Hi Dima, On 2018-09-01, Dima Pasechnik <dimp...@gmail.com> wrote: > Sage does not need that broken and obsolete package, it can talk to an > instance of Macaulay2 (usually called M2) > in the PATH. See > http://doc.sagemath.org/html/en/reference/interfaces/sage/interfaces/macaulay2.html
I tried to find out how to install Macaulay2 on Ubuntu, and it seems to be a bit awkward, adding obscure repositories etc. I didn't install it, yet. And since the whole thing is eventually supposed to be part of my group cohomology package, I am a bit reluctant to rely on something that isn't optional but experimental. Also, I just tried frobby. My experiences: The frobby interface by default returns the multigraded Hilbert series. I consider it a bug that the coefficients of the multigraded series are the same as the domain of coefficients of the given ideal --- because apparently one needs to interprete the multigraded Hilbert series modulo 2, for otherwise the result is wrong: sage: R.<x,y,z,w>=QQ[] sage: I = R*[x^3,x^2*y,x*z] sage: D = ~PowerSeriesRing(QQ,'x,y,z,w')((x-1)*(y-1)*(z-1)*(w-1)) sage: frobby.hilbert(I) x^3*y*z + x^3*y + x^3*z + x^2*y*z + x^3 + x^2*y + x*z + 1 sage: (frobby.hilbert(I)*D)[:4] 1 + x + y + z + w + x^2 + x*y + 2*x*z + x*w + y^2 + y*z + y*w + z^2 + z*w + w^2 + 2*x^3 + 2*x^2*y + 2*x^2*z + x^2*w + x*y^2 + 2*x*y*z + x*y*w + 2*x*z^2 + 2*x*z*w + x*w^2 + y^3 + y^2*z + y^2*w + y*z^2 + y*z*w + y*w^2 + z^3 + z^2*w + z*w^2 + w^3 + O(x, y, z, w)^12 So, as you can see, the monomial x*z has coefficient 2, but should have coefficient 0, as it is not a standard monomial. Or do I misinterprete it? I tested it on the example that I currently care most about: It is the mod-2 cohomology ring of a certain finite group; the cohomology has a minimal generating set of 78 generators out to degree 11, and the quotient relations form an ideal that has a minimal generating set of 2589 elements of maximal degree 22 (the Krull dimension is 5). In order to compute its so-called filter degree type, I need to compute the first Hilbert series of several quotients of that ring. The following happens when I trie to compute the Hilbert series of the relation ideal: - Singular's "hilb(Rels,1,ringweights(basering))" fails with an int overflow. - My implementation (basically an implementation of a well known algorithm using singular-via-pexpect to deal with the ideals) needs about one minute to compute the first Hilbert series, using about 20% of my computer's memory. - Frobby needed substantially more than one minute, and then I needed to interrupt it because it was eating up 70% of my computer's memory. And even if it were finishing, I still needed to convert the multigraded series (that apparently ought to be over ZZ/2) into a univariate series (over ZZ). Can you tell me how to transform a Singular ideal into LattE or CoCoA, so that I can try it, too? Best regards, Simon -- 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.
