Add solver for linear Diophantine equations#159
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xavierleroy wants to merge 1 commit intoocaml:masterfrom
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Add solver for linear Diophantine equations#159xavierleroy wants to merge 1 commit intoocaml:masterfrom
xavierleroy wants to merge 1 commit intoocaml:masterfrom
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Solves linear Diophantine equations of one variable. Generalization of the Chinese remainder theorem.
xavierleroy
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This PR adds
Z.solve_linear_congruences, a solver for linear Diophantine equations of one variable:This includes the Chinese remainder theorem as a special case (with aᵢ = 1).
I wrote this code several times in the past, once to implement RSA in Cryptokit, the other times for programming / mathematical puzzles such as the Euler project. The interface and implementation in this PR is taken from https://github.com/gmevel/euler-lib , which uses OCaml's plain
intinstead of arbitrary-precision integers.Maybe this function is too specialized for a library such as Zarith. On the other hand, it's nontrivial code that nicely complements the existing number-theoretic functions of Zarith.