LinearOrdinaryOperatorPolynomialSolutions

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LinearOrdinaryOperatorPolynomialSolutions

$\begin{usage} import from LinearOrdinaryOperatorPolynomialSolutions(R, F, $\iota$, RX, RXY, FX) \end{usage}$

$\begin{params} {\em R} & \htmlref{\texttt{IntegralDomain}}{IntegralDomain} & A... ... F\\ & \htmlref{\texttt{CommutativeRing}}{CommutativeRing} &\\\end{params}$

$\begin{descr} LinearOrdinaryOperatorPolynomialSolutions(R, F, $\iota$, RX, RXY,... ... differential or recurrence operators with polynomial coefficients. \end{descr}$

Exports

`kernel`:	(RXY, Z) $\to$ V FX	Polynomial solutions
`particularSolution`:	(RXY, Z, FX) $\to$ `Partial` FX	A polynomial solution
	(RXY, Z, V FX) $\to$ V FX	Some polynomial solutions
`solve`:	(RXY, Z, FX) $\to$ (V FX, `Partial` FX)	Polynomial solutions
	(RXY, Z, V FX) $\to$ (V FX, V FX)	Polynomial solutions

if has RationalRootRing then

`kernel`:	RXY $\to$ V FX	Polynomial solutions
`parametricSolve`:	(RXY, V FX) $\to$ (V FX, M F)	Polynomial solutions
`particularSolution`:	(RXY, FX) $\to$ `Partial` FX	A polynomial solution
	(RXY, V FX) $\to$ V FX	Some polynomial solutions
`solve`:	(RXY, FX) $\to$ (V FX, `Partial` FX)	Polynomial solutions
	(RXY, V FX) $\to$ (V FX, V FX)	Polynomial solutions

where
M == DenseMatrix

V == Vector

Z == Integer

Subsections

Next: kernel Up: Solutions of Differential and Previous: kernel Contents Index

Manuel Bronstein 2000-12-13