[sage-support] Re: simplification options
Hi Michael, On 2019-03-11, Michael Beeson wrote: > I tried various simplification functions.I suppose I could start over, > not using "symbolic expressions" but > declaring K to be a suitable field or ring, maybe a quadratic extension of > the field of rational functions in a. > That is probably the "right" way to do it. Probably! > But I wish there were a simpler way. Why do you think using a sub-optimal far too general tool (e.g., symbolic variables when in fact the problem is about polynomial) is "simpler"? Best regards, Simon -- 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: simplification options
Le lundi 11 mars 2019 19:05:04 UTC+1, Michael Beeson a écrit :
>
> I appreciate Eric's post, and I do use subs sometimes, but it makes me
> nervous since
> it will happily substitute any old thing you tell it to, even an
> incorrect thing. So, if your idea
> is to check a computation, it is a dangerous thing.
>
In order to minimize the error risk in the substitution, note that you can
use the Python variable b defined as
b = sqrt(1-a^2)
in the argument of subs(), thereby avoiding any duplicate code. The whole
code becomes then
sage: var('p,q,r,a') # note: no b at this stage
(p, q, r, a)
sage: b = sqrt(1-a^2)
sage: eq = (p*a+r*b+q)^2
sage: eq = eq.expand(); eq
a^2*p^2 - a^2*r^2 + 2*sqrt(-a^2 + 1)*a*p*r + 2*a*p*q + 2*sqrt(-a^2 + 1)*q*r
+ q^2 + r^2
sage: eq.subs({b: SR.var('b')})
a^2*p^2 + 2*a*b*p*r - a^2*r^2 + 2*a*p*q + 2*b*q*r + q^2 + r^2
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[sage-support] Re: simplification options
On Monday, March 11, 2019 at 11:05:04 AM UTC-7, Michael Beeson wrote: > > I appreciate Eric's post, and I do use subs sometimes, but it makes me > nervous since > it will happily substitute any old thing you tell it to, even an > incorrect thing. So, if your idea > is to check a computation, it is a dangerous thing. True, if you put > only correct equations in, > you'll usually get correct ones out. > Checking a result is usually much easier: Take the original form of the equation, subtract the simplified form, and check that the difference is divisible by the relations you impose, such as b^2-(1-a^2). No special normal forms are required, just a divisibility test. This gets more complicated when there are more relations, because then you'll need an ideal membership test, but then you can just present that as "the computational tool" (plus, with a bit of luck you can extract the way in which the difference can be expressed in terms of the generating relations. The algorithm in principle encounters that information on the way) -- 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: simplification options
I appreciate Eric's post, and I do use subs sometimes, but it makes me nervous since it will happily substitute any old thing you tell it to, even an incorrect thing. So, if your idea is to check a computation, it is a dangerous thing. True, if you put only correct equations in, you'll usually get correct ones out. -- 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: simplification options
What about something like
sage: var('p,q,r,a')
(p, q, r, a)
sage: b = sqrt(1-a^2)
sage: eq = (p*a+r*b+q)^2
sage: eq = eq.expand(); eq
a^2*p^2 - a^2*r^2 + 2*sqrt(-a^2 + 1)*a*p*r + 2*a*p*q + 2*sqrt(-a^2 + 1)*q*r
+ q^2 + r^2
sage: b = var('b')
sage: eq.subs({sqrt(1-a^2): b})
a^2*p^2 + 2*a*b*p*r - a^2*r^2 + 2*a*p*q + 2*b*q*r + q^2 + r^2
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[sage-support] Re: simplification of symbolic expressions
On 2013-11-22, John Cremona john.crem...@gmail.com wrote: 1. It is a fact that if a^2+b^2=1 then arcsin(a)+arcsin(b)=pi/2, but how can I get this to happen automatically? I have an expression which comes out as arcsin(1/3*sqrt(3)*sqrt(2)) + arcsin(1/3*sqrt(3)) which I would like to get simplified in this way. I think this can be achieved via simplification rules in Maxima. I don't know if there are other ways to get the same result elsewhere in Sage (if so I am interested to hear about it -- I wouldn't mind adopting some ideas into Maxima). Here's what I have. matchdeclare (aa, lambda ([e], not atom(e) and op(e) = nounify(asin))); matchdeclare (xx, lambda ([e], atom(e) or op(e) # nounify(asin))); tellsimpafter (aa + xx, xx + FOO1 (aa)); FOO1(a):=if op(a) = + then FOO2 (a) else a; FOO2(a):=(a:args(a), for i thru length(a) do (for j from i + 1 thru length(a) do if a[i] # 0 then (FOO3 (a[i], a[j]), if %% # false then [a[i], a[j]] : [%%, 0])), apply (+, a)); FOO3(u,v):=if is (equal (args(u)[1]^2 + args(v)[1]^2, 1)) = true then %pi/2; If there are any asin terms, call FOO1 on them. If there's more than one, FOO1 gets an expression like asin(u) + asin(v) + ... (otherwise it's just asin(u)), so call FOO2 on the + expression. FOO2 marches thru the list of asin terms and tries to combine them two by two (via FOO3). With that I get the following: (%i9) asin(sqrt(3)*sqrt(2)/3) + asin(sqrt(3)/3); (%o9) %pi/2 (%i10) asin(sqrt(3)*sqrt(2)/3) + asin(sqrt(3)/3) - 1; (%o10) %pi/2-1 (%i11) asin(sqrt(3)*sqrt(2)/3) + asin(sqrt(3)/3) - x + y; (%o11) y-x+%pi/2 (%i12) asin(sqrt(3)*sqrt(2)/3) + asin(sqrt(3)/3) - asin(x) + u; (%o12) -asin(x)+u+%pi/2 (%i13) asin(sqrt(3)*sqrt(2)/3) + asin(sqrt(3)/3) + asin(sqrt(1 - u^2)) + asin (u); (%o13) %pi This is just what I got from some half-hearted hacking; I'm sure there are serious limitations. Good luck, have fun, hope this helps. Robert Dodier -- 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 http://groups.google.com/group/sage-support. For more options, visit https://groups.google.com/groups/opt_out.
