**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. 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 It's even possible the Singular developers aren't naive. **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 [email protected]. > To post to this group, send email to [email protected]. > 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 [email protected]. To post to this group, send email to [email protected]. Visit this group at https://groups.google.com/group/sage-devel. For more options, visit https://groups.google.com/d/optout.
