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Numerical algorithms for problems in analysis and algebra, scientific computation

11 votes
Accepted

Compute an arbitrary decimal place of $\pi$

Yes, there are such algorithms. -- See e.g. Xavier Gourdon: Computation of the $n$-th decimal digit of $\pi$ with low memory. There also is the Bailey-Borwein-Plouffe formula already mentioned by Geof …
Stefan Kohl's user avatar
  • 19.6k
6 votes

Algorithm for solving systems of linear Diophantine inequalities

GAP provides a function NullspaceIntMat which solves systems of linear diophantine equations. The documentation says: 25.1-2 SolutionIntMat * SolutionIntMat( mat, vec ) ───────────────────────────── …
Stefan Kohl's user avatar
  • 19.6k
2 votes

How to calculate log or exp of a value in GF(2^n) using log/exp table of GF((2^k)^m) where n...

Efficient algorithms to compute in finite fields are based on Conway polynomials. Such algorithms are implemented in several computer algebra systems, for example in GAP. For details, see e.g. the cha …
Stefan Kohl's user avatar
  • 19.6k