[sage-support] Re: Simplification Issue Implicates Canonical Form
On Feb 22, 2:37 am, JamesHDavenport j.h.davenp...@bath.ac.uk wrote: Canonical form and simplify aren't the same thing (necessarily). See Carette,J., Understanding Expression Simplification. Proc. ISSAC 2004 (ed. J. Gutierrez), ACM Press, New York, 2004, pp. 72-79. I don't have access to that source but I completely agree, noting that the passage you quoted discusses the results of full_simplify(). What I've reported is primarily a bug in Sage simplification. However, the underlying cause appears to be an issue with the GiNaC canonical form, which apparently tends to proliferate radicals of small integers. Given Sage's dependence upon GiNaC's canonical form, unless Sage aggressively simplifies such expressions, Sage users will see many more expressions like -(3*sqrt(-2/3*(2*(3*sqrt(-2*sqrt(5) + 5) - 2*sqrt(5) +3)/ (sqrt(-2*sqrt(5) + 5) - sqrt(5) + 2) - 3)*el + 1/9*(3*sqrt(-2*sqrt(5)+ 5) - 2*sqrt(5) + 3)^2/(sqrt(-2*sqrt(5) + 5) - sqrt(5) + 2)^2) - (3*sqrt(-2*sqrt(5) + 5) - 2*sqrt(5) + 3)/(sqrt(-2*sqrt(5) + 5) - sqrt(5)+ 2))/(2*(3*sqrt(-2*sqrt(5) + 5) - 2*sqrt(5) + 3)/ (sqrt(-2*sqrt(5) + 5)- sqrt(5) + 2) - 3) My system engineering gut feel is that it would be desirable to address this particular simplification issue closer to the source rather than to try to engineer around it on the simplification end. When I get some free time, I'm going to raise this issue on GiNaC- list. I'm not sure how soon that will be though. -Mark -- 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] Re: Simplification Issue Implicates Canonical Form
Try http://www.cas.mcmaster.ca/~carette/publications/simplification.pdf The real point is that GiNaC's canonical form has different goals from a 'simplify' command in the sense of minimal complexity. One really needs to separate the two, and I don;t know how easy that is with the current design. James On Feb 22, 5:18 pm, Mark Rahner rah...@alum.mit.edu wrote: On Feb 22, 2:37 am, JamesHDavenport j.h.davenp...@bath.ac.uk wrote: Canonical form and simplify aren't the same thing (necessarily). See Carette,J., Understanding Expression Simplification. Proc. ISSAC 2004 (ed. J. Gutierrez), ACM Press, New York, 2004, pp. 72-79. I don't have access to that source but I completely agree, noting that the passage you quoted discusses the results of full_simplify(). What I've reported is primarily a bug in Sage simplification. However, the underlying cause appears to be an issue with the GiNaC canonical form, which apparently tends to proliferate radicals of small integers. Given Sage's dependence upon GiNaC's canonical form, unless Sage aggressively simplifies such expressions, Sage users will see many more expressions like -(3*sqrt(-2/3*(2*(3*sqrt(-2*sqrt(5) + 5) - 2*sqrt(5) +3)/ (sqrt(-2*sqrt(5) + 5) - sqrt(5) + 2) - 3)*el + 1/9*(3*sqrt(-2*sqrt(5)+ 5) - 2*sqrt(5) + 3)^2/(sqrt(-2*sqrt(5) + 5) - sqrt(5) + 2)^2) - (3*sqrt(-2*sqrt(5) + 5) - 2*sqrt(5) + 3)/(sqrt(-2*sqrt(5) + 5) - sqrt(5)+ 2))/(2*(3*sqrt(-2*sqrt(5) + 5) - 2*sqrt(5) + 3)/ (sqrt(-2*sqrt(5) + 5)- sqrt(5) + 2) - 3) My system engineering gut feel is that it would be desirable to address this particular simplification issue closer to the source rather than to try to engineer around it on the simplification end. When I get some free time, I'm going to raise this issue on GiNaC- list. I'm not sure how soon that will be though. -Mark -- 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] Re: Simplification Issue Implicates Canonical Form
So once it comes back to Sage, its internal representation goes back to the Ginac one. Doh! So much for a possible workaround involving maxima. Dox, I was using full_simplify() and also the handful of simplify methods it invokes. Evaluate a.full_simplify? to see their names. Nils, trivial comparison is a major reason to use a canonical form but it isn't an argument that favors a particular canonical form. For example, to simplify your example expressions, I would factor the 6 inside the radical and continue with substitutions as I recommended. The resulting expressions would be easy to compare because they would be identical: 2/sqrt(6) - 2/(sqrt(3)*sqrt(2)) - sqrt(2)/sqrt(3) sqrt(6)/3 - (sqrt(3)*sqrt(2))/3 - sqrt(2)/sqrt(3) My initial problem was the severe obfuscation that resulted when extra factors added by the canonical form refused to cancel and then replicated geometrically. Severe obfuscation is obviously a bad thing. It grows out of simple obfuscation of much simpler expressions. Should ( 1/7 * sqrt(21) ).full_simplify() produce 1/7*sqrt(3)*sqrt(7) when sqrt(3)/sqrt(7) is an option? Having fewer factors is an important part of being simpler. In the more complicated expression, the factors involving 7s aren't even adjacent. I don't know if the more complicated forms are required for GiNaC to perform efficiently. However, from an interactive user's perspective, this issue is perplexing because it only involves the representation of constants. What could be simpler? (pun intended) -Mark -- 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] Re: Simplification Issue Implicates Canonical Form
On Feb 21, 9:36 pm, Mark Rahner rah...@alum.mit.edu wrote: So once it comes back to Sage, its internal representation goes back to the Ginac one. My initial problem was the severe obfuscation that resulted when extra factors added by the canonical form refused to cancel and then replicated geometrically. Severe obfuscation is obviously a bad thing. It grows out of simple obfuscation of much simpler expressions. Should ( 1/7 * sqrt(21) ).full_simplify() produce 1/7*sqrt(3)*sqrt(7) when sqrt(3)/sqrt(7) is an option? Having fewer factors is an important part of being simpler. In the more complicated expression, the factors involving 7s aren't even adjacent. I don't know if the more complicated forms are required for GiNaC to perform efficiently. However, from an interactive user's perspective, this issue is perplexing because it only involves the representation of constants. What could be simpler? (pun intended) Canonical form and simplify aren't the same thing (necessarily). See Carette,J., Understanding Expression Simplification. Proc. ISSAC 2004 (ed. J. Gutierrez), ACM Press, New York, 2004, pp. 72-79. -- 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] Re: Simplification Issue Implicates Canonical Form
