source: branches/f4grobner/termlist.lisp

;;; -*-  Mode: Lisp -*- 
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;;;                                                                              
;;;  Copyright (C) 1999, 2002, 2009, 2015 Marek Rychlik <rychlik@u.arizona.edu>          
;;;                                                                              
;;;  This program is free software; you can redistribute it and/or modify        
;;;  it under the terms of the GNU General Public License as published by        
;;;  the Free Software Foundation; either version 2 of the License, or           
;;;  (at your option) any later version.                                         
;;;                                                                              
;;;  This program is distributed in the hope that it will be useful,             
;;;  but WITHOUT ANY WARRANTY; without even the implied warranty of              
;;;  MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the               
;;;  GNU General Public License for more details.                                
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;;;  You should have received a copy of the GNU General Public License           
;;;  along with this program; if not, write to the Free Software                 
;;;  Foundation, Inc., 59 Temple Place - Suite 330, Boston, MA 02111-1307, USA.  
;;;                                                                              
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(defpackage "TERMLIST"
  (:use :cl :monom :ring :ring-and-order :term)
  (:export "TERMLIST-SUGAR"
           "TERMLIST-CONTRACT"
           "TERMLIST-EXTEND"
           "TERMLIST-ADD-VARIABLES"
           "TERMLIST-LT"
           "TERMLIST-LM"
           "TERMLIST-LC"
           "SCALAR-MUL"
           "SCALAR-TIMES-TERMLIST"
           "TERM-MUL-LST"
           "TERMLIST-TIMES-TERM"
           "TERM-TIMES-TERMLIST"
           "MONOM-TIMES-TERM"
           "MONOM-TIMES-TERMLIST"
           "TERMLIST-UMINUS"
           "TERMLIST-ADD"
           "TERMLIST-SUB"
           "TERMLIST-MUL"
           "TERMLIST-UNIT"
           "TERMLIST-EXPT"))

(in-package :termlist)

(proclaim '(optimize (speed 3) (space 0) (safety 0) (debug 0)))

(defun termlist-sugar (p &aux (sugar -1))
  (declare (fixnum sugar))
  (dolist (term p sugar)
    (setf sugar (max sugar (term-sugar term)))))

(defun termlist-contract (p &optional (k 1))
  "Eliminate first K variables from a polynomial P."
  (mapcar #'(lambda (term) 
              (declare (type term term))
              (make-term :monom (monom-contract (term-monom term) k)
                         :coeff (term-coeff term)))
          p))

(defun termlist-ncontract (p &optional (k 1))
  "Eliminate first K variables from a polynomial P. Destructive version."
  (mapc #'(lambda (term) 
            (declare (type term term))
            (setf (term-monom term) (monom-contract (term-monom term) k)))
        p))

(defun termlist-extend (p &optional (m (make-monom :dimension 1)))
  "Extend every monomial in a polynomial P by inserting at the
beginning of every monomial the list of powers M."
  (mapcar #'(lambda (term) 
              (declare (type term term))
              (make-term :monom (monom-append m (term-monom term))
                         :coeff (term-coeff term)))
          p))

(defun termlist-add-variables (p n)
  "Add N variables to a polynomial P by inserting zero powers
at the beginning of each monomial."
  (declare (fixnum n))
  (mapcar #'(lambda (term)
              (declare (type term term))
              (make-term :monom (monom-append (make-monom :dimension n)
                                              (term-monom term))
                         :coeff (term-coeff term)))
          p))


;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;
;;
;; Low-level polynomial arithmetic done on 
;; lists of terms
;;
;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;

(defmacro termlist-lt (p) `(car ,p))
(defun termlist-lm (p) (term-monom (termlist-lt p)))
(defun termlist-lc (p) (term-coeff (termlist-lt p)))

(define-modify-macro scalar-mul (c) coeff-mul)

(defun scalar-times-termlist (ring c p)
  "Multiply scalar C by a polynomial P. This function works
even if there are divisors of 0."
  (declare (ring ring))
  (mapcan
   #'(lambda (term)
       (let ((c1 (funcall (ring-mul ring) c (term-coeff term))))
         (unless (funcall (ring-zerop ring) c1)
           (list (make-term :monom (term-monom term) :coeff c1)))))
   p))


(defun term-mul-lst (ring term1 term2)
  "A special version of term multiplication. Returns (LIST TERM) where
TERM is the product of the terms TERM1 TERM2, or NIL when the product
is 0. This definition takes care of divisors of 0 in the coefficient
ring."
  (declare (ring ring) (type term term1 term2))
  (let ((c (funcall (ring-mul ring) (term-coeff term1) (term-coeff term2))))
    (unless (funcall (ring-zerop ring) c)
      (list (make-term :monom (monom-mul (term-monom term1) (term-monom term2)) 
                       :coeff c)))))

(defun term-times-termlist (ring term f)
  (declare (type ring ring) (type term term))
  (mapcan #'(lambda (term-f) (term-mul-lst ring term term-f)) f))

