[sage-devel] Re: evaluation of polynomials in several variables
I opened a separate ticket #10946 for this issue. Hopefully someone with better knowledge of keywords, evaluations, polynomials, singulars and such will find a way to solve it. Thanks for the comments. Chris. -- To post to this group, send an email to sage-devel@googlegroups.com To unsubscribe from this group, send an email to sage-devel+unsubscr...@googlegroups.com For more options, visit this group at http://groups.google.com/group/sage-devel URL: http://www.sagemath.org
[sage-devel] Re: evaluation of polynomials in several variables
> Given f in R[x,y], I think f(x=a, y=b) should do exactly the same > thing as f(a,b). The parent should be the same as R.base_ring()(0) + a > + b. +1 > The difficult case is what to do for f(x=5). Should that be the same > as f(x=5, y=y) or a univariate polynomial? I would certainly read f(x=5) as short for f(x=5,y=y). Hence (by the same reasoning as above) I would expect a bivariate polynomial as answer. -- To post to this group, send an email to sage-devel@googlegroups.com To unsubscribe from this group, send an email to sage-devel+unsubscr...@googlegroups.com For more options, visit this group at http://groups.google.com/group/sage-devel URL: http://www.sagemath.org
[sage-devel] Re: evaluation of polynomials in several variables
> Given f in R[x,y], I think f(x=a, y=b) should do exactly the same > thing as f(a,b). The parent should be the same as R.base_ring()(0) + a > + b. +1 > The difficult case is what to do for f(x=5). Should that be the same > as f(x=5, y=y) or a univariate polynomial? I would certainly read f(x=5) as short for f(x=5, y=y), hence (by the same reasoning as above) expect a bivariate polynomial as answer. -- To post to this group, send an email to sage-devel@googlegroups.com To unsubscribe from this group, send an email to sage-devel+unsubscr...@googlegroups.com For more options, visit this group at http://groups.google.com/group/sage-devel URL: http://www.sagemath.org
[sage-devel] Re: evaluation of polynomials in several variables
> > No I am against changing this. For two reasons, when working with > > polynomials in variable names liks "k", "p". It is not always easy to > > remember which was the first and which was the second variable. Then > > it is very handy to pass keywords for evaluation - but still to expect > > a base_ring element. > > +1 (but where is the second reason?) Well, given that my message got posted three times, there are 3 reasons already :) The other (which I forgot to include in the end) is that it would probably imply a lot of changes throughout the full sage code and many people might be used to the syntax. > > Instead I think we should check that all variables are evaluated. This > > would be consistent with the call f(2,3) which screams when the number > > of variables is not correct. Even better, we could check if the result > > is really a ring element after substitution, which is easy to do. E.g. > > I would allow > > f = x*(x+y) > > f(x=0) > > but not > > f(x=1) > > I don't like this approach. I would allow both f(x=0) and f(x=1), in > both cases returning a univariate polynomial. Mathematically I fully agreee with you. I would expect an element of R[x,y]/(x) = R[x,y]/(x-1) = R[y] in both cases. But if we want to stick to the principle that the type should be the same for all returned answers, we would have to do f.subs() gives back an element of the parent of f and f(..) gives back an element of the base-ring of f and hence it would only be allowed to be used in case the evaluation really yields an element in there. My suggestion above is based on the fact that it is very easy to check if the result is in the base_ring. Maybe it is just as easy to check if the length of the keywords is equal to the number of variables. Chris. -- To post to this group, send an email to sage-devel@googlegroups.com To unsubscribe from this group, send an email to sage-devel+unsubscr...@googlegroups.com For more options, visit this group at http://groups.google.com/group/sage-devel URL: http://www.sagemath.org
[sage-devel] Re: evaluation of polynomials in several variables
Hi Chris, On 14 Mrz., 23:31, chris wuthrich wrote: > I hope we agree that evaluation (meaning evaluation of all variables > by some elements in a ring) should yield an element of the ring. I > don't mind if subs should give back a polynomial in all cases. > > [Aside: Strangely this is not the case for symbolic expressions. I am > sure there must have been a discussion on this and I missed it. E.g. > f(x) = sin(x) > f(1.).floor() > does not work.] Well, f(1.) is in fact contained in the base ring of the parent of f, so everything is formally fine: sage: f.parent() Callable function ring with arguments (x,) sage: f.parent().base_ring() Symbolic Ring sage: f(1.).parent() Symbolic Ring > No I am against changing this. For two reasons, when working with > polynomials in variable names liks "k", "p". It is not always easy to > remember which was the first and which was the second variable. Then > it is very handy to pass keywords for evaluation - but still to expect > a base_ring element. +1 (but where is the second reason?) > Instead I think we should check that all variables are evaluated. This > would be consistent with the call f(2,3) which screams when the number > of variables is not correct. Even better, we could check if the result > is really a ring element after substitution, which is easy to do. E.g. > I would allow > f = x*(x+y) > f(x=0) > but not > f(x=1) I don't like this approach. I would allow both f(x=0) and f(x=1), in both cases returning a univariate polynomial. Cheers, Simon -- To post to this group, send an email to sage-devel@googlegroups.com To unsubscribe from this group, send an email to sage-devel+unsubscr...@googlegroups.com For more options, visit this group at http://groups.google.com/group/sage-devel URL: http://www.sagemath.org
