# Polynomial Interfaces to Singular¶

AUTHORS:

• Martin Albrecht <malb@informatik.uni-bremen.de> (2006-04-21)

• Robert Bradshaw: Re-factor to avoid multiple inheritance vs. Cython (2007-09)

Added non-prime finite fields to _singular_init_ (2012-1-22)

TESTS:

sage: R = PolynomialRing(GF(2**8,'a'),10,'x', order='invlex')
True
sage: P.<a,b> = PolynomialRing(GF(7), 2)
sage: f = (a^3 + 2*b^2*a)^7; f
a^21 + 2*a^7*b^14

class sage.rings.polynomial.polynomial_singular_interface.PolynomialRing_singular_repr

Implements methods to convert polynomial rings to Singular.

This class is a base class for all univariate and multivariate polynomial rings which support conversion from and to Singular rings.

class sage.rings.polynomial.polynomial_singular_interface.Polynomial_singular_repr

Implements coercion of polynomials to Singular polynomials.

This class is a base class for all (univariate and multivariate) polynomial classes which support conversion from and to Singular polynomials.

Due to the incompatibility of Python extension classes and multiple inheritance, this just defers to module-level functions.

sage.rings.polynomial.polynomial_singular_interface.can_convert_to_singular(R)

Returns True if this ring’s base field or ring can be represented in Singular, and the polynomial ring has at least one generator. If this is True then this polynomial ring can be represented in Singular.

The following base rings are supported: finite fields, rationals, number fields, and real and complex fields.

EXAMPLES:

sage: from sage.rings.polynomial.polynomial_singular_interface import can_convert_to_singular
sage: can_convert_to_singular(PolynomialRing(QQ, names=['x']))
True

sage: can_convert_to_singular(PolynomialRing(QQ, names=[]))
False


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Isolate Real Roots of Real Polynomials