diff options
| author | dos-reis <gdr@axiomatics.org> | 2008-04-03 04:23:42 +0000 |
|---|---|---|
| committer | dos-reis <gdr@axiomatics.org> | 2008-04-03 04:23:42 +0000 |
| commit | 001e19b08ba7fb1b9e6f6bdb44a82ba3db3fc532 (patch) | |
| tree | da9e2fe5d81ff4cd7709d12e44b8c3e348b8a8e3 /src/algebra/ore.spad.pamphlet | |
| parent | a7bab9a6c2070d05e2dbd256ce455079c8ced385 (diff) | |
| download | open-axiom-001e19b08ba7fb1b9e6f6bdb44a82ba3db3fc532.tar.gz | |
Replace `^=' with `~='.
Diffstat (limited to 'src/algebra/ore.spad.pamphlet')
| -rw-r--r-- | src/algebra/ore.spad.pamphlet | 18 |
1 files changed, 9 insertions, 9 deletions
diff --git a/src/algebra/ore.spad.pamphlet b/src/algebra/ore.spad.pamphlet index 1c567ebf..ebdc406a 100644 --- a/src/algebra/ore.spad.pamphlet +++ b/src/algebra/ore.spad.pamphlet @@ -30,7 +30,7 @@ UnivariateSkewPolynomialCategory(R:Ring): ++ \spad{l = sum(monomial(a(i),i), i = 0..n)}. minimumDegree: $ -> NonNegativeInteger ++ minimumDegree(l) is the smallest \spad{k} such that - ++ \spad{a(k) ^= 0} if + ++ \spad{a(k) ~= 0} if ++ \spad{l = sum(monomial(a(i),i), i = 0..n)}. leadingCoefficient: $ -> R ++ leadingCoefficient(l) is \spad{a(n)} if @@ -146,14 +146,14 @@ UnivariateSkewPolynomialCategory(R:Ring): coefficients l == ans:List(R) := empty() - while l ^= 0 repeat + while l ~= 0 repeat ans := concat(leadingCoefficient l, ans) l := reductum l ans a:R * y:% == z:% := 0 - while y ^= 0 repeat + while y ~= 0 repeat z := z + monomial(a * leadingCoefficient y, degree y) y := reductum y z @@ -165,7 +165,7 @@ UnivariateSkewPolynomialCategory(R:Ring): if R has IntegralDomain then l exquo a == ans:% := 0 - while l ^= 0 repeat + while l ~= 0 repeat (u := (leadingCoefficient(l) exquo a)) case "failed" => return "failed" ans := ans + monomial(u::R, degree l) @@ -205,7 +205,7 @@ UnivariateSkewPolynomialCategory(R:Ring): a0 := a u0:% := v:% := 1 v0:% := u:% := 0 - while b ^= 0 repeat + while b ~= 0 repeat qr := leftDivide(a, b) (a, b) := (b, qr.remainder) (u0, u):= (u, u0 - u * qr.quotient) @@ -216,7 +216,7 @@ UnivariateSkewPolynomialCategory(R:Ring): zero? a => b zero? b => a degree a < degree b => ncgcd(b, a, ncrem) - while b ^= 0 repeat (a, b) := (b, ncrem(a, b)) + while b ~= 0 repeat (a, b) := (b, ncrem(a, b)) a extended(a, b, eea) == @@ -240,7 +240,7 @@ UnivariateSkewPolynomialCategory(R:Ring): a0 := a u0:% := v:% := 1 v0:% := u:% := 0 - while b ^= 0 repeat + while b ~= 0 repeat qr := rightDivide(a, b) (a, b) := (b, qr.remainder) (u0, u):= (u, u0 - qr.quotient * u) @@ -392,7 +392,7 @@ UnivariateSkewPolynomialCategoryOps(R, C): Exports == Implementation where times(x, y, sigma, delta) == zero? y => 0 z:C := 0 - while x ^= 0 repeat + while x ~= 0 repeat z := z + termPoly(leadingCoefficient x, degree x, y, sigma, delta) x := reductum x z @@ -402,7 +402,7 @@ UnivariateSkewPolynomialCategoryOps(R, C): Exports == Implementation where (u := subtractIfCan(n, 1)) case "failed" => a * y n1 := u::N z:C := 0 - while y ^= 0 repeat + while y ~= 0 repeat m := degree y b := leadingCoefficient y z := z + termPoly(a, n1, monomial(sigma b, m + 1), sigma, delta) |