[1] | 1 | ;;; -*- Mode: Common-Lisp; Package: String-Grobner; Base: 10 -*-
|
---|
| 2 | #|
|
---|
| 3 | $Id: string-grobner.lisp,v 1.3 2009/01/22 04:07:58 marek Exp $
|
---|
| 4 | *--------------------------------------------------------------------------*
|
---|
| 5 | | Copyright (C) 1994, Marek Rychlik (e-mail: rychlik@math.arizona.edu) |
|
---|
| 6 | | Department of Mathematics, University of Arizona, Tucson, AZ 85721 |
|
---|
| 7 | | |
|
---|
| 8 | | Everyone is permitted to copy, distribute and modify the code in this |
|
---|
| 9 | | directory, as long as this copyright note is preserved verbatim. |
|
---|
| 10 | *--------------------------------------------------------------------------*
|
---|
| 11 | |#
|
---|
| 12 |
|
---|
| 13 |
|
---|
| 14 | (defpackage "STRING-GROBNER"
|
---|
| 15 | (:export
|
---|
| 16 | string-normal-form
|
---|
| 17 | string-grobner
|
---|
| 18 | string-colon-ideal
|
---|
| 19 | string-ideal-polysaturation-1
|
---|
| 20 | string-ideal-saturation-1
|
---|
| 21 | string-ideal-polysaturation
|
---|
| 22 | string-ideal-saturation
|
---|
| 23 | string-poly-lcm
|
---|
| 24 | string-ideal-intersection
|
---|
| 25 | string-elimination-ideal
|
---|
| 26 | string-read-poly)
|
---|
| 27 | (:use "ORDER" "MONOM" "PARSE" "PRINTER" "GROBNER" "TERM" "POLY"
|
---|
| 28 | "COEFFICIENT-RING" "COMMON-LISP"))
|
---|
| 29 |
|
---|
| 30 | (in-package "STRING-GROBNER")
|
---|
| 31 |
|
---|
[48] | 32 | (proclaim '(optimize (speed 3) (space 0) (safety 0) (debug 0)))
|
---|
[1] | 33 |
|
---|
| 34 | (defun string-normal-form (f fl vars
|
---|
| 35 | &key
|
---|
| 36 | (stream t)
|
---|
| 37 | (print t)
|
---|
| 38 | (order #'lex>)
|
---|
| 39 | (top-reduction-only nil)
|
---|
| 40 | (ring *coefficient-ring*)
|
---|
| 41 | (suppress-value t)
|
---|
| 42 | &aux (vars (read-vars vars)))
|
---|
| 43 | (let ((f (parse-string-to-sorted-alist f vars order))
|
---|
| 44 | (fl (parse-string-to-sorted-alist fl vars order)))
|
---|
| 45 | (format stream "~&Args:")
|
---|
| 46 | (poly-print fl vars stream)
|
---|
| 47 | (let ((nf (normal-form (copy-tree f) (rest fl) order top-reduction-only ring)))
|
---|
| 48 | (terpri stream)
|
---|
| 49 | (when print
|
---|
| 50 | (poly-print
|
---|
| 51 | nf
|
---|
| 52 | vars
|
---|
| 53 | stream))
|
---|
| 54 | (if suppress-value (values) nf))))
|
---|
| 55 |
|
---|
| 56 | (defun string-grobner (plist vars
|
---|
| 57 | &key (order #'lex>)
|
---|
| 58 | (start 0)
|
---|
| 59 | (stream t)
|
---|
| 60 | (reduce t)
|
---|
| 61 | (reduce-before t)
|
---|
| 62 | (suppress-value t)
|
---|
| 63 | (top-reduction-only nil)
|
---|
| 64 | (ring *coefficient-ring*)
|
---|
| 65 | (print t)
|
---|
| 66 | &aux (vars (read-vars vars)))
|
---|
| 67 | ;; Turn on some phancy tracing to see the action better
|
---|
| 68 | (let ((grobner-fun
|
---|
| 69 | (if reduce #'reduced-grobner #'grobner))
|
---|
| 70 | (plist (parse-string-to-sorted-alist plist vars order)))
|
---|
| 71 | (format stream "~&Args:")
|
---|
| 72 | (poly-print plist vars stream)
|
---|
| 73 | (setf plist (rest plist))
|
---|
| 74 | (when reduce-before (setf plist (reduction plist order ring)))
|
---|
| 75 | (let ((gb (funcall grobner-fun plist order start top-reduction-only ring)))
|
---|
| 76 | (terpri stream)
|
---|
| 77 | (when print
|
---|
| 78 | (poly-print
|
---|
| 79 | (cons '[ gb)
|
---|
| 80 | vars
|
---|
| 81 | stream))
|
---|
| 82 | (if suppress-value (values) gb))))
|
---|
| 83 |
|
---|
| 84 | (defun string-elimination-ideal (flist vars k
|
---|
| 85 | &key (stream t)
|
---|
| 86 | (key #'identity)
|
---|
| 87 | (primary-order #'grevlex>)
|
---|
| 88 | (secondary-order #'grevlex>)
|
---|
| 89 | (suppress-value t)
|
---|
| 90 | (order (elimination-order