On Feb 18, 8:24 pm, Mark Rahner rah...@alum.mit.edu wrote: I appreciate that background info. I hadn't tried invoking maxima because I read somewhere that simplify() used maxima. I must've been reading outdated material. As you stated, maxima does the correct thing. Because Sage can invoke maxima, perhaps I have a work around. Well, it *does* use maxima, but in this case it just sends it to Maxima and back. So once it comes back to Sage, its internal representation goes back to the Ginac one. You're right that this issue should be considered in the context of powers. In that context, I think it is even more clear that 5^(-1/2) is simpler than (1/5) * 5^(1/2). Leaving the additional term doesn't seem like a big deal, but by preventing subsequent simplifications, and by combining and recombining with other large expressions, it can have highly undesirable effects. I took a quick look at ginsh, the GiNaC interactive shell. It converts 1/sqrt(5) to 1/5*sqrt(5) so I suspect that this issue can be traced to the GiNaC canonical form. I'm not a CAS expert but I know a Great, then that solves it. I haven't had a working ginsh for a while, so I didn't check to make sure. fair amount about computer system interfaces and I'm sure this issue adversely impacts the user experience. Nobody would select equation obfuscation mode given the choice. However, there may be other reasons for this choice. I hesitate to critique either the GiNaC or Maxima folks (or anyone else) on thorny canonicalization of simplification questions. I think this issue should be taken up with the GiNaC folks. Do they hang out in this group? One or two are on the sage-devel list.Or you can ask on https://www.ginac.de/mailman/listinfo/ginac-devel, I think. -- 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] Re: Simplification Issue Implicates Canonical Form
On Feb 18, 5:24 pm, Mark Rahner rah...@alum.mit.edu wrote: converts 1/sqrt(5) to 1/5*sqrt(5) so I suspect that this issue can be traced to the GiNaC canonical form. Yes, it does so for a very good reason: By simplifying expressions this way, you're sure to recognize equal expressions. Compare 2/ sqrt(6) and sqrt(6)/3, for instance. You'll easily recognize they're equal if you remove sqrts from the denominator. By sacrificing the apparent simplicity of 1/sqrt(5) to get 1/5*sqrt(5), one big problem in deciding if algebraic numbers are equal disappears completely (there are still other ones, due to the fact that expressions line sqrt(1+sqrt(2)) are ambiguous). It's a standard convention to deal with fractions involving roots. It's often taught in schools. -- 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] Re: Simplification Issue Implicates Canonical Form
I appreciate that background info. I hadn't tried invoking maxima because I read somewhere that simplify() used maxima. I must've been reading outdated material. As you stated, maxima does the correct thing. Because Sage can invoke maxima, perhaps I have a work around. You're right that this issue should be considered in the context of powers. In that context, I think it is even more clear that 5^(-1/2) is simpler than (1/5) * 5^(1/2). Leaving the additional term doesn't seem like a big deal, but by preventing subsequent simplifications, and by combining and recombining with other large expressions, it can have highly undesirable effects. I took a quick look at ginsh, the GiNaC interactive shell. It converts 1/sqrt(5) to 1/5*sqrt(5) so I suspect that this issue can be traced to the GiNaC canonical form. I'm not a CAS expert but I know a fair amount about computer system interfaces and I'm sure this issue adversely impacts the user experience. Nobody would select equation obfuscation mode given the choice. I think this issue should be taken up with the GiNaC folks. Do they hang out in this group? -Mark -- 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] Re: Simplification Issue Implicates Canonical Form
In some previous incarnation, where Sage used Maxima for things like this, your simplification happened. (%i1) 1/sqrt(5); 1 (%o1) --- sqrt(5) (%i2) sqrt(5)/5; 1 (%o2) --- sqrt(5) Now we use Ginac for basic symbolic stuff. Once in a while we (i.e., Burcin) changes some internal representation, or Ginac does. But in general I think it just goes for positive powers - you may want to read its documentation. In particular, sqrt is not a builtin function (square root (not a GiNaC function, rather an alias for pow(x, numeric(1, 2, so the behavior is analogous to sage: 1/5^(1/3) 1/5*5^(2/3) Naturally, GiNaC is Not a CAS, so perhaps that is one reason for the distinction. You are also right about black arts! So I don't pretend to judge Maxima *or* Ginac on this one. I'm sorry if that doesn't help, but it might give you some background, at least. - kcrisman -- 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] Re: Simplification / Latex question
As far as I understand from your previous comments, a way to extract the
exponential functions from the expression is all you need. You don't
really need to walk through the tree. Here is one way to do this:
sage: t = exp(x+y)*(x-y)*(exp(y)+exp(z-y))
sage: t
(e^(-y + z) + e^y)*(x - y)*e^(x + y)
sage: w = SR.wild()
sage: t.find(exp(w))
[e^(-y + z), e^(x + y), e^y]
You can then change the expressions in the given array and substitute
new values for them:
Did you define res in between? Maybe this? Just a guess.
sage: res = t.find(exp(w))
sage: t.subs({res[1]: sin(res[1].operands()[0])})
(e^(-y + z) + e^y)*(x - y)*sin(x + y)
The .operands()[0] syntax is really cumbersome. We need a shortcut for
this. I thought .op(0) worked for pynac expressions before we switched
from the maxima backend.
