From: Marcelo F. <mf...@us...> - 2017-03-19 14:00:04
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--- ** [bugs:#3295] Incorrect integral of rational expression of trigonometric function ** **Status:** open **Group:** None **Labels:** integrate wrong result **Created:** Sun Mar 19, 2017 02:00 PM UTC by Marcelo Forets **Last Updated:** Sun Mar 19, 2017 02:00 PM UTC **Owner:** nobody integrate((2*cos(2*%pi*x) - cos(4*%pi*x)) / (5 - 4*cos(2*%pi*x)), x, 0, 1); returns 23/24 (tested in maxima-online.org), but the result should be 1/4. See also: https://trac.sagemath.org/ticket/17968 --- Sent from sourceforge.net because max...@li... is subscribed to https://sourceforge.net/p/maxima/bugs/ To unsubscribe from further messages, a project admin can change settings at https://sourceforge.net/p/maxima/admin/bugs/options. Or, if this is a mailing list, you can unsubscribe from the mailing list. |
From: Marcelo F. <mf...@us...> - 2017-03-19 14:02:01
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ooops.. posted the wrong link! See also: https://trac.sagemath.org/ticket/21440 --- ** [bugs:#3295] Incorrect integral of rational expression of trigonometric function ** **Status:** open **Group:** None **Labels:** integrate wrong result **Created:** Sun Mar 19, 2017 02:00 PM UTC by Marcelo Forets **Last Updated:** Sun Mar 19, 2017 02:00 PM UTC **Owner:** nobody integrate((2*cos(2*%pi*x) - cos(4*%pi*x)) / (5 - 4*cos(2*%pi*x)), x, 0, 1); returns 23/24 (tested in maxima-online.org), but the result should be 1/4. See also: https://trac.sagemath.org/ticket/17968 --- Sent from sourceforge.net because max...@li... is subscribed to https://sourceforge.net/p/maxima/bugs/ To unsubscribe from further messages, a project admin can change settings at https://sourceforge.net/p/maxima/admin/bugs/options. Or, if this is a mailing list, you can unsubscribe from the mailing list. |
From: David S. <tom...@us...> - 2017-03-19 20:59:58
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- Description has changed: Diff: ~~~~ --- old +++ new @@ -1,4 +1,4 @@ -integrate((2*cos(2*%pi*x) - cos(4*%pi*x)) / (5 - 4*cos(2*%pi*x)), x, 0, 1); +`integrate((2*cos(2*%pi*x) - cos(4*%pi*x)) / (5 - 4*cos(2*%pi*x)), x, 0, 1);` returns 23/24 (tested in maxima-online.org), but the result should be 1/4. ~~~~ - **Comment**: Corrected formatting --- ** [bugs:#3295] Incorrect integral of rational expression of trigonometric function ** **Status:** open **Group:** None **Labels:** integrate wrong result **Created:** Sun Mar 19, 2017 02:00 PM UTC by Marcelo Forets **Last Updated:** Sun Mar 19, 2017 02:02 PM UTC **Owner:** nobody `integrate((2*cos(2*%pi*x) - cos(4*%pi*x)) / (5 - 4*cos(2*%pi*x)), x, 0, 1);` returns 23/24 (tested in maxima-online.org), but the result should be 1/4. See also: https://trac.sagemath.org/ticket/17968 --- Sent from sourceforge.net because max...@li... is subscribed to https://sourceforge.net/p/maxima/bugs/ To unsubscribe from further messages, a project admin can change settings at https://sourceforge.net/p/maxima/admin/bugs/options. Or, if this is a mailing list, you can unsubscribe from the mailing list. |
From: David S. <tom...@us...> - 2017-03-19 21:04:07
