Re: [sage-support] integrate(sec(t)*tan(t),t,0,pi/3), why does definite integral of trig functions give error?
On Sun, Dec 27, 2009 at 9:22 AM, Martin Rubey wrote: > William Stein writes: > >> On Sun, Dec 27, 2009 at 12:42 AM, Martin Rubey >> wrote: >>> ceterum censeo 2: >>> The problem -- which is a serious one -- is that Sage's symbolic integration is by default done using Maxima (this is currently the main way in which Maxima is used in Sage; the other big way is for solving symbolic equations). >>> >>> For my ears (well, eyes :-) this sounds like an insult. (and I'm >>> certainly not a maxima developer.) >> >> We are shipping a central critical component of Sage -- the symbolic >> integration function -- which none of us fully understand or know how >> to fix bugs in. This *is* a problem. > > If that's the reason (and I agree it's a very good reason), why don't > you state just this? You're absolutely right, I should just state this: We are shipping a central critical component of Sage -- the symbolic integration function -- which none of us fully understand or know how to fix bugs in. This *is* a problem. William -- To post to this group, send email to sage-support@googlegroups.com To unsubscribe from this group, send email to sage-support+unsubscr...@googlegroups.com For more options, visit this group at http://groups.google.com/group/sage-support URL: http://www.sagemath.org
Re: [sage-support] integrate(sec(t)*tan(t),t,0,pi/3), why does definite integral of trig functions give error?
William Stein writes: > On Sun, Dec 27, 2009 at 12:42 AM, Martin Rubey > wrote: >> ceterum censeo 2: >> >>> The problem -- which is a serious one -- is that Sage's symbolic >>> integration is by default done using Maxima (this is currently the >>> main way in which Maxima is used in Sage; the other big way is for >>> solving symbolic equations). >> >> For my ears (well, eyes :-) this sounds like an insult. (and I'm >> certainly not a maxima developer.) > > We are shipping a central critical component of Sage -- the symbolic > integration function -- which none of us fully understand or know how > to fix bugs in. This *is* a problem. If that's the reason (and I agree it's a very good reason), why don't you state just this? (it's not a technical issue I criticise, but I hope that's obvious.) Martin -- To post to this group, send email to sage-support@googlegroups.com To unsubscribe from this group, send email to sage-support+unsubscr...@googlegroups.com For more options, visit this group at http://groups.google.com/group/sage-support URL: http://www.sagemath.org
Re: [sage-support] integrate(sec(t)*tan(t),t,0,pi/3), why does definite integral of trig functions give error?
On Sun, Dec 27, 2009 at 12:42 AM, Martin Rubey wrote: > ceterum censeo 2: > >> The problem -- which is a serious one -- is that Sage's symbolic >> integration is by default done using Maxima (this is currently the >> main way in which Maxima is used in Sage; the other big way is for >> solving symbolic equations). > > For my ears (well, eyes :-) this sounds like an insult. (and I'm > certainly not a maxima developer.) We are shipping a central critical component of Sage -- the symbolic integration function -- which none of us fully understand or know how to fix bugs in. This *is* a problem. See [1] and [2] for some discussions about how not understanding the components of your software can be a serious problem. -- William [1] http://www.joelonsoftware.com/articles/fog07.html [2] http://www.wired.com/magazine/2009/12/fail_duke_nukem/ -- To post to this group, send email to sage-support@googlegroups.com To unsubscribe from this group, send email to sage-support+unsubscr...@googlegroups.com For more options, visit this group at http://groups.google.com/group/sage-support URL: http://www.sagemath.org
Re: [sage-support] integrate(sec(t)*tan(t),t,0,pi/3), why does definite integral of trig functions give error?
ceterum censeo 2: > The problem -- which is a serious one -- is that Sage's symbolic > integration is by default done using Maxima (this is currently the > main way in which Maxima is used in Sage; the other big way is for > solving symbolic equations). For my ears (well, eyes :-) this sounds like an insult. (and I'm certainly not a maxima developer.) Why don't you just say something like: | The problem is that Maxima assumes that a user is at the terminal | answering questions. (By the way, Christian Krattenthaler's hyp and hyp.q for mathematica are two brilliant packages that assume the very same thing. This doesn't make the package less brilliant) I can imagine (but I don't know) that the maxima developers are unwilling (or even unable) to change that behaviour. In this case one could state precisely this: | And the maxima developers are unwilling/unable to change this | behaviour. Statements like the one above are one of the reasons I am unwilling to really join sage. Martin -- To post to this group, send email to sage-support@googlegroups.com To unsubscribe from this group, send email to sage-support+unsubscr...@googlegroups.com For more options, visit this group at http://groups.google.com/group/sage-support URL: http://www.sagemath.org
Re: [sage-support] integrate(sec(t)*tan(t),t,0,pi/3), why does definite integral of trig functions give error?
On Wed, Dec 23, 2009 at 10:10 PM, Ben Woodruff wrote:
> Hi all. This is my first post to the discussions groups I've been
> following for the last 4 months. I used Sage in my first semester
> calculus class this last semester, and plan to move every class I can
> over to Sage during the next few years. Giving the students something
> they can use anywhere they go without forking over thousands of
> dollars has a huge advantage. As such, I'm going to start doing a
> better job of posting errors when they arise and I can't figure out
> how to resolve them.
