[1] | 1 | head 1.4;
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| 2 | access;
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| 3 | symbols;
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| 4 | locks; strict;
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| 5 | comment @;;; @;
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| 6 |
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| 7 |
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| 8 | 1.4
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| 9 | date 2009.01.22.04.05.32; author marek; state Exp;
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| 10 | branches;
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| 11 | next 1.3;
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| 12 |
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| 13 | 1.3
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| 14 | date 2009.01.19.09.28.20; author marek; state Exp;
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| 15 | branches;
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| 16 | next 1.2;
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| 17 |
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| 18 | 1.2
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| 19 | date 2009.01.19.07.51.29; author marek; state Exp;
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| 20 | branches;
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| 21 | next 1.1;
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| 22 |
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| 23 | 1.1
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| 24 | date 2009.01.19.07.00.23; author marek; state Exp;
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| 25 | branches;
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| 26 | next ;
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| 27 |
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| 28 |
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| 29 | desc
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| 30 | @@
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| 31 |
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| 32 |
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| 33 | 1.4
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| 34 | log
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| 35 | @*** empty log message ***
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| 36 | @
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| 37 | text
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| 38 | @#|
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| 39 | $Id$
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| 40 | *--------------------------------------------------------------------------*
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| 41 | | Copyright (C) 1994, Marek Rychlik (e-mail: rychlik@@math.arizona.edu) |
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| 42 | | Department of Mathematics, University of Arizona, Tucson, AZ 85721 |
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| 43 | | |
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| 44 | | Everyone is permitted to copy, distribute and modify the code in this |
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| 45 | | directory, as long as this copyright note is preserved verbatim. |
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| 46 | *--------------------------------------------------------------------------*
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| 47 | |#
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| 48 | (defpackage "POLY-GCD"
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| 49 | (:export poly-gcd poly-content poly-pseudo-divide poly-primitive-part
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| 50 | poly-pseudo-remainder)
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| 51 | (:use "ORDER" "POLY" "DIVISION" "COMMON-LISP"))
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| 52 |
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| 53 | (in-package "POLY-GCD")
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| 54 |
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| 55 | #+debug(proclaim '(optimize (speed 0) (debug 3)))
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| 56 | #-debug(proclaim '(optimize (speed 3) (debug 0)))
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| 57 |
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| 58 | ;; This package calculates GCD of polynomials over integers.
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| 59 | ;; They are assumed to be ordered lexicographically.
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| 60 | ;;
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| 61 | ;; The algorithm is that on p. 57 of Geddes, Czapor, Labahn
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| 62 | ;; Given polynomials a(x),b(x) in D[x] where D is a UFD, we
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| 63 | ;; compute g(x)=GCD(a(x),b(x))
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| 64 | ;; Assume that the poly's are sorted lexicographically
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| 65 |
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| 66 | (defun poly-gcd (a b)
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| 67 | (cond
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| 68 | ((endp a) b)
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| 69 | ((endp b) a)
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| 70 | ((endp (caar a)) ;scalar
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| 71 | (list (cons nil (gcd (cdar a) (cdar b)))))
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| 72 | (t
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| 73 | (do* ((r nil (poly-pseudo-remainder c d))
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| 74 | (c (poly-primitive-part a) d)
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| 75 | (d (poly-primitive-part b) (poly-primitive-part r)))
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| 76 | ((endp d)
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| 77 | (poly* (poly-extend
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| 78 | (poly-gcd (poly-content a) (poly-content b)))
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| 79 | c))))))
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| 80 |
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| 81 | ;; Perform a pseudo-division in k[x2,....,xn][x1]
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| 82 | ;; Assume that the terms are sorted according to decreasing powers of x1
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| 83 | ;; p.297 of Cox
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| 84 | (defun poly-pseudo-divide (f g)
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| 85 | (multiple-value-bind (lg grest)
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| 86 | (lpart g)
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| 87 | (do* ((m (mdeg g))
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| 88 | (dm (poly-extend lg))
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| 89 | (lpart nil (multiple-value-list (lpart r)))
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| 90 | (lr nil (car lpart))
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| 91 | (lrest nil (cadr lpart))
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| 92 | (term nil (poly-extend lr (list (- (mdeg r) m))))
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| 93 | (r f (poly- (poly* dm lrest)
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| 94 | (poly* term grest)))
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| 95 | (q nil (append (poly* dm q) term)))
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| 96 | ((or (endp r) (< (mdeg r) m))
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| 97 | (values q r)))))
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| 98 |
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| 99 |
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| 100 | (defun poly-pseudo-remainder (f g)
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| 101 | (second (multiple-value-list (poly-pseudo-divide f g))))
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| 102 |
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| 103 | ;; Degree in main variable
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| 104 | (defun mdeg (b) (caaar b))
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| 105 |
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| 106 | ;; Leading coefficient in the first variable; a poly in k[x2,...,xn]
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| 107 | (defun lcoeff (b)
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| 108 | (first (multiple-value-list (lpart b))))
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| 109 |
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| 110 | (defun lrest (b)
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| 111 | (second (multiple-value-list (lpart b))))
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| 112 |
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| 113 | (defun lpart (b)
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| 114 | (do ((mdeg (mdeg b))
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| 115 | (b b (rest b))
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| 116 | (b1 nil (cons (cons (cdaar b) (cdar b)) b1)))
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| 117 | ((or (endp b) (/= (caaar b) mdeg))
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| 118 | (values (reverse b1) b))))
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| 119 |
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| 120 | ;; Divide f by its content
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| 121 | (defun poly-primitive-part (f)
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| 122 | (cond
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| 123 | ((endp (caar f)) ;scalar
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| 124 | f)
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| 125 | (t
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| 126 | (poly-exact-divide f (poly-extend (poly-content f))))))
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| 127 |
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| 128 |
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| 129 | (defun poly-content (f)
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| 130 | (cond
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| 131 | ((endp f) (error "Zero argument"))
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| 132 | (t (multiple-value-bind (lc r)
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| 133 | (lpart f)
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| 134 | (cond
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| 135 | ((endp r) lc)
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| 136 | ((and (= (length lc) 1)
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| 137 | (every #'zerop (caar lc))
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| 138 | (or (= (cdar lc) 1)
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| 139 | (= (cdar lc) -1))) ;lc is 1 or -1
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| 140 | lc)
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| 141 | (t (poly-gcd lc (poly-content r))))))))
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| 142 | @
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| 143 |
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| 144 |
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| 145 | 1.3
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| 146 | log
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| 147 | @*** empty log message ***
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| 148 | @
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| 149 | text
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| 150 | @d18 2
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| 151 | a19 2
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| 152 | ;;(proclaim '(optimize (speed 0) (debug 3)))
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| 153 | (proclaim '(optimize (speed 3) (debug 0)))
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| 154 | @
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| 155 |
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| 156 |
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| 157 | 1.2
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| 158 | log
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| 159 | @*** empty log message ***
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| 160 | @
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| 161 | text
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| 162 | @d18 2
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| 163 | a19 1
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| 164 | (proclaim '(optimize (speed 0) (debug 3)))
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| 165 | @
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| 166 |
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| 167 |
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| 168 | 1.1
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| 169 | log
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| 170 | @Initial revision
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| 171 | @
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| 172 | text
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| 173 | @d2 1
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| 174 | a2 1
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| 175 | $Id: poly-gcd.lisp,v 1.12 1997/12/13 07:11:59 marek Exp $
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| 176 | d18 1
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| 177 | @
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