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sagemath
GitHub Repository: sagemath/sagelib
 Path: blob/master/sage/geometry/polyhedron/base_RDF.py
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"""

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Base class for polyhedra over ``RDF``.

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"""

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from sage.rings.all import RDF

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from base import Polyhedron_base

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class Polyhedron_RDF(Polyhedron_base):

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    """

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    Base class for polyhedra over ``RDF``.

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    TESTS::

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        sage: p = Polyhedron([(0,0)], base_ring=RDF);  p

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        A 0-dimensional polyhedron in RDF^2 defined as the convex hull of 1 vertex

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        sage: TestSuite(p).run()

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    """

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    # 1e-6 is the cddf+ default fuzzy zero cutoff

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    def _is_zero(self, x):

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        """

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        Test whether ``x`` is zero.

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        INPUT:

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        - ``x`` -- a number in the base ring.

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        OUTPUT:

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        Boolean.

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        EXAMPLES::

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            sage: p = Polyhedron([(0,0)], base_ring=RDF)

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            sage: p._is_zero(0)

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            True

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            sage: p._is_zero(1e-3)

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            False

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        This is a fuzzy zero for floating-point numbers::

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            sage: p._is_zero(1e-10)

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            True

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        """

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        return abs(x)<=1e-6

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    def _is_nonneg(self, x):

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        """

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        Test whether ``x`` is nonnegative.

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        INPUT:

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        - ``x`` -- a number in the base ring.

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        OUTPUT:

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        Boolean.

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        EXAMPLES::

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            sage: p = Polyhedron([(0,0)], base_ring=RDF)

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            sage: p._is_nonneg(1)

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            True

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            sage: p._is_nonneg(-1e-3)

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            False

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        This is a fuzzy zero for floating-point numbers::

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            sage: p._is_nonneg(-1e-10)

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            True

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        """

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        return x>=-1e-6

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    def _is_positive(self, x):

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        """

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        Test whether ``x`` is positive.

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        INPUT:

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        - ``x`` -- a number in the base ring.

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        OUTPUT:

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        Boolean.

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        EXAMPLES::

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            sage: p = Polyhedron([(0,0)], base_ring=RDF)

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            sage: p._is_positive(1)

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            True

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            sage: p._is_positive(0)

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            True

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        This is a fuzzy zero for floating-point numbers::

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            sage: p._is_positive(-1e-10)

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            True

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        """

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        return x>=-1e-6

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    _base_ring = RDF

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