Comments for Flux http://dlpeterson.com/blog Dynamics, Python, Open Source, Bikes Tue, 25 Aug 2009 23:11:07 -0700 http://wordpress.org/?v=2.8.4 hourly 1 Comment on PyDy / Sympy progress by Aaron Meurer http://dlpeterson.com/blog/2009/05/21/pydy-sympy-progress/comment-page-1/#comment-91 Aaron Meurer Tue, 25 Aug 2009 23:11:07 +0000 http://dlpeterson.com/blog/?p=7#comment-91 We were talking about it on IRC the other day. Reducing using multi-argument identities like sin(x)**2 == 1/2 - cos(2*x)/2 can be done by converting sin(x) into (exp(I*x) - exp(-I*x))/(2*I) and expanding it. It does work, at least for that identity, though it might not be the most efficient way to do it. We were talking about it on IRC the other day. Reducing using multi-argument identities like sin(x)**2 == 1/2 – cos(2*x)/2 can be done by converting sin(x) into (exp(I*x) – exp(-I*x))/(2*I) and expanding it.

It does work, at least for that identity, though it might not be the most efficient way to do it.

]]> Comment on PyDy / Sympy progress by admin http://dlpeterson.com/blog/2009/05/21/pydy-sympy-progress/comment-page-1/#comment-90 admin Tue, 25 Aug 2009 20:45:50 +0000 http://dlpeterson.com/blog/?p=7#comment-90 I'm not sure exactly what you mean by Euler replacement, but I have found that for my application, replacing all instances of cos(?)**2 with 1-sin(?)**2 and expanding seems to do the trick. These expression keep popping up in my Vector expressions when working with multiple reference frames. ~Luke I’m not sure exactly what you mean by Euler replacement, but I have found that for my application, replacing all instances of cos(?)**2 with 1-sin(?)**2 and expanding seems to do the trick. These expression keep popping up in my Vector expressions when working with multiple reference frames.
~Luke

]]> Comment on PyDy / Sympy progress by smichr http://dlpeterson.com/blog/2009/05/21/pydy-sympy-progress/comment-page-1/#comment-89 smichr Tue, 25 Aug 2009 05:39:34 +0000 http://dlpeterson.com/blog/?p=7#comment-89 Hi Like, Stopped by #sympy but didn't find you there. Would just doing a Euler replacement of trig funcs followed by a powsimp and back-replacement handle a large majority of the simplification necessary? /c Hi Like,

Stopped by #sympy but didn’t find you there. Would just doing a Euler replacement of trig funcs followed by a powsimp and back-replacement handle a large majority of the simplification necessary?

/c

]]> Comment on Developments in PyDy by vks http://dlpeterson.com/blog/2009/08/12/developments-in-pydy/comment-page-1/#comment-84 vks Fri, 14 Aug 2009 07:26:13 +0000 http://dlpeterson.com/blog/?p=97#comment-84 We really have to improve sympy that functions work as good as symbols... We really have to improve sympy that functions work as good as symbols…

]]> Comment on New trig functions by admin http://dlpeterson.com/blog/2009/07/20/new-trig-functions/comment-page-1/#comment-46 admin Mon, 20 Jul 2009 20:05:42 +0000 http://dlpeterson.com/blog/?p=86#comment-46 The reason is because I programmed it based off what Wolfram Alpha returns: http://www53.wolframalpha.com/input/?i=sin(arccot(x)) The rationale for returning this result is that it is valid for all real x, positive or negative. I believe it is also valid for complex x as well. I think with Fabian's assumption system, Sympy will be able to convert 1/(x*sqrt(1+1/x**2)) to 1/sqrt(1+x**2) for x>0, but I don't think this should be programmed into the trig functions themselves. The reason is because I programmed it based off what Wolfram Alpha returns:
http://www53.wolframalpha.com/input/?i=sin(arccot(x))

The rationale for returning this result is that it is valid for all real x, positive or negative. I believe it is also valid for complex x as well.

I think with Fabian’s assumption system, Sympy will be able to convert 1/(x*sqrt(1+1/x**2)) to 1/sqrt(1+x**2) for x>0, but I don’t think this should be programmed into the trig functions themselves.

