diff options
| author | dos-reis <gdr@axiomatics.org> | 2011-03-10 18:14:47 +0000 |
|---|---|---|
| committer | dos-reis <gdr@axiomatics.org> | 2011-03-10 18:14:47 +0000 |
| commit | 3018eca8731c1ebfc07487d6ba305c82090b4dca (patch) | |
| tree | 2977f65419c43b201a65e63a8bcf55dfaa443639 /src/algebra/catdef.spad.pamphlet | |
| parent | d39e317cd51e0f251d485df1948e2a85a4007048 (diff) | |
| download | open-axiom-3018eca8731c1ebfc07487d6ba305c82090b4dca.tar.gz | |
* algebra/catdef.spad.pamphlet (CharacteristicNonZero)
[charthRoot]: Now return Maybe %.
(PolynomialFactorizationExplicit) [charthRoot]: Likewise.
* algebra/ffcat.spad.pamphlet (FiniteAlgebraicExtensionField):
Propagate change.
* algebra/fraction.spad.pamphlet (Fraction) [charthRoot]: Likewise.
* algebra/poly.spad.pamphlet (UnivariatePolynomialSquareFree):
Likewise.
* algebra/polycat.spad.pamphlet (PolynomialCategory): Likewise.
Diffstat (limited to 'src/algebra/catdef.spad.pamphlet')
| -rw-r--r-- | src/algebra/catdef.spad.pamphlet | 16 |
1 files changed, 9 insertions, 7 deletions
diff --git a/src/algebra/catdef.spad.pamphlet b/src/algebra/catdef.spad.pamphlet index 694d169f..7dfc10fc 100644 --- a/src/algebra/catdef.spad.pamphlet +++ b/src/algebra/catdef.spad.pamphlet @@ -377,7 +377,7 @@ CancellationAbelianMonoid(): Category == AbelianMonoid with ++ Description: ++ Rings of Characteristic Non Zero CharacteristicNonZero():Category == Ring with - charthRoot: % -> Union(%,"failed") + charthRoot: % -> Maybe % ++ charthRoot(x) returns the pth root of x ++ where p is the characteristic of the ring. @@ -1706,9 +1706,9 @@ PolynomialFactorizationExplicit(): Category == Definition where ++ whose \spad{p}-th powers (p is the characteristic of the domain) ++ are a solution of the homogenous linear system represented ++ by m, or "failed" is there is no such vector. - charthRoot: % -> Union(%,"failed") - ++ charthRoot(r) returns the \spad{p}-th root of r, or "failed" - ++ if none exists in the domain. + charthRoot: % -> Maybe % + ++ charthRoot(r) returns the \spad{p}-th root of r, or + ++ \spad{nothing} if none exists in the domain. -- this is a special case of conditionP, but often the one we want add gcdPolynomial(f,g) == @@ -1725,11 +1725,13 @@ PolynomialFactorizationExplicit(): Category == Definition where -- to take p'th root of f, solve the system X-fY=0, -- so solution is [x,y] -- with x^p=X and y^p=Y, then (x/y)^p = f - zero? f => 0 + zero? f => just 0 m:Matrix % := matrix [[1,-f]] ans:= conditionP m - ans case "failed" => "failed" - (ans.1) exquo (ans.2) + ans case "failed" => nothing + r := (ans.1) exquo (ans.2) + r case "failed" => nothing + just r if % has Field then solveLinearPolynomialEquation(lf,g) == multiEuclidean(lf,g)$P |