On Fri, Sep 14, 2018 at 9:00 AM, Peter Luschny <peter.lusc...@gmail.com> wrote: > How can I speed up this computation? > > H.<i,j,k> = QuaternionAlgebra(SR, -1, -1)
Do NOT use SR. Instead use QQ(x). Then it is 100x faster than Mathematica... R.<x> = QQ[] K = R.fraction_field() H.<i,j,k> = QuaternionAlgebra(K, -1, -1) def Q(a, b, c, d): return H(a + b*i + c*j + d*k) def P(n): return Q(x+1,1,1,1)*P(n-1) if n > 0 else Q(1,0,0,0) def p(n): return P(n)[0].numerator().list() for n in (0..20): print [n], p(n) This takes 0.05s walltime. See https://share.cocalc.com/share/4a5f0542-5873-4eed-a85c-a18c706e8bcd/support/2018-09-14-091151-quat.sagews?viewer=share Also, if you want to actually push things further, note that your function P depends on all smaller values of P, so you could make this massively faster by making P use @cached_function, like this: R.<x> = QQ[] K = R.fraction_field() H.<i,j,k> = QuaternionAlgebra(K, -1, -1) def Q(a, b, c, d): return H(a + b*i + c*j + d*k) @cached_function def P(n): return Q(x+1,1,1,1)*P(n-1) if n > 0 else Q(1,0,0,0) def p(n): return P(n)[0].numerator().list() for n in (0..20): print [n], p(n) This takes 0.01s walltime, and will work for 20 replaced by a much larger number. Read about this cached_function decorator: http://doc.sagemath.org/html/en/reference/misc/sage/misc/cachefunc.html > def Q(a, b, c, d): return H(a + b*i + c*j + d*k) > def P(n): return Q(x+1,1,1,1)*P(n-1) if n > 0 else Q(1,0,0,0) > def p(n): return P(n)[0].list() > for n in (0..20): print [n], p(n) > > [0] [1] > [1] [1, 1] > [2] [-2, 2, 1] > [3] [-8, -6, 3, 1] > [4] [-8, -32, -12, 4, 1] > [5] [16, -40, -80, -20, 5, 1] > [6] [64, 96, -120, -160, -30, 6, 1] > ... > > With Mathematica this takes 6 sec, with Sage it takes > hours, (in fact I interrupted after n=15). > > Thanks, Peter > > > -- > You received this message because you are subscribed to the Google Groups > "sage-support" group. > To unsubscribe from this group and stop receiving emails from it, send an > email to sage-support+unsubscr...@googlegroups.com. > To post to this group, send email to sage-support@googlegroups.com. > Visit this group at https://groups.google.com/group/sage-support. > 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-support" group. To unsubscribe from this group and stop receiving emails from it, send an email to sage-support+unsubscr...@googlegroups.com. To post to this group, send email to sage-support@googlegroups.com. Visit this group at https://groups.google.com/group/sage-support. For more options, visit https://groups.google.com/d/optout.