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Maxima's antiderivative has a discontinuity at `x=1/2`, which it doesn't detect, so it just does `F(1)-F(0)`. I believe that's where the error comes from. --- ** [bugs:#3295] Incorrect integral of rational expression of trigonometric function ** **Status:** open **Group:** None **Labels:** integrate wrong result **Created:** Sun Mar 19, 2017 02:00 PM UTC by Marcelo Forets **Last Updated:** Sun Mar 19, 2017 08:59 PM UTC **Owner:** nobody `integrate((2*cos(2*%pi*x) - cos(4*%pi*x)) / (5 - 4*cos(2*%pi*x)), x, 0, 1);` returns 23/24 (tested in maxima-online.org), but the result should be 1/4. See also: https://trac.sagemath.org/ticket/17968 --- Sent from sourceforge.net because max...@li... is subscribed to https://sourceforge.net/p/maxima/bugs/ To unsubscribe from further messages, a project admin can change settings at https://sourceforge.net/p/maxima/admin/bugs/options. Or, if this is a mailing list, you can unsubscribe from the mailing list. |
From: Robert D. <rob...@us...> - 2017-03-20 04:48:50
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I dunno if ignoring the discontinuity is the only problem here. `integrate(..., x, 0, 1/2)` returns 23/24 which seems to be incorrect (should be 1/8 I guess). `integrate(..., x)` returns an antiderivative and then `ev(%, x = 1/2 - foo) - ev(%, x = 0)` followed by `limit(%, foo, 0, plus)` yields 1/8. I don't know where it goes wrong. --- ** [bugs:#3295] Incorrect integral of rational expression of trigonometric function ** **Status:** open **Group:** None **Labels:** integrate wrong result **Created:** Sun Mar 19, 2017 02:00 PM UTC by Marcelo Forets **Last Updated:** Sun Mar 19, 2017 09:04 PM UTC **Owner:** nobody `integrate((2*cos(2*%pi*x) - cos(4*%pi*x)) / (5 - 4*cos(2*%pi*x)), x, 0, 1);` returns 23/24 (tested in maxima-online.org), but the result should be 1/4. See also: https://trac.sagemath.org/ticket/17968 --- Sent from sourceforge.net because max...@li... is subscribed to https://sourceforge.net/p/maxima/bugs/ To unsubscribe from further messages, a project admin can change settings at https://sourceforge.net/p/maxima/admin/bugs/options. Or, if this is a mailing list, you can unsubscribe from the mailing list. |
From: number Z. <nu...@us...> - 2017-06-13 17:44:09
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The same problem here: ~~~ integrate( (1 / %pi) * sqrt(r) * (1 - r) * (cos(2 * psi) - 1) * ( (cos((phi + psi)/2)) / (1 - 2*r*cos(phi + psi) + r^2) + (cos((phi - psi)/2)) / (1 - 2*r*cos(phi - psi) + r^2) ) , psi, 0, %pi ); ~~~ Numerical solution seems to be right (it is calculated at `r=0.99`; at `r=1.00` it should be `cos(2 * phi) - 1`), but symbolic one is radically different. Note that it is calculated using `ldefint`; `integrate` yields similarly looking non-smooth function (full of `atan(tan(phi))`) Attachments: - [Screenshot_20170613_203910.png](https://sourceforge.net/p/maxima/bugs/_discuss/thread/33c559a3/9485/attachment/Screenshot_20170613_203910.png) (17.5 kB; image/png) - [Screenshot_20170613_203840.png](https://sourceforge.net/p/maxima/bugs/_discuss/thread/33c559a3/9485/attachment/Screenshot_20170613_203840.png) (18.4 kB; image/png) --- ** [bugs:#3295] Incorrect integral of rational expression of trigonometric function ** **Status:** open **Group:** None **Labels:** integrate wrong result **Created:** Sun Mar 19, 2017 02:00 PM UTC by Marcelo Forets **Last Updated:** Sun Mar 19, 2017 09:04 PM UTC **Owner:** nobody `integrate((2*cos(2*%pi*x) - cos(4*%pi*x)) / (5 - 4*cos(2*%pi*x)), x, 0, 1);` returns 23/24 (tested in maxima-online.org), but the result should be 1/4. See also: https://trac.sagemath.org/ticket/17968 --- Sent from sourceforge.net because max...@li... is subscribed to https://sourceforge.net/p/maxima/bugs/ To unsubscribe from further messages, a project admin can change settings at https://sourceforge.net/p/maxima/admin/bugs/options. Or, if this is a mailing list, you can unsubscribe from the mailing list. |