRIC SIMPLIFICATIONS ***% | ||
+ | |||
+ | % ELEMENTARY ANGLE VALUES % | ||
+ | |||
+ | COS (0); | ||
+ | @: 1 | ||
+ | |||
+ | |||
+ | ? SIN (#PI/2); | ||
+ | @: 1 | ||
+ | |||
+ | |||
+ | ? SIN (37*# | ||
+ | @: 3^0.5 / 2 | ||
+ | |||
+ | |||
+ | ? % EQUIVALENT FUNCTIONS % | ||
+ | |||
+ | TAN(X) * COS(X); | ||
+ | @: SIN (X) | ||
+ | |||
+ | |||
+ | ? % MULTIPLE ANGLES EXPANSION % | ||
+ | |||
+ | SIN (2*X); | ||
+ | @: 2 * COS(X) * SIN(X) | ||
+ | |||
+ | |||
+ | ? COS(3*X); | ||
+ | @: 4*COS(X)^3 - 3*COS(X) | ||
+ | |||
+ | |||
+ | ? % ANGLE SUMS EXPANSION % | ||
+ | |||
+ | COS (X-Y); | ||
+ | @: COS(X)*COS(Y) + SIN(X)*SIN(Y) | ||
+ | |||
+ | |||
+ | ? % COMBINATION EXPANSIONS % | ||
+ | |||
+ | EG: SIN (2*X+Y); | ||
+ | @: 2*COS(X)^2*SIN(Y) + 2*COS(X)*COS(Y)*SIN(X) - SIN( | ||
+ | Y) | ||
+ | |||
+ | |||
+ | ? | ||
+ | %*** REPRESENT EQUATIONS | ||
+ | |||
+ | EQN: 2*X+7 == A^2 - X^2/X - 3; | ||
+ | @: 7+2*X == -3-X+A^2 | ||
+ | |||
+ | |||
+ | ? % STEP BY STEP SOLUTION FOR X % | ||
+ | |||
+ | EQN: EQN + X - 7; | ||
+ | @: 3*X == -10+A^2 | ||
+ | |||
+ | |||
+ | ? EQN: EQN/3; | ||
+ | @: X == (-10+A^2)/ | ||
+ | |||
+ | |||
+ | ? | ||
+ | %*** CALCULUS OPERATIONS | ||
+ | |||
+ | % FIND DERIVATIVES % | ||
+ | |||
+ | DIF (3*X^2 + 5*X - 4, X); | ||
+ | @: 5 + 6*X | ||
+ | |||
+ | |||
+ | ? DIF (LN(X)^2, X); | ||
+ | @: 2*LN(X) / X | ||
+ | |||
+ | |||
+ | ? DIF (#E^X^2, X); | ||
+ | @: 2 * #E^X^2 * X | ||
+ | |||
+ | |||
+ | ? DIF (P*SIN(X) + X^2, X); | ||
+ | @: 2*X + P*COS(X) | ||
+ | |||
+ | |||
+ | ? % FIND INTEGRALS % | ||
+ | |||
+ | INT (2*X - 1/X, X); | ||
+ | @: X^2 - LN(X) | ||
+ | |||
+ | |||
+ | ? INT (X * #E^X^2 * SIN(# | ||
+ | @: -COS(# | ||
+ | |||
+ | |||
+ | ? INT (LN(LN(X))/ | ||
+ | @: LN(X)*LN(LN(X)) - LN(X) | ||
+ | |||
+ | |||
+ | ? | ||
+ | %*** | ||
+ | |||
+ | % TAYLOR SERIES EXPANSION FUNCTION % | ||
+ | |||
+ | FUNCTION TAYLOR (EXPN, X, A, N, | ||
+ | % Locals: % J, C, ANS, NUMNUM, DENNUM), | ||
+ | NUMNUM: DENNUM: 30, | ||
+ | J: ANS: 0, | ||
+ | C: 1, | ||
+ | LOOP | ||
+ | ANS: ANS + C * EVSUB (EXPN, X, A), | ||
+ | WHEN J=N, ANS EXIT, | ||
+ | EXPN: DIF (EXPN, X), | ||
+ | J: J + 1, | ||
+ | C: C * (X-A) / J, | ||
+ | ENDLOOP, | ||
+ | ENDFUN ; | ||
+ | @: *** REDEFINED: TAYLOR | ||
+ | | ||
+ | |||
+ | |||
+ | ? % TAYLOR SERIES EXPANSION % | ||
+ | |||
+ | TAYLOR (#E^X, X, 0, 6); | ||
+ | @: 1 + X + X^2/2 + X^3/6 + X^4/24 + X^5/120 + X^6/ | ||
+ | 720 | ||
+ | |||
+ | |||
+ | ? TAYLOR (SIN(X), X, 0, 8); | ||
+ | @: X - X^3/6 + X^5/120 - X^7/5040 | ||
+ | |||
+ | |||
+ | ? TAYLOR (#E^SIN(X), X, 0, 4); | ||
+ | @: 1 + X + X^2/2 - X^4/8 | ||
+ | |||
+ | |||
+ | ? | ||
+ | MOVD (' | ||
+ | |||
+ | ? RDS ()$ | ||
+ | |||
+ | ? ^C | ||
+ | </ |