Python QQ.random_element方法代码示例

# 需要导入模块: from sage.rings.all import QQ [as 别名]
# 或者: from sage.rings.all.QQ import random_element [as 别名]
def test_add_commutes(trials, verbose=False):
    r"""
    This is a simple demonstration of the :func:`random_testing` decorator and
    its recommended usage.

    We test that addition is commutative over rationals.

    EXAMPLES::

        sage: from sage.misc.random_testing import test_add_commutes
        sage: test_add_commutes(2, verbose=True, seed=0)
        a == -4, b == 0 ...
        Passes!
        a == -1/2, b == -1/95 ...
        Passes!
        sage: test_add_commutes(10)
        sage: test_add_commutes(1000) # long time
    """
    from sage.rings.all import QQ
    for _ in xrange(trials):
        a = QQ.random_element()
        b = QQ.random_element()
        if verbose:
            print "a == %s, b == %s ..." % (a, b)
        assert(a+b == b+a)
        if verbose:
            print "Passes!"

# 需要导入模块: from sage.rings.all import QQ [as 别名]
# 或者: from sage.rings.all.QQ import random_element [as 别名]
    def random_element(self):
        r"""
        Return a random element of `\Q/n\Z`.

        The denominator is selected
        using the ``1/n`` distribution on integers, modified to return
        a positive value.  The numerator is then selected uniformly.

        EXAMPLES::

            sage: G = QQ/(6*ZZ)
            sage: G.random_element()
            47/16
            sage: G.random_element()
            1
            sage: G.random_element()
            3/5
        """
        if self.n == 0:
            return self(QQ.random_element())
        d = ZZ.random_element()
        if d >= 0:
            d = 2 * d + 1
        else:
            d = -2 * d
        n = ZZ.random_element((self.n * d).ceil())
        return self(n / d)

# 需要导入模块: from sage.rings.all import QQ [as 别名]
# 或者: from sage.rings.all.QQ import random_element [as 别名]
def test_add_is_mul(trials, verbose=False):
    r"""
    This example demonstrates a failing :func:`random_testing` test,
    and shows how to reproduce the error.

    DO NOT USE THIS AS AN EXAMPLE OF HOW TO USE
    :func:`random_testing`!  Instead, look at
    :func:`sage.misc.random_testing.test_add_commutes`.

    We test that ``a+b == a*b``, for *a*, *b* rational.  This is of
    course false, so the test will almost always fail.

    EXAMPLES::

        sage: from sage.misc.random_testing import test_add_is_mul

    We start by testing that we get reproducible results when setting
    *seed* to 0.

    ::

        sage: test_add_is_mul(2, verbose=True, seed=0)
        a == -4, b == 0 ...
        Random testing has revealed a problem in test_add_is_mul
        Please report this bug!  You may be the first
        person in the world to have seen this problem.
        Please include this random seed in your bug report:
        Random seed: 0
        AssertionError()

    Normally in a ``@random_testing`` doctest, we would leave off the
    ``verbose=True`` and the ``# random``.  We put it in here so that we can
    verify that we are seeing the exact same error when we reproduce
    the error below.

    ::

        sage: test_add_is_mul(10, verbose=True) # random
        a == -2/7, b == 1 ...
        Random testing has revealed a problem in test_add_is_mul
        Please report this bug!  You may be the first
        person in the world to have seen this problem.
        Please include this random seed in your bug report:
        Random seed: 216390410596009428782506007128692114173
        AssertionError()

    OK, now assume that some user has reported a
    :func:`test_add_is_mul` failure.  We can specify the same
    *random_seed* that was found in the bug report, and we will get the
    exact same failure so that we can debug the "problem".

    ::

        sage: test_add_is_mul(10, verbose=True, seed=216390410596009428782506007128692114173)
        a == -2/7, b == 1 ...
        Random testing has revealed a problem in test_add_is_mul
        Please report this bug!  You may be the first
        person in the world to have seen this problem.
        Please include this random seed in your bug report:
        Random seed: 216390410596009428782506007128692114173
        AssertionError()
    """
    from sage.rings.all import QQ
    for _ in xrange(trials):
        a = QQ.random_element()
        b = QQ.random_element()
        if verbose:
            print "a == %s, b == %s ..." % (a, b)
        assert(a+b == a*b)
        if verbose:
            print "Passes!"