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[sage-support] Re: Simplification / Latex question
On 6/24/10 6:15 AM, kcrisman wrote: Right. This crops up in the middle of a more complicated expression. If I could figure out how to break the expression up in the right way, then I guess I could search for parts that are exponential functions, take the log of those, and then simplify the logs. I know how to ultimately find all the pieces of the function with .operands(), but I don't then know any way to put them back together with the proper operators. Maybe there's a way to access the parsed I believe there is, but I can't figure out how to do it without going through fast_callable, which doesn't seem right. This information is in Pynac, but I can't find a method or underscore method that accesses it. This is now http://trac.sagemath.org/sage_trac/ticket/9329 . See http://sagenb.org/home/pub/1760/ for an example of creating an expression tree (in that worksheet, the expression tree is used to make a mathematica expression...) Thanks, Jason -- 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: Simplification / Latex question
On 06/26/2010 03:26:06 PM, Jason Grout wrote: On 6/24/10 6:15 AM, kcrisman wrote: Right. This crops up in the middle of a more complicated expression. If I could figure out how to break the expression up in the right way, then I guess I could search for parts that are exponential functions, take the log of those, and then simplify the logs. I know how to ultimately find all the pieces of the function with .operands(), but I don't then know any way to put them back together with the proper operators. Maybe there's a way to access the parsed I believe there is, but I can't figure out how to do it without going through fast_callable, which doesn't seem right. This information is in Pynac, but I can't find a method or underscore method that accesses it. This is now http://trac.sagemath.org/sage_trac/ticket/9329 . See http://sagenb.org/home/pub/1760/ for an example of creating an expression tree (in that worksheet, the expression tree is used to make a mathematica expression...) Hey, that's really cool. Thanks! BTW, at this point, after the further Latex discussion, I realize that my original problem was really more related to Ticket #9314 than to the expression itself (at least, that's what I'm currently speculating). But, especially with that example, it's pretty clear to me what to do if I need to parse an expression. I believe that Ticket #9329 was generated in response to my original post, before I understood that there was a Latex issue involved. I believe that Ticket #9329 should be deleted (closed or whatever). -Mike -- 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] Re: Simplification / Latex question
I believe that Ticket #9329 was generated in response to my original post, before I understood that there was a Latex issue involved. I believe that Ticket #9329 should be deleted (closed or whatever). But part of your question was also to try to simplify more complicated expressions, and it does seem reasonable that we could provide a full nested expression tree for symbolic expressions (rather than having to iterate something by hand), since we do so for fast_callable (I think?). Just because we might not do it anytime soon doesn't mean we can't have a ticket for it! We usually only close tickets it is clear are duplicates or things we won't fix or are too vague; things which no one is motivated to provide just stay that way until someone shows up (and you'd be surprised how many stay open for 1 year and all of a sudden get someone working on them). I do hope the LaTeX issue gets resolved for you soon, though. - kcrisman -- 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: Simplification / Latex question
On 06/26/2010 05:21:21 PM, kcrisman wrote: I believe that Ticket #9329 was generated in response to my original post, before I understood that there was a Latex issue involved. I believe that Ticket #9329 should be deleted (closed or whatever). But part of your question was also to try to simplify more complicated expressions, and it does seem reasonable that we could provide a full nested expression tree for symbolic expressions (rather than having to iterate something by hand), since we do so for fast_callable (I think?). Just because we might not do it anytime soon doesn't mean we can't have a ticket for it! We usually only close tickets it is clear are duplicates or things we won't fix or are too vague; things which no one is motivated to provide just stay that way until someone shows up (and you'd be surprised how many stay open for 1 year and all of a sudden get someone working on them). OK, sure, that makes sense. I do hope the LaTeX issue gets resolved for you soon, though. My current theory is that it will be resolved if Ticket #9314 gets fixed. But I don't really know that for sure :-) - kcrisman -- 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 -- 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] Re: Simplification / Latex question
Dear Mike, Just to follow up: There is further discussion at http://trac.sagemath.org/sage_trac/ticket/9329 if you are interested in saying exactly what sort of data structure would enable you to perform the simplifications you would like to without having to create a custom Maxima simplification routine. - kcrisman -- 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: Simplification / Latex question
On 06/25/2010 06:07:02 AM, kcrisman wrote:
Dear Mike,
Just to follow up:
There is further discussion at
http://trac.sagemath.org/sage_trac/ticket/9329
if you are interested in saying exactly what sort of data structure
would enable you to perform the simplifications you would like to
without having to create a custom Maxima simplification routine.
- kcrisman
Well ... I can see how one might work one's way
through the expression, using the operator() and operands()
functions. And, I suppose, I can see how one could then build
up the equivalent expression, having modified one of the
operands in a certain way. So, I don't suppose that there is
actually any need for a custom data structure to do this.
I guess it's really just a question of whether the way
these expressions sometimes display in latex bothers me
enough to do something about it, other than just complain.
Although ... I guess I'm still a bit confused as to why
this happens, even given the form of the exponential.
sage: f = e^(2*I*pi*n*x - 2*I*pi*n)
sage: latex(f)
e^{\left(\left(2 I\right) \, \pi n x + \left(-2 I\right) \, \pi
n\right)}
Still, I shouldn't really get +(-2i) right? I think you
mentioned something about Pynac (another program I know
nothing about). It seems like trying to fix this just
involves learning too much of a learning curve for me
to contemplate.
-Mike
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[sage-support] Re: Simplification / Latex question
sage: n=var('n')
sage: f=e^(i*x*pi*n-i*2*pi*n)
sage: f.simplify_full()
e^(I*pi*n*x - 2*I*pi*n)
# Is there a way I can get this to simplify?
This apparently isn't even that easy in Maxima.
Maxima 5.21.1http://maxima.sourceforge.net
using Lisp ECL 10.4.1
Distributed under the GNU Public License. See the file COPYING.
Dedicated to the memory of William Schelter.
The function bug_report() provides bug reporting information.
