CoCalc -- base

GitHub Repository: sagemath/sagesmc
Path: blob/master/src/sage/geometry/polyhedron/base_QQ.py
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"""
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Base class for polyhedra over `\QQ`
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"""
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from sage.rings.all import QQ
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from base import Polyhedron_base
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class Polyhedron_QQ(Polyhedron_base):
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    """
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    Base class for Polyhedra over `\QQ`
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    TESTS::
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        sage: p = Polyhedron([(0,0)], base_ring=QQ);  p
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        A 0-dimensional polyhedron in QQ^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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    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=QQ)
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            sage: p._is_zero(0)
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            True
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            sage: p._is_zero(1/100000)
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            False
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        """
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        return x==0
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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=QQ)
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            sage: p._is_nonneg(1)
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            True
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            sage: p._is_nonneg(-1/100000)
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            False
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        """
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        return x>=0
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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=QQ)
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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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            False
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        """
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        return x>0
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    _base_ring = QQ
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