Re: [sage-support] Re: integrate(sec(t)*tan(t),t,0,pi/3), why does definite integral of trig functions give error?
Robert Bradshaw writes: > Sage has an input form as well: > > sage: R. = QQ[] > sage: sage_input(t^3-t) > R. = QQ[] > t^3 - t > > sage: R. = GF(101)[] > sage: sage_input(random_matrix(ZZ, 2, 2) + t) > R. = GF(101)[] > matrix(R, [[t, 1], [96, t + 98]]) Oh, this is wonderful! (ideally, i.e., for many types it is not implemented, but it's mostly a triviality) we'd have something like ($elt (MyType myop) arg1 arg2 ...) for myop(arg1, arg2, ...)$MyType Of course, since there may be several operations myop in MyType, the types of arg1, arg2, etc. should be specified too. >> I think we would need a FriCAS-SAGE programmer, who implements a >> dictionary style translation between the two type systems. But maybe >> I'm too optimistic here... > > Well, I'm pretty sure there's not a FriCAS equivalent of every Sage > type, and vice-versa, but even doing a little better would be very > useful (right now, it doesn't do anything that's not just passing > strings back and forth. Exactly. 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] Re: integrate(sec(t)*tan(t),t,0,pi/3), why does definite integral of trig functions give error?
On Dec 26, 2009, at 12:42 PM, Martin Rubey wrote:
> William Stein writes:
>
>>> I admit however, that calling FriCAS from sage is very awkward,
>>> since
>>> the interface is absolutely dumb.
>>
>> Could you please give constructive criticism instead? I for one
>> appreciate the work Bill Page did at Sage Days 2 to write an axiom
>> interface. I think enumerating some specific criticism of it would
>> be
>> more useful. If you've already done so, maybe you could post a link?
>
> I also think that Bill Page did and does a good job.
>
> The main thing that's missing is a proper way to translate between
> fricas and sage types.
Yes.
> Eg: (without understanding the issues involved...)
>
>>> sage: fricas.integrate('sec(t)*tan(t)','t=0..%pi/3','"noPole"')
>>> 1
>
> why is it, that I can't write
>
> fricas.integrate(sec(t)*tan(t),(t,0,%pi/3),"noPole")
You can do fricas.eval("...any valid fricas command..."), though
fricas.integrate(...) and integrate(..., algorithm='fricas') should
work much better.
> (and I think that "SegmentBinding", i.e., something of the form
>
>t=a..
>
> or
>
>t=a..b
>
> is something missing from sage. On the other hand, "=" seems to be
> reserved for keyword arguments and assignment in python, except that
> sage uses it at least in "limit" also in the sense of an equation.
Yes, that is correct. The decision to stay close to Python is a
constraint in some ways, but in many others is a huge benefit.
> I would have expected "==".)
> FriCAS has a type called InputForm, which (in an ideal world) captures
> the semantics of any given object. (I guess, it's somewhat similar to
> the pickle mechanism?)
Sage has an input form as well:
sage: R. = QQ[]
sage: sage_input(t^3-t)
R. = QQ[]
t^3 - t
sage: R. = GF(101)[]
sage: sage_input(random_matrix(ZZ, 2, 2) + t)
R. = GF(101)[]
matrix(R, [[t, 1], [96, t + 98]])
Pickling is a binary representation, more optimized for compactness
and speed (and also may store pre-computed cached data).
> I think we would need a FriCAS-SAGE programmer, who implements a
> dictionary style translation between the two type systems. But maybe
> I'm too optimistic here...
Well, I'm pretty sure there's not a FriCAS equivalent of every Sage
type, and vice-versa, but even doing a little better would be very
useful (right now, it doesn't do anything that's not just passing
strings back and forth.
- Robert
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Re: [sage-support] Re: integrate(sec(t)*tan(t),t,0,pi/3), why does definite integral of trig functions give error?
William Stein writes:
>> I admit however, that calling FriCAS from sage is very awkward, since
>> the interface is absolutely dumb.
>
> Could you please give constructive criticism instead? I for one
> appreciate the work Bill Page did at Sage Days 2 to write an axiom
> interface. I think enumerating some specific criticism of it would be
> more useful. If you've already done so, maybe you could post a link?
I also think that Bill Page did and does a good job.
The main thing that's missing is a proper way to translate between
fricas and sage types.
Eg: (without understanding the issues involved...)
>> sage: fricas.integrate('sec(t)*tan(t)','t=0..%pi/3','"noPole"')
>> 1
why is it, that I can't write
fricas.integrate(sec(t)*tan(t),(t,0,%pi/3),"noPole")
(and I think that "SegmentBinding", i.e., something of the form
t=a..
or
t=a..b
is something missing from sage. On the other hand, "=" seems to be
reserved for keyword arguments and assignment in python, except that
sage uses it at least in "limit" also in the sense of an equation. I
would have expected "==".)
FriCAS has a type called InputForm, which (in an ideal world) captures
the semantics of any given object. (I guess, it's somewhat similar to
the pickle mechanism?)
I think we would need a FriCAS-SAGE programmer, who implements a
dictionary style translation between the two type systems. But maybe
I'm too optimistic here...
Martin
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Re: [sage-support] Re: integrate(sec(t)*tan(t),t,0,pi/3), why does definite integral of trig functions give error?
On Sat, Dec 26, 2009 at 8:28 AM, Robert Dodier wrote: > On Dec 24, 11:18 am, William Stein wrote: > >> 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. > > For the record, I believe that strengthening the assume > system would be the shortest path towards solving the > problem which started this thread. > (As opposed to revising or reimplementing the code > for definite integration.) Cool. I didn't know that. What do you have in mind? 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] Re: integrate(sec(t)*tan(t),t,0,pi/3), why does definite integral of trig functions give error?
On Sat, Dec 26, 2009 at 7:18 AM, Martin Rubey
wrote:
> Jason Grout writes:
>
>> 3. Use an alternative system for evaluating the integral, like sympy or
>> mathematica_free
>
> ceterum censeo:
>
> sage: fricas.integrate('sec(t)*tan(t)','t=0..%pi/3','"noPole"')
> 1
>
>
> the noPole argument instructs FriCAS to ignore possible poles that the
> integral without limits could have:
>
> sage: fricas.integrate('sec(t)*tan(t)','t')
>
> cos(t) + 1
> --
> cos(t)
>
> I admit however, that calling FriCAS from sage is very awkward, since
> the interface is absolutely dumb.
Could you please give constructive criticism instead?I for one
appreciate the work Bill Page did at Sage Days 2 to write an axiom
interface. I think enumerating some specific criticism of it would
be more useful. If you've already done so, maybe you could post a
link?
William
>
> I think that's a shame, because FriCAS is quite good at differential
> algebra.
>
> Martin
>
> --
> To post to this group, send email to sage-support@googlegroups.com
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>
--
William Stein
Associate Professor of Mathematics
University of Washington
http://wstein.org
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Re: [sage-support] Re: integrate(sec(t)*tan(t),t,0,pi/3), why does definite integral of trig functions give error?
Jason Grout writes:
> 3. Use an alternative system for evaluating the integral, like sympy or
> mathematica_free
ceterum censeo:
sage: fricas.integrate('sec(t)*tan(t)','t=0..%pi/3','"noPole"')
1
the noPole argument instructs FriCAS to ignore possible poles that the
integral without limits could have:
sage: fricas.integrate('sec(t)*tan(t)','t')
cos(t) + 1
--
cos(t)
I admit however, that calling FriCAS from sage is very awkward, since
the interface is absolutely dumb.
I think that's a shame, because FriCAS is quite good at differential
algebra.
Martin
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