519
Comment:
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1699
Summarize tickets #3678, #4218, #4494, #4899
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* Powers of polynomial variables (Alex Ghitza) -- Report an error message when a determinate of a (multivariate) polynomial is raised to a fractional exponent. Previously, raising a polynomial determinate to a fractional power has the effect of rounding the exponent to an integer. As yet, fractional powers is not supported. * Extensions of finite fields (Alex Ghitza) -- Implements methods {{{random_element()}}} and {{{order()}}} for quotients of polynomial rings. The method {{{random_element()}}} returns the number of elements of a quotient ring, and {{{order()}}} returns a random element of a quotient ring. * Conjugates for integer, rational and real numbers (Alex Ghitza) -- Implements trivial {{{conjugate()}}} methods for elements over the integers, rationals, and reals. Conjugates work (trivially) for matrices over rings that embed canonically into the real numbers. * Square roots of Galois field elements (John Cremona, William Stein) -- Improve the square root of an element of a Galois field {{{GF(2^e)}}}, where {{{e > 15}}}. Previously, this works fine except for the square root of 1, where 1 is an element of {{{GF(2^e)}}} for {{{e > 15}}}. |
Sage 3.2.3 Release Tour
Sage 3.2.3 was released on FIXME. For the official, comprehensive release notes, see sage-3.2.3.txt.
Algebra
- Powers of polynomial variables (Alex Ghitza) -- Report an error message when a determinate of a (multivariate) polynomial is raised to a fractional exponent. Previously, raising a polynomial determinate to a fractional power has the effect of rounding the exponent to an integer. As yet, fractional powers is not supported.
Extensions of finite fields (Alex Ghitza) -- Implements methods random_element() and order() for quotients of polynomial rings. The method random_element() returns the number of elements of a quotient ring, and order() returns a random element of a quotient ring.
Conjugates for integer, rational and real numbers (Alex Ghitza) -- Implements trivial conjugate() methods for elements over the integers, rationals, and reals. Conjugates work (trivially) for matrices over rings that embed canonically into the real numbers.
Square roots of Galois field elements (John Cremona, William Stein) -- Improve the square root of an element of a Galois field GF(2^e), where e > 15. Previously, this works fine except for the square root of 1, where 1 is an element of GF(2^e) for e > 15.
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