subresultants.py 文件源码

def PSC(F, G, x):
    """PSC(F, G, x) returns a set with the non-zero principal subresultant
    coefficients (psc) of the two polynomials F and G with respect to the
    variable x.

    If the degree of the polynomial F is strictly less than the degree of
    the polynomial G, then F and G are interchanged.

    Extended psc beyond the n-th are not considered, where n is the minimum
    of the degrees of F and G with respect to x.

    >>> PSC(0, 0, var('x'))
    set()
    >>> PSC(poly('2*x'), poly('3*y'), var('x'))
    {3*y}
    >>> PSC(poly('2*x'), poly('3*y + 5*x**2'), var('x')) == {12*var('y'), 2}
    True
    >>> PSC(poly('x**3'), poly('x**3 + x'), var('x'))
    {1}
    """
    subs = subresultants(F, G, x)
    s = set()
    i = len(subs) - 1
    if i < 0:
        return s
    currDeg = degree(subs[i], x)
    while i > 0:
        nextDeg = degree(subs[i-1], x)
        s.add( LC(subs[i], x)**(nextDeg-currDeg) )
        currDeg = nextDeg
        i -= 1
    return s


# Execute doctest when run from the command line