Python densetools.dmp_eval函数代码示例

def test_dmp_eval_in():
    assert dmp_eval_in(f_6, -2, 1, 3, ZZ) == dmp_eval(dmp_swap(f_6, 0, 1, 3, ZZ), -2, 3, ZZ)
    assert dmp_eval_in(f_6, 7, 1, 3, ZZ) == dmp_eval(dmp_swap(f_6, 0, 1, 3, ZZ), 7, 3, ZZ)
    assert dmp_eval_in(f_6, -2, 2, 3, ZZ) == dmp_swap(dmp_eval(dmp_swap(f_6, 0, 2, 3, ZZ), -2, 3, ZZ), 0, 1, 2, ZZ)
    assert dmp_eval_in(f_6, 7, 2, 3, ZZ) == dmp_swap(dmp_eval(dmp_swap(f_6, 0, 2, 3, ZZ), 7, 3, ZZ), 0, 1, 2, ZZ)

    f = [[[45L]], [[]], [[]], [[-9L], [-1L], [], [3L, 0L, 10L, 0L]]]

    assert dmp_eval_in(f, -2, 2, 2, ZZ) == [[45], [], [], [-9, -1, 0, -44]]

def test_dmp_eval_in():
    assert dmp_eval_in(
        f_6, -2, 1, 3, ZZ) == dmp_eval(dmp_swap(f_6, 0, 1, 3, ZZ), -2, 3, ZZ)
    assert dmp_eval_in(
        f_6, 7, 1, 3, ZZ) == dmp_eval(dmp_swap(f_6, 0, 1, 3, ZZ), 7, 3, ZZ)
    assert dmp_eval_in(f_6, -2, 2, 3, ZZ) == dmp_swap(
        dmp_eval(dmp_swap(f_6, 0, 2, 3, ZZ), -2, 3, ZZ), 0, 1, 2, ZZ)
    assert dmp_eval_in(f_6, 7, 2, 3, ZZ) == dmp_swap(
        dmp_eval(dmp_swap(f_6, 0, 2, 3, ZZ), 7, 3, ZZ), 0, 1, 2, ZZ)

    f = [[[long(45)]], [[]], [[]], [[long(-9)], [-1], [], [long(3), long(0), long(10), long(0)]]]

    assert dmp_eval_in(f, -2, 2, 2, ZZ) == \
        [[45], [], [], [-9, -1, 0, -44]]

def test_dmp_eval():
    assert dmp_eval([], 3, 0, ZZ) == 0

    assert dmp_eval([[]], 3, 1, ZZ) == []
    assert dmp_eval([[[]]], 3, 2, ZZ) == [[]]

    assert dmp_eval([[1, 2]], 0, 1, ZZ) == [1, 2]

    assert dmp_eval([[[1]]], 3, 2, ZZ) == [[1]]
    assert dmp_eval([[[1, 2]]], 3, 2, ZZ) == [[1, 2]]

    assert dmp_eval([[3, 2], [1, 2]], 3, 1, ZZ) == [10, 8]
    assert dmp_eval([[[3, 2]], [[1, 2]]], 3, 2, ZZ) == [[10, 8]]

def test_dmp_diff_eval_in():
    assert dmp_diff_eval_in(f_6, 2, 7, 1, 3, ZZ) == \
        dmp_eval(dmp_diff(dmp_swap(f_6, 0, 1, 3, ZZ), 2, 3, ZZ), 7, 3, ZZ)

def dmp_zz_modular_resultant(f, g, p, u, K):
    """
    Compute resultant of ``f`` and ``g`` modulo a prime ``p``.

    **Examples**

    >>> from sympy.polys.domains import ZZ
    >>> from sympy.polys.euclidtools import dmp_zz_modular_resultant

    >>> f = ZZ.map([[1], [1, 2]])
    >>> g = ZZ.map([[2, 1], [3]])

    >>> dmp_zz_modular_resultant(f, g, ZZ(5), 1, ZZ)
    [-2, 0, 1]

    """
    if not u:
        return gf_int(dup_prs_resultant(f, g, K)[0] % p, p)

    v = u - 1

    n = dmp_degree(f, u)
    m = dmp_degree(g, u)

    N = dmp_degree_in(f, 1, u)
    M = dmp_degree_in(g, 1, u)

    B = n*M + m*N

    D, a = [K.one], -K.one
    r = dmp_zero(v)

    while dup_degree(D) <= B:
        while True:
            a += K.one

            if a == p:
                raise HomomorphismFailed('no luck')

            F = dmp_eval_in(f, gf_int(a, p), 1, u, K)

            if dmp_degree(F, v) == n:
                G = dmp_eval_in(g, gf_int(a, p), 1, u, K)

                if dmp_degree(G, v) == m:
                    break

        R = dmp_zz_modular_resultant(F, G, p, v, K)
        e = dmp_eval(r, a, v, K)

        if not v:
            R = dup_strip([R])
            e = dup_strip([e])
        else:
            R = [R]
            e = [e]

        d = K.invert(dup_eval(D, a, K), p)
        d = dup_mul_ground(D, d, K)
        d = dmp_raise(d, v, 0, K)

        c = dmp_mul(d, dmp_sub(R, e, v, K), v, K)
        r = dmp_add(r, c, v, K)

        r = dmp_ground_trunc(r, p, v, K)

        D = dup_mul(D, [K.one, -a], K)
        D = dup_trunc(D, p, K)

    return r

def dmp_zz_heu_gcd(f, g, u, K):
    """
    Heuristic polynomial GCD in ``Z[X]``.

