gistfile1.txt

(defun rischexpvar (expexpflag flag l)
  (prog (lcm y m p alphar beta gamma delta r s
	 tt denom k wl wv i ytemp ttemp yalpha f a expg n yn yd)
     (desetq (f a expg n) l)
     (cond ((or (pzerop a) (pzerop (car a)))
	    (return (cond ((null flag) (rzero))
			  (t (rischzero))))))
     (setq denom (ratdenominator f))
     (setq p (findpr (cdr (partfrac a mainvar))
		     (cdr (partfrac f mainvar))))
     (setq lcm (plcm (ratdenominator a) p))
     (setq y (ratpl (spderivative (cons 1 p) mainvar)
		    (ratqu f p)))
     (setq lcm (plcm lcm (ratdenominator y)))
     (setq r (car (ratqu lcm p)))
     (setq s (car (r* lcm y)))
     (setq tt (car (r* a lcm)))
     (setq beta (pdegree r mainvar))
     (setq gamma (pdegree s mainvar))
     (setq delta (pdegree tt mainvar))
     (setq alphar (max (- (1+ delta) beta)
		       (- delta gamma)))
     (setq m 0)
     (cond ((equal (1- beta) gamma)
	    (setq y (r* -1
			(ratqu (polcoef s gamma)
			       (polcoef r beta))))
	    (and (equal (cdr y) 1)
		 (numberp (car y))
		 (setq m (car y)))))
     (setq alphar (max alphar m))
     (if (minusp alphar)
	 (return (if flag (cxerfarg (rzero) expg n a) nil)))
     (cond ((not (and (equal alphar m) (not (zerop m))))
	    (go down2)))
     (setq k (+ alphar beta -2))
     (setq wl nil)
     l2   (setq wv (list (cons (polcoef tt k) 1)))
     (setq i alphar)
     l1   (setq wv
		(cons (r+ (r* (cons i 1)
			      (polcoef r (+ k 1 (- i))))
			  (cons (polcoef s (+ k (- i))) 1))
		      wv))
     (decf i)
     (cond ((> i -1) (go l1)))
     (setq wl (cons wv wl))
     (decf k)
     (cond ((> k -1) (go l2)))
     (setq y (lsa wl))
     (if (or (eq y 'singular) (eq y 'inconsistent))
	 (cond ((null flag) (return nil))
	       (t (return (cxerfarg (rzero) expg n a)))))
     (setq k 0)
     (setq lcm 0)
     (setq y (cdr y))
     l3   (setq lcm
		(r+ (r* (car y) (pexpt (list mainvar 1 1) k))
		    lcm))
     (incf k)
     (setq y (cdr y))
     (cond ((null y)
	    (return (cond ((null flag) (ratqu lcm p))
			  (t (list (r* (ratqu lcm p)
				       (cons (list expg n 1) 1))
				   0))))))
     (go l3)
     down2 (cond ((> (1- beta) gamma)
		 (setq k (+ alphar (1- beta)))
		 (setq denom '(ratti alphar (polcoef r beta) t)))
		((< (1- beta) gamma)
		 (setq k (+ alphar gamma))
		 (setq denom '(polcoef s gamma)))
		(t (setq k (+ alphar gamma))
		   (setq denom
			 '(ratpl (ratti alphar (polcoef r beta) t)
			   (polcoef s gamma)))))
     (setq y 0)
     loop (setq yn (polcoef (ratnumerator tt) k)
		yd (r* (ratdenominator tt) ;DENOM MAY BE 0
		       (cond ((zerop alphar) (polcoef s gamma))
			     (t (eval denom))) ))
     (cond ((rzerop yd)
	    (cond ((pzerop yn) (setq k (1- k) alphar (1- alphar))
		   (go loop))		;need more constraints?
		  (t (cond
		       ((null flag) (return nil))
		       (t (return (cxerfarg (rzero) expg n a)))))))
	   (t (setq yalpha (ratqu yn yd))))
     (setq ytemp (r+ y (r* yalpha
			   (cons (list mainvar alphar 1) 1) )))
     (setq ttemp (r- tt (r* yalpha
			    (r+ (r* s (cons (list mainvar alphar 1) 1))
				(r* r alphar
				    (list mainvar (1- alphar) 1))))))
     (decf k)
     (decf alphar)
     (cond ((< alphar 0)
	    (cond
	      ((rzerop ttemp)
	       (cond
		 ((null flag) (return (ratqu ytemp p)))
		 (t (return (list (ratqu (r* ytemp (cons (list expg n 1) 1))
					 p)
				  0)))))
	      ((null flag) (return nil))
	      ((and (risch-constp (setq ttemp (ratqu ttemp lcm)))
		    $erfflag
		    (equal (pdegree (car (get expg 'rischarg)) mainvar) 2)
		    (equal (pdegree (cdr (get expg 'rischarg)) mainvar) 0))
	       (return (list (ratqu (r* ytemp (cons (list expg n 1) 1)) p)
			     (erfarg2 (r* n (get expg 'rischarg)) ttemp))))
	      (t (return
		   (cxerfarg
		    (ratqu (r* y (cons (list expg n 1) 1)) p)
		    expg
		    n
		    (ratqu tt lcm)))))))
     (setq y ytemp)
     (setq tt ttemp)
     (go loop)))