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3

4

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6
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From: SourceForge.net <noreply@so...>  20110910 06:11:31

Bugs item #3407069, was opened at 20110910 09:11 Message generated for change (Tracker Item Submitted) made by aleksasd You can respond by visiting: https://sourceforge.net/tracker/?func=detail&atid=104933&aid=3407069&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 Private: No Submitted By: Aleksas (aleksasd) Assigned to: Nobody/Anonymous (nobody) Summary: radcan bug Initial Comment: "radcan" bug We calculate the integral of (%i1) f:1/((x1)*sqrt(8*x^2+4*x+3)); (%o1) 1/((x1)*sqrt(8*x^2+4*x+3)) (%i2) assume(x<1)$ (%i3) integrate(f,x)$ sol:factor(%); (%o4) asin((6*x5)/(2*sqrt(7)*(x1))) Test of solution(the first method): (%i5) diff(sol,x)f$ factor(%); (%o6) 0 (%i7) is(%=0); (%o7) true Test of solution(the second method): (%i8) diff(sol,x)f$ radcan(%); (%o9) (2*sqrt(8*x^2+4*x+3))/(8*x^312*x^2+x+3) (%i10) is(%=0); (%o10) false I think that "radcan" has bug  You can respond by visiting: https://sourceforge.net/tracker/?func=detail&atid=104933&aid=3407069&group_id=4933 
From: SourceForge.net <noreply@so...>  20110910 05:44:01

Bugs item #3405408, was opened at 20110907 12:31 Message generated for change (Comment added) made by aleksasd You can respond by visiting: https://sourceforge.net/tracker/?func=detail&atid=104933&aid=3405408&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 Private: No Submitted By: Aleksas (aleksasd) Assigned to: Nobody/Anonymous (nobody) Summary: integrate bug Initial Comment: Wrong: (%i1) integrate(acos((x1/2)/sqrt(1x^2)),x); (%o1) (%pi*x)/2 The result should be (%i2) sol:(2^(3/2)*x*acos((2*x1)/(2*sqrt(1x^2))) sqrt(2)*asin((10*x+1)/(2*sqrt(7)*(x+1))) +sqrt(2)*asin((6*x5)/(2*sqrt(7)*(x1))) +asin((4*x1)/sqrt(7)))/2^(3/2)$ Test of sol: (%i3) f:acos((x1/2)/sqrt(1x^2))$ (%i4) diff(sol,x)f,radcan; (%o4) 0 (%i5) is(%=0); (%o5) true Next a detailed solution has bug: (%i6) load(bypart)$ (%i7) assume(abs(x)<1); (%o7) [abs(x)<1] (%i8) byparts(f,x,f,x),factor$ (%i9) sol1:ev(%, nouns),factor$ Test of sol1: (%i10) diff(sol1,x)f,radcan$ (%i11) is(%=0); (%o11) false Note: this integral is from http://www.math.utexas.edu/pipermail/maxima/2011/025866.html (%i12) S1:'integrate(acos((2*c+k*u)/sqrt((1k^2/4)*(1u^2))),u)$ (%i13) subst([k=2/sqrt(5),c=1/2/sqrt(5)],S1),factor; (%o13) integrate(acos((2*u1)/(2*sqrt(1u^2))),u)  Comment By: Aleksas (aleksasd) Date: 20110910 08:44 Message: Correct value of integrate(acos((x1/2)/sqrt(1x^2)),x) and "radcan" bug (%i1) f:acos((x1/2)/sqrt(1x^2))$ (%i2) load(bypart)$ (%i3) assume(abs(x)<1)$ (%i4) byparts(f,x,f,1),factor$ (%i5) sol2:ev(%, nouns),factor; (%o5) (2^(3/2)*x*acos((2*x1)/(2*sqrt(1x^2))) sqrt(2)*asin((10*x+1)/(2*sqrt(7)*(x+1))) sqrt(2)*asin((6*x5)/(2*sqrt(7)*(x1))) +asin((4*x1)/sqrt(7)))/2^(3/2) Test of solution(the first method): (%i6) diff(sol2,x)f$ factor(%); (%o7) 0 (%i8) is(%=0); (%o8) true Test of solution(the second method): (%i9) diff(sol2,x)f$ radcan(%); (%o10) 1/((%i*x%i)*sqrt(8*x^24*x3)) (%i11) is(%=0); (%o11) false I think that solution sol2 is correct and "radcan" has bug (%i12) build_info()$ Maxima version: 5.25.0 Maxima build date: 12:0 8/2/2011 Host type: i686pcmingw32 Lisp implementation type: Clozure Common Lisp Lisp implementation version: Version 1.7r14925M (WindowsX8632)  Comment By: Aleksas (aleksasd) Date: 20110907 13:11 Message: WolframAlpha solution of this problem is not correct. The result is undefined for x=0 (in real domain).  You can respond by visiting: https://sourceforge.net/tracker/?func=detail&atid=104933&aid=3405408&group_id=4933 