5 papers
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…
Determining Points on Handwritten Mathematical Symbols
Rui Hu, Stephen M. Watt
In a variety of applications, such as handwritten mathematics and diagram labelling, it is common to have symbols of many different sizes in use and for the writing not to follow s…
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…