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## [Maxima-bugs] [ maxima-Bugs-820770 ] plog(x^2)=>2*log(x)

 [Maxima-bugs] [ maxima-Bugs-820770 ] plog(x^2)=>2*log(x) From: SourceForge.net - 2003-10-09 17:40:40 ```Bugs item #820770, was opened at 2003-10-09 13:40 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=820770&group_id=4933 Category: None Group: None Status: Open Resolution: None Priority: 5 Submitted By: Stavros Macrakis (macrakis) Assigned to: Nobody/Anonymous (nobody) Summary: plog(x^2)=>2*log(x) Initial Comment: Plog is advertised as the principal branch of the complex-valued natural logarithm with -%PI < CARG(X) <= +%PI This sounds very useful, and presumes that the regular 'log' function represents something other than the principal branch -- perhaps all branches as a multivalued function? But plog(x^2) simplifies to 2*log(x) (after asking whether x is non-zero). This simplification is incorrect for x=-1. The main meaning of plog appears to be that it will *carry out* the logarithm when the imagpart is a multiple of %pi/4. makelist([log(x),plog(x)],x,[1,%i,1+%i,%i*2,2+%i]) => [[0,0], [LOG(%I), %I*%PI/2 ], [LOG(%I+1), LOG(2)/2+%I*%PI/4 ], [LOG(2*%I), LOG(2)+%I*%PI/2 ], [LOG(%I+2), PLOG(%I+2) ] ] And the only use of plog within Maxima is by defint. I am not even sure that defint actually needs plog (as opposed to plain log) -- maybe it is some sort of vestige? ---------------------------------------------------------------------- You can respond by visiting: https://sourceforge.net/tracker/?func=detail&atid=104933&aid=820770&group_id=4933 ```

 [Maxima-bugs] [ maxima-Bugs-820770 ] plog(x^2)=>2*log(x) From: SourceForge.net - 2003-10-09 17:40:40 ```Bugs item #820770, was opened at 2003-10-09 13:40 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=820770&group_id=4933 Category: None Group: None Status: Open Resolution: None Priority: 5 Submitted By: Stavros Macrakis (macrakis) Assigned to: Nobody/Anonymous (nobody) Summary: plog(x^2)=>2*log(x) Initial Comment: Plog is advertised as the principal branch of the complex-valued natural logarithm with -%PI < CARG(X) <= +%PI This sounds very useful, and presumes that the regular 'log' function represents something other than the principal branch -- perhaps all branches as a multivalued function? But plog(x^2) simplifies to 2*log(x) (after asking whether x is non-zero). This simplification is incorrect for x=-1. The main meaning of plog appears to be that it will *carry out* the logarithm when the imagpart is a multiple of %pi/4. makelist([log(x),plog(x)],x,[1,%i,1+%i,%i*2,2+%i]) => [[0,0], [LOG(%I), %I*%PI/2 ], [LOG(%I+1), LOG(2)/2+%I*%PI/4 ], [LOG(2*%I), LOG(2)+%I*%PI/2 ], [LOG(%I+2), PLOG(%I+2) ] ] And the only use of plog within Maxima is by defint. I am not even sure that defint actually needs plog (as opposed to plain log) -- maybe it is some sort of vestige? ---------------------------------------------------------------------- You can respond by visiting: https://sourceforge.net/tracker/?func=detail&atid=104933&aid=820770&group_id=4933 ```