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## maxima-bugs

 [Maxima-bugs] [ maxima-Bugs-1051437 ] Trig integral error From: SourceForge.net - 2004-10-21 12:21:37 ```Bugs item #1051437, was opened at 2004-10-21 22:21 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=1051437&group_id=4933 Category: None Group: None Status: Open Resolution: None Priority: 5 Submitted By: David Billinghurst (billingd) Assigned to: Nobody/Anonymous (nobody) Summary: Trig integral error Initial Comment: The integral of 2*COT(x)^2*COS(2*x)/(CSC(2*x)+COT(2*x)); is wrong for maxima-5.9.1 (%i1) display2d:false; (%o1) FALSE (%i2) h: 2*COT(x)^2*COS(2*x)/(CSC(2*x)+COT(2*x)); (%o2) 2*COT(x)^2*COS(2*x)/(CSC(2*x)+COT(2*x)) (%i3) ih:integrate(h,x); (%o3) (2*LOG(SIN(x)^2+COS(x)^2+2*COS(x)+1) +2*LOG(SIN(x)^2+COS(x)^2-2*COS(x)+1) +COS(2*x)) /2 (%i4) ev(ih,x=1.0,numer)-ev(ih,x=0.5,numer); (%o4) .6469013090248041 (%i5) quad_qags(h,x,0.5,1); (%o5) [.1686767378171631,3.37999776996994E- 15,21,0] (%i6) h2:trigsimp(trigexpand(h)); (%o6) (4*COS(x)^3-2*COS(x))/SIN(x) (%i7) ih2:integrate(h2,x); (%o7) LOG(COS(x)+1)+LOG(COS(x)-1)+2*COS(x)^2 (%i8) ev(ih2,x=1.0,numer)-ev(ih2,x=0.5,numer); (%o8) .1686767378171636 The integral over 0.5 < x < 1.0 at %o4 differs from the numerical integral %o5 and the analytic integral of an equivalent expression %o8. ---------------------------------------------------------------------- You can respond by visiting: https://sourceforge.net/tracker/?func=detail&atid=104933&aid=1051437&group_id=4933 ```
 [Maxima-bugs] [ maxima-Bugs-1051437 ] Trig integral error From: SourceForge.net - 2004-10-21 12:29:04 ```Bugs item #1051437, was opened at 2004-10-21 22:21 Message generated for change (Comment added) made by billingd You can respond by visiting: https://sourceforge.net/tracker/?func=detail&atid=104933&aid=1051437&group_id=4933 Category: None Group: None Status: Open Resolution: None Priority: 5 Submitted By: David Billinghurst (billingd) Assigned to: Nobody/Anonymous (nobody) Summary: Trig integral error Initial Comment: The integral of 2*COT(x)^2*COS(2*x)/(CSC(2*x)+COT(2*x)); is wrong for maxima-5.9.1 (%i1) display2d:false; (%o1) FALSE (%i2) h: 2*COT(x)^2*COS(2*x)/(CSC(2*x)+COT(2*x)); (%o2) 2*COT(x)^2*COS(2*x)/(CSC(2*x)+COT(2*x)) (%i3) ih:integrate(h,x); (%o3) (2*LOG(SIN(x)^2+COS(x)^2+2*COS(x)+1) +2*LOG(SIN(x)^2+COS(x)^2-2*COS(x)+1) +COS(2*x)) /2 (%i4) ev(ih,x=1.0,numer)-ev(ih,x=0.5,numer); (%o4) .6469013090248041 (%i5) quad_qags(h,x,0.5,1); (%o5) [.1686767378171631,3.37999776996994E- 15,21,0] (%i6) h2:trigsimp(trigexpand(h)); (%o6) (4*COS(x)^3-2*COS(x))/SIN(x) (%i7) ih2:integrate(h2,x); (%o7) LOG(COS(x)+1)+LOG(COS(x)-1)+2*COS(x)^2 (%i8) ev(ih2,x=1.0,numer)-ev(ih2,x=0.5,numer); (%o8) .1686767378171636 The integral over 0.5 < x < 1.0 at %o4 differs from the numerical integral %o5 and the analytic integral of an equivalent expression %o8. ---------------------------------------------------------------------- >Comment By: David Billinghurst (billingd) Date: 2004-10-21 22:29 Message: Logged In: YES user_id=365569 Once this is fixed, activate equation (22) in share/contrib/diffequations/tests/rtestode_murphy1.mac ---------------------------------------------------------------------- You can respond by visiting: https://sourceforge.net/tracker/?func=detail&atid=104933&aid=1051437&group_id=4933 ```
