Ignore:
Timestamp:
Jul 6, 2011, 4:41:07 PM (13 years ago)
Author:
Frank Seelisch <seelisch@…>
Branches:
(u'fieker-DuVal', '117eb8c30fc9e991c4decca4832b1d19036c4c65')(u'spielwiese', '79dfb9a6d258bfeb991428bdb25b8f55e9e809b2')
Children:
6c19d854882ab99fd19b9b972a32606106c2f2ee
Parents:
2d3091c7bb239cd4787574560ab475ac88621da7
git-author:
Frank Seelisch <seelisch@mathematik.uni-kl.de>2011-07-06 16:41:07+02:00
git-committer:
Mohamed Barakat <mohamed.barakat@rwth-aachen.de>2011-11-09 12:39:12+01:00
Message:
handled nested fractions (when over Q), found bug in longrat.cc (see coeffs_test.h:507)
File:
1 edited

Legend:

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  • libpolys/polys/ext_fields/transext.h

    r2d3091c r06df101  
    99*           transcendental variables t_1, ..., t_s, where s >= 1.
    1010*           Denoting the implemented coeffs object by cf, then these numbers
    11 *           are represented as quotients of polynomials in the polynomial
    12 *           ring K[t_1, .., t_s] represented by cf->extring.
     11*           are represented as quotients of polynomials living in the
     12*           polynomial ring K[t_1, .., t_s] represented by cf->extring.
     13*
     14*           An element of K(t_1, .., t_s) may have numerous representations,
     15*           due to the possibility of common polynomial factors in the
     16*           numerator and denominator. This problem is handled by a
     17*           cancellation heuristic: Each number "knows" its complexity
     18*           which is 0 if and only if common factors have definitely been
     19*           cancelled, and some positive integer otherwise.
     20*           Each arithmetic operation of two numbers with complexities c1
     21*           and c2 will result in a number of complexity c1 + c2 + some
     22*           penalty (specific for each arithmetic operation; see constants
     23*           in the *.h file). Whenever the resulting complexity exceeds a
     24*           certain threshold (see constant in the *.h file), then the
     25*           cancellation heuristic will call 'factory' to compute the gcd
     26*           and cancel it out in the given number. (This definite cancel-
     27*           lation will also be performed at the beginning of ntWrite,
     28*           ensuring that any output is free of common factors.
     29*           For the special case of K = Q (i.e., when computing over the
     30*           rationals), this definite cancellation procedure will also take
     31*           care of nested fractions: If there are fractional coefficients
     32*           in the numerator or denominator of a number, then this number
     33*           is being replaced by a quotient of two polynomials over Z, or
     34*           - if the denominator is a constant - by a polynomial over Q.
    1335*/
    1436
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