## [Maxima-bugs] [ maxima-Bugs-831354 ] beta(-2,1) inconsistent

 [Maxima-bugs] [ maxima-Bugs-831354 ] beta(-2,1) inconsistent From: SourceForge.net - 2003-10-27 21:46:45 ```Bugs item #831354, was opened at 2003-10-27 16:45 Message generated for change (Tracker Item Submitted) made by Item Submitter You can respond by visiting: https://sourceforge.net/tracker/?func=detail&atid=104933&aid=831354&group_id=4933 Category: None Group: None Status: Open Resolution: None Priority: 5 Submitted By: Stavros Macrakis (macrakis) Assigned to: Nobody/Anonymous (nobody) Summary: beta(-2,1) inconsistent Initial Comment: beta(-2, 1) => -1/2 beta(-2.0, 1) => -0.5 BUT beta(-2.0, 1.0) => -0.25 The fundamental problem is that beta(x,y) is undefined as a continuous real function of both x and y at (-2,1), but that beta(x,1) can be extended to be a well- behaved continuous function of x, namely 1/x. This is essentially the same case as x^y at (0,0). Right now, Maxima simplifies x^0=>1 and 0^x=>0 (just like beta(x,1)). The difference is that Maxima gives an error for 0^0, 0.0^0, etc. Longer-term, it would be nice if 0^x kept as a side- condition (x # 0) of the simplification, but for now.... ---------------------------------------------------------------------- You can respond by visiting: https://sourceforge.net/tracker/?func=detail&atid=104933&aid=831354&group_id=4933 ```

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 [Maxima-bugs] [ maxima-Bugs-831354 ] beta(-2,1) inconsistent From: SourceForge.net - 2003-10-27 21:46:45 ```Bugs item #831354, was opened at 2003-10-27 16:45 Message generated for change (Tracker Item Submitted) made by Item Submitter You can respond by visiting: https://sourceforge.net/tracker/?func=detail&atid=104933&aid=831354&group_id=4933 Category: None Group: None Status: Open Resolution: None Priority: 5 Submitted By: Stavros Macrakis (macrakis) Assigned to: Nobody/Anonymous (nobody) Summary: beta(-2,1) inconsistent Initial Comment: beta(-2, 1) => -1/2 beta(-2.0, 1) => -0.5 BUT beta(-2.0, 1.0) => -0.25 The fundamental problem is that beta(x,y) is undefined as a continuous real function of both x and y at (-2,1), but that beta(x,1) can be extended to be a well- behaved continuous function of x, namely 1/x. This is essentially the same case as x^y at (0,0). Right now, Maxima simplifies x^0=>1 and 0^x=>0 (just like beta(x,1)). The difference is that Maxima gives an error for 0^0, 0.0^0, etc. Longer-term, it would be nice if 0^x kept as a side- condition (x # 0) of the simplification, but for now.... ---------------------------------------------------------------------- You can respond by visiting: https://sourceforge.net/tracker/?func=detail&atid=104933&aid=831354&group_id=4933 ```
 [Maxima-bugs] [ maxima-Bugs-831354 ] beta(-2,1) inconsistent From: SourceForge.net - 2006-07-11 05:03:42 ```Bugs item #831354, was opened at 2003-10-27 14:45 Message generated for change (Comment added) made by robert_dodier You can respond by visiting: https://sourceforge.net/tracker/?func=detail&atid=104933&aid=831354&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: 5 Submitted By: Stavros Macrakis (macrakis) Assigned to: Nobody/Anonymous (nobody) Summary: beta(-2,1) inconsistent Initial Comment: beta(-2, 1) => -1/2 beta(-2.0, 1) => -0.5 BUT beta(-2.0, 1.0) => -0.25 The fundamental problem is that beta(x,y) is undefined as a continuous real function of both x and y at (-2,1), but that beta(x,1) can be extended to be a well- behaved continuous function of x, namely 1/x. This is essentially the same case as x^y at (0,0). Right now, Maxima simplifies x^0=>1 and 0^x=>0 (just like beta(x,1)). The difference is that Maxima gives an error for 0^0, 0.0^0, etc. Longer-term, it would be nice if 0^x kept as a side- condition (x # 0) of the simplification, but for now.... ---------------------------------------------------------------------- >Comment By: Robert Dodier (robert_dodier) Date: 2006-07-10 23:03 Message: Logged In: YES user_id=501686 Same behavior observed in 5.9.3cvs. About simplifying 0^x to 'if x # 0 then 0 else 1, that is certainly workable with unevaluated conditionals, see share/contrib/boolsimp/ for a proposed implementation. ---------------------------------------------------------------------- You can respond by visiting: https://sourceforge.net/tracker/?func=detail&atid=104933&aid=831354&group_id=4933 ```
 [Maxima-bugs] [ maxima-Bugs-831354 ] beta(-2,1) inconsistent From: SourceForge.net - 2009-02-14 18:30:21 ```Bugs item #831354, was opened at 2003-10-27 22:45 Message generated for change (Comment added) made by crategus You can respond by visiting: https://sourceforge.net/tracker/?func=detail&atid=104933&aid=831354&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: Closed >Resolution: Fixed Priority: 5 Private: No Submitted By: Stavros Macrakis (macrakis) Assigned to: Nobody/Anonymous (nobody) Summary: beta(-2,1) inconsistent Initial Comment: beta(-2, 1) => -1/2 beta(-2.0, 1) => -0.5 BUT beta(-2.0, 1.0) => -0.25 The fundamental problem is that beta(x,y) is undefined as a continuous real function of both x and y at (-2,1), but that beta(x,1) can be extended to be a well- behaved continuous function of x, namely 1/x. This is essentially the same case as x^y at (0,0). Right now, Maxima simplifies x^0=>1 and 0^x=>0 (just like beta(x,1)). The difference is that Maxima gives an error for 0^0, 0.0^0, etc. Longer-term, it would be nice if 0^x kept as a side- condition (x # 0) of the simplification, but for now.... ---------------------------------------------------------------------- >Comment By: Dieter Kaiser (crategus) Date: 2009-02-14 19:30 Message: A consistent and correct handling of the Beta function with a negative integer or an float or bigfloat representation has been implemented. These are the new results: (%i3) beta(-2,1); (%o3) -1/2 (%i4) beta(-2,1.0); (%o4) -0.5 (%i5) beta(-2.0,1); (%o5) -0.5 (%i6) beta(-2.0,1.0); (%o6) -0.5 (%i7) beta(-2,1.0b0); (%o7) -5.0b-1 (%i8) beta(-2b0,1); (%o8) -5.0b-1 (%i9) beta(-2b0,1b0); (%o9) -5.0b-1 Closing this bug report as fixed. Dieter Kaiser ---------------------------------------------------------------------- Comment By: Robert Dodier (robert_dodier) Date: 2006-07-11 07:03 Message: Logged In: YES user_id=501686 Same behavior observed in 5.9.3cvs. About simplifying 0^x to 'if x # 0 then 0 else 1, that is certainly workable with unevaluated conditionals, see share/contrib/boolsimp/ for a proposed implementation. ---------------------------------------------------------------------- You can respond by visiting: https://sourceforge.net/tracker/?func=detail&atid=104933&aid=831354&group_id=4933 ```

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