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From: SourceForge.net <noreply@so...>  20100419 20:47:31

Bugs item #2989321, was opened at 20100419 15:22 Message generated for change (Comment added) made by alex108 You can respond by visiting: https://sourceforge.net/tracker/?func=detail&atid=104933&aid=2989321&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 Private: No Submitted By: Nobody/Anonymous (nobody) Assigned to: Nobody/Anonymous (nobody) Summary: integrate(rational func) > choses incorrect branch in atan? Initial Comment: integrate((x^4+x^2+4)/(x^67*x^4+14*x^2+1),x,2,2); gives $0.$ >From reading "Improving Exact Integrals From Symbolic Algebra Systems" by Fateman and Kahan, page 5, this should be $2\pi.$  Comment By: Aleksas Domarkas (alex108) Date: 20100419 23:47 Message: For integrating we define block "int_rac(f,x)": (%i1) int_rac(f,x):=block('integrate(f,x),map(gfactor,%%), ev(%%,nouns),rectform(%%),logcontract(%%))$ 1 example (%i2) integrate((x^4+x^2+4)/(x^67*x^4+14*x^2+1),x); (%o2) integrate((x^4+x^2+4)/(x^67*x^4+14*x^2+1),x) (%i3) f:first(%); (%o3) (x^4+x^2+4)/(x^67*x^4+14*x^2+1) We find antiderivative F : (%i4) F:int_rac(f,x); (%o4) atan2(x^21,x^34*x) Test: (%i5) diff(F,x),ratsimp; (%o5) (x^4+x^2+4)/(x^67*x^4+14*x^2+1) (%i6) limit(F,x,1,minus); (%o6) %pi (%i7) limit(F,x,1,plus); (%o7) %pi Then F is discontinous at x=1. (%i8) wxplot2d([f,F], [x,5,5],[y,5,5])$ (%t8) << Graphics >> Function f is even. Then (%i13) 'integrate(f,x,2,2)=2*(ev(F,x=0)ev(F,x=2)); (%o13) integrate((x^4+x^2+4)/(x^67*x^4+14*x^2+1),x,2,2)=2*%pi 2 example (%i10) S:integrate(1/(x^4+6*x^2+1),x); (%o10) integrate(1/(x^4+6*x^2+1),x) (%i11) sol:int_rac(1/(x^4+6*x^2+1),x); (%o11) (2^(5/2)*atan((2*x)/(x^2+1))+4*atan(x/(sqrt(2)+1))+4*atan(x/(sqrt(2)1)))/2^(9/2) Test: (%i12) diff(%,x),ratsimp; (%o12) 1/(x^4+6*x^2+1)  Comment By: Raymond Toy (rtoy) Date: 20100419 16:37 Message: Maxima converts this integral to an integral from 0 to inf. This new integral is evaluted using resides, and maxima fails to find the roots of the denominator: 9*x^642*x^5+1031*x^41932*x^3+1031*x^242*x+9 Maxima erroneously returns 0 in this case.  You can respond by visiting: https://sourceforge.net/tracker/?func=detail&atid=104933&aid=2989321&group_id=4933 
From: SourceForge.net <noreply@so...>  20100419 13:37:41

Bugs item #2989321, was opened at 20100419 08:22 Message generated for change (Comment added) made by rtoy You can respond by visiting: https://sourceforge.net/tracker/?func=detail&atid=104933&aid=2989321&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 Private: No Submitted By: Nobody/Anonymous (nobody) Assigned to: Nobody/Anonymous (nobody) Summary: integrate(rational func) > choses incorrect branch in atan? Initial Comment: integrate((x^4+x^2+4)/(x^67*x^4+14*x^2+1),x,2,2); gives $0.$ >From reading "Improving Exact Integrals From Symbolic Algebra Systems" by Fateman and Kahan, page 5, this should be $2\pi.$  >Comment By: Raymond Toy (rtoy) Date: 20100419 09:37 Message: Maxima converts this integral to an integral from 0 to inf. This new integral is evaluted using resides, and maxima fails to find the roots of the denominator: 9*x^642*x^5+1031*x^41932*x^3+1031*x^242*x+9 Maxima erroneously returns 0 in this case.  You can respond by visiting: https://sourceforge.net/tracker/?func=detail&atid=104933&aid=2989321&group_id=4933 
From: SourceForge.net <noreply@so...>  20100419 12:22:33

Bugs item #2989321, was opened at 20100419 12:22 Message generated for change (Tracker Item Submitted) made by nobody You can respond by visiting: https://sourceforge.net/tracker/?func=detail&atid=104933&aid=2989321&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 Private: No Submitted By: Nobody/Anonymous (nobody) Assigned to: Nobody/Anonymous (nobody) Summary: integrate(rational func) > choses incorrect branch in atan? Initial Comment: integrate((x^4+x^2+4)/(x^67*x^4+14*x^2+1),x,2,2); gives $0.$ >From reading "Improving Exact Integrals From Symbolic Algebra Systems" by Fateman and Kahan, page 5, this should be $2\pi.$  You can respond by visiting: https://sourceforge.net/tracker/?func=detail&atid=104933&aid=2989321&group_id=4933 