Ticket #6315: trac_6315-part2.patch

File trac_6315-part2.patch, 2.3 KB (added by was, 8 years ago)
  • doc/en/bordeaux_2008/birds_other.rst

    # HG changeset patch
    # User William Stein <wstein@gmail.com>
    # Date 1314086654 25200
    # Node ID 163bbb17e4a31bc94ede007aa62bb53928f0c979
    # Parent  005cedfeed1cb3b214b0ef4946cd9b2d2c8008e6
    trac 6315 - part 2: optional doctest failure -- caused by mistakes in lectures on number theory rst book
    
    diff --git a/doc/en/bordeaux_2008/birds_other.rst b/doc/en/bordeaux_2008/birds_other.rst
    a b  
    221221---------------------------------------
    222222
    223223Sage uses Bill Hart and David Harvey's GPL'd Flint C library for
    224 arithmetic in :math:`\ZZ[x]`. Its main claim to fame is that it
    225 is the world's fastest for polynomial multiplication, e.g., in the
    226 benchmark below it is 3 times faster than NTL and twice as fast as
    227 Magma. Behind the scenes it contains some carefully tuned discrete
    228 Fourier transform code (which I know nearly nothing about).
     224arithmetic in :math:`\ZZ[x]`. Its main claim to fame is that it is the
     225world's fastest for polynomial multiplication, e.g., in the benchmark
     226below it is faster than NTL and Magma on some systems (though such
     227benchmarks of course change as software improves).  Behind the scenes
     228Flint contains some carefully tuned discrete Fourier transform code.
    229229
    230230::
    231231
     
    242242    sage: ff = magma(f); gg = magma(g)  #optional - magma
    243243    sage: s = 'time v := [%s * %s : i in [1..10^5]];'%(ff.name(), gg.name()) #optional - magma
    244244    sage: magma.eval(s)     #optional - magma
    245     'Time: 17.120'
    246     sage: (17.120/10^5)*10^(6)    # convert to microseconds
    247     171.200000000000
     245    'Time: ...'
    248246
    249247Singular: Multivariate Polynomial Arithmetic
    250248--------------------------------------------
     
    252250Multivariate polynomial arithmetic in many cases uses Singular in
    253251library mode (due to Martin Albrecht), which is quite fast. For example,
    254252below we do the Fateman benchmark over the finite field of order
    255 32003.
     25332003, and compare the timing with Magma.
    256254
    257255::
    258256
     
    264262    sage: pp = magma(p); qq = magma(q) #optional - magma
    265263    sage: s = 'time w := %s*%s;'%(pp.name(),qq.name()) #optional - magma
    266264    sage: magma.eval(s) #optional - magma
    267     'Time: 1.480'
     265    'Time: ...'
    268266
    269 Notice that the multiplication takes about four times as long in
    270 Magma.
    271267