>
> Here is the issue. When I evaluate
>
> sage: var('t')
> sage: integrate(sec(t)*tan(t),t,0,pi/3)
>
> I get the error message
>
>>Traceback (click to the left for traceback)
>>...
>>Is cos(t) positive, negative, or zero?
>
> I can get the correct solution of 1 by executing
>
> sage: var('t')
> sage: F(t)=integrate(sec(t)*tan(t),t)
> sage: F(pi/3)-F(0)
>
> Similar issues arise with other trig functions. The command
>
> sage: integrate(csc(x)*cot(x),x,pi/3,pi/2)
>
> gives the error message
>
>>Traceback (click to the left for traceback)
>>...
>>Is sin(x) positive, negative, or zero?
>
> Any ideas why Sage cannot complete this definite integral? I would
> prefer to have Sage give the answers without using an assuming
> commands, since by specifying the bounds are between 0 and pi/3 I am
> already declaring cos(x)>0 and x to be real.
>
> Could this be related to
> http://trac.sagemath.org/sage_trac/ticket/6956
No.
The problem -- which is a serious one -- is that Sage's symbolic
integration is by default done using Maxima (this is currently the
main way in which Maxima is used in Sage; the other big way is for
solving symbolic equations). Maxima has a somewhat weak assumptions
system and was designed in the 1960s when the assumption that a user
was at the terminal happily answering questions -- a sort of
conversation -- was considered reasonable.
Sympy is the only other program in Sage that does symbolic
integration, and you can access it by doing for example
sage: integrate(sin(t),t,0,pi/3, algorithm='sympy')
However, it only works on a small class of fairly simple integrals.
Until we Sage developers write our own symbolic integration
implementation, we'll continue to have similar issues to what you
complain about above. I'm for doing that.
In the meantime, I hope we can find ways around the issues that arise
by using assume.
-- William
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Re: [sage-support] integrate(sec(t)*tan(t),t,0,pi/3), why does definite integral of trig functions give error?
Ben Woodruff wrote: > Hi all. This is my first post to the discussions groups I've been > following for the last 4 months. I used Sage in my first semester > calculus class this last semester, and plan to move every class I can > over to Sage during the next few years. Giving the students something > they can use anywhere they go without forking over thousands of > dollars has a huge advantage. Sorry I can't answer your question. I'm not a Sage user, though I've spent a lot of time porting Sage to Sun's Solaris operating system, so I will be able to use it, on what I consider is an excellent operating system. But I could not resist commenting on one of your points here. Giving students something they can use outside university is a huge plus which teaching Sage has compared to teaching Mathematica. I learned Mathematica as a postgraduate researcher and used it at university quite a bit. Then when I left university, suddenly I find few places use it. Most places can't afford to, or insist staff use something cheaper. (At Marconi Optical Components I had to use Mathcad if I wanted maths software.) A hunt for jobs mentioning Mathematica on job sites brings up very few hits. Learning Mathematica is a bit like learning your way around campus - useful while you are at university, but your might as well forget it once you leave. In my honest opinion, it is almost irresponsible for universities to teach Mathematica. I'm not a fan of Microsoft's products (I use Sun's Solaris rather than Microsoft Windows most of the time). But nobody can accuse schools of being irresponsible teaching children Word or Excel, as those skills are wanted by employers. The same can not be said for Mathematica. I know little about Maple or Macsyma and accept that MATLAB is wanted by a number of employers. Of course there are other advantages/disadvantages to open-source software, but here is not the place for a open-source vs closed-source debate. Dave -- To post to this group, send email to sage-support@googlegroups.com To unsubscribe from this group, send email to sage-support+unsubscr...@googlegroups.com For more options, visit this group at http://groups.google.com/group/sage-support URL: http://www.sagemath.org
[sage-support] integrate(sec(t)*tan(t),t,0,pi/3), why does definite integral of trig functions give error?
Hi all. This is my first post to the discussions groups I've been
following for the last 4 months. I used Sage in my first semester
calculus class this last semester, and plan to move every class I can
over to Sage during the next few years. Giving the students something
they can use anywhere they go without forking over thousands of
dollars has a huge advantage. As such, I'm going to start doing a
better job of posting errors when they arise and I can't figure out
how to resolve them.
Here is the issue. When I evaluate
sage: var('t')
sage: integrate(sec(t)*tan(t),t,0,pi/3)
I get the error message
>Traceback (click to the left for traceback)
>...
>Is cos(t) positive, negative, or zero?
I can get the correct solution of 1 by executing
sage: var('t')
sage: F(t)=integrate(sec(t)*tan(t),t)
sage: F(pi/3)-F(0)
Similar issues arise with other trig functions. The command
sage: integrate(csc(x)*cot(x),x,pi/3,pi/2)
gives the error message
>Traceback (click to the left for traceback)
>...
>Is sin(x) positive, negative, or zero?
Any ideas why Sage cannot complete this definite integral? I would
prefer to have Sage give the answers without using an assuming
commands, since by specifying the bounds are between 0 and pi/3 I am
already declaring cos(x)>0 and x to be real.
Could this be related to
http://trac.sagemath.org/sage_trac/ticket/6956
Thanks for the great product.
Ben Woodruff
BYU-Idaho
--
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