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#35 powerseries((x+1)/(1-2*x^2), x, 0);
If powerseries is called with a monomial as the numerator, it factors it
out before expansion:
(%i9) powerseries((x)/(1-2*x), x, 0);
inf
====
\ i5 i5 + 1 i5
(%o9) - x > (- 2) (- 1) x
/
====
i5 = 0
If the numerator is a polynomial, powerseries tries to do a partial fraction
expansion before powerseries expansion:
(%i8) powerseries((x+1)/(1-2*x), x, 0);
inf
====
\ i4 i4 + 1 i4
3 > (- 2) (- 1) x
/
====
i4 = 0 1
(%o8) - -------------------------------- - -
2 2
If partial fraction expansion fails, the power series fails:
(%i1) powerseries((1+x)/(1-2*x^2), x, 0);
(%o1) Unable to expand
This patch keeps going if partial fraction expansion fails, factoring out
the numerator and doing power series expansion of the denominator only:
(%i7) powerseries((x+1)/(1-2*x^2), x, 0);
inf
====
\ i3 i3 + 1 2 i3
(%o7) (- x - 1) > (- 2) (- 1) x
/
====
i3 = 0
*** ./series.lisp 2007/05/20 11:34:20 1.1
--- ./series.lisp 2007/05/20 13:01:55
***************
*** 174,194 ****
(defun ratexand1 (n d)
(and $verbose
! (prog2 (mtell "Trying partial fraction expansion of ")
(show-exp (list '(mquotient) n d))
(terpri)))
(funcall #'(lambda (*ratexp)
! (m+l (mapcar #'ratexp
! (funcall #'(lambda (l)
! (cond ((eq (caar l) 'mplus)
! (and $verbose
! (mtell "which is ")
! (show-exp l))
! (cdr l))
! (t (throw 'psex
! '(err (mtext)
! "Partial fraction expansion failed")))))
! ($partfrac (div* n d) var)))))
t))
^L
(defun sratsubst (gcd num den)
--- 174,197 ----
(defun ratexand1 (n d)
(and $verbose
! (prog2 (mtell "Trying partial fraction expansion of ~%")
(show-exp (list '(mquotient) n d))
(terpri)))
(funcall #'(lambda (*ratexp)
! (let ((l ($partfrac (div* n d) var)))
! (cond ((eq (caar l) 'mplus)
! (and $verbose
! (mtell "which is ~%")
! (show-exp l))
! (m+l (mapcar #'ratexp
! (cdr l))))
! ((poly? n var)
! (and $verbose
! (mtell "Partial fraction expansion failed, expanding denominator only~%"))
! (m* n (ratexp (m// 1 d))))
! (t (throw 'psex
! '(err (mtext)
! "Partial fraction expansion failed"))))))
t))
^L
(defun sratsubst (gcd num den)
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File Added: series.lisp.diff
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Here is a verison of series.lisp with an implementation of the
rational expansion theorem for distinct roots. Some test cases:
/* two simple roots */
powerseries((1)/((1-2*x)*(1-3*x)), x, 0);
/* fibonacci */
powerseries((1)/(1-x-x^2), x, 0);
/* 1 1 2 2 4 4 8 8 */
powerseries((1+x)/(1-2*x^2), x, 0);
/* multiple root */
powerseries((1+x)/(1-x)^2, x, 0);
/* numerator higher order poly than denom */
powerseries((1+x^3)/(1-x-x^2), x, 0);
/* zero root in denom */
powerseries((1)/((1-2*x)*(x)), x, 0);
/* one simple and one repeated root in denom */
powerseries((1+x+x^2)/((1-2*x)*(1+x)^2), x, 0);
/* gcd of exps is two */
powerseries((1-x^2)/(1-4*x^2+x^4), x, 0);
File Added: series.lisp