[1] | 1 | #|
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| 2 | $Id: poly-with-sugar.lisp,v 1.3 2009/01/22 04:06:12 marek Exp $
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| 3 | *--------------------------------------------------------------------------*
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| 4 | | Copyright (C) 1994, Marek Rychlik (e-mail: rychlik@math.arizona.edu) |
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| 5 | | Department of Mathematics, University of Arizona, Tucson, AZ 85721 |
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| 6 | | |
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| 7 | | Everyone is permitted to copy, distribute and modify the code in this |
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| 8 | | directory, as long as this copyright note is preserved verbatim. |
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| 9 | *--------------------------------------------------------------------------*
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| 10 | |#
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| 11 | (defpackage "POLY-WITH-SUGAR"
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| 12 | (:export poly-with-sugar-poly
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| 13 | poly-with-sugar-tail
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| 14 | poly-with-sugar-sugar
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| 15 | monom-sugar
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| 16 | term-sugar
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| 17 | monom-times-poly-with-sugar
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| 18 | scalar-times-poly-with-sugar
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| 19 | term-times-poly-with-sugar
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| 20 | minus-poly-with-sugar
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| 21 | poly-with-sugar+
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| 22 | poly-with-sugar-
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| 23 | poly-with-sugar-op
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| 24 | poly-with-sugar-zerop
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| 25 | poly-with-sugar-nreverse
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| 26 | poly-with-sugar-append
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| 27 | poly-with-sugar-lm
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| 28 | poly-with-sugar-lc
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| 29 | poly-with-sugar-lt
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| 30 | poly-add-sugar)
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| 31 | (:use "ORDER" "MONOM" "TERM" "TERM" "POLY" "COEFFICIENT-RING" "COMMON-LISP"))
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| 32 |
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| 33 | (in-package "POLY-WITH-SUGAR")
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| 34 |
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[53] | 35 | (proclaim '(optimize (speed 3) (space 0) (safety 0) (debug 0)))
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[1] | 36 |
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| 37 | ;;----------------------------------------------------------------
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| 38 | ;; BASIC OPERATIONS ON POLYNOMIALS of many variables WITH SUGAR
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| 39 | ;; Hybrid operations involving polynomials and monomials or terms
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| 40 | ;;----------------------------------------------------------------
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| 41 | ;; The representation is as follows:
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| 42 | ;;
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| 43 | ;; polynomial-with-sugar: (poly . sugar)
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| 44 | ;;
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| 45 | ;;----------------------------------------------------------------
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| 46 |
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| 47 | (defun poly-with-sugar-poly (p) (car p))
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| 48 | (defun poly-with-sugar-sugar (p) (cdr p))
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| 49 | (defun poly-with-sugar-tail (p) (cons (cdar p) (cdr p)))
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| 50 |
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| 51 | (defsetf poly-with-sugar-poly (p) (poly)
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| 52 | `(setf (car ,p) ,poly))
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| 53 |
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| 54 | (defsetf poly-with-sugar-sugar (p) (sugar)
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| 55 | `(setf (cdr ,p) ,sugar))
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| 56 |
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| 57 | (defsetf poly-with-sugar-tail (p) (tail)
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| 58 | `(setf (cdar ,p) ,tail))
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| 59 |
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| 60 | ;;----------------------------------------------------------------
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| 61 | ;; Sugar of monomials and terms
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| 62 | ;; The total degree is used
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| 63 | ;;----------------------------------------------------------------
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| 64 | (defun monom-sugar (m)
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| 65 | (total-degree m))
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| 66 |
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| 67 | (defun coefficient-sugar (c ring)
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| 68 | (funcall (ring-length ring) c))
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| 69 |
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| 70 | (defun term-sugar (term ring)
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| 71 | (declare (ignore ring))
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| 72 | (monom-sugar (term-monom term)))
