On Sun, 2 Sep 2018, 15:15 Simon King, <simon.k...@uni-jena.de> wrote:
> > Since this post summarises replies to various posts in this thread and to > an off-list message, I am making this a reply to the top of the thread. > It probably should get subject line "sorry state of basic open-source commutative altebra" :-) > Objective: As a *small* part of some group cohomology computations, I need > to compute the first Hilbert series of certain homogeneous ideals in > graded-commutative rings, with respect to given degree weights of the > ring generators. > > Problem: The data are in Singular, thus, Singular is the natural > candidate to do the job. Unfortunately, some of my rings have too many > variables, which means that Singular's "hilb(...,1)" command suffers > from an int overflow. > It would be good to submit a Singular bug report with an example at https://github.com/Singular/Sources It's silly to see an overflow in such a case. Do you understand where exactly you are hitting intvec limitations: https://www.singular.uni-kl.de/Manual/4-0-3/sing_455.htm#SEC494 Potential ways out: I am listing potential approaches to achieve the > objective. In all cases I tell what is good or bad in that approach, in > some cases I need more support or answers. > > 1. Create an implementation in Sage, that does the ideal computations in > Singular-via-pexpect and does the bigint computations in Sage. > Good: It works even in big examples. > Bad: In the cases in which Singular works, Singular is a lot faster. > Bad - more code to maintain... :-) 2. Create an implementation in Singular that doesn't use intvec (which > has a 32 bit limitation) but a different data structure, or get the > Singular developers to do so. > Bad: I didn't try to implement it myself; Singular devs didn't > answer yet. > we should try - it could be that the fix is very easy. In particular that 32-bit limitations are from almost obsolete 32-bit processors, IMHO. Using 'long' instead would remedy a lot... 3. Use frobby. > Good: It works in small examples. > Bad: On some big example, it is slower than 1. and fails due to > memory problems. And one would need a conversion from multigraded > to univariate Hilbert series. > ==> Frobby is no serious option. > yep, frobby is not maintained, too... 4. Use LattE/normaliz. > Bad: I have no idea how. > 5. Use Macaulay2 > Bad: (a) The experimental spkg is broken, it won't install. > experimental package is dead, IMHO. Creating special gc-aware versions of several Sage packages and in addition adding more dependincies needed by M2 is a lot of hard work (if specific Linux distos have trouble packaging it properly, this rings a bell...) (b) The installation instructions for Ubuntu on the project > pages are rather verbose and require adding obscure > repositories. > (c) Installation from sources (release-1.12 from github): > i. Although I installed all dependencies listed in the > INSTALL file, "make" fails because additionally givaro > is required. And 'export MAKE="make -j3"' makes Macaulay2 > believe that gnu make is not installed. > ii. I tried installation in a Sage shell, as givaro is > in Sage. However, "make" fails as follows: > /home/king/Projekte/Macaulay2/M2/M2/usr-host/include/fflas-ffpack/fflas/fflas_ftrsm_src.inl:279:27: > error: ‘openblas_set_num_threads’ was not declared in this scope > openblas_set_num_threads(__FFLASFFPACK_OPENBLAS_NUM_THREADS); > ^ > cc1plus: warning: unrecognized command line option ‘-Wno-mismatched-tags’ > ../../include/config.Makefile:226: recipe for target 'interface.o' failed > make[2]: *** [interface.o] Error 1 > make[2]: Leaving directory > '/home/king/Projekte/Macaulay2/M2/M2/Macaulay2/d' > Makefile:20: recipe for target 'all-in-d' failed > make[1]: *** [all-in-d] Error 2 > ==> Currently Macaulay2 is no option. > 6. Use CoCoA(Lib). > Good: "sage -i cocoalib" works. CoCoA is known for a focus on Hilbert > driven computations, thus, is supposed to be good for the job. > Bad: (a) Apparently the optional package only provides the CoCoA > library (plus headers, of course), but no Cython bindings. > (b) The cocoa documentation is not installed in the proper > place, but in SAGE_LOCAL/include/CoCoA/doc. And this is the > full documentation of the hilbert() function (I am not joking): > """ > hey!!! write something more! > > I'm just using the C code I wrote for CoCoA-4. It will be > entirely rewritten in C++ > > The only usable function is > > RingElem HilbertNumeratorMod(PolyRing HSRing, ideal I); > > but it works ONLY if I is a monomial ideal. HSRing is the > ring where the Hilbert Series Numerator should live. > """ > ==> CoCoALib seriously lacks documentation and has no Sage bindings, and > thus currently it is no option. > CoCoAlib is essentially a two-person project. I know John Abbott, one of the two, reasonably well, could we get him involved? > > QUESTIONS: > - Are people trying to create cython bindings for CoCoALib? > - How do I use LattE or normaliz? Perhaps Matthias Koeppe knows? I cc to him. Say: > sage: R.<x,y,z,w>=QQ[] > sage: I = R*[x^3,x^2*y,x*z] > And now how can I compute the first Hilbert series, with given degrees > for x,y,z? > - How to make Macaulay2? > The core of M2 is essentially a two-person project. They are very approachable, but often busy. Try their github... (I have mixed experience with building M2. IMHO they make it harder by not using automake...) Cheers, Dima > 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. > -- 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.