(%i5) radcan(%e^(%pi*n-2*%pi));
%pi n - 2 %pi
(%o5) %e
(%i6) expand(%e^(%pi*n-2*%pi));
%pi n - 2 %pi
(%o6) %e
There are several Maxima experts on the list, though, who may know
about a flag to set in such a case to factor the exponent first. I
couldn't find one in the simplification documentation for Maxima, but
it may be elsewhere.
Well, I hope to hear from one of these Maxima experts!
Of course, you can do this ahead of time:
sage: e^((n*pi-pi*2).factor())
e^((n - 2)*pi)
but this is probably not what you want.
Right. This crops up in the middle of a more complicated
expression. If I could figure out how to break the expression
up in the right way, then I guess I could search for parts
that are exponential functions, take the log of those, and
then simplify the logs. I know how to ultimately find all
the pieces of the function with .operands(), but I don't
then know any way to put them back together with the
proper operators. Maybe there's a way to access the parsed
I believe there is, but I can't figure out how to do it without going
through fast_callable, which doesn't seem right. This information is
in Pynac, but I can't find a method or underscore method that accesses
it. This is now http://trac.sagemath.org/sage_trac/ticket/9329 .
tree of the expression? But of course that's crazy.
There must be a normal way to simplify it!
I don't know about that. Many other discussions about 'obvious'
simplifications have led me to agree that this is a much harder
problem than one thinks.
On the other hand, it can be hard to find references to additional
packages in Maxima that might do this; it turns out that lots of
things one wants to do are not automatically available. Try
http://maxima.sourceforge.net/docs/manual/en/maxima_71.html#SEC298 for
ways you might be able to do this directly in Maxima, though I
couldn't see for sure if that is part of its functionality.
sage: maxima_console()
(%i4) demo(facexp);
Annoyingly, it continues this thing of asking whether 2*%pi is an
integer which one often sees...
I hope this helps.
- kcrisman
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Re: [sage-support] Re: Simplification / Latex question
On 06/24/2010 06:15:52 AM, kcrisman wrote:
sage: n=var('n')
sage: f=e^(i*x*pi*n-i*2*pi*n)
sage: f.simplify_full()
e^(I*pi*n*x - 2*I*pi*n)
# Is there a way I can get this to simplify?
This apparently isn't even that easy in Maxima.
Maxima 5.21.1http://maxima.sourceforge.net
using Lisp ECL 10.4.1
Distributed under the GNU Public License. See the file COPYING.
Dedicated to the memory of William Schelter.
The function bug_report() provides bug reporting information.
(%i5) radcan(%e^(%pi*n-2*%pi));
%pi n - 2 %pi
(%o5) %e
(%i6) expand(%e^(%pi*n-2*%pi));
%pi n - 2 %pi
(%o6) %e
There are several Maxima experts on the list, though, who may know
about a flag to set in such a case to factor the exponent first.
I
couldn't find one in the simplification documentation for Maxima,
but
it may be elsewhere.
Well, I hope to hear from one of these Maxima experts!
Of course, you can do this ahead of time:
sage: e^((n*pi-pi*2).factor())
e^((n - 2)*pi)
but this is probably not what you want.
Right. This crops up in the middle of a more complicated
expression. If I could figure out how to break the expression
up in the right way, then I guess I could search for parts
that are exponential functions, take the log of those, and
then simplify the logs. I know how to ultimately find all
the pieces of the function with .operands(), but I don't
then know any way to put them back together with the
proper operators. Maybe there's a way to access the parsed
I believe there is, but I can't figure out how to do it without going
through fast_callable, which doesn't seem right. This information is
in Pynac, but I can't find a method or underscore method that accesses
it. This is now http://trac.sagemath.org/sage_trac/ticket/9329 .
tree of the expression? But of course that's crazy.
There must be a normal way to simplify it!
I don't know about that. Many other discussions about 'obvious'
simplifications have led me to agree that this is a much harder
problem than one thinks.
On the other hand, it can be hard to find references to additional
packages in Maxima that might do this; it turns out that lots of
things one wants to do are not automatically available. Try
http://maxima.sourceforge.net/docs/manual/en/maxima_71.html#SEC298 for
ways you might be able to do this directly in Maxima, though I
couldn't see for sure if that is part of its functionality.
sage: maxima_console()
(%i4) demo(facexp);
Annoyingly, it continues this thing of asking whether 2*%pi is an
integer which one often sees...
I hope this helps.
- kcrisman
This is all good information, thanks. It helps to at least know
that I'm not missing something obvious. It's the combination with
that latex issue that results in some really ugly output.
I've noticed too about how maxima continues to ask things that
(it would seem) you have already told it. I guess it would be
in my best interests to learn more about maxima.
Thanks again,
-Mike
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[sage-support] Re: Simplification / Latex question
I've noticed too about how maxima continues to ask things that (it would seem) you have already told it. I guess it would be in my best interests to learn more about maxima. If you are serious about doing symbolic manipulation that you can control from within Sage, yes. That said, various people will note that things it would seem you told it are often things that are provably undecidable or something like that. Good luck! - kcrisman -- 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: Simplification / Latex question
On 06/22/2010 12:41:17 PM, kcrisman wrote:
sage: n=var('n')
sage: f=e^(i*x*pi*n-i*2*pi*n)
sage: f.simplify_full()
e^(I*pi*n*x - 2*I*pi*n)
# Is there a way I can get this to simplify?
This apparently isn't even that easy in Maxima.
Maxima 5.21.1 http://maxima.sourceforge.net
using Lisp ECL 10.4.1
Distributed under the GNU Public License. See the file COPYING.
Dedicated to the memory of William Schelter.
The function bug_report() provides bug reporting information.
(%i5) radcan(%e^(%pi*n-2*%pi));
%pi n - 2 %pi
(%o5) %e
(%i6) expand(%e^(%pi*n-2*%pi));
%pi n - 2 %pi
(%o6) %e
There are several Maxima experts on the list, though, who may know
about a flag to set in such a case to factor the exponent first. I
couldn't find one in the simplification documentation for Maxima, but
it may be elsewhere.
Well, I hope to hear from one of these Maxima experts!
