UnivariateSkewPolynomialCategoryTools

Next: apply Up: Univariate Skew Polynomials and Previous: rightLcm Contents Index

UnivariateSkewPolynomialCategoryTools

$\begin{usage} import from UnivariateSkewPolynomialCategoryTools(R, C) \end{usage}$

$\begin{params} {\em R} & \htmlref{\texttt{Ring}}{Ring} & The coefficient ring\... ...{UnivariateSkewPolynomialCategory} R & A skew--polynomial type\\\end{params}$

$\begin{descr} UnivariateSkewPolynomialCategoryTools(R, C) provides the univaria... ...gma$\ and $\delta$\ functions determining the skew polynomial ring. \end{descr}$

Exports

apply: (C, R, R, MOR, R $\to$ R) $\to$ R Apply a skew-polynomial to a scalar

times: (C, C, MOR, R $\to$ R) $\to$ C Product of skew-polynomials

if R has IntegralDomain then

`leftExactQuotient`:	(C, C, MOR, R $\to$ R) $\to$ `Partial` C	Left exact quotient
`monicLeftDivide`:	(C, C, MOR, R $\to$ R) $\to$ (C, C)	Left Euclidean division
`monicRightDivide`:	(C, C, MOR, R $\to$ R) $\to$ (C, C)	Right Euclidean division
`rightExactQuotient`:	(C, C, MOR, R $\to$ R) $\to$ `Partial` C	Right exact quotient

if R has Field then
leftDivide: (C, C, MOR, R $\to$ R) $\to$ (C, C) Left Euclidean division

rightDivide: (C, C, MOR, R $\to$ R) $\to$ (C, C) Right Euclidean division

where
MOR == Automorphism R

Subsections

Next: apply Up: Univariate Skew Polynomials and Previous: rightLcm Contents Index

Manuel Bronstein 2000-12-13

`apply`:	(C, R, R, MOR, R $\to$ R) $\to$ R	Apply a skew-polynomial to a scalar
`times`:	(C, C, MOR, R $\to$ R) $\to$ C	Product of skew-polynomials

`leftDivide`:	(C, C, MOR, R $\to$ R) $\to$ (C, C)	Left Euclidean division
`rightDivide`:	(C, C, MOR, R $\to$ R) $\to$ (C, C)	Right Euclidean division