diff options
Diffstat (limited to 'src/algebra/manip.spad.pamphlet')
| -rw-r--r-- | src/algebra/manip.spad.pamphlet | 30 |
1 files changed, 10 insertions, 20 deletions
diff --git a/src/algebra/manip.spad.pamphlet b/src/algebra/manip.spad.pamphlet index e112a811..17fb455a 100644 --- a/src/algebra/manip.spad.pamphlet +++ b/src/algebra/manip.spad.pamphlet @@ -33,8 +33,7 @@ FactoredFunctions(M:IntegralDomain): Exports == Implementation where Implementation ==> add nthRoot(ff, n) == coeff:M := 1 --- radi:List(M) := (one? unit ff => empty(); [unit ff]) - radi:List(M) := (((unit ff) = 1) => empty(); [unit ff]) + radi:List(M) := (one? unit ff => empty(); [unit ff]) lf := factors ff d:N := empty? radi => gcd(concat(n, [t.exponent::N for t in lf]))::N @@ -100,8 +99,7 @@ PolynomialRoots(E, V, R, P, F):Exports == Implementation where zroot : (Z, N) -> Record(exponent:N, coef:Z, radicand:Z) zroot(x, n) == --- zero? x or one? x => [1, x, 1] - zero? x or (x = 1) => [1, x, 1] + zero? x or one? x => [1, x, 1] s := nthRoot(squareFree x, n) [s.exponent, s.coef, */s.radicand] @@ -164,8 +162,7 @@ PolynomialRoots(E, V, R, P, F):Exports == Implementation where else nthr(x, n) == nthRoot(squareFree x, n) froot(x, n) == --- zero? x or one? x => [1, x, 1] - zero? x or (x = 1) => [1, x, 1] + zero? x or one? x => [1, x, 1] sn := nthr(numer x, n) sd := nthr(denom x, n) pn := rsplit(sn.radicand) @@ -358,18 +355,15 @@ AlgebraicManipulations(R, F): Exports == Implementation where q := univariate(p, k) while (d := degree q) > 0 repeat term := --- one?(g := gcd(d, n)) => monomial(1, k, d) - ((g := gcd(d, n)) = 1) => monomial(1, k, d) + one?(g := gcd(d, n)) => monomial(1, k, d) monomial(1, kernel(operator k, [a,(n quo g)::F], height k), d quo g) ans := ans + leadingCoefficient(q)::F * term::F q := reductum q leadingCoefficient(q)::F + ans inroot(op, x, n) == --- one? x => x - (x = 1) => x --- (x ~= -1) and (one?(num := numer x) or (num = -1)) => - (x ~= -1) and (((num := numer x) = 1) or (num = -1)) => + one? x => x + (x ~= -1) and (one?(num := numer x) or (num = -1)) => inv inroot(op, (num * denom x)::F, n) (u := isExpt(x, op)) case "failed" => kernel(op, [x, n::F]) pr := u::Record(var:K, exponent:Integer) @@ -648,13 +642,11 @@ TranscendentalManipulations(R, F): Exports == Implementation where not (terms case "failed") => logArgs(terms) expt : Union(POW, "failed") := isPower(e) --- (expt case POW) and not one? expt.exponent => - (expt case POW) and not (expt.exponent = 1) => + (expt case POW) and not one? expt.exponent => simplifyLog(expt.val)**(expt.exponent) kers : List K := kernels e --- not(one?(#kers)) => e -- Have a constant - not(((#kers) = 1)) => e -- Have a constant + not(one?(#kers)) => e -- Have a constant kernel(operator first kers,[simplifyLog(u) for u in argument first kers]) @@ -666,10 +658,8 @@ TranscendentalManipulations(R, F): Exports == Implementation where expandpow k == a := expandPower first(arg := argument k) b := expandPower second arg --- ne:F := (one? numer a => 1; numer(a)::F ** b) - ne:F := (((numer a) = 1) => 1; numer(a)::F ** b) --- de:F := (one? denom a => 1; denom(a)::F ** (-b)) - de:F := (((denom a) = 1) => 1; denom(a)::F ** (-b)) + ne:F := (one? numer a => 1; numer(a)::F ** b) + de:F := (one? denom a => 1; denom(a)::F ** (-b)) ne * de termexp p == |