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From: SourceForge.net <noreply@so...>  20080927 19:16:12

Bugs item #1093138, was opened at 20041230 08:05 Message generated for change (Comment added) made by crategus You can respond by visiting: https://sourceforge.net/tracker/?func=detail&atid=104933&aid=1093138&group_id=4933 Please note that this message will contain a full copy of the comment thread, including the initial issue submission, for this request, not just the latest update. Category: Lisp Core Group: None Status: Closed >Resolution: Fixed Priority: 3 Private: No Submitted By: Robert Dodier (robert_dodier) Assigned to: Nobody/Anonymous (nobody) Summary: double factorial defn incorrect for noninteger operand Initial Comment: The double factorial x!! yields an incorrect result for x other than an integer. It appears that x!! is computed as the product x*(x2)*(x4)*...*y, where y is the least term (x2*k) s.t. x2*k > 1. This agrees with published defns (Arfken, Mathworld) for positive integers but not otherwise. Mathworld (http://mathworld.wolfram.com/DoubleFactorial.html) states a formula for z!!, z complex, translated into Maxima as follows  doublefact (z) := block ([a: 1+2*zcos(%pi*z), b: cos(%pi*z)1], 2^(a/4) * %pi^(b/4) * gamma(1+z/2)); It seems that Maxima could evaluate this function for noninteger arguments. Note that Maxima translates input x!! into an noun form genfact (x, x/2, 2).  >Comment By: Dieter Kaiser (crategus) Date: 20080927 21:16 Message: Change resolution to "fixed".  Comment By: Dieter Kaiser (crategus) Date: 20080927 14:30 Message: Closing this bug report. The function $genfact(x,y,z) no longer gives wrong results. A function factorial_double has been implemented. Dieter Kaiser  Comment By: Dieter Kaiser (crategus) Date: 20080922 00:17 Message: In a first step (asum.lisp, Rev. 1.30) the numerical evaluation of the function genfact(x,y,z) is specialized to integer arguments within the following range x, y, z, integer and z <= x and y <= x/z. For non valid integers a Maxima error is thrown. For all other numbers Maxima returns a noun form. With this changes Maxima no longer calculate wrong results. To get more general results for real and complex values for the Double factorial function a new function factorial_double has been suggested on the mailing list. Because Maxima no longer gets incorrect results this bug report could be closed. Dieter Kaiser  You can respond by visiting: https://sourceforge.net/tracker/?func=detail&atid=104933&aid=1093138&group_id=4933 
From: SourceForge.net <noreply@so...>  20080927 12:30:37

Bugs item #1093138, was opened at 20041230 08:05 Message generated for change (Comment added) made by crategus You can respond by visiting: https://sourceforge.net/tracker/?func=detail&atid=104933&aid=1093138&group_id=4933 Please note that this message will contain a full copy of the comment thread, including the initial issue submission, for this request, not just the latest update. Category: Lisp Core Group: None >Status: Closed Resolution: None Priority: 3 Private: No Submitted By: Robert Dodier (robert_dodier) Assigned to: Nobody/Anonymous (nobody) Summary: double factorial defn incorrect for noninteger operand Initial Comment: The double factorial x!! yields an incorrect result for x other than an integer. It appears that x!! is computed as the product x*(x2)*(x4)*...*y, where y is the least term (x2*k) s.t. x2*k > 1. This agrees with published defns (Arfken, Mathworld) for positive integers but not otherwise. Mathworld (http://mathworld.wolfram.com/DoubleFactorial.html) states a formula for z!!, z complex, translated into Maxima as follows  doublefact (z) := block ([a: 1+2*zcos(%pi*z), b: cos(%pi*z)1], 2^(a/4) * %pi^(b/4) * gamma(1+z/2)); It seems that Maxima could evaluate this function for noninteger arguments. Note that Maxima translates input x!! into an noun form genfact (x, x/2, 2).  >Comment By: Dieter Kaiser (crategus) Date: 20080927 14:30 Message: Closing this bug report. The function $genfact(x,y,z) no longer gives wrong results. A function factorial_double has been implemented. Dieter Kaiser  Comment By: Dieter Kaiser (crategus) Date: 20080922 00:17 Message: In a first step (asum.lisp, Rev. 1.30) the numerical evaluation of the function genfact(x,y,z) is specialized to integer arguments within the following range x, y, z, integer and z <= x and y <= x/z. For non valid integers a Maxima error is thrown. For all other numbers Maxima returns a noun form. With this changes Maxima no longer calculate wrong results. To get more general results for real and complex values for the Double factorial function a new function factorial_double has been suggested on the mailing list. Because Maxima no longer gets incorrect results this bug report could be closed. Dieter Kaiser  You can respond by visiting: https://sourceforge.net/tracker/?func=detail&atid=104933&aid=1093138&group_id=4933 
From: SourceForge.net <noreply@so...>  20080927 12:27:41

Bugs item #1486452, was opened at 20060511 14:09 Message generated for change (Comment added) made by crategus You can respond by visiting: https://sourceforge.net/tracker/?func=detail&atid=104933&aid=1486452&group_id=4933 Please note that this message will contain a full copy of the comment thread, including the initial issue submission, for this request, not just the latest update. Category: Lisp Core  Simplification Group: None Status: Open Resolution: None Priority: 3 Private: No Submitted By: Barton Willis (willisbl) Assigned to: Nobody/Anonymous (nobody) Summary: minfactorial doesn't look inside "!" Initial Comment: The minfactorial function doesn't look inside the factorial function. So it misses some simplifications that it could do: (%i1) (n!/(n1)!)!; (%o1) (n!/(n1)!)! (%i2) minfactorial(%); (%o2) (n!/(n1)!)! < could be n! (%i3) build_info(); Maxima version: 5.9.3 Maxima build date: 0:52 3/20/2006 host type: i686pcmingw32 lispimplementationtype: GNU Common Lisp (GCL) lispimplementationversion: GCL 2.6.7 Barton  >Comment By: Dieter Kaiser (crategus) Date: 20080927 14:27 Message: When we implement the simplification of expressions like factorial(n+m) and factorial (nm) with integer m, the factorials simplifies immediatly. The simplification depends on the Maxima User flag $factoriol_expand. This could be the implementation of the expansion: ((and $factorial_expand (mplusp y) (integerp (cadr y))) ;; factorial(z+m) and m integer. Expand. (let ((m (cadr y)) (n (simplify (cons '(mplus) (cddr y))))) (cond ((>= m 0) (mul (simplify (list '($pochhammer) (add n 1) m)) (simplify (list '(mfactorial) n)))) ((< m 0) (setq m ( m)) (div (mul (power 1 m) (simplify (list '(mfactorial) n))) (simplify (list '($pochhammer) (mul 1 n) m))))))) This is the result without simplification and minfactorial: (%i15) (n!/(n1)!)!; (%o15) (n!/(n1)!)! (%i16) minfactorial(%); (%o16) (n!/(n1)!)! Now we set the flag to expand the Factorials: (%i18) factorial_expand:true$ (%i20) factorial(n+2); (%o20) (n+1)*(n+2)*n! (%i21) factorial(n2); (%o21) n!/((1n)*n) The epression of this bug report simplifies: (%i22) (n!/(n1)!)!; (%o22) n! Because the simplification is done by the simplifier we have no problems with nested expressions. This mechanism of simplification has already be implemented for Double factorial, the Gamma function and the Incomplete Gamma function. Dieter Kaiser  You can respond by visiting: https://sourceforge.net/tracker/?func=detail&atid=104933&aid=1486452&group_id=4933 