Of course, you can do this ahead of time:
sage: e^((n*pi-pi*2).factor())
e^((n - 2)*pi)
but this is probably not what you want.
Right. This crops up in the middle of a more complicated
expression. If I could figure out how to break the expression
up in the right way, then I guess I could search for parts
that are exponential functions, take the log of those, and
then simplify the logs. I know how to ultimately find all
the pieces of the function with .operands(), but I don't
then know any way to put them back together with the
proper operators. Maybe there's a way to access the parsed
tree of the expression? But of course that's crazy.
There must be a normal way to simplify it!
sage: latex(f)
e^{\left(I \, \pi n x + \left(-2 I\right) \, \pi n\right)}
# Why the extra parentheses around -2I ?
No idea. Pynac usually handles these sorts of things; I'm not sure
whether I would call it a bug, though it does seem strange. Perhaps
Pynac represents this as a complex internally and so this happens?
Burcin will know :)
- kcrisman
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[sage-support] Re: Simplification / Latex question
sage: n=var('n')
sage: f=e^(i*x*pi*n-i*2*pi*n)
sage: f.simplify_full()
e^(I*pi*n*x - 2*I*pi*n)
# Is there a way I can get this to simplify?
This apparently isn't even that easy in Maxima.
Maxima 5.21.1 http://maxima.sourceforge.net
using Lisp ECL 10.4.1
Distributed under the GNU Public License. See the file COPYING.
Dedicated to the memory of William Schelter.
The function bug_report() provides bug reporting information.
(%i5) radcan(%e^(%pi*n-2*%pi));
%pi n - 2 %pi
(%o5) %e
(%i6) expand(%e^(%pi*n-2*%pi));
%pi n - 2 %pi
(%o6) %e
There are several Maxima experts on the list, though, who may know
about a flag to set in such a case to factor the exponent first. I
couldn't find one in the simplification documentation for Maxima, but
it may be elsewhere.
Of course, you can do this ahead of time:
sage: e^((n*pi-pi*2).factor())
e^((n - 2)*pi)
but this is probably not what you want.
sage: latex(f)
e^{\left(I \, \pi n x + \left(-2 I\right) \, \pi n\right)}
# Why the extra parentheses around -2I ?
No idea. Pynac usually handles these sorts of things; I'm not sure
whether I would call it a bug, though it does seem strange. Perhaps
Pynac represents this as a complex internally and so this happens?
Burcin will know :)
- kcrisman
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[sage-support] Re: Simplification
On May 14, 3:57 am, Laurent moky.m...@gmail.com wrote:
Hello
Hi Laurent,
x,y=var('x,y')
s = x*y2 + x*(-y2 - x2 + 1) + x3 - x
print simplify(s)
Answer :
2 2 2 3
x y + x (- y - x + 1) + x - x
+
I'm quite disappointed that Sage do not notice that s=0. Do I miss
something ?
Btw, the function simplify_full does not exist ... so I suppose that I
*do* miss something.
Yes, it does exist for me :)
--
| Sage Version 3.4.2, Release Date: 2009-05-04 |
| Type notebook() for the GUI, and license() for information.|
--
sage: x,y=var('x,y')
sage: s = x*y^2 + x*(-y^2 - x^2 + 1) + x^3 - x; s
x*y^2 + x*(-y^2 - x^2 + 1) + x^3 - x
sage: s.simplify()
x*y^2 + x*(-y^2 - x^2 + 1) + x^3 - x
sage: s.simplify_full()
0
My version is extracted from the tar.gz downloaded from the website :
| Sage Version 3.4.1, Release Date: 2009-04-21 |
| Type notebook() for the GUI, and license() for information. |
--
Should I install some additional proposed packages
?http://www.sagemath.org/download-packages.html
Thanks
Laurent
Cheers,
Michael
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[sage-support] Re: Simplification
Dear Laurent,
On May 14, 12:57 pm, Laurent moky.m...@gmail.com wrote:
Btw, the function simplify_full does not exist ... so I suppose that I
*do* miss something.
Yes. simplify_full is not a function but a method (after all, python
is object oriented).
So, you can do:
sage: x,y=var('x,y')
sage: s = x*y^2 + x*(-y^2 - x^2 + 1) + x^3 - x
sage: s
x*y^2 + x*(-y^2 - x^2 + 1) + x^3 - x
sage: s.simplify_full()
0
Btw, for getting a list of methods, the TAB-Key helps. For example,
type in
sage: s.sim
and press the TAB-key. Then a list appears:
s.simplify s.simplify_log s.simplify_trig
s.simplify_exp s.simplify_radical
s.simplify_full s.simplify_rational
And these are all attributes/methods of s whose names start with
'sim'.
Best regards,
Simon
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[sage-support] Re: Simplification
On May 14, 2009, at 3:57 AM, Laurent wrote:
Hello
x,y=var('x,y')
s = x*y2 + x*(-y2 - x2 + 1) + x3 - x
print simplify(s)
Answer :
2 22 3
x y + x (- y - x + 1) + x - x
+
I'm quite disappointed that Sage do not notice that s=0. Do I miss
something ?
Btw, the function simplify_full does not exist ... so I suppose that I
*do* miss something.
Simplification doesn't expand by default. This is by design (e.g. one
might argue that (1+x)^100 is more simplified than its expanded
form). However, Sage is able to tell that this is zero:
sage: var('x,y')
(x, y)
sage: s = x*y^2 + x*(-y^2 - x^2 + 1) + x^3 - x
sage: s.simplify()
x*y^2 + x*(-y^2 - x^2 + 1) + x^3 - x
sage: s.simplify_full()
0
sage: s.simplify_rational()
0
sage: s.expand()
0
Or over the (orders of magnitude faster) polynomial ring:
sage: R.x,y = QQ[]
sage: s = x*y^2 + x*(-y^2 - x^2 + 1) + x^3 - x; s
0
- Robert
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[sage-support] Re: Simplification
On May 14, 12:57 pm, Laurent moky.m...@gmail.com wrote: Btw, the function simplify_full does not exist ... so I suppose that I *do* miss something. Yes. simplify_full is not a function but a method (after all, python is object oriented). Thanks all. Indeed, simplify_all(s) provokes an error while s.simplify_all() provides 0. Quite logical. I still have some psychological inability to speak with Sage as I speak with my python interpreter ;) Good afternoon Laurent --~--~-~--~~~---~--~~ 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 URLs: http://www.sagemath.org -~--~~~~--~~--~--~---
[sage-support] Re: Simplification/Rewrite Rules?