    Given univariate polynomials ``f`` and ``g`` in ``Z[X]``, returns
    their GCD and cofactors, i.e. polynomials ``h``, ``cff`` and ``cfg``
    such that::

          h = gcd(f, g), cff = quo(f, h) and cfg = quo(g, h)

    The algorithm is purely heuristic which means it may fail to compute
    the GCD. This will be signaled by raising an exception. In this case
    you will need to switch to another GCD method.

    The algorithm computes the polynomial GCD by evaluating polynomials
    f and g at certain points and computing (fast) integer GCD of those
    evaluations. The polynomial GCD is recovered from the integer image
    by interpolation. The evaluation proces reduces f and g variable by
    variable into a large integer.  The final step  is to verify if the
    interpolated polynomial is the correct GCD. This gives cofactors of
    the input polynomials as a side effect.

    **Examples**

    >>> from sympy.polys.domains import ZZ
    >>> from sympy.polys.euclidtools import dmp_zz_heu_gcd

    >>> f = ZZ.map([[1], [2, 0], [1, 0, 0]])
    >>> g = ZZ.map([[1], [1, 0], []])

    >>> dmp_zz_heu_gcd(f, g, 1, ZZ)
    ([[1], [1, 0]], [[1], [1, 0]], [[1], []])

    **References**

    1. [Liao95]_

    """
    if not u:
        return dup_zz_heu_gcd(f, g, K)

    result = _dmp_rr_trivial_gcd(f, g, u, K)

    if result is not None:
        return result

    df = dmp_degree(f, u)
    dg = dmp_degree(g, u)

    gcd, f, g = dmp_ground_extract(f, g, u, K)

    f_norm = dmp_max_norm(f, u, K)
    g_norm = dmp_max_norm(g, u, K)

    B = 2*min(f_norm, g_norm) + 29

    x = max(min(B, 99*K.sqrt(B)),
            2*min(f_norm // abs(dmp_ground_LC(f, u, K)),
                  g_norm // abs(dmp_ground_LC(g, u, K))) + 2)

    for i in xrange(0, HEU_GCD_MAX):
        ff = dmp_eval(f, x, u, K)
        gg = dmp_eval(g, x, u, K)

        v = u - 1

        if not (dmp_zero_p(ff, v) or dmp_zero_p(gg, v)):
            h, cff, cfg = dmp_zz_heu_gcd(ff, gg, v, K)

            h = _dmp_zz_gcd_interpolate(h, x, v, K)
            h = dmp_ground_primitive(h, u, K)[1]

            cff_, r = dmp_div(f, h, u, K)

            if dmp_zero_p(r, u):
                cfg_, r = dmp_div(g, h, u, K)

                if dmp_zero_p(r, u):
                    h = dmp_mul_ground(h, gcd, u, K)
                    return h, cff_, cfg_

            cff = _dmp_zz_gcd_interpolate(cff, x, v, K)

            h, r = dmp_div(f, cff, u, K)

            if dmp_zero_p(r, u):
                cfg_, r = dmp_div(g, h, u, K)

                if dmp_zero_p(r, u):
                    h = dmp_mul_ground(h, gcd, u, K)
                    return h, cff, cfg_

            cfg = _dmp_zz_gcd_interpolate(cfg, x, v, K)

            h, r = dmp_div(g, cfg, u, K)

            if dmp_zero_p(r, u):
                cff_, r = dmp_div(f, h, u, K)

                if dmp_zero_p(r, u):
#.........这里部分代码省略.........

def dmp_zz_modular_resultant(f, g, p, u, K):
    """
    Compute resultant of `f` and `g` modulo a prime `p`.

    Examples
    ========

    >>> from sympy.polys import ring, ZZ
    >>> R, x,y = ring("x,y", ZZ)

    >>> f = x + y + 2
    >>> g = 2*x*y + x + 3

    >>> R.dmp_zz_modular_resultant(f, g, 5)
    -2*y**2 + 1

    """
    if not u:
        return gf_int(dup_prs_resultant(f, g, K)[0] % p, p)

    v = u - 1

    n = dmp_degree(f, u)
    m = dmp_degree(g, u)

    N = dmp_degree_in(f, 1, u)
    M = dmp_degree_in(g, 1, u)

    B = n*M + m*N

    D, a = [K.one], -K.one
    r = dmp_zero(v)

    while dup_degree(D) <= B:
        while True:
            a += K.one

            if a == p:
                raise HomomorphismFailed('no luck')

            F = dmp_eval_in(f, gf_int(a, p), 1, u, K)

            if dmp_degree(F, v) == n:
                G = dmp_eval_in(g, gf_int(a, p), 1, u, K)

                if dmp_degree(G, v) == m:
                    break

        R = dmp_zz_modular_resultant(F, G, p, v, K)
        e = dmp_eval(r, a, v, K)

        if not v:
            R = dup_strip([R])
            e = dup_strip([e])
        else:
            R = [R]
            e = [e]

        d = K.invert(dup_eval(D, a, K), p)
        d = dup_mul_ground(D, d, K)
        d = dmp_raise(d, v, 0, K)

        c = dmp_mul(d, dmp_sub(R, e, v, K), v, K)
        r = dmp_add(r, c, v, K)

        r = dmp_ground_trunc(r, p, v, K)

        D = dup_mul(D, [K.one, -a], K)
        D = dup_trunc(D, p, K)

    return r