diff options
Diffstat (limited to 'src/algebra/algfunc.spad.pamphlet')
| -rw-r--r-- | src/algebra/algfunc.spad.pamphlet | 12 |
1 files changed, 4 insertions, 8 deletions
diff --git a/src/algebra/algfunc.spad.pamphlet b/src/algebra/algfunc.spad.pamphlet index fbbe96dc..30cbb285 100644 --- a/src/algebra/algfunc.spad.pamphlet +++ b/src/algebra/algfunc.spad.pamphlet @@ -121,8 +121,7 @@ AlgebraicallyClosedField(): Category == Join(Field,RadicalCategory) with binomialRoots(p, y, fn) == -- p = a * x**n + b alpha := assign(x := new(y)$Symbol, fn(p, x)) --- one?(n := degree p) => [ alpha ] - ((n := degree p) = 1) => [ alpha ] + one?(n := degree p) => [ alpha ] cyclo := cyclotomic(n, monomial(1,1)$SUP)$NumberTheoreticPolynomialFunctions(SUP) beta := assign(x := new(y)$Symbol, fn(cyclo, x)) [alpha*beta**i for i in 0..(n-1)::NonNegativeInteger] @@ -384,8 +383,7 @@ AlgebraicFunction(R, F): Exports == Implementation where monomial? q => 0 (d := degree q) <= 0 => error "rootOf: constant polynomial" --- one? d=> - leadingCoefficient(reductum q) / leadingCoefficient q - (d = 1) => - leadingCoefficient(reductum q) / leadingCoefficient q + one? d=> - leadingCoefficient(reductum q) / leadingCoefficient q ((rx := retractIfCan(x)@Union(SE, "failed")) case SE) and ((r := UP2R q) case UPR) => rootOf(r::UPR, rx::SE)::F kernel(opalg, [q x, x]) @@ -403,8 +401,7 @@ AlgebraicFunction(R, F): Exports == Implementation where inrootof(q, x) == monomial? q => 0 (d := degree q) <= 0 => error "rootOf: constant polynomial" --- one? d => - leadingCoefficient(reductum q) /leadingCoefficient q - (d = 1) => - leadingCoefficient(reductum q) /leadingCoefficient q + one? d => - leadingCoefficient(reductum q) /leadingCoefficient q kernel(opalg, [q x, x]) evaluate(opalg, ialg)$BasicOperatorFunctions1(F) @@ -443,8 +440,7 @@ AlgebraicFunction(R, F): Exports == Implementation where inroot l == zero?(n := retract(second l)@Z) => error "root: exponent = 0" --- one?(x := first l) or one? n => x - ((x := first l) = 1) or (n = 1) => x + one?(x := first l) or one? n => x (r := retractIfCan(x)@Union(R,"failed")) case R => iroot(r::R,n) (u := isExpt(x)) case Record(var:K, exponent:Z) => pr := u::Record(var:K, exponent:Z) |