[sage-support] Re: Unexpected behaviour of derivatives on power series
I would have expected that with Laurent series but they don't do the expected, either: sage: R.=LaurentSeriesRing(SR) sage: f = 1 + O(x^2) sage: f.derivative(1) O(x^1) sage: f.derivative(2) 0 sage: f.derivative(3) 0 -- You received this message because you are subscribed to the Google Groups "sage-support" group. To unsubscribe from this group and stop receiving emails from it, send an email to sage-support+unsubscr...@googlegroups.com. To post to this group, send email to sage-support@googlegroups.com. Visit this group at https://groups.google.com/group/sage-support. For more options, visit https://groups.google.com/d/optout.
[sage-support] Re: simplifying radicals of trigonometric expressions
We need documentation on symbolic simplification... sage: sin(x/(x^2 + x)).normalize() sin(1/(x + 1)) sage: factor(cos(x)^3 - 3*cos(x)^2 - cos(x) + 6) (cos(x)^2 - cos(x) - 3)*(cos(x) - 2) sage: factor(sqrt(cos(x)^3 - 3*cos(x)^2 - cos(x) + 6)) sqrt(cos(x)^3 - 3*cos(x)^2 - cos(x) + 6) sage: from sympy import factor as sfactor sage: sfactor(sqrt(cos(x)^3 - 3*cos(x)^2 - cos(x) + 6)) sqrt((cos(x) - 2)*(cos(x)**2 - cos(x) - 3)) On Friday, January 13, 2017 at 11:12:26 AM UTC+1, Enrique Artal wrote: > > I would like to know how to handle with this issue. Consider a function > f=sqrt(cos(x)^3 - 3*cos(x)^2 - cos(x) + 6). It is possible to deal with > this function for standard procedures like numerical_integral in (-1,1). If > one considers f.canonicalize_radical() it is presented as sqrt(cos(x)^2 - > cos(x) - 3)*sqrt(cos(x) - 2), which avoids numerical integration in > particular since each factor is complex in (-1,1). It is not solved if x is > declared as a real variable (with domain='real'). For this particular > function, it is not hard to avoid the issue, but if it appears in more > complex expressions, it is less obvious. > -- You received this message because you are subscribed to the Google Groups "sage-support" group. To unsubscribe from this group and stop receiving emails from it, send an email to sage-support+unsubscr...@googlegroups.com. To post to this group, send email to sage-support@googlegroups.com. Visit this group at https://groups.google.com/group/sage-support. For more options, visit https://groups.google.com/d/optout.
Re: [sage-support] simplifying radicals of trigonometric expressions
Thanks! I did not expect a particular simplification of the function; the problem is that the given simplification caused problems. This function appeared as a factor in the computation of the curvature of some spatial curve. El domingo, 15 de enero de 2017, 15:50:06 (UTC+1), Michael Orlitzky escribió: > > On 01/14/2017 03:42 AM, Enrique Artal wrote: > > This is true. The problem is that if not used, simple expressions keep > to > > be too much complicated. Is there any compromise? > > > > There is simplify_full() which should be safe for all expressions, and > simplify_real() that assumes everything is real. Those two methods use > our Maxima backend. > > The sympy backend has improved a lot, too. There's no easy way to get > access to it, but something like this should work: > > sage: import sympy > sage: f = sin(x/(x^2 + x)) > sage: sympy.simplify(sympy.sympify(f)) > sin(1/(x + 1)) > > In the case of f = sqrt(cos(x)^3 - 3*cos(x)^2 - cos(x) + 6), did you > have any particular simplification in mind? I don't see anything obvious > that can be done. > > -- You received this message because you are subscribed to the Google Groups "sage-support" group. To unsubscribe from this group and stop receiving emails from it, send an email to sage-support+unsubscr...@googlegroups.com. To post to this group, send email to sage-support@googlegroups.com. Visit this group at https://groups.google.com/group/sage-support. For more options, visit https://groups.google.com/d/optout.
[sage-support] Unexpected behaviour of derivatives on power series
When differentiating elements of power series rings, I do not get the
expected result. Below is a minimal example:
R. = PowerSeriesRing(SR)
f = 1 + O(x^2)
f.derivative(1)
f.derivative(2)
f.derivative(3)
The first derivative gives `O(x^1)` as expected and similarly the second
gives `O(x^0)`. However, the third derivative, rather than giving `O(x^0)`
again as expected, gives `O(x^{-1})`. Is this a bug or is this the desired
behaviour for some reason?
Note: as well as my local installation, I was able to reproduce this bug on
SageMath Cloud.
(I apologise if I'm doing something stupid as I'm only newly trying to
switch to Sage from Mathematica.)
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Re: [sage-support] simplifying radicals of trigonometric expressions
On 01/14/2017 03:42 AM, Enrique Artal wrote: > This is true. The problem is that if not used, simple expressions keep to > be too much complicated. Is there any compromise? > There is simplify_full() which should be safe for all expressions, and simplify_real() that assumes everything is real. Those two methods use our Maxima backend. The sympy backend has improved a lot, too. There's no easy way to get access to it, but something like this should work: sage: import sympy sage: f = sin(x/(x^2 + x)) sage: sympy.simplify(sympy.sympify(f)) sin(1/(x + 1)) In the case of f = sqrt(cos(x)^3 - 3*cos(x)^2 - cos(x) + 6), did you have any particular simplification in mind? I don't see anything obvious that can be done. -- You received this message because you are subscribed to the Google Groups "sage-support" group. To unsubscribe from this group and stop receiving emails from it, send an email to sage-support+unsubscr...@googlegroups.com. To post to this group, send email to sage-support@googlegroups.com. Visit this group at https://groups.google.com/group/sage-support. For more options, visit https://groups.google.com/d/optout.
