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Fixed bug 14177

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bezout-binary did not handle negative numbers correctly.
This commit is contained in:
Jens Axel Søgaard 2013-12-08 22:13:21 +01:00 committed by Vincent St-Amour
parent 8f6af94221
commit 0909acc473
1 changed files with 23 additions and 3 deletions
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26
pkgs/math-pkgs/math-lib/math/private/number-theory/divisibility.rkt
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@ -42,9 +42,29 @@
(if (= r 0)
(list ub vb)
(loop b r ub vb (- ua (* q ub)) (- va (* q vb))))))
(if (> a b)
(loop a b 1 0 0 1)
(loop b a 0 1 1 0)))
(: start : Integer Integer -> (List Integer Integer))
(define (start a b)
(if (> a b)
(loop a b 1 0 0 1)
(loop b a 0 1 1 0)))
(cond [(and (positive? a) (positive? b))
(start a b)]
[(and (negative? a) (negative? b))
(define uv (start (- a) (- b)))
(list (- (car uv)) (- (cadr uv)))]
[(and (negative? a) (positive? b))
; choose k s.t. a+kb>0
(define k (+ (quotient (- a) b) 1))
(define uv (start (+ a (* k b)) b))
(define u (car uv)) (define v (cadr uv))
(list u (+ (* u k) v))]
[(and (positive? a) (negative? b))
; choose k s.t. ak+b>0
(define k (+ (quotient (- b) a) 1))
(define uv (start a (+ (* k a) b)))
(define u (car uv)) (define v (cadr uv))
(list (+ u (* k v)) v)]
[else (error "Internal error in bezout-binary")]))
; (bezout a b c ...) -> (list u v w ...) <=> gcd(a,b,c,...) = au + bv + cw + ...
(: bezout : Integer Integer * -> (Listof Integer))