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7f918cf1 CE |
1 | (* Copyright (C) 1999-2006 Henry Cejtin, Matthew Fluet, Suresh |
2 | * Jagannathan, and Stephen Weeks. | |
3 | * | |
4 | * MLton is released under a BSD-style license. | |
5 | * See the file MLton-LICENSE for details. | |
6 | *) | |
7 | ||
8 | signature EUCLIDEAN_RING_STRUCTS = | |
9 | sig | |
10 | include RING_WITH_IDENTITY | |
11 | ||
12 | (* Two elements a, b are "unit equivalent" if there is a unit element u | |
13 | * such that au = b. | |
14 | *) | |
15 | ||
16 | val divMod: t * t -> t * t | |
17 | val metric: t -> Pervasive.IntInf.int | |
18 | (* Monics should be an (infinite) stream of all (except for zero and one) | |
19 | * the representatives of the unit equivalence classes in nondecreasing | |
20 | * order of metric. | |
21 | *) | |
22 | val monics: t Stream.t | |
23 | (* Map an element to the representative of its unit equivalence class. *) | |
24 | val unitEquivalent: t -> t | |
25 | end | |
26 | ||
27 | signature EUCLIDEAN_RING = | |
28 | sig | |
29 | include EUCLIDEAN_RING_STRUCTS | |
30 | ||
31 | val div: t * t -> t | |
32 | val divides: t * t -> bool | |
33 | val extendedEuclid: t * t -> t * t * t | |
34 | val extendedEuclidTerm: t * t * (t * t -> bool) -> t * t * t | |
35 | val factor: t -> (t * Pervasive.Int.int) list | |
36 | val gcd: t * t -> t | |
37 | val isComposite: t -> bool | |
38 | val isPrime: t -> bool | |
39 | val lcm: t * t -> t | |
40 | val primes: t Stream.t | |
41 | val mod: t * t -> t | |
42 | end |