Module multi_polynomial_libsingular

File: sage/rings/polynomial/multi_polynomial_libsingular.pyx (starting at line 1)

Multivariate polynomials via libSINGULAR.

This file implements multivariate polynomials over certain fields via
the shared library interface to \SINGULAR and thus this implementation
is quite efficient. Supported base fields are $\QQ$ and $\F_{p^n}$.

However, in this shared library mode no support for the \Singular
interpreter is provided which means that only a basic subset of
\Singular's capabilities are available, i.e. those written in
C/C++. All of \Singular's capabilities are however available through
the pexpect interface and convenient conversion methods are provided.

AUTHORS:
    -- Martin Albrecht (2007-01): initial implementation
    -- Joel Mohler (2008-01): misc improvements, polishing

TODO:
   -- implement Real, Complex, NumberFields

TESTS:
    sage: P.<x,y,z> = QQ[]
    sage: loads(dumps(P)) == P
    True
    sage: loads(dumps(x)) == x
    True
    sage: P.<x,y,z> = GF(2^8,'a')[]
    sage: loads(dumps(P)) == P
    True
    sage: loads(dumps(x)) == x
    True
    sage: P.<x,y,z> = GF(127)[]
    sage: loads(dumps(P)) == P
    True
    sage: loads(dumps(x)) == x
    True

File: sage/rings/polynomial/multi_polynomial_libsingular.pyx (starting at line 1378)

inverse function for MPolynomialRing_libsingular.__reduce__

EXAMPLE:
    sage: P.<x,y> = PolynomialRing(QQ)
    sage: loads(dumps(P)) == P # indirect doctest
    True

File: sage/rings/polynomial/multi_polynomial_libsingular.pyx (starting at line 3957)

Deserialize an \code{MPolynomial_libsingular} object

INPUT:
    R -- the base ring
    d -- a Python dictionary as returned by MPolynomial_libsingular.dict

EXAMPLE:
    sage: P.<x,y> = PolynomialRing(QQ)
    sage: loads(dumps(x)) == x # indirect doctest
    True