|
---|
| 91 | k
|
---|
| 92 | :primary-order primary-order
|
---|
| 93 | :secondary-order secondary-order
|
---|
| 94 | ))
|
---|
| 95 | &aux (vars (read-vars vars)))
|
---|
| 96 | (let ((id (ring-intersection
|
---|
| 97 | (string-grobner flist vars
|
---|
| 98 | :order order
|
---|
| 99 | :suppress-value nil
|
---|
| 100 | :stream stream
|
---|
| 101 | :print nil)
|
---|
| 102 | k :key key)))
|
---|
| 103 | (poly-print (cons '[ id) vars stream)
|
---|
| 104 | (if suppress-value (values) id)))
|
---|
| 105 |
|
---|
| 106 |
|
---|
| 107 | (defun string-ideal-intersection (f g vars
|
---|
| 108 | &key (order #'lex>)
|
---|
| 109 | (top-reduction-only nil)
|
---|
| 110 | (ring *coefficient-ring*)
|
---|
| 111 | (stream t)
|
---|
| 112 | (suppress-value t)
|
---|
| 113 | &aux (vars (read-vars vars))
|
---|
| 114 | (f (parse-string-to-sorted-alist
|
---|
| 115 | f vars order))
|
---|
| 116 | (g (parse-string-to-sorted-alist
|
---|
| 117 | g vars order)))
|
---|
| 118 | (let ((id (ideal-intersection (rest f) (rest g) order top-reduction-only ring)))
|
---|
| 119 | (poly-print (cons '[ id) vars stream)
|
---|
| 120 | (if suppress-value (values) id)))
|
---|
| 121 |
|
---|
| 122 | (defun string-poly-lcm (f g vars
|
---|
| 123 | &key (order #'lex>)
|
---|
| 124 | (ring *coefficient-ring*)
|
---|
| 125 | (stream t)
|
---|
| 126 | (suppress-value t)
|
---|
| 127 | &aux (vars (read-vars vars))
|
---|
| 128 | (f (parse-string-to-sorted-alist
|
---|
| 129 | f vars order))
|
---|
| 130 | (g (parse-string-to-sorted-alist
|
---|
| 131 | g vars order)))
|
---|
| 132 | (let ((lcm (poly-lcm f g order ring)))
|
---|
| 133 | (poly-print lcm vars stream)
|
---|
| 134 | (if suppress-value (values) lcm)))
|
---|
| 135 |
|
---|
| 136 | (defun string-ideal-saturation-1 (F p vars
|
---|
| 137 | &key (order #'lex>) (start 0)
|
---|
| 138 | (top-reduction-only nil)
|
---|
| 139 | (ring *coefficient-ring*)
|
---|
| 140 | (stream t)
|
---|
| 141 | (suppress-value t)
|
---|
| 142 | &aux (vars (read-vars vars))
|
---|
| 143 | (F (parse-string-to-sorted-alist
|
---|
| 144 | F vars order))
|
---|
| 145 | (p (parse-string-to-sorted-alist
|
---|
| 146 | p vars order)))
|
---|
| 147 | (let ((id (ideal-saturation-1 (rest F) p order start top-reduction-only ring)))
|
---|
| 148 | (poly-print (cons '[ id) vars stream)
|
---|
| 149 | (if suppress-value (values) id)))
|
---|
| 150 |
|
---|
| 151 | (defun string-ideal-polysaturation-1 (F plist vars
|
---|
| 152 | &key (order #'lex>) (start 0)
|
---|
| 153 | (top-reduction-only nil)
|
---|
| 154 | (ring *coefficient-ring*)
|
---|
| 155 | (stream t)
|
---|
| 156 | (suppress-value t)
|
---|
| 157 | &aux (vars (read-vars vars))
|
---|
| 158 | (F (parse-string-to-sorted-alist
|
---|
| 159 | F vars order))
|
---|
| 160 | (plist (parse-string-to-sorted-alist
|
---|
| 161 | plist vars order)))
|
---|
| 162 | (format stream "~&Args1:")
|
---|
| 163 | (poly-print F vars stream)
|
---|
| 164 | (format stream "~&Args2:")
|
---|
| 165 | (poly-print plist vars stream)
|
---|
| 166 | (terpri stream)
|
---|
| 167 | (let ((id (ideal-polysaturation-1 (rest F) (rest plist) order start top-reduction-only ring)))
|
---|
| 168 | (poly-print (cons '[ id) vars stream)
|
---|
| 169 | (if suppress-value (values) id)))
|
---|
| 170 |
|
---|
| 171 | (defun string-ideal-saturation (F G vars
|
---|
| 172 | &key (order #'lex>) (start 0)
|
---|
| 173 | (top-reduction-only nil)
|
---|
| 174 | (ring *coefficient-ring*)
|
---|
| 175 | (stream t)
|
---|
| 176 | (suppress-value t)
|
---|
| 177 | &aux (vars (read-vars vars))
|
---|
| 178 | (F (parse-string-to-sorted-alist
|
---|
| 179 | F vars order))
|
---|
| 180 | (G (parse-string-to-sorted-alist
|
---|
