[Maxima-bugs] [ maxima-Bugs-3038883 ] In general exp(z)^a --> exp(z*a) not correct

 [Maxima-bugs] [ maxima-Bugs-3038883 ] In general exp(z)^a --> exp(z*a) not correct From: SourceForge.net - 2010-09-23 21:08:21 ```Bugs item #3038883, was opened at 2010-08-03 17:59 Message generated for change (Comment added) made by crategus You can respond by visiting: https://sourceforge.net/tracker/?func=detail&atid=104933&aid=3038883&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: Dieter Kaiser (crategus) Assigned to: Nobody/Anonymous (nobody) Summary: In general exp(z)^a --> exp(z*a) not correct Initial Comment: Maxima always simplifies exp(z)^a --> exp(a*z) In general this is only correct for -%pi < imagpart(z) <= %pi or a an integer. This is an example with z = 3/2*%i*%pi and a = 1/2. First we calculate exp(z)^a: (%i2) sqrt(exp(3/2*%i*%pi)),rectform,factor; (%o2) -(%i-1)/sqrt(2) The result for exp(a*z) differs by the sign: (%i3) exp(3/4*%i*%pi),rectform,factor; (%o3) (%i-1)/sqrt(2) Remark: In the first example Maxima immediately simplifies exp(3/2*%i*%pi) --> -%i. Therefore, the simplification exp(z)^a is not applied. Dieter Kaiser ---------------------------------------------------------------------- >Comment By: Dieter Kaiser (crategus) Date: 2010-09-23 23:08 Message: Fixed in simp.lisp revision 1.116. Closing this bug report as fixed. Dieter Kaiser ---------------------------------------------------------------------- Comment By: Dieter Kaiser (crategus) Date: 2010-08-03 22:33 Message: In addition: The problem is that Maxima simplifies (x^a)^b --> x^(a*b), when x is positive, but this condition is not enough to be correct in general. This is an example: (%i2) assume(x>0)\$ (%i3) (x^a)^b; (%o3) x^(a*b) This type of simplification is correct only if one of the following conditions holds: (1) b an integer (correctly implemented) or (2) -1 < a <= 1 (not implemented) or (3) -%pi < imagpart(a*log(x)) <= %pi (not implemented) Dieter Kaiser ---------------------------------------------------------------------- You can respond by visiting: https://sourceforge.net/tracker/?func=detail&atid=104933&aid=3038883&group_id=4933 ```

 [Maxima-bugs] [ maxima-Bugs-3038883 ] In general exp(z)^a --> exp(z*a) not correct From: SourceForge.net - 2010-08-03 15:59:59 ```Bugs item #3038883, was opened at 2010-08-03 17:59 Message generated for change (Tracker Item Submitted) made by crategus You can respond by visiting: https://sourceforge.net/tracker/?func=detail&atid=104933&aid=3038883&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 Private: No Submitted By: Dieter Kaiser (crategus) Assigned to: Nobody/Anonymous (nobody) Summary: In general exp(z)^a --> exp(z*a) not correct Initial Comment: Maxima always simplifies exp(z)^a --> exp(a*z) In general this is only correct for -%pi < imagpart(z) <= %pi or a an integer. This is an example with z = 3/2*%i*%pi and a = 1/2. First we calculate exp(z)^a: (%i2) sqrt(exp(3/2*%i*%pi)),rectform,factor; (%o2) -(%i-1)/sqrt(2) The result for exp(a*z) differs by the sign: (%i3) exp(3/4*%i*%pi),rectform,factor; (%o3) (%i-1)/sqrt(2) Remark: In the first example Maxima immediately simplifies exp(3/2*%i*%pi) --> -%i. Therefore, the simplification exp(z)^a is not applied. Dieter Kaiser ---------------------------------------------------------------------- You can respond by visiting: https://sourceforge.net/tracker/?func=detail&atid=104933&aid=3038883&group_id=4933 ```