 [Maxima-bugs] [ maxima-Bugs-1051437 ] Trig integral error From: SourceForge.net - 2006-02-16 15:27:00 ```Bugs item #1051437, was opened at 2004-10-21 08:21 Message generated for change (Comment added) made by rtoy You can respond by visiting: https://sourceforge.net/tracker/?func=detail&atid=104933&aid=1051437&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: None Group: None Status: Open Resolution: None Priority: 5 Submitted By: David Billinghurst (billingd) Assigned to: Nobody/Anonymous (nobody) Summary: Trig integral error Initial Comment: The integral of 2*COT(x)^2*COS(2*x)/(CSC(2*x)+COT(2*x)); is wrong for maxima-5.9.1 (%i1) display2d:false; (%o1) FALSE (%i2) h: 2*COT(x)^2*COS(2*x)/(CSC(2*x)+COT(2*x)); (%o2) 2*COT(x)^2*COS(2*x)/(CSC(2*x)+COT(2*x)) (%i3) ih:integrate(h,x); (%o3) (2*LOG(SIN(x)^2+COS(x)^2+2*COS(x)+1) +2*LOG(SIN(x)^2+COS(x)^2-2*COS(x)+1) +COS(2*x)) /2 (%i4) ev(ih,x=1.0,numer)-ev(ih,x=0.5,numer); (%o4) .6469013090248041 (%i5) quad_qags(h,x,0.5,1); (%o5) [.1686767378171631,3.37999776996994E- 15,21,0] (%i6) h2:trigsimp(trigexpand(h)); (%o6) (4*COS(x)^3-2*COS(x))/SIN(x) (%i7) ih2:integrate(h2,x); (%o7) LOG(COS(x)+1)+LOG(COS(x)-1)+2*COS(x)^2 (%i8) ev(ih2,x=1.0,numer)-ev(ih2,x=0.5,numer); (%o8) .1686767378171636 The integral over 0.5 < x < 1.0 at %o4 differs from the numerical integral %o5 and the analytic integral of an equivalent expression %o8. ---------------------------------------------------------------------- >Comment By: Raymond Toy (rtoy) Date: 2006-02-16 10:26 Message: Logged In: YES user_id=28849 This seems to be a bug in the Risch integrator. If you trace(?rischint), you can see h is converted to exponential form and the Risch integrator returns log(exp(%i*x)+1)+log(exp(%i*x)-1)+(exp(2*%i*x)-4*%i*x)/4. However integrate(trigsimp(exponentialize(h)),x); (which uses the Risch integrator too!) returns 2*log(%e^(%i*x)+1)+2*log(%e^(%i*x)-1)+%e^(2*%i*x)/2+%e^-(2*%i*x)/2-2*%i*x I think this simplifies to log(2*cos(x)+2)+log(2-2*cos(x))+cos(2*x) Differentiating this produces something equal to h. ---------------------------------------------------------------------- Comment By: David Billinghurst (billingd) Date: 2004-10-21 08:29 Message: Logged In: YES user_id=365569 Once this is fixed, activate equation (22) in share/contrib/diffequations/tests/rtestode_murphy1.mac ---------------------------------------------------------------------- You can respond by visiting: https://sourceforge.net/tracker/?func=detail&atid=104933&aid=1051437&group_id=4933 ```
 [Maxima-bugs] [ maxima-Bugs-1051437 ] Trig integral error From: SourceForge.net - 2006-04-10 04:09:12 ```Bugs item #1051437, was opened at 2004-10-21 06:21 Message generated for change (Settings changed) made by robert_dodier You can respond by visiting: https://sourceforge.net/tracker/?func=detail&atid=104933&aid=1051437&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 - Integration Group: None Status: Open Resolution: None Priority: 5 Submitted By: David Billinghurst (billingd) Assigned to: Nobody/Anonymous (nobody) Summary: Trig integral error Initial Comment: The integral of 2*COT(x)^2*COS(2*x)/(CSC(2*x)+COT(2*x)); is wrong for maxima-5.9.1 (%i1) display2d:false; (%o1) FALSE (%i2) h: 2*COT(x)^2*COS(2*x)/(CSC(2*x)+COT(2*x)); (%o2) 2*COT(x)^2*COS(2*x)/(CSC(2*x)+COT(2*x)) (%i3) ih:integrate(h,x); (%o3) (2*LOG(SIN(x)^2+COS(x)^2+2*COS(x)+1) +2*LOG(SIN(x)^2+COS(x)^2-2*COS(x)+1) +COS(2*x)) /2 (%i4) ev(ih,x=1.0,numer)-ev(ih,x=0.5,numer); (%o4) .6469013090248041 (%i5) quad_qags(h,x,0.5,1); (%o5) [.1686767378171631,3.37999776996994E- 15,21,0] (%i6) h2:trigsimp(trigexpand(h)); (%o6) (4*COS(x)^3-2*COS(x))/SIN(x) (%i7) ih2:integrate(h2,x); (%o7) LOG(COS(x)+1)+LOG(COS(x)-1)+2*COS(x)^2 (%i8) ev(ih2,x=1.0,numer)-ev(ih2,x=0.5,numer); (%o8) .1686767378171636 The integral over 0.5 < x < 1.0 at %o4 differs from the numerical integral %o5 and the analytic integral of an equivalent expression %o8. ---------------------------------------------------------------------- Comment By: Raymond Toy (rtoy) Date: 2006-02-16 08:26 Message: Logged In: YES user_id=28849 This seems to be a bug in the Risch integrator. If you trace(?rischint), you can see h is converted to exponential form and the Risch integrator returns