;; 4/4/08 RJF
;; I can't find the hashtable polynomial multiplication, so I'll rewrite it.
;; multivar version, sparse monomials
;; pack exponent version
;;(setf size 10) ; much larger after testing
;;(setf  mem (make-array size :fill-pointer 0 ))
;;(dotimes (i size) (vector-push-extend (make-array 2 :element-type 'double-float :initial-element 0.0d0) mem))

(defun ptimes(r s)
  (let ((ans  (make-hash-table :test 'eql ))
	(m nil)
	(q 0.0d0))
    (declare (double-float q)(optimize (speed 3)(safety 0)))
    (maphash #'(lambda(ex v)		 ; exponent, coefficient-list
		  (declare  (double-float ex)
			    (type (simple-array double-float 1) v))
		 (maphash #'(lambda (ex2 v2)
			      (declare(double-float ex2)
				        (type (simple-array double-float 1) v2))
			      (setf q (+ ex ex2))
			      (setf m (gethash q ans nil)) ; is there an entry?
			      (if (null m)(setf m (setf (gethash q ans) 
							   (make-array 1 :element-type 'double-float 
								       :initial-element 0.0d0))))
 ;make an entry
			  ;    (format t "~%make entry for ~s"q)
			      (incf (the double-float (aref m 0))
				    (* (the double-float (aref v 0))
				       (the double-float (aref v2 0)))))r))   s)
    ans))

(defun ppower(r n)
  (cond((= n 0) 1)
       ((= n 1) r)
       (t (ptimes r (ppower r (1- n))))))

(defun list2hash(k)  
  (let ((ans (make-hash-table :test 'eql))
	)
    (dolist (i k ans)
      (setf (gethash  (cdr i) ans)
	(make-array 1 :element-type 'double-float :initial-element (coerce (car i) 'double-float))))))

(defun pdump(r)(maphash #'(lambda(key val)(format t "~%~a*x^~a" (aref val 0)key)) r))