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- Rational and integer zeros of a univariate polynomial
- using fast modular methods.
- Author: F.J.Wright@Maths.QMW.ac.uk
- Version 1.05, 2 Oct 1994
- The operators r_solve and i_solve take a single univariate polynomial (or
- polynomial equation) as argument, and optionally the variable as second
- argument, and return respectively the sets of rational and integer zeros.
- Any denominator is completely ignored! See the test/demo file rsolve.tst
- for examples.
- Default output format is the same as used by solve (including respecting
- the multiplicities switch), but optional arguments allow other output
- formats (see the source file rsolve.red for details). Solutions of
- degenerate equations are expressed by r_solve and i_solve using the
- operators ARBRAT (which is new) and ARBINT respectively.
- Computing only the integer zeros is slightly more efficient than extracting
- them from the rational zeros. This algorithm appears to be faster than
- solve by a factor that depends on the example, but typically up to about 2,
- and gives more convenient output if only integer or rational zeros are
- required.
- The algorithm used is that described by R. Loos (1983): Computing rational
- zeros of integral polynomials by p-adic expansion. SIAM J. Computing. 12,
- 286--293.
- The switch TRSOLVE turns on tracing of the algorithm.
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