On Nov 24, 2008, at 8:45 PM, William Stein wrote:
On Mon, Nov 24, 2008 at 4:46 PM, Tim Lahey [EMAIL PROTECTED]
wrote:
Hi,
Is there a specific way to add rules (and apply them) to rewrite
expressions in Sage?
Such as, log(a)-log(b) = log(a/b)
I need this (and others) in order to properly compare the integration
results from Sage to the list of integrals I have. I'm trying to put
together a suite of integration tests for both correctness and
timing.
I don't know if one can do the above (maybe with pynac it is
possible).
However, in the meantime could you at least improperly compare
the results for pseudo-correctness by evaluating both answers
at a bunch of randomly chosen points and see if they differ by a
constant?
I'll check the maxima docs. Unfortunately, at the moment, it doesn't
look like one can use the new symbolics with the standard (maxima)
integration.
If I do, I get:
sage: var('x,a,b',ns=1)
(x, a, b)
sage: f16 = x/(a*x+b)^3
sage: f16.integrate(x)
---
AttributeErrorTraceback (most recent call
last)
/Users/tjlahey/ipython console in module()
AttributeError: 'sage.symbolic.expression.Expression' object has no
attribute 'integrate'
I can easily run timing comparisons between maxima and FriCAS, but
because
of how sympy does things (with its separate variables), I'll have to run
them separately. Comparing maxima and FriCAS, the timings are pretty
close on
both for most of the ones I've tried. A few were much longer in FriCAS.
I have a pretty long list of integrals to go through and I've only
done 16.
Cheers,
Tim.
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[sage-support] Re: Simplification/Rewrite Rules?
On Mon, Nov 24, 2008 at 6:03 PM, Tim Lahey [EMAIL PROTECTED] wrote:
On Nov 24, 2008, at 8:45 PM, William Stein wrote:
On Mon, Nov 24, 2008 at 4:46 PM, Tim Lahey [EMAIL PROTECTED]
wrote:
Hi,
Is there a specific way to add rules (and apply them) to rewrite
expressions in Sage?
Such as, log(a)-log(b) = log(a/b)
I need this (and others) in order to properly compare the integration
results from Sage to the list of integrals I have. I'm trying to put
together a suite of integration tests for both correctness and
timing.
I don't know if one can do the above (maybe with pynac it is
possible).
However, in the meantime could you at least improperly compare
the results for pseudo-correctness by evaluating both answers
at a bunch of randomly chosen points and see if they differ by a
constant?
I'll check the maxima docs. Unfortunately, at the moment, it doesn't
look like one can use the new symbolics with the standard (maxima)
integration.
True.
If I do, I get:
sage: var('x,a,b',ns=1)
(x, a, b)
sage: f16 = x/(a*x+b)^3
sage: f16.integrate(x)
---
AttributeErrorTraceback (most recent call
last)
/Users/tjlahey/ipython console in module()
AttributeError: 'sage.symbolic.expression.Expression' object has no
attribute 'integrate'
Yep, that's not implemented.
I can easily run timing comparisons between maxima and FriCAS, but
because
of how sympy does things (with its separate variables), I'll have to run
them separately. Comparing maxima and FriCAS, the timings are pretty
close on
both for most of the ones I've tried. A few were much longer in FriCAS.
I have a pretty long list of integrals to go through and I've only
done 16.
Many thanks for doing this!
William
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[sage-support] Re: Simplification/Rewrite Rules?
On Nov 24, 2008, at 9:05 PM, William Stein wrote: I can easily run timing comparisons between maxima and FriCAS, but because of how sympy does things (with its separate variables), I'll have to run them separately. Comparing maxima and FriCAS, the timings are pretty close on both for most of the ones I've tried. A few were much longer in FriCAS. I have a pretty long list of integrals to go through and I've only done 16. Many thanks for doing this! William No problem. Once it's done it should help as automated tests for both monitoring performance and correctness. I'll be happy to donate them to the cause. It's going to take a while. The timeit routines give results that look like: 5 loops, best of 3: 50 ms per loop Does anybody have something to pull out the specific time (50ms)? Cheers, Tim. --- Tim Lahey PhD Candidate, Systems Design Engineering University of Waterloo --~--~-~--~~~---~--~~ To post to this group, send email to sage-support@googlegroups.com To unsubscribe from this group, send email to [EMAIL PROTECTED] For more options, visit this group at http://groups.google.com/group/sage-support URLs: http://www.sagemath.org -~--~~~~--~~--~--~---
[sage-support] Re: Simplification/Rewrite Rules?
On Nov 24, 6:17 pm, Tim Lahey [EMAIL PROTECTED] wrote:
On Nov 24, 2008, at 9:05 PM, William Stein wrote:
Hi,
I can easily run timing comparisons between maxima and FriCAS, but
because
of how sympy does things (with its separate variables), I'll have
to run
them separately. Comparing maxima and FriCAS, the timings are pretty
close on
both for most of the ones I've tried. A few were much longer in
FriCAS.
I have a pretty long list of integrals to go through and I've only
done 16.
Many thanks for doing this!
William
No problem. Once it's done it should help as automated tests for both
monitoring performance and correctness. I'll be happy to donate them
to the cause. It's going to take a while.
The timeit routines give results that look like:
5 loops, best of 3: 50 ms per loop
Does anybody have something to pull out the specific time (50ms)?
We have a timeit doctest framework that is supposed to hunt for speed
regressions. It is merged in 3.2, but we need infrastructure to
compare the output from several runs.
