diff options
Diffstat (limited to 'src/algebra/manip.spad.pamphlet')
| -rw-r--r-- | src/algebra/manip.spad.pamphlet | 43 |
1 files changed, 22 insertions, 21 deletions
diff --git a/src/algebra/manip.spad.pamphlet b/src/algebra/manip.spad.pamphlet index afdb165c..e112a811 100644 --- a/src/algebra/manip.spad.pamphlet +++ b/src/algebra/manip.spad.pamphlet @@ -420,7 +420,7 @@ TranscendentalManipulations(R, F): Exports == Implementation where K ==> Kernel F P ==> SparseMultivariatePolynomial(R, K) UP ==> SparseUnivariatePolynomial P - POWER ==> "%power"::Symbol + POWER ==> '%power POW ==> Record(val: F,exponent: Z) PRODUCT ==> Record(coef : Z, var : K) FPR ==> Fraction Polynomial R @@ -593,11 +593,11 @@ TranscendentalManipulations(R, F): Exports == Implementation where sum : F := 0 arg : F := 1 for term in l repeat - is?(term,"log"::Symbol) => + is?(term,'log) => arg := arg * simplifyLog(first(argument(first(kernels(term))))) -- Now look for multiples, including negative ones. prod : Union(PRODUCT, "failed") := isMult(term) - (prod case PRODUCT) and is?(prod.var,"log"::Symbol) => + (prod case PRODUCT) and is?(prod.var,'log) => arg := arg * simplifyLog ((first argument(prod.var))**(prod.coef)) sum := sum+term sum+log(arg) @@ -606,11 +606,11 @@ TranscendentalManipulations(R, F): Exports == Implementation where simplifyLog1(numerator e)/simplifyLog1(denominator e) simplifyLog1(e:F):F == - freeOf?(e,"log"::Symbol) => e + freeOf?(e,'log) => e -- Check for n*log(u) prod : Union(PRODUCT, "failed") := isMult(e) - (prod case PRODUCT) and is?(prod.var,"log"::Symbol) => + (prod case PRODUCT) and is?(prod.var,'log) => log simplifyLog ((first argument(prod.var))**(prod.coef)) termList : Union(List(F),"failed") := isTimes(e) @@ -635,7 +635,7 @@ TranscendentalManipulations(R, F): Exports == Implementation where i : NonNegativeInteger := 0 while (not(foundLog) and (i < #terms)) repeat i := i+1 - if is?(terms.i,"log"::Symbol) then + if is?(terms.i,'log) then args : List F := argument(retract(terms.i)@K) setelt(terms,i, log simplifyLog1(first(args)**(*/exprs))) foundLog := true @@ -678,7 +678,7 @@ TranscendentalManipulations(R, F): Exports == Implementation where lpow := select(is?(#1, POWER)$K, lk := variables p)$List(K) for k in lk repeat d := degree(p, k) - if is?(k, "exp"::Symbol) then + if is?(k, 'exp) then exponent := exponent + d * first argument k else if not is?(k, POWER) then -- Expand arguments to functions as well ... MCD 23/1/97 @@ -747,7 +747,7 @@ TranscendentalManipulations(R, F): Exports == Implementation where arg := [htrigs x for x in argument k]$List(F) num := univariate(numer f, k) den := univariate(denom f, k) - is?(op, "exp"::Symbol) => + is?(op,'exp) => g1 := cosh(a := first arg) + sinh(a) g2 := cosh(a) - sinh(a) supexp(num,g1,g2,b:= (degree num)::Z quo 2)/supexp(den,g1,g2,b) @@ -770,7 +770,7 @@ TranscendentalManipulations(R, F): Exports == Implementation where logexpand k == nullary?(op := operator k) => k::F - is?(op, "log"::Symbol) => + is?(op,'log) => exlog(numer(x := expandLog first argument k)) - exlog denom x op [expandLog x for x in argument k]$List(F) @@ -778,24 +778,23 @@ TranscendentalManipulations(R, F): Exports == Implementation where nullary?(op := operator k) => k::F is?(op, POWER) => expandpow k arg := first argument k - is?(op, "sec"::Symbol) => inv expand cos arg - is?(op, "csc"::Symbol) => inv expand sin arg - is?(op, "log"::Symbol) => - exlog(numer(x := expand arg)) - exlog denom x + is?(op,'sec) => inv expand cos arg + is?(op,'csc) => inv expand sin arg + is?(op,'log) => exlog(numer(x := expand arg)) - exlog denom x num := numer arg den := denom arg (b := (reductum num) / den) ~= 0 => a := (leadingMonomial num) / den - is?(op, "exp"::Symbol) => exp(expand a) * expand(exp b) - is?(op, "sin"::Symbol) => + is?(op,'exp) => exp(expand a) * expand(exp b) + is?(op,'sin) => sin(expand a) * expand(cos b) + cos(expand a) * expand(sin b) - is?(op, "cos"::Symbol) => + is?(op,'cos) => cos(expand a) * expand(cos b) - sin(expand a) * expand(sin b) - is?(op, "tan"::Symbol) => + is?(op,'tan) => ta := tan expand a tb := expand tan b (ta + tb) / (1 - ta * tb) - is?(op, "cot"::Symbol) => + is?(op,'cot) => cta := cot expand a ctb := expand cot b (cta * ctb - 1) / (ctb + cta) @@ -815,16 +814,18 @@ TranscendentalManipulations(R, F): Exports == Implementation where -- pass3 groups exponentials together simplify0 x == simplifyExp eval(eval(x, - ["tan"::Symbol,"cot"::Symbol,"sec"::Symbol,"csc"::Symbol, - "tanh"::Symbol,"coth"::Symbol,"sech"::Symbol,"csch"::Symbol], + ['tan,'cot,'sec,'csc, + 'tanh,'coth,'sech,'csch], [t2t,c2t,s2c,c2s,th2th,ch2th,sh2ch,ch2sh]), - ["sin"::Symbol, "sinh"::Symbol], [2, 2], [s2c2, sh2ch2]) + ['sin, 'sinh], [2, 2], [s2c2, sh2ch2]) @ \section{License} <<license>>= --Copyright (c) 1991-2002, The Numerical ALgorithms Group Ltd. --All rights reserved. +--Copyright (C) 2007-2009, Gabriel Dos Reis. +--All rights reserved. -- --Redistribution and use in source and binary forms, with or without --modification, are permitted provided that the following conditions are |