diff options
Diffstat (limited to 'src/algebra/ore.spad.pamphlet')
| -rw-r--r-- | src/algebra/ore.spad.pamphlet | 6 |
1 files changed, 5 insertions, 1 deletions
diff --git a/src/algebra/ore.spad.pamphlet b/src/algebra/ore.spad.pamphlet index ebdc406a..9617f107 100644 --- a/src/algebra/ore.spad.pamphlet +++ b/src/algebra/ore.spad.pamphlet @@ -464,7 +464,7 @@ UnivariateSkewPolynomialCategoryOps(R, C): Exports == Implementation where )abbrev domain ORESUP SparseUnivariateSkewPolynomial ++ Author: Manuel Bronstein ++ Date Created: 19 October 1993 -++ Date Last Updated: 1 February 1994 +++ Date Last Updated: September, 2008 ++ Description: ++ This is the domain of sparse univariate skew polynomials over an Ore ++ coefficient field. @@ -479,6 +479,10 @@ SparseUnivariateSkewPolynomial(R:Ring, sigma:Automorphism R, delta: R -> R): x:% * y:% == times(x, y, sigma, delta) apply(p, c, r) == apply(p, c, r, sigma, delta) + x:% ** n:PositiveInteger == expt(x,n)$RepeatedSquaring(%) + x:% ** n:NonNegativeInteger == + zero? n => 1 + expt(x,n::PositiveInteger)$RepeatedSquaring(%) if R has IntegralDomain then monicLeftDivide(a, b) == monicLeftDivide(a, b, sigma) |