Python Poly.all_coeffs方法代码示例

# 需要导入模块: from sympy.polys import Poly [as 别名]
# 或者: from sympy.polys.Poly import all_coeffs [as 别名]
def _sqrt_symbolic_denest(a, b, r):
    """Given an expression, sqrt(a + b*sqrt(b)), return the denested
    expression or None.

    Algorithm:
    If r = ra + rb*sqrt(rr), try replacing sqrt(rr) in ``a`` with
    (y**2 - ra)/rb, and if the result is a quadratic, ca*y**2 + cb*y + cc, and
    (cb + b)**2 - 4*ca*cc is 0, then sqrt(a + b*sqrt(r)) can be rewritten as
    sqrt(ca*(sqrt(r) + (cb + b)/(2*ca))**2).

    Examples
    ========

    >>> from sympy.simplify.sqrtdenest import _sqrt_symbolic_denest, sqrtdenest
    >>> from sympy import sqrt, Symbol
    >>> from sympy.abc import x

    >>> a, b, r = 16 - 2*sqrt(29), 2, -10*sqrt(29) + 55
    >>> _sqrt_symbolic_denest(a, b, r)
    sqrt(-2*sqrt(29) + 11) + sqrt(5)

    If the expression is numeric, it will be simplified:

    >>> w = sqrt(sqrt(sqrt(3) + 1) + 1) + 1 + sqrt(2)
    >>> sqrtdenest(sqrt((w**2).expand()))
    1 + sqrt(2) + sqrt(1 + sqrt(1 + sqrt(3)))

    Otherwise, it will only be simplified if assumptions allow:

    >>> w = w.subs(sqrt(3), sqrt(x + 3))
    >>> sqrtdenest(sqrt((w**2).expand()))
    sqrt((sqrt(sqrt(sqrt(x + 3) + 1) + 1) + 1 + sqrt(2))**2)

    Notice that the argument of the sqrt is a square. If x is made positive
    then the sqrt of the square is resolved:

    >>> _.subs(x, Symbol('x', positive=True))
    sqrt(sqrt(sqrt(x + 3) + 1) + 1) + 1 + sqrt(2)
    """

    a, b, r = map(sympify, (a, b, r))
    rval = _sqrt_match(r)
    if not rval:
        return None
    ra, rb, rr = rval
    if rb:
        y = Dummy('y', positive=True)
        try:
            newa = Poly(a.subs(sqrt(rr), (y**2 - ra)/rb), y)
        except PolynomialError:
            return None
        if newa.degree() == 2:
            ca, cb, cc = newa.all_coeffs()
            cb += b
            if _mexpand(cb**2 - 4*ca*cc).equals(0):
                z = sqrt(ca*(sqrt(r) + cb/(2*ca))**2)
                if z.is_number:
                    z = _mexpand(Mul._from_args(z.as_content_primitive()))
                return z

# 需要导入模块: from sympy.polys import Poly [as 别名]
# 或者: from sympy.polys.Poly import all_coeffs [as 别名]
def _solve_inequality(ie, s):
    """ A hacky replacement for solve, since the latter only works for
        univariate inequalities. """
    from sympy import Poly
    if not ie.rel_op in ('>', '>=', '<', '<='):
        raise NotImplementedError
    expr = ie.lhs - ie.rhs
    p = Poly(expr, s)
    if p.degree() != 1:
        raise NotImplementedError('%s' % ie)
    a, b = p.all_coeffs()
    if a.is_positive:
        return ie.func(s, -b/a)
    elif a.is_negative:
        return ie.func(-b/a, s)
    else:
        raise NotImplementedError

# 需要导入模块: from sympy.polys import Poly [as 别名]
# 或者: from sympy.polys.Poly import all_coeffs [as 别名]
def _solve_inequality(ie, s):
    """ A hacky replacement for solve, since the latter only works for
        univariate inequalities. """
    if not ie.rel_op in (">", ">=", "<", "<="):
        raise NotImplementedError
    expr = ie.lhs - ie.rhs
    try:
        p = Poly(expr, s)
    except PolynomialError:
        raise NotImplementedError
    if p.degree() != 1:
        raise NotImplementedError("%s" % ie)
    a, b = p.all_coeffs()
    if a.is_positive:
        return ie.func(s, -b / a)
    elif a.is_negative:
        return ie.func(-b / a, s)
    else:
        raise NotImplementedError

# 需要导入模块: from sympy.polys import Poly [as 别名]
# 或者: from sympy.polys.Poly import all_coeffs [as 别名]
def _solve_inequality(ie, s):
    """ A hacky replacement for solve, since the latter only works for
        univariate inequalities. """
    expr = ie.lhs - ie.rhs
    try:
        p = Poly(expr, s)
        if p.degree() != 1:
            raise NotImplementedError
    except (PolynomialError, NotImplementedError):
        try:
            return reduce_rational_inequalities([[ie]], s)
        except PolynomialError:
            return solve_univariate_inequality(ie, s)
    a, b = p.all_coeffs()
    if a.is_positive or ie.rel_op in ('!=', '=='):
        return ie.func(s, -b/a)
    elif a.is_negative:
        return ie.reversed.func(s, -b/a)
    else:
        raise NotImplementedError

# 需要导入模块: from sympy.polys import Poly [as 别名]
# 或者: from sympy.polys.Poly import all_coeffs [as 别名]
def _solve_inequality(ie, s, assume=True):
    """ A hacky replacement for solve, since the latter only works for
        univariate inequalities. """
    if not ie.rel_op in ('>', '>=', '<', '<='):
        raise NotImplementedError
    expr = ie.lhs - ie.rhs
    try:
        p = Poly(expr, s)
        if p.degree() != 1:
            raise NotImplementedError
    except (PolynomialError, NotImplementedError):
        try:
            n, d = expr.as_numer_denom()
            return reduce_rational_inequalities([[ie]], s, assume=assume)
        except PolynomialError:
            return solve_univariate_inequality(ie, s, assume=assume)
    a, b = p.all_coeffs()
    if a.is_positive:
        return ie.func(s, -b/a)
    elif a.is_negative:
        return ie.func(-b/a, s)
    else:
        raise NotImplementedError