Name
Abstract | ||
|---|---|---|
We use filters of open sets to provide a semantics justifying formally the use of infinity in informal limit calculations in calculus, and in the same kind of calculations in computer algebra. We compare the behavior of these filters to the way Mathematica behaves when calculating with in- finity. A proper semantics for computer algebra expressions is necessary not only for the correct application of those methods, but also in order to use results and methods from computer algebra in theorem provers. The computer algebra method under discussion in this paper is the use of rewrite rules to evaluate limits involving infinity. Unlike in other areas of computer algebra, where the problem has been a mismatch between a known semantics and implementations, we here provide the first precise semantics. |
Year | DOI | Venue |
|---|---|---|
2005 | 10.1007/3-540-45470-5_23 | J. Symb. Comput. |
Keywords | Field | DocType |
Computer algebra,High school calculus,Semantics,Limits,Filters,Infinity,Interval arithmetic,Non-standard analysis | Subalgebra,Term algebra,Discrete mathematics,Computer science,Infinity,Symbolic computation,Filtered algebra,Current algebra,Two-element Boolean algebra,Calculus,Algebra representation | Journal |
Volume | Issue | ISSN |
39 | 5 | Journal of Symbolic Computation |
ISBN | Citations | PageRank |
3-540-43865-3 | 3 | 0.70 |
References | Authors | |
1 | 2 | |
Name | Order | Citations | PageRank |
|---|---|---|---|
| Michael Beeson | 1 | 22 | 4.09 |
| Freek Wiedijk | 2 | 381 | 43.24 |