 [Maxima-bugs] [ maxima-Bugs-3038883 ] In general exp(z)^a --> exp(z*a) not correct From: SourceForge.net - 2010-08-03 20:33:33 ```Bugs item #3038883, was opened at 2010-08-03 17:59 Message generated for change (Comment added) made by crategus You can respond by visiting: https://sourceforge.net/tracker/?func=detail&atid=104933&aid=3038883&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 Private: No Submitted By: Dieter Kaiser (crategus) Assigned to: Nobody/Anonymous (nobody) Summary: In general exp(z)^a --> exp(z*a) not correct Initial Comment: Maxima always simplifies exp(z)^a --> exp(a*z) In general this is only correct for -%pi < imagpart(z) <= %pi or a an integer. This is an example with z = 3/2*%i*%pi and a = 1/2. First we calculate exp(z)^a: (%i2) sqrt(exp(3/2*%i*%pi)),rectform,factor; (%o2) -(%i-1)/sqrt(2) The result for exp(a*z) differs by the sign: (%i3) exp(3/4*%i*%pi),rectform,factor; (%o3) (%i-1)/sqrt(2) Remark: In the first example Maxima immediately simplifies exp(3/2*%i*%pi) --> -%i. Therefore, the simplification exp(z)^a is not applied. Dieter Kaiser ---------------------------------------------------------------------- >Comment By: Dieter Kaiser (crategus) Date: 2010-08-03 22:33 Message: In addition: The problem is that Maxima simplifies (x^a)^b --> x^(a*b), when x is positive, but this condition is not enough to be correct in general. This is an example: (%i2) assume(x>0)\$ (%i3) (x^a)^b; (%o3) x^(a*b) This type of simplification is correct only if one of the following conditions holds: (1) b an integer (correctly implemented) or (2) -1 < a <= 1 (not implemented) or (3) -%pi < imagpart(a*log(x)) <= %pi (not implemented) Dieter Kaiser ---------------------------------------------------------------------- You can respond by visiting: https://sourceforge.net/tracker/?func=detail&atid=104933&aid=3038883&group_id=4933 ```
 [Maxima-bugs] [ maxima-Bugs-3038883 ] In general exp(z)^a --> exp(z*a) not correct From: SourceForge.net - 2010-09-23 21:08:21 ```Bugs item #3038883, was opened at 2010-08-03 17:59 Message generated for change (Comment added) made by crategus You can respond by visiting: https://sourceforge.net/tracker/?func=detail&atid=104933&aid=3038883&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: Dieter Kaiser (crategus) Assigned to: Nobody/Anonymous (nobody) Summary: In general exp(z)^a --> exp(z*a) not correct Initial Comment: Maxima always simplifies exp(z)^a --> exp(a*z) In general this is only correct for -%pi < imagpart(z) <= %pi or a an integer. This is an example with z = 3/2*%i*%pi and a = 1/2. First we calculate exp(z)^a: (%i2) sqrt(exp(3/2*%i*%pi)),rectform,factor; (%o2) -(%i-1)/sqrt(2) The result for exp(a*z) differs by the sign: (%i3) exp(3/4*%i*%pi),rectform,factor; (%o3) (%i-1)/sqrt(2) Remark: In the first example Maxima immediately simplifies exp(3/2*%i*%pi) --> -%i. Therefore, the simplification exp(z)^a is not applied. Dieter Kaiser ---------------------------------------------------------------------- >Comment By: Dieter Kaiser (crategus) Date: 2010-09-23 23:08 Message: Fixed in simp.lisp revision 1.116. Closing this bug report as fixed. Dieter Kaiser ---------------------------------------------------------------------- Comment By: Dieter Kaiser (crategus) Date: 2010-08-03 22:33 Message: In addition: The problem is that Maxima simplifies (x^a)^b --> x^(a*b), when x is positive, but this condition is not enough to be correct in general. This is an example: (%i2) assume(x>0)\$ (%i3) (x^a)^b; (%o3) x^(a*b) This type of simplification is correct only if one of the following conditions holds: (1) b an integer (correctly implemented) or (2) -1 < a <= 1 (not implemented) or (3) -%pi < imagpart(a*log(x)) <= %pi (not implemented) Dieter Kaiser ---------------------------------------------------------------------- You can respond by visiting: https://sourceforge.net/tracker/?func=detail&atid=104933&aid=3038883&group_id=4933 ```