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src/HOL/NumberTheory/README

author | paulson |

Thu, 03 Aug 2000 10:46:01 +0200 | |

changeset 9508 | 4d01dbf6ded7 |

child 9545 | c1d9500e2927 |

permissions | -rw-r--r-- |

Chinese Remainder Theorem, Wilsons Theorem, etc., by T M Masmussen

IntPrimes dvd relation, GCD, Euclid's extended algorithm, primes, congruences (all on the Integers) Comparable to 'Primes' theory but dvd is included here as it is not present in 'IntDiv'. Also includes extended GCD and congruences not present in 'Primes'. Also a few extra theorems concerning 'mod' Maybe it should be split/merged - at least given another name? Chinese The Chinese Remainder Theorem for an arbitrary finite number of equations. (The one-equation case is included in 'IntPrimes') Uses functions for indicing. Maybe 'funprod' and 'funsum' should be based on general 'fold' on indices? IntPowerFact Power function on Integers (exponent is still Nat), Factorial on integers and recursively defined set including all Integers from 2 up to a. Plus definition of product of finite set. Should probably be split/merged with other theories? BijectionRel Inductive definitions of bijections between two different sets and between the same set. Theorem for relating the two definitions EulerFermat Fermat's Little Theorem extended to Euler's Totient function. More abstract approach than Boyer-Moore (which seems necessary to achieve the extended version) WilsonRuss Wilson's Theorem following quite closely Russinoff's approach using Boyer-Moore (using finite sets instead of lists, though) WilsonBij Wilson's Theorem using a more "abstract" approach based on bijections between sets. Does not use Fermat's Little Theorem (unlike Russinoff)