(defun termlist-times-term (ring f term)
  (declare (ring ring) (type term term))
  (mapcan #'(lambda (term-f) (term-mul-lst ring term-f term)) f))

(defun monom-times-term (m term)
  (declare (type monom m) (type term term))
  (make-term :monom (monom-mul m (term-monom term)) :coeff (term-coeff term)))

(defun monom-times-termlist (m f)
  (declare (type monom m))
  (cond
    ((null f) nil)
    (t
     (mapcar #'(lambda (x) (monom-times-term m x)) f))))

(defun termlist-uminus (ring f)
  (declare (ring ring))
  (mapcar #'(lambda (x)
              (make-term :monom (term-monom x)
                         :coeff (funcall (ring-uminus ring) (term-coeff x))))
          f))

(defun termlist-add (ring-and-order p q 
                     &aux 
                       (ring (ro-ring ring-and-order))
                       (order (ro-order ring-and-order)))
  (declare (ring-and-order ring-and-order) (type list p q))
  (do (r)
      ((cond
         ((endp p)
          (setf r (revappend r q)) t)
         ((endp q)
          (setf r (revappend r p)) t)
         (t
          (multiple-value-bind
                (lm-greater lm-equal)
              (funcall order (termlist-lm p) (termlist-lm q))
            (cond
              (lm-equal
               (let ((s (funcall (ring-add ring) (termlist-lc p) (termlist-lc q))))
                 (unless (funcall (ring-zerop ring) s) ;check for cancellation
                   (setf r (cons (make-term :monom (termlist-lm p) :coeff s) r)))
                 (setf p (cdr p) q (cdr q))))
              (lm-greater
               (setf r (cons (car p) r)
                     p (cdr p)))
              (t (setf r (cons (car q) r)
                       q (cdr q)))))
          nil))
       r)))

(defun termlist-sub (ring-and-order p q
                     &aux 
                       (ring (ro-ring ring-and-order))
                       (order (ro-order ring-and-order)))
  (declare (ring-and-order ring-and-order) (type list p q))
  (do (r)
      ((cond
         ((endp p)
          (setf r (revappend r (termlist-uminus ring q)))
          t)
         ((endp q)
          (setf r (revappend r p))
          t)
         (t
          (multiple-value-bind
                (mgreater mequal)
              (funcall order (termlist-lm p) (termlist-lm q))
            (cond
              (mequal
               (let ((s (funcall (ring-sub ring) (termlist-lc p) (termlist-lc q))))
                 (unless (funcall (ring-zerop ring) s) ;check for cancellation
                   (setf r (cons (make-term :monom (termlist-lm p) :coeff s) r)))
                 (setf p (cdr p) q (cdr q))))
              (mgreater
               (setf r (cons (car p) r)
                     p (cdr p)))
              (t (setf r (cons (make-term :monom (termlist-lm q)
                                          :coeff (funcall (ring-uminus ring) (termlist-lc q))) r)
                       q (cdr q)))))
          nil))
       r)))

;; Multiplication of polynomials
;; Non-destructive version
(defun termlist-mul (ring-and-order p q
                     &aux (ring (ro-ring ring-and-order)))
  (declare (ring-and-order ring-and-order))
  (cond ((or (endp p) (endp q)) nil)    ;p or q is 0 (represented by NIL)
        ;; If p=p0+p1 and q=q0+q1 then pq=p0q0+p0q1+p1q
        ((endp (cdr p))
         (term-times-termlist ring (car p) q))
        ((endp (cdr q))
         (termlist-times-term ring p (car q)))
        (t
         (let ((head (term-mul-lst ring (termlist-lt p) (termlist-lt q)))
               (tail (termlist-add ring-and-order
                                   (term-times-termlist ring (car p) (cdr q))
                                   (termlist-mul ring-and-order (cdr p) q))))
           (cond ((null head) tail)
                 ((null tail) head)
                 (t (nconc head tail)))))))

(defun termlist-unit (ring dim)
  (declare (ring ring) (fixnum dim))
  (list (make-term :monom (make-monom :dimension dim)
                   :coeff (funcall (ring-unit ring)))))


(defun termlist-expt (ring-and-order poly n 
                      &aux
                        (ring (ro-ring ring-and-order))
                        (dim (monom-dimension (termlist-lm poly))))
  (declare (ring-and-order ring-and-order) (type fixnum n dim))
  (cond
    ((minusp n) (error "termlist-expt: Negative exponent."))
    ((endp poly) (if (zerop n) (termlist-unit ring dim) nil))
    (t
     (do ((k 1 (ash k 1))
          (q poly (termlist-mul ring-and-order q q)) ;keep squaring
          (p (termlist-unit ring dim) (if (not (zerop (logand k n))) (termlist-mul ring-and-order p q) p)))
         ((> k n) p)
       (declare (fixnum k))))))