Name
Abstract | ||
|---|---|---|
A standard method for finding a rational number from its values modulo a collection of primes is to determine its value modulo the product of the primes via Chinese remaindering, and then use Farey sequences for rational reconstruction. Successively enlarging the set of primes if needed, this method is guaranteed to work if we restrict ourselves to "good" primes. Depending on the particular application, however, there may be no efficient way of identifying good primes. In the algebraic and geometric applications we have in mind, the final result consists of an a priori unknown ideal (or module) which is found via a construction yielding the (reduced) Grobner basis of the ideal. In this context, we discuss a general setup for modular and, thus, potentially parallel algorithms which can handle "bad" primes. A new key ingredient is an error tolerant algorithm for rational reconstruction via Gaussian reduction. |
Year | DOI | Venue |
|---|---|---|
2015 | 10.1090/mcom/2951 | MATHEMATICS OF COMPUTATION |
Keywords | Field | DocType |
Rational reconstruction,Farey map | Discrete mathematics,Rational number,Algebraic geometry,Algebra,Modulo,Mathematical analysis,A priori and a posteriori,Commutative algebra,Modular design,Mathematics,Farey sequence,Rational reconstruction | Journal |
Volume | Issue | ISSN |
84 | 296 | 0025-5718 |
Citations | PageRank | References |
5 | 0.67 | 6 |
Authors | ||
4 | ||
Name | Order | Citations | PageRank |
|---|---|---|---|
| Janko Boehm | 1 | 5 | 2.36 |
| Wolfram Decker | 2 | 26 | 8.41 |
| Claus Fieker | 3 | 73 | 14.37 |
| Gerhard Pfister | 4 | 83 | 12.74 |