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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.

Build

Coercion

Commutative Algebra

Doctest

Documentation

Graphics

Interfaces

Linear Algebra

Miscellaneous

Modular Forms

Notebook

Number Theory

Optional Packages

Packages

Solaris

ReleaseTours/sage-3.2.3 (last edited 2020-05-03 18:36:32 by mkoeppe)