4 papers · 1 filter
Algorithms for Linear Ordinary Differential Operators
Jean Della Dora, Stephen M. Watt
We describe an implementation in Scratchpad II of linear ordinary differential operators over a differential ring, acting on a module equipped with a compatible derivation. The abs…
Efficient Quotients of Non-Commutative Polynomials
Stephen M. Watt
It is shown how to compute quotients efficiently in non-commutative univariate polynomial rings. This extends earlier work where efficient generic quotients were studied with a pri…
Efficient Generic Quotients Using Exact Arithmetic
Stephen M. Watt
The usual formulation of efficient division uses Newton iteration to compute an inverse in a related domain where multiplicative inverses exist. On one hand, Newton iteration allow…
Symbolic Domain Decomposition
Jacques Carette, Alan P. Sexton, Volker Sorge +1
Decomposing the domain of a function into parts has many uses in mathematics. A domain may naturally be a union of pieces, a function may be defined by cases, or different boundary…