[sage-devel] Re: evaluation of polynomials in several variables
Hi Robert, On 14 Mrz., 23:29, Robert Bradshaw wrote: > > Yes, but the fact that f(2,3) has a different parent than f(x=2,y=3) > > has a high probability of being troublesome. > > Given f in R[x,y], I think f(x=a, y=b) should do exactly the same > thing as f(a,b). The parent should be the same as R.base_ring()(0) + a > + b. +1. I think that f.__call__(*args,**kwds) of a polynomial f in variables x,y,z should behave like a Python function of signature f(x,y,z,**kwds). In particular, f(1,2,z=3, foo='bar') should do exactly the same as f(1,2,3,foo='bar'). Note that currently the situation is not very consistent. On the one hand, we already have the behaviour that you wish: sage: R. = ZZ[] sage: P. = QQ[] sage: f = x+y sage: parent(f(a,b)) Multivariate Polynomial Ring in a, b over Rational Field sage: parent(f(x=a,y=b)) Multivariate Polynomial Ring in a, b over Rational Field sage: parent(f(1,b)) Multivariate Polynomial Ring in a, b over Rational Field But on the other hand, we have the inconsistency that started this thread: sage: parent(f(x=1,y=2)) Multivariate Polynomial Ring in x, y over Integer Ring sage: parent(f(1,2)) Integer Ring > The difficult case is what to do for f(x=5). Should that be the same > as f(x=5, y=y) or a univariate polynomial? I tend to believe that if you evaluate k variables of a polynomial with n variables then the result should be a polynomial with n-k variables. That having said, I wonder whether one should really make a special case for k==n: Should the result be an element of the base ring, or should it actually be a polynomial in zero variables? Cheers, Simon -- To post to this group, send an email to sage-devel@googlegroups.com To unsubscribe from this group, send an email to sage-devel+unsubscr...@googlegroups.com For more options, visit this group at http://groups.google.com/group/sage-devel URL: http://www.sagemath.org
[sage-devel] Re: evaluation of polynomials in several variables
I hope we agree that evaluation (meaning evaluation of all variables by some elements in a ring) should yield an element of the ring. I don't mind if subs should give back a polynomial in all cases. [Aside: Strangely this is not the case for symbolic expressions. I am sure there must have been a discussion on this and I missed it. E.g. f(x) = sin(x) f(1.).floor() does not work.] > I agree that thats the only valid question here: is f(x=2,y=3) substitution > or evaluation? The call syntax suggests evaluation, but keywords allow you > to only substitute some variables. I'm tempted to say that since its not > obvious we shouldn't have the function at all, that is, don't allow keyword > arguments in _call_. No I am against changing this. For two reasons, when working with polynomials in variable names liks "k", "p". It is not always easy to remember which was the first and which was the second variable. Then it is very handy to pass keywords for evaluation - but still to expect a base_ring element. Instead I think we should check that all variables are evaluated. This would be consistent with the call f(2,3) which screams when the number of variables is not correct. Even better, we could check if the result is really a ring element after substitution, which is easy to do. E.g. I would allow f = x*(x+y) f(x=0) but not f(x=1) Chris. -- To post to this group, send an email to sage-devel@googlegroups.com To unsubscribe from this group, send an email to sage-devel+unsubscr...@googlegroups.com For more options, visit this group at http://groups.google.com/group/sage-devel URL: http://www.sagemath.org
Re: [sage-devel] Re: evaluation of polynomials in several variables
On Fri, Mar 11, 2011 at 8:42 AM, Simon King wrote: > On 11 Mrz., 17:24, Volker Braun wrote: >> Substitution should always try to return the same type (i.e. same parent) if >> possible. Anything else will just be a constant source of bugs where your >> code works with generic polynomial input, but not for constants. > > Yes, but the fact that f(2,3) has a different parent than f(x=2,y=3) > has a high probability of being troublesome. Given f in R[x,y], I think f(x=a, y=b) should do exactly the same thing as f(a,b). The parent should be the same as R.base_ring()(0) + a + b. The difficult case is what to do for f(x=5). Should that be the same as f(x=5, y=y) or a univariate polynomial? - Robert -- To post to this group, send an email to sage-devel@googlegroups.com To unsubscribe from this group, send an email to sage-devel+unsubscr...@googlegroups.com For more options, visit this group at http://groups.google.com/group/sage-devel URL: http://www.sagemath.org
