On Thursday, February 16, 2017 at 7:46:18 AM UTC, Dima Pasechnik wrote: > > > > On Thursday, February 16, 2017 at 6:59:04 AM UTC, William wrote: >> >> **Disclaimer: I consider myself very naive about computational >> commutative algebra, especially with floating point numbers. Dima, >> thanks for answering the question, but I think you are maybe jumping >> to wronc conclusions. See below. ** >> >> > The backend that actually does this computation is Singular, adn it >> does not do floating point numbers (in this context for sure). >> >> It's possible you are completely wrong. > > > well, not 100% :-) > I maintain that it's well-known how to get examples of Groebner bases of > ideas which will not be > representable with original precision---if you work in RR(n), for some n, > say. > I don't know what Singular does, but it cannot always work in limited > precision, full stop. >

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here you can see an example of Singular's Groebner basis computation returning a wrong result for polynomials with (low precision) floating point coeffcients: https://trac.sagemath.org/ticket/22387#comment:2 (and Sage 7.4 unable to make sense of this Singular output, but that's another story) > They also "do" Groebner bases for monomial orders for which termination is > not guaranteed... > > > >> Half the intro examples in >> the "make a ring" section of the Singular manual are floating point: >> https://www.singular.uni-kl.de/Manual/4-0-3/sing_29.htm >> >> ~$ singular >> SINGULAR / >> A Computer Algebra System for Polynomial Computations / version >> 4.1.0 >> 0< >> by: W. Decker, G.-M. Greuel, G. Pfister, H. Schoenemann \ Nov 2016 >> FB Mathematik der Universitaet, D-67653 Kaiserslautern \ >> > ring r = (real,50),(x,y,z),dp; >> > poly f=x3+yx2+3y+4; >> > qring q=std(maxideal(2)); >> > basering; >> // characteristic : 0 (real:50 digits, additional 50 digits) >> // number of vars : 3 >> // block 1 : ordering dp >> // : names x y z >> // block 2 : ordering C >> // quotient ring from ideal >> _[1]=z2 >> _[2]=yz >> _[3]=xz >> _[4]=y2 >> _[5]=xy >> _[6]=x2 >> > poly g=fetch(r, f); >> > g; >> x3+x2y+3*y+4 >> > 4.5*g; >> 4.5*x3+4.5*x2y+13.5*y+18 >> > reduce(g,std(0)); >> 3*y+4 >> > >> >> > I have opened https://trac.sagemath.org/ticket/22387 to deal with >> this. >> >> Please fix this, e.g., the ticket should point out that Sage appeared >> to work and provide results before. >> >> Just because you think it's nuts to use floating point numbers in the >> context of commutative algebra doesn't mean it is... It's a whole >> research area, e.g., >> >> http://link.springer.com/chapter/10.1007/978-3-540-87827-8_23 >> > > a paper from 2008 with one citation and one self-citation is not a "whole > research area", come on... > > >> >> It's even possible the Singular developers aren't naive. >> > > well, they are not - although they allow the users to shoot themselves in > all the feet around them. > > >> >> **Disclaimer: I consider myself very naive about computational >> commutative algebra, especially with floating point numbers.** >> >> William >> >> > >> > On Thursday, February 16, 2017 at 5:32:42 AM UTC, Matthew Macauley >> wrote: >> >> >> >> Typing the following: >> >> >> >> >> >> P.<x,y,z> = PolynomialRing(RR, 3, order='lex'); P >> >> I = ideal(x^2+y^2+z^2-1, x^2-y+z^2, x-z); I >> >> B = I.groebner_basis(); B >> >> >> >> >> >> gives a brutal error (type it into SageMathCell and you'll see). >> >> >> >> >> >> Seth Sullivant suggested that it's due to a roundoff error, because it >> >> works with fields such as "QQ" or "GF(3)", etc. That said, I am 99% >> sure >> >> that it's a relatively new error, because I have typed in those exact >> lines >> >> in previous semesters (it's from a HW problem that I assigned) and I >> haven't >> >> had any prior issues. >> > >> > -- >> > You received this message because you are subscribed to the Google >> Groups >> > "sage-devel" group. >> > To unsubscribe from this group and stop receiving emails from it, send >> an >> > email to sage-devel+...@googlegroups.com. >> > To post to this group, send email to sage-...@googlegroups.com. >> > Visit this group at https://groups.google.com/group/sage-devel. >> > For more options, visit https://groups.google.com/d/optout. >> >> >> >> -- >> William (http://wstein.org) >> > -- You received this message because you are subscribed to the Google Groups "sage-devel" group. To unsubscribe from this group and stop receiving emails from it, send an email to sage-devel+unsubscr...@googlegroups.com. To post to this group, send email to sage-devel@googlegroups.com. Visit this group at https://groups.google.com/group/sage-devel. For more options, visit https://groups.google.com/d/optout.