]]> Comment on New trig functions by Aaron Meurer http://dlpeterson.com/blog/2009/07/20/new-trig-functions/comment-page-1/#comment-45 Aaron Meurer Mon, 20 Jul 2009 18:43:44 +0000 http://dlpeterson.com/blog/?p=86#comment-45 Is there a reason that sin(arccot(x)) returns 1/(x*sqrt(1+1/x^2)) instead of 1/sqrt(1+x^2). That is what Maple returns for me. I realize that the two are only equal when x is positive, but Maple plots of sin(arccot(x)), 1/(x*sqrt(1+1/x^2)), and 1/sqrt(1+x^2) reveal that sin(arccot(x)) == 1/sqrt(1+x^2) (the other one is negative for negative x). I don't know much about how these need to be handled so that they remain valid for complex x, but a simple right triangle tells me that sin(arccot(x)) should be 1/sqrt(x**2 + 1) Is there a reason that sin(arccot(x)) returns 1/(x*sqrt(1+1/x^2)) instead of 1/sqrt(1+x^2). That is what Maple returns for me. I realize that the two are only equal when x is positive, but Maple plots of sin(arccot(x)), 1/(x*sqrt(1+1/x^2)), and 1/sqrt(1+x^2) reveal that sin(arccot(x)) == 1/sqrt(1+x^2) (the other one is negative for negative x).

I don’t know much about how these need to be handled so that they remain valid for complex x, but a simple right triangle tells me that sin(arccot(x)) should be 1/sqrt(x**2 + 1)

]]> Comment on sin, cos, tan, cot, sec, csc by admin http://dlpeterson.com/blog/2009/06/15/sin-cos-tan-cot-sec-csc/comment-page-1/#comment-16 admin Wed, 17 Jun 2009 00:01:06 +0000 http://dlpeterson.com/blog/?p=66#comment-16 I haven't done anything yet. If I understand it correctly, would expand_trig just apply the double angle formula if the arg of the trig function was an Add instance? I haven’t done anything yet. If I understand it correctly, would expand_trig just apply the double angle formula if the arg of the trig function was an Add instance?

]]> Comment on sin, cos, tan, cot, sec, csc by Aaron Meurer http://dlpeterson.com/blog/2009/06/15/sin-cos-tan-cot-sec-csc/comment-page-1/#comment-14 Aaron Meurer Tue, 16 Jun 2009 03:41:31 +0000 http://dlpeterson.com/blog/?p=66#comment-14 Have you or are you planning on doing any work on expand_trig? I'm asking because I am currently working on refactoring expand for issue 1455 (see http://groups.google.com/group/sympy/browse_thread/thread/3fb7a3036c0b9d87) Have you or are you planning on doing any work on expand_trig? I’m asking because I am currently working on refactoring expand for issue 1455 (see http://groups.google.com/group/sympy/browse_thread/thread/3fb7a3036c0b9d87)

]]> Comment on Progress on trigsimp(), .eval() method of sin, cos, tan, and PyDy printing by Fabian Pedregosa http://dlpeterson.com/blog/2009/06/02/progress-on-trigsimp-eval-method-of-sin-cos-tan-and-pydy-printing/comment-page-1/#comment-8 Fabian Pedregosa Wed, 03 Jun 2009 12:08:38 +0000 http://dlpeterson.com/blog/?p=29#comment-8 Hi Luke! Checked yesterday your branch trigsimp, tested a little bit, it looks good! Hi Luke!

Checked yesterday your branch trigsimp, tested a little bit, it looks good!

]]> Comment on Progress on trigsimp(), .eval() method of sin, cos, tan, and PyDy printing by admin http://dlpeterson.com/blog/2009/06/02/progress-on-trigsimp-eval-method-of-sin-cos-tan-and-pydy-printing/comment-page-1/#comment-7 admin Wed, 03 Jun 2009 00:27:49 +0000 http://dlpeterson.com/blog/?p=29#comment-7 Thanks for the link, that will be good testing grounds for my new implementation of trigsimp. Thanks for the link, that will be good testing grounds for my new implementation of trigsimp.

]]>