[sage-devel] Re: evaluation of polynomials in several variables
I hope we agree that evaluation (meaning evaluation of all variables by some elements in a ring) should yield an element of the ring. I don't mind if subs should give back a polynomial in all cases. [Aside: Strangely this is not the case for symbolic expressions. I am sure there must have been a discussion on this and I missed it. E.g. f(x) = sin(x) f(1.).floor() does not work.] > I agree that thats the only valid question here: is f(x=2,y=3) substitution > or evaluation? The call syntax suggests evaluation, but keywords allow you > to only substitute some variables. I'm tempted to say that since its not > obvious we shouldn't have the function at all, that is, don't allow keyword > arguments in _call_. No I am against changing this. For two reasons, when working with polynomials in variable names liks "k", "p". It is not always easy to remember which was the first and which was the second variable. Then it is very handy to pass keywords for evaluation - but still to expect a base_ring element. Instead I think we should check that all variables are evaluated. This would be consistent with the call f(2,3) which screams when the number of variables is not correct. Even better, we could check if the result is really a ring element after substitution, which is easy to do. E.g. I would allow f = x*(x+y) f(x=0) but not f(x=1) Chris. -- To post to this group, send an email to sage-devel@googlegroups.com To unsubscribe from this group, send an email to sage-devel+unsubscr...@googlegroups.com For more options, visit this group at http://groups.google.com/group/sage-devel URL: http://www.sagemath.org
[sage-devel] Re: evaluation of polynomials in several variables
I hope we agree that evaluation (meaning evaluation of all variables by some elements in a ring) should yield an element of the ring. I don't mind if subs should give back a polynomial in all cases. [Aside: Strangely this is not the case for symbolic expressions. I am sure there must have been a discussion on this and I missed it. E.g. f(x) = sin(x) f(1.).floor() does not work.] > I agree that thats the only valid question here: is f(x=2,y=3) substitution > or evaluation? The call syntax suggests evaluation, but keywords allow you > to only substitute some variables. I'm tempted to say that since its not > obvious we shouldn't have the function at all, that is, don't allow keyword > arguments in _call_. No I am against changing this. For two reasons, when working with polynomials in variable names liks "k", "p". It is not always easy to remember which was the first and which was the second variable. Then it is very handy to pass keywords for evaluation - but still to expect a base_ring element. Instead I think we should check that all variables are evaluated. This would be consistent with the call f(2,3) which screams when the number of variables is not correct. Even better, we could check if the result is really a ring element after substitution, which is easy to do. E.g. I would allow f = x*(x+y) f(x=0) but not f(x=1) Chris. -- To post to this group, send an email to sage-devel@googlegroups.com To unsubscribe from this group, send an email to sage-devel+unsubscr...@googlegroups.com For more options, visit this group at http://groups.google.com/group/sage-devel URL: http://www.sagemath.org
[sage-devel] Re: evaluation of polynomials in several variables
I agree that thats the only valid question here: is f(x=2,y=3) substitution or evaluation? The call syntax suggests evaluation, but keywords allow you to only substitute some variables. I'm tempted to say that since its not obvious we shouldn't have the function at all, that is, don't allow keyword arguments in _call_. -- To post to this group, send an email to sage-devel@googlegroups.com To unsubscribe from this group, send an email to sage-devel+unsubscr...@googlegroups.com For more options, visit this group at http://groups.google.com/group/sage-devel URL: http://www.sagemath.org
[sage-devel] Re: evaluation of polynomials in several variables
On 11 Mrz., 17:24, Volker Braun wrote: > Substitution should always try to return the same type (i.e. same parent) if > possible. Anything else will just be a constant source of bugs where your > code works with generic polynomial input, but not for constants. Yes, but the fact that f(2,3) has a different parent than f(x=2,y=3) has a high probability of being troublesome. -- To post to this group, send an email to sage-devel@googlegroups.com To unsubscribe from this group, send an email to sage-devel+unsubscr...@googlegroups.com For more options, visit this group at http://groups.google.com/group/sage-devel URL: http://www.sagemath.org
[sage-devel] Re: evaluation of polynomials in several variables
Substitution should always try to return the same type (i.e. same parent) if possible. Anything else will just be a constant source of bugs where your code works with generic polynomial input, but not for constants. -- To post to this group, send an email to sage-devel@googlegroups.com To unsubscribe from this group, send an email to sage-devel+unsubscr...@googlegroups.com For more options, visit this group at http://groups.google.com/group/sage-devel URL: http://www.sagemath.org