log(exp(%i*x)+1)+log(exp(%i*x)-1)+(exp(2*%i*x)-4*%i*x)/4. However integrate(trigsimp(exponentialize(h)),x); (which uses the Risch integrator too!) returns 2*log(%e^(%i*x)+1)+2*log(%e^(%i*x)-1)+%e^(2*%i*x)/2+%e^-(2*%i*x)/2-2*%i*x I think this simplifies to log(2*cos(x)+2)+log(2-2*cos(x))+cos(2*x) Differentiating this produces something equal to h. ---------------------------------------------------------------------- Comment By: David Billinghurst (billingd) Date: 2004-10-21 06:29 Message: Logged In: YES user_id=365569 Once this is fixed, activate equation (22) in share/contrib/diffequations/tests/rtestode_murphy1.mac ---------------------------------------------------------------------- You can respond by visiting: https://sourceforge.net/tracker/?func=detail&atid=104933&aid=1051437&group_id=4933 ```
 [Maxima-bugs] [ maxima-Bugs-1051437 ] Trig integral error From: SourceForge.net - 2008-02-23 18:50:50 ```Bugs item #1051437, was opened at 2004-10-21 08:21 Message generated for change (Comment added) made by dgildea You can respond by visiting: https://sourceforge.net/tracker/?func=detail&atid=104933&aid=1051437&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 - Integration Group: None >Status: Closed >Resolution: Fixed Priority: 5 Private: No Submitted By: David Billinghurst (billingd) Assigned to: Nobody/Anonymous (nobody) Summary: Trig integral error Initial Comment: The integral of 2*COT(x)^2*COS(2*x)/(CSC(2*x)+COT(2*x)); is wrong for maxima-5.9.1 (%i1) display2d:false; (%o1) FALSE (%i2) h: 2*COT(x)^2*COS(2*x)/(CSC(2*x)+COT(2*x)); (%o2) 2*COT(x)^2*COS(2*x)/(CSC(2*x)+COT(2*x)) (%i3) ih:integrate(h,x); (%o3) (2*LOG(SIN(x)^2+COS(x)^2+2*COS(x)+1) +2*LOG(SIN(x)^2+COS(x)^2-2*COS(x)+1) +COS(2*x)) /2 (%i4) ev(ih,x=1.0,numer)-ev(ih,x=0.5,numer); (%o4) .6469013090248041 (%i5) quad_qags(h,x,0.5,1); (%o5) [.1686767378171631,3.37999776996994E- 15,21,0] (%i6) h2:trigsimp(trigexpand(h)); (%o6) (4*COS(x)^3-2*COS(x))/SIN(x) (%i7) ih2:integrate(h2,x); (%o7) LOG(COS(x)+1)+LOG(COS(x)-1)+2*COS(x)^2 (%i8) ev(ih2,x=1.0,numer)-ev(ih2,x=0.5,numer); (%o8) .1686767378171636 The integral over 0.5 < x < 1.0 at %o4 differs from the numerical integral %o5 and the analytic integral of an equivalent expression %o8. ---------------------------------------------------------------------- >Comment By: Dan Gildea (dgildea) Date: 2008-02-23 13:50 Message: Logged In: YES user_id=1797506 Originator: NO Fixed in risch.lisp rev 1.15. (%i4) h : 2*cot(x)^2*cos(2*x)/(csc(2*x)+cot(2*x)); (%o4) 2*cot(x)^2*cos(2*x)/(csc(2*x)+cot(2*x)) (%i5) ih:integrate(h,x); (%o5) log(sin(x)^2+cos(x)^2+2*cos(x)+1)+log(sin(x)^2+cos(x)^2-2*cos(x)+1) +cos(2*x) (%i6) ev(ih,x=1.0,numer)-ev(ih,x=0.5,numer); (%o6) 0.168676737817163 ---------------------------------------------------------------------- Comment By: Raymond Toy (rtoy) Date: 2006-02-16 10:26 Message: Logged In: YES user_id=28849 This seems to be a bug in the Risch integrator. If you trace(?rischint), you can see h is converted to exponential form and the Risch integrator returns log(exp(%i*x)+1)+log(exp(%i*x)-1)+(exp(2*%i*x)-4*%i*x)/4. However integrate(trigsimp(exponentialize(h)),x); (which uses the Risch integrator too!) returns 2*log(%e^(%i*x)+1)+2*log(%e^(%i*x)-1)+%e^(2*%i*x)/2+%e^-(2*%i*x)/2-2*%i*x I think this simplifies to log(2*cos(x)+2)+log(2-2*cos(x))+cos(2*x) Differentiating this produces something equal to h. ---------------------------------------------------------------------- Comment By: David Billinghurst (billingd) Date: 2004-10-21 08:29 Message: Logged In: YES user_id=365569 Once this is fixed, activate equation (22) in share/contrib/diffequations/tests/rtestode_murphy1.mac ---------------------------------------------------------------------- You can respond by visiting: https://sourceforge.net/tracker/?func=detail&atid=104933&aid=1051437&group_id=4933 ```