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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35 | (proclaim '(optimize (speed 0) (debug 3)))
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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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