But I guess you are asking if timeit('foo') could return the time so
that one can do something with the data? I am not sure how that is
possible, but the timeit doctesting framework somehow does it.
Cheers,
Tim.
Cheers,
Michael
---
Tim Lahey
PhD Candidate, Systems Design Engineering
University of Waterloo
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[sage-support] Re: Simplification/Rewrite Rules?
On Nov 24, 2008, at 9:21 PM, mabshoff wrote:
We have a timeit doctest framework that is supposed to hunt for speed
regressions. It is merged in 3.2, but we need infrastructure to
compare the output from several runs.
But I guess you are asking if timeit('foo') could return the time so
that one can do something with the data? I am not sure how that is
possible, but the timeit doctesting framework somehow does it.
I know I could parse the output, but I thought someone might have done
it and it sounds like the timeit doctest framework might do it.
Where can I find this in the source so I can see how it is doing it?
Thanks,
Tim.
---
Tim Lahey
PhD Candidate, Systems Design Engineering
University of Waterloo
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[sage-support] Re: Simplification/Rewrite Rules?
On Mon, Nov 24, 2008 at 6:31 PM, Tim Lahey [EMAIL PROTECTED] wrote: I know I could parse the output, but I thought someone might have done it and it sounds like the timeit doctest framework might do it. Where can I find this in the source so I can see how it is doing it? You can do this in 3.2: sage: s = timeit.eval(2+3) sage: s 625 loops, best of 3: 942 ns per loop sage: s.stats (625, 3, 3, 942.230224609375, 'ns') The code is in sage/misc/sage_timeit.py and sage/misc/sage_timeit_class.py. --Mike --~--~-~--~~~---~--~~ To post to this group, send email to sage-support@googlegroups.com To unsubscribe from this group, send email to [EMAIL PROTECTED] For more options, visit this group at http://groups.google.com/group/sage-support URLs: http://www.sagemath.org -~--~~~~--~~--~--~---
[sage-support] Re: Simplification/Rewrite Rules?
On Nov 24, 7:03 pm, Tim Lahey [EMAIL PROTECTED] wrote: On Nov 24, 2008, at 9:51 PM, Mike Hansen wrote: You can do this in 3.2: sage: s = timeit.eval(2+3) sage: s 625 loops, best of 3: 942 ns per loop sage: s.stats (625, 3, 3, 942.230224609375, 'ns') The code is in sage/misc/sage_timeit.py and sage/misc/ sage_timeit_class.py. Thanks a lot. This will definitely help. Yep. Cheers, You should consider creating one or a couple large files with the integrals for doctesting and stuff them into $SAGE_ROOT/devel/tests. Hopefully it can be arranged to feed the input into Maxima/Axiom/Maple/ MMA/sympy and so on and compare the result as well as performance. If you find a bunch of integrals the OS programs cannot do or where a result is incorrect I am sure those projects will be more than happy to get bug reports. Tim. Cheers, Michael --~--~-~--~~~---~--~~ To post to this group, send email to sage-support@googlegroups.com To unsubscribe from this group, send email to [EMAIL PROTECTED] For more options, visit this group at http://groups.google.com/group/sage-support URLs: http://www.sagemath.org -~--~~~~--~~--~--~---
[sage-support] Re: Simplification/Rewrite Rules?
On Nov 24, 2008, at 10:07 PM, mabshoff wrote:
You should consider creating one or a couple large files with the
integrals for doctesting and stuff them into $SAGE_ROOT/devel/tests.
Hopefully it can be arranged to feed the input into Maxima/Axiom/
Maple/
MMA/sympy and so on and compare the result as well as performance. If
you find a bunch of integrals the OS programs cannot do or where a
result is incorrect I am sure those projects will be more than happy
to get bug reports.
Initially, I'm using the integrals set I got from Tim Daly at the Axiom
project. His are from the Schaum's integral tables. He has a total of
25 separate files. I've finished the first file. So, I'm not checking
those results, just performance. I will be checking both Maxima and
Sympy
for correctness, though. I've already found one integral that Axiom and
Sympy get correct, but Maxima fails because it requests additional
information during the integration:
var('x,a,b,n')
f22 = (a*x+b)^n
aa = f22.integrate(x)
In fact, SymPy gets the same answer as Schaum's while FriCAS needs
a rewrite rule applied to the results to match Schaum's.
Cheers,
Tim.
---
Tim Lahey
PhD Candidate, Systems Design Engineering
University of Waterloo
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[sage-support] Re: Simplification/Rewrite Rules?
On Mon, Nov 24, 2008 at 6:17 PM, Tim Lahey [EMAIL PROTECTED] wrote:
On Nov 24, 2008, at 9:05 PM, William Stein wrote:
I can easily run timing comparisons between maxima and FriCAS, but
because
of how sympy does things (with its separate variables), I'll have
to run
them separately. Comparing maxima and FriCAS, the timings are pretty
close on
both for most of the ones I've tried. A few were much longer in
FriCAS.
I have a pretty long list of integrals to go through and I've only
done 16.
Many thanks for doing this!
William
No problem. Once it's done it should help as automated tests for both
monitoring performance and correctness. I'll be happy to donate them
to the cause. It's going to take a while.
The timeit routines give results that look like:
5 loops, best of 3: 50 ms per loop
Does anybody have something to pull out the specific time (50ms)?
In Sage-3.2 somebody (thanks!) nicely refactored the timeit code
somewhat, so that this is well supported. This is probably related
to the doctest improvements that mabshoff just mentioned.
Anyway, here is an example:
sage: from sage.misc.sage_timeit import sage_timeit
sage: a = sage_timeit('3^1',globals())
sage: a
625 loops, best of 3: 35.2 µs per loop
sage: type(a)
type 'instance'
sage: a.stats
(625, 3, 3, 35.214614868164062, '\xc2\xb5s')
sage:a.__repr__??
def __repr__(self):
return %d loops, best of %d: %.*g %s per loop % self.stats
The stats are:
(number, repeat, precision, best * scaling[order], units[order])
It would be nice if you contribute some new integration doctests or
something even before you have something massive and
comprehensive.
William
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