| 181 | G vars order)))
|
---|
| 182 | (let ((id (ideal-saturation (rest F) (rest G) order start top-reduction-only ring)))
|
---|
| 183 | (poly-print (cons '[ id) vars stream)
|
---|
| 184 | (if suppress-value (values) id)))
|
---|
| 185 |
|
---|
| 186 | (defun string-ideal-polysaturation (F ideal-list vars
|
---|
| 187 | &key (order #'lex>) (start 0)
|
---|
| 188 | (top-reduction-only nil)
|
---|
| 189 | (ring *coefficient-ring*)
|
---|
| 190 | (stream t)
|
---|
| 191 | (suppress-value t)
|
---|
| 192 | &aux (vars (read-vars vars))
|
---|
| 193 | (F (parse-string-to-sorted-alist
|
---|
| 194 | F vars order))
|
---|
| 195 | (ideal-list
|
---|
| 196 | (mapcar #'(lambda (G) (parse-string-to-sorted-alist
|
---|
| 197 | G vars order))
|
---|
| 198 | ideal-list)))
|
---|
| 199 | (format stream "~&Args1:")
|
---|
| 200 | (poly-print F vars stream)
|
---|
| 201 | (format stream "~&Args2:")
|
---|
| 202 | (dolist (G ideal-list)
|
---|
| 203 | (poly-print G vars stream))
|
---|
| 204 | (terpri stream)
|
---|
| 205 | (let ((id (ideal-polysaturation (rest F) (mapcar #'rest ideal-list) order start top-reduction-only ring)))
|
---|
| 206 | (poly-print (cons '[ id) vars stream)
|
---|
| 207 | (if suppress-value (values) id)))
|
---|
| 208 |
|
---|
| 209 |
|
---|
| 210 |
|
---|
| 211 | (defun string-colon-ideal (F G vars
|
---|
| 212 | &key (top-reduction-only nil)
|
---|
| 213 | (ring *coefficient-ring*)
|
---|
| 214 | (stream t)
|
---|
| 215 | (order #'lex>)
|
---|
| 216 | (suppress-value t)
|
---|
| 217 | &aux (vars (read-vars vars))
|
---|
| 218 | (F (parse-string-to-sorted-alist
|
---|
| 219 | F vars order))
|
---|
| 220 | (G (parse-string-to-sorted-alist
|
---|
| 221 | G vars order)))
|
---|
| 222 | (format stream "~&Args1:")
|
---|
| 223 | (poly-print F vars stream)
|
---|
| 224 | (format stream "~&Args2:")
|
---|
| 225 | (poly-print G vars stream)
|
---|
| 226 | (let ((id (colon-ideal (rest F) (rest G) order top-reduction-only ring)))
|
---|
| 227 | (poly-print (cons '[ id) vars stream)
|
---|
| 228 | (if suppress-value (values) id)))
|
---|
| 229 |
|
---|
| 230 | ;;----------------------------------------------------------------
|
---|
| 231 | ;; An enhanced polynomial reader
|
---|
| 232 | ;;----------------------------------------------------------------
|
---|
| 233 | (defun string-read-poly (F vars
|
---|
| 234 | &key (order #'lex>)
|
---|
| 235 | (suppress-value nil)
|
---|
| 236 | (stream t)
|
---|
| 237 | (convert-rational-to-integer t)
|
---|
| 238 | &aux (vars (read-vars vars))
|
---|
| 239 | (F (parse-string-to-sorted-alist F vars order)))
|
---|
| 240 | (when convert-rational-to-integer
|
---|
| 241 | (if (eq (car F) '[)
|
---|
| 242 | (setf F (cons (car F) (mapcar #'poly-rational-to-integer (rest F))))
|
---|
| 243 | (setf F (poly-rational-to-integer F))))
|
---|
| 244 | (format stream "~&Args:")
|
---|
| 245 | (poly-print F vars stream)
|
---|
| 246 | (terpri stream)
|
---|
| 247 | (if suppress-value (values) F))
|
---|
| 248 |
|
---|
| 249 |
|
---|
| 250 | ;; Multiply by lcm of denominators of coefficients
|
---|
| 251 | (defun poly-rational-to-integer (p &optional (ring *coefficient-ring*))
|
---|
| 252 | (let ((c (apply (ring-lcm ring) (mapcar (ring-denominator ring) (mapcar #'cdr p)))))
|
---|
| 253 | (scalar-times-poly c p ring)))
|
---|
| 254 |
|
---|
| 255 | (defun read-vars (string-or-list)
|
---|
| 256 | "Read a list of variables, specified either as a list of symbols or a string
|
---|
| 257 | listing variables in the form of a comma-separated list, delimited by [,]"
|
---|
| 258 | (typecase string-or-list
|
---|
| 259 | (list string-or-list)
|
---|
| 260 | (string (with-input-from-string (s string-or-list) (rest (parse s))))))
|
---|