Hi Simon, Thank you for your insight, and let me state that I find InfinitePolynomialRing useful in combinatorics to deal with (truncated) multivariate generating functions with apriori unknown number of variables, and so basic operations (such as differentiation) on polynomials would be very welcome here. Btw, is there InfinitePowerSeriesRing or alike available by any chance?
>From what you said, I think it should be easy to fix (making it work) at least ISSUE#2 -- one just needs to extend the underlying finite PolynomialRing with the differentiating variable(s) before delegating the actual differentiation to it. I think as a temporary fix for ISSUE#2, one can create an polynomial being a sum of all variables that may ever appear later to make sure that the underlying PolynomialRing knows about them all upfront. Regards, Max On Wednesday, September 8, 2021 at 10:30:21 AM UTC-4 Simon King wrote: > Hi Max, > > On 2021-09-08, Max Alekseyev <max...@gmail.com> wrote: > > I've found a couple of issues with differentiation in > InfinitePolynomialRing > > > > (ISSUE #1) Differentiation fails in InfinitePolynomialRing(QQ), e.g. the > > following code > > > > R.<x> = InfinitePolynomialRing(QQ) > > f = x[0] + x[1] > > derivative(f,x[1]) > > > > gives an error > > TypeError: Argument 'var' has incorrect type (expected > > > sage.rings.polynomial.multi_polynomial_libsingular.MPolynomial_libsingular, > > got InfinitePolynomial_dense) > > Sure, that's not supposed to work. InfinitePolynomialRing knows nothing > about symbolic calculus. That would be the job of symbolic expressions. > > > However, if we replace QQ with something more sophisticated, > > differentiation starts suddenly work: > > > > K.<u> = PolynomialRing(QQ) > > R.<x> = InfinitePolynomialRing(K) > > f = x[0] + x[1] > > derivative(f,x[1]) > > > > gives 1 as expected. > > Interesting. That's not supposed to work either. > > A possible explanation: InfinitePolynomialRing uses a *finite* > polynomial ring under the hood, which is extended when a generator > is requested with a higher index. > > If I recall correctly, methods that aren't explicitly implemented for > elements of InfinitePolynomialRing are forwarded to the underlying finite > polynomials. That could explain why it works at all. But I don't know > why it only works if the base ring is a polynomial ring. > > > (ISSUE #2) Slightly modifying the second example above: > > > > K.<u> = PolynomialRing(QQ) > > R.<x> = InfinitePolynomialRing(K) > > f = x[0] + x[1] > > derivative(f,x[2]) > > > > we get an error > > ValueError: cannot differentiate with respect to x_2 > > > > However, if we try to execute the same 'derivative(f,x[2])' command > again > > in the same Sage session, it will succeed. > > > So, it appears that if we differentiate with respect to a new variable, > > which was not accessed before, then differentiation would fail. I hope > this > > is not an intended behavior and can be easily fixed. > > When you create f, then it is implemented based on a ring with two > variables > x0 and x1. Thus, a method of an element of K['x0','x1'] is called, on > x[2], which K['x0','x1'] doesn't know about. But by calling x[2], the > underlying finite ring in the meantime is extended to K['x0', 'x1', > 'x2'], thus, when you try to differentiate a second time, it is done in > a ring in which x2 is known. > > At least that's my guess. > > As I said, differentiation is not supposed to work. But I (as original > author) don't fully understand *why* it sometimes works and how to fix > that (by "fix", I mean "make it not work and, in the best case, suggest > to convert to a symbolic expression"). > > InfinitePolynomialRing was created for a very narrow purpose, namely > computing symmetric Gröbner bases. In particular, calculus was not in > the scope. If someone wants to extend its functionality, I wouldn't > mind though. > > 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 view this discussion on the web visit https://groups.google.com/d/msgid/sage-support/f87e8c26-1bca-4958-8ad1-774fcfc0258dn%40googlegroups.com.
