Changeset 06df101 in git for libpolys/polys/ext_fields/transext.h
 Timestamp:
 Jul 6, 2011, 4:41:07 PM (12 years ago)
 Branches:
 (u'spielwiese', '0d6b7fcd9813a1ca1ed4220cfa2b104b97a0a003')
 Children:
 6c19d854882ab99fd19b9b972a32606106c2f2ee
 Parents:
 2d3091c7bb239cd4787574560ab475ac88621da7
 gitauthor:
 Frank Seelisch <seelisch@mathematik.unikl.de>20110706 16:41:07+02:00
 gitcommitter:
 Mohamed Barakat <mohamed.barakat@rwthaachen.de>20111109 12:39:12+01:00
 File:

 1 edited
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libpolys/polys/ext_fields/transext.h
r2d3091c r06df101 9 9 * transcendental variables t_1, ..., t_s, where s >= 1. 10 10 * 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. 13 35 */ 14 36
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