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From: Raymond Toy <rtoy@us...>  20070622 16:51:08

Update of /cvsroot/maxima/maxima/src In directory sc8prcvs16.sourceforge.net:/tmp/cvsserv13838/src Modified Files: defint.lisp Log Message: Bug [ 1552789 ] integrate(1/(sin(x)^2+1),x,1,1+%pi) Integral is no longer slow, but does return the wrong answer. This fixes the problem with the wrong answer. src/defint.lisp: o Basically, need to convert tan(x) to sin(x)/cos(x) so POLESININTERVAL can find the poles of tan(x). This probably needs refinement. tests/rtest15.mac: o Add test from this bug report o Add an additional related test. Index: defint.lisp =================================================================== RCS file: /cvsroot/maxima/maxima/src/defint.lisp,v retrieving revision 1.47 retrieving revision 1.48 diff u d r1.47 r1.48  defint.lisp 19 Jun 2007 15:51:44 0000 1.47 +++ defint.lisp 22 Jun 2007 16:50:25 0000 1.48 @@ 887,7 +887,19 @@ ;;;This function works only on things with ATAN's in them now. (defun samesheetsubs (exp ll ul &aux ans)  (let ((poles (atanpoles exp ll ul))) + ;; POLESININTERVAL doesn't know about the poles of tan(x). Call + ;; trigsimp to convert tan into sin/cos, which POLESININTERVAL + ;; knows how to handle. + ;; + ;; XXX Should we fix POLESININTERVAL instead? + ;; + ;; XXX Is calling trigsimp too much? Should we just only try to + ;; substitute sin/cos for tan? + ;; + ;; XXX Should the result try to convert sin/cos back into tan? (A + ;; call to trigreduce would do it, among other things.) + (let* ((exp (mfuncall '$trigsimp exp)) + (poles (atanpoles exp ll ul))) ;;POLES > ((mlist) ((mequal) ((%atan) foo) replacement) ......) ;;We can then use $SUBSTITUTE (setq ans ($limit exp var ll '$plus)) 
From: Raymond Toy <rtoy@us...>  20070622 16:50:40

Update of /cvsroot/maxima/maxima/tests In directory sc8prcvs16.sourceforge.net:/tmp/cvsserv13838/tests Modified Files: rtest15.mac Log Message: Bug [ 1552789 ] integrate(1/(sin(x)^2+1),x,1,1+%pi) Integral is no longer slow, but does return the wrong answer. This fixes the problem with the wrong answer. src/defint.lisp: o Basically, need to convert tan(x) to sin(x)/cos(x) so POLESININTERVAL can find the poles of tan(x). This probably needs refinement. tests/rtest15.mac: o Add test from this bug report o Add an additional related test. Index: rtest15.mac =================================================================== RCS file: /cvsroot/maxima/maxima/tests/rtest15.mac,v retrieving revision 1.60 retrieving revision 1.61 diff u d r1.60 r1.61  rtest15.mac 12 Jun 2007 02:47:05 0000 1.60 +++ rtest15.mac 22 Jun 2007 16:50:27 0000 1.61 @@ 743,3 +743,19 @@ log((x^2+1)^(1/4)/sqrt(x)+1)/8log((x^2+1)^(1/4)/sqrt(x)1)/8 +atan((x^2+1)^(1/4)/sqrt(x))/4 +(x^2+1)^(1/4)/(sqrt(x)*(2*(x^2+1)/x^22))$ + +/* + * Bug [ 1552789 ] integrate(1/(sin(x)^2+1),x,1,1+%pi) + * + * This bug said it was slow. That's no longer true, but the result + * was wrong. + * + * This has been fixed for this particular case. + */ +integrate(1/(sin(x)^2+1),x,1,1+%pi); +%pi/sqrt(2); + +/* A few more related tests. I think these are right */ +integrate(1/(sin(x)^2+1),x,1,1+4*%pi); +2*sqrt(2)*%pi; + 