I believe that mpz size is the right number of limbs for a FLINT fmpz. Bill.
2009/9/15 Robert Bradshaw <rober...@math.washington.edu>: > On Sep 14, 2009, at 3:47 PM, Sebastian Pancratz wrote: > >> Dear all, >> >> The implementation of QQ[] using FLINT is making lots of progress and >> it seems as if everything should be *much* faster than it is now. >> >> At the moment, I've got two questions. First one is about the design >> of the gcd method, and possibly affects other rings too. The second >> method is pretty implementation specific; I'd be grateful if someone >> with a good knowledge of FLINT and GMP could please have a look at it, >> because otherwise it might lead to some difficult bugs later. >> >> 1. >> >> Given rational polynomials a and b, what should gcd(a,b) return? The >> problem arises since the gcd is only defined up to rational units. I >> think the two sound options are either the monic normalisation, or a >> primitive integer polynomial with positive leading coefficient. >> >> Personally, I would be in favour of the second choice, because in the >> new implementation using FLINT, the polynomial is represented as an >> integer polynomial with a positive integer denominator coprime to the >> content of the numerator. If in a higher level block of code calls >> are made to gcd on a frequent basis, this would be faster than if gcd >> always had to return the monic version. >> >> Here are two other examples from SAGE (ignoring the case gcd(0,0) == >> 0): >> >> - Integers: Positive values. >> - Rationals: 1. >> - Integer polynomials: Polynomial with positive leading >> coefficient. >> - Polynomials over Z/nZ via FLINT: Not quite sure, except that gcd >> (a,0) == a and gcd(0,b) == b. By the way, working in (Z/27Z)[t], gcd >> (3*t+2, (3*t+2)*(t^3 + t - 1)) returns 1, which looks like a bug. In >> any case, enforcing gcd(a,0) == a leads to an inconsistent >> normalisation, so it might also be a good idea to think about what gcd >> should return working in (Z/nZ)[t]. >> >> I'd appreciate your input on how to normalise the gcd output. > > I would expect monic polynomials. > >> 2. >> >> One of the input methods for rational polynomials needs to take a SAGE >> Rational. In particular, it needs to initialise an integer of type >> fmpz_t and set it to the value of an integer of type mpz_t. The >> following block of code illustrates the problem (although it doesn't >> exactly like this appear in my code): >> >> # Assume that x a rational is of type mpq_t, properly initialised >> to some value. >> # Want to set den to the denominator of x. >> cdef fmpz_t den >> cdef unsigned long limbs >> limbs = mpz_size(mpq_denref(x)) # TODO: Check that fmpz and mpz >> limbs are compatible! >> den = fmpz_init(limbs) >> mpz_to_fmpz(den, mpq_denref(x)) >> >> I am afraid that this way, the call "fmpz_init(limbs)" might not >> allocate enough room for the value I want to store. I have worked >> with GMP (using C code) before, but this is the first time that I am >> working with FLINT and hence fmpz_t's. Can someone please confirm >> that the above code does the right thing, or let me know how to do >> this? > > Bill Hart would be the one who knows this. > > - Robert > > --~--~---------~--~----~------------~-------~--~----~ To post to this group, send an email to sage-devel@googlegroups.com To unsubscribe from this group, send an email to sage-devel-unsubscr...@googlegroups.com For more options, visit this group at http://groups.google.com/group/sage-devel URL: http://www.sagemath.org -~----------~----~----~----~------~----~------~--~---
