source: branches/f4grobner/termlist.lisp@ 153

;;; -*-  Mode: Lisp; Package: Maxima; Syntax: Common-Lisp; Base: 10 -*- 
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;;;  Copyright (C) 1999, 2002, 2009, 2015 Marek Rychlik <rychlik@u.arizona.edu>          
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;;;  This program is free software; you can redistribute it and/or modify        
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(in-package :grobner)

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;;
;; Low-level polynomial arithmetic done on 
;; lists of terms
;;
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(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."
  (mapcan
   #'(lambda (term)
       (let ((c1 (funcall (ring-mul ring) c (term-coeff term))))
         (unless (funcall (ring-zerop ring) c1)
           (list (make-term (term-monom term) c1)))))
   p))


(defun term-mul (ring term1 term2)
  "Returns (LIST TERM) wheter 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."
  (let ((c (funcall (ring-mul ring) (term-coeff term1) (term-coeff term2))))
    (unless (funcall (ring-zerop ring) c)
      (list (make-term (monom-mul (term-monom term1) (term-monom term2)) c)))))

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

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

(defun monom-times-term (m term)
  (make-term (monom-mul m (term-monom term)) (term-coeff term)))

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

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

(defun termlist-add (ring p q)
  (declare (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)
             (monomial-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 (termlist-lm p) 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 p q)
  (declare (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)
             (monomial-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 (termlist-lm p) 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 (termlist-lm q) (funcall (ring-uminus ring) (termlist-lc q))) r)
                     q (cdr q)))))
         nil))
       r)))

;; Multiplication of polynomials
;; Non-destructive version
(defun termlist-mul (ring p q)
  (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 ring (termlist-lt p) (termlist-lt q)))
               (tail (termlist-add ring (term-times-termlist ring (car p) (cdr q))
                                   (termlist-mul ring (cdr p) q))))
           (cond ((null head) tail)
                 ((null tail) head)
                 (t (nconc head tail)))))))
                    
(defun termlist-unit (ring dimension)
  (declare (fixnum dimension))
  (list (make-term (make-monom dimension :initial-element 0)
                   (funcall (ring-unit ring)))))

(defun termlist-expt (ring poly n &aux (dim (monom-dimension (termlist-lm poly))))
  (declare (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 q q))       ;keep squaring
         (p (termlist-unit ring dim) (if (not (zerop (logand k n))) (termlist-mul ring p q) p)))
        ((> k n) p)
      (declare (fixnum k))))))