UnivariateTaylorSeriesCategory

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UnivariateTaylorSeriesCategory

$\begin{usage} UnivariateTaylorSeriesCategory~R: Category \end{usage}$

$\begin{params} {\em R} & \htmlref{\texttt{SumitType}}{SumitType} & The coeffic... ...main\\ & \htmlref{\texttt{ArithmeticType}}{ArithmeticType} &\\\end{params}$

$\begin{descr} UnivariateTaylorSeriesCategory~R is the category of univariate Taylor series with coefficients in R. \end{descr}$

Exports

`UnivariateFreeAlgebra` R
`degree`:	% $\to$ `Partial` `Integer`	upper bound on the degree
`expand`:	(Rx: UPC R, R) $\to$ Rx $\to$ %	series expansion around a point
`finite?`:	% $\to$ `Boolean`	check whether the support is finite
`series`:	`Sequence` R $\to$ %	creation of a series

where
UPC == UnivariatePolynomialCategory

if has CommutativeRing then
differentiate: % $\to$ % Differentiation

(%, Integer) $\to$ %

if has CommutativeRing and has QRing then
integrate: % $\to$ % Integration

(%, Integer) $\to$ %

Subsections

Next: degree,finite? Up: Univariate Polynomials and Series Previous: yun Contents Index

Manuel Bronstein 2000-12-13

`differentiate`:	% $\to$ %	Differentiation
	(%, `Integer`) $\to$ %