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;;; ratpow version 0.3 4 June 2015
;;;
;;; Copyright 2013-2015 Stavros Macrakis
;;; Released under the LGPL (http://www.gnu.org/copyleft/lesser.html)
;;; These functions operate on the *numerator* of a CRE
;;; to find the exponents in the denominator, use ratXXpow(ratdenom(...))
;;; ratp_hipow -- highest power of the main variable in a CRE polynomial
;;; ratp_lopow -- lowest power of the main variable in a CRE polynomial
;;; ratp_coeffs -- list of powers and coefficients of the main variable
;;; ratp_dense_coeffs -- list of coefficients of the main variable, highest first
;;; ratp_dense_coeffs_lo -- list of coefficients of the main variable, lowest first
;; To get a list of vars in a CRE, use showratvars
;;; ratp_hipow( expr, var ) => highest power of var in ratnumer(expr)
;;; ratp_hipow( x^(5/2) + x^2 , x) => 2
;;; ratp_hipow( x^(5/2) + x^2 , sqrt(x)) => 5
(defun $ratp_hipow (e v) (ratp_pow e v 'hipow))
;;; ratp_lopow( expr, var ) => lowest power of var in ratnumer(expr)
;;; ratp_lopow( x^(5/2) + x^3 , x) => 0
;; CRE is {x}^3 + {x^(1/2)}^5 * {x}^0, where {} denotes kernels
(defun $ratp_lopow (e v) (ratp_pow e v 'lopow))
;;; ratp_coeffs( expr, var ) => list of powers/coefficients in ratnumer(expr)
;;; returned coefficients are in CRE form except for numbers
;;; ratp_coeffs( 4*x^3 + x + sqrt(x), x) => [[3,4],[1,1],[0,sqrt(x)]]
(defun $ratp_coeffs (e v) (ratp_pow e v 'sparse_coeffs))
;;; ratp_dense_coeffs( expr, var ) => list of coefficients in ratnumer(expr), highest first
;;; returned coefficients are in CRE form except for numbers
;;; ratp_dense_coeffs( 4*x^3 + x + sqrt(x), x) => [4,0,1,sqrt(x)]
(defun $ratp_dense_coeffs (e v) (ratp_pow e v 'dense_coeffs))
;;; ratp_dense_coeffs_lo( expr, var ) => list of coefficients in ratnumer(expr), lowest first
;;; returned coefficients are in CRE form except for numbers
;;; ratp_dense_coeffs_lo( 4*x^3 + x + sqrt(x), x) => [sqrt(x),1,0,4]
(defun $ratp_dense_coeffs_lo (e v) (ratp_pow e v 'dense_coeffs_low))
(defun ratp_pow (e v func)
(if (mbagp e)
(simplify (cons (list (caar e))
(mapcar #'(lambda (i) (ratp_pow i v func)) (cdr e))))
(let* ((e ($rat (if ($taylorp e) ($ratdisrep e) e) v)) ; change main variable if necessary
(mrat (car e))
(kernels (caddr mrat))
(gensyms (cadddr mrat))
(mainvar-gensym (nth (1- (length kernels)) gensyms))
(numerat (cadr e))
(res ())
(lis
(if (or (pcoefp numerat)
(not (eq (car numerat) mainvar-gensym)))
(list 0 numerat)
(cdr numerat))))
(cond ((eq func 'hipow) (car lis))
((eq func 'lopow) (car (last lis 2)))
(t (setq kernels (butlast kernels 1))
(setq mrat (list 'mrat 'simp kernels gensyms))
;;; Putprop needed for pdisrep, but not part-rat
;;; (mapc #'(lambda (y z) (putprop y z 'disrep)) gensyms kernels)
(cond
((eq func 'sparse_coeffs)
(do ((lis lis (cddr lis)))
((null lis)
(cons '(mlist simp) (nreverse res)))
(push (list '(mlist simp)
(car lis)
(part-rat mrat (cadr lis)))
res)))
((memq func '(dense_coeffs dense_coeffs_low))
(do ((lis lis (cddr lis))
(pow (car lis) (1- pow)))
((null lis)
(cons '(mlist simp)
(if (eq func 'dense_coeffs_low)
res
(nreverse res))))
(while (> pow (car lis))
(push 0 res)
(setq pow (1- pow)))
(push (part-rat mrat (cadr lis)) res)))))))))
(defun part-rat (mrat expr)
(if (pcoefp expr)
expr
(list* mrat expr 1)))
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