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| 73 |
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| 74 | ;;----------------------------------------------------------------
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| 75 | ;; Initialize sugar of an ordinary polynomial
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| 76 | ;;----------------------------------------------------------------
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| 77 | (defun poly-add-sugar (poly ring)
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| 78 | (cons poly
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| 79 | (apply #'max (mapcar #'(lambda (term) (term-sugar term ring)) poly))))
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| 80 |
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| 81 | ;; Multiplies scalar c by a polynomial p
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| 82 | (defun scalar-times-poly-with-sugar (c p ring)
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| 83 | (cons (scalar-times-poly c (poly-with-sugar-poly p) ring)
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| 84 | (poly-with-sugar-sugar p)))
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| 85 |
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| 86 | ;; Multiplies term m by a poly-with-sugar f
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| 87 | (defun term-times-poly-with-sugar (term f ring)
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| 88 | (cons (term-times-poly term (poly-with-sugar-poly f) ring)
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| 89 | (+ (poly-with-sugar-sugar f) (term-sugar term ring))))
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| 90 |
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| 91 | ;; Multiply a monom by a poly-with-sugarnomial
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| 92 | (defun monom-times-poly-with-sugar (m f)
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| 93 | (cons
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| 94 | (monom-times-poly m (poly-with-sugar-poly f))
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| 95 | (+ (poly-with-sugar-sugar f) (monom-sugar m))))
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| 96 |
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| 97 | ;; Changes the sign of the polynomial f with sugar
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| 98 | (defun minus-poly-with-sugar (f ring)
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| 99 | (cons
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| 100 | (minus-poly (poly-with-sugar-poly f) ring)
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| 101 | (poly-with-sugar-poly f)))
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| 102 |
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| 103 | ;; Addition and subtraction of polynomials with sugar
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| 104 | (defun poly-with-sugar+ (p q pred ring)
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| 105 | (cons
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| 106 | (poly+ (poly-with-sugar-poly p) (poly-with-sugar-poly q) pred ring)
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| 107 | (max (poly-with-sugar-sugar p) (poly-with-sugar-sugar q))))
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| 108 |
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| 109 | ;; Addition and subtraction of polynomials with sugar
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| 110 | (defun poly-with-sugar- (p q pred ring)
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| 111 | (cons
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| 112 | (poly- (poly-with-sugar-poly p) (poly-with-sugar-poly q) pred ring)
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| 113 | (max (poly-with-sugar-sugar p) (poly-with-sugar-sugar q))))
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| 114 |
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| 115 | ;; Implement f-term*g
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| 116 | (defun poly-with-sugar-op (f term g pred ring)
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| 117 | (poly-with-sugar- f (term-times-poly-with-sugar term g ring) pred ring))
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| 118 |
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| 119 |
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| 120 | ;; Destructively reverse the order of terms in a polynomial with sugar
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| 121 | (defun poly-with-sugar-nreverse (p)
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| 122 | (setf (poly-with-sugar-poly p) (nreverse (poly-with-sugar-poly p)))
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| 123 | p)
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| 124 |
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| 125 | ;; Append two polynomials with sugar, which are assumed to be
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| 126 | ;; sorted and all terms of q are smaller than terms of p
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| 127 | (defun poly-with-sugar-append (p q)
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| 128 | (cons (append (poly-with-sugar-poly p) (poly-with-sugar-poly q))
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| 129 | (max (poly-with-sugar-sugar p) (poly-with-sugar-sugar q))))
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| 130 |
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| 131 | (defun poly-with-sugar-zerop (p)
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| 132 | (poly-zerop (poly-with-sugar-poly p)))
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| 133 |
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| 134 | (defun poly-with-sugar-lm (p)
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| 135 | (lm (poly-with-sugar-poly p)))
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| 136 |
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| 137 | (defun poly-with-sugar-lc (p)
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| 138 | (lc (poly-with-sugar-poly p)))
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| 139 |
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| 140 | (defun poly-with-sugar-lt (p)
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| 141 | (lt (poly-with-sugar-poly p)))
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