Sage / Python: 来自非空生成器的空元组

Question

Sage 的新手，我运行遇到了这段代码的以下问题：

    abc2 = ((x * d).numerator() for x in abc)
    for x in abc2:
        show (type(x))
        show (gcd (x.coefficients()))
    g = (gcd (x.coefficients()) for x in abc2)
    print ("g =", tuple(g))

打印以下输出：

<class 'sage.rings.polynomial.multi_polynomial_libsingular.MPolynomial_libsingular'>
177282774041995797378340812360777728/101
<class 'sage.rings.polynomial.multi_polynomial_libsingular.MPolynomial_libsingular'>
177282774041995797378340812360777728
<class 'sage.rings.polynomial.multi_polynomial_libsingular.MPolynomial_libsingular'>
177282774041995797378340812360777728
g = ()

正如您可以从循环中的打印中推断的那样，按照 gcd (x.coefficients()) 的预期计算了 3 个 gcds。但是，当循环后在生成器中使用 gcd (x.coefficients()) 时，生成器是空的，我希望它有 3 个元素？

我在这里错过了什么？我检查了生成的.py文件，那部分没有改变，所以我对Python的理解是错误的？

$ sage --version
SageMath version 9.0, Release Date: 2020-01-01

仅供参考，这是完整的 Sage 代码，上面的片段从第 24 行开始：

#!/usr/bin/env sage

R.<a,b,c> = QQ[]
    
def to_xy (abc, E):
    (a2, a1) = E
    (a, b, c) = abc

    d = 6*a + 6*b - c
    x = -28 * (a + b + 2*c) / d
    y = 364 * (a - b) / d
    return (x, y)


def to2_abc (P, E):
    """ Get back from a point P = (x,y) on
        E: y^2 = x^3 + a2 x^2 + a1 x  to (a,b,c).
    """
    (x,y) = P

    abc = (-56/101 - 12 * x, 56 - x + y, 56 - x - y)

    d = lcm (x.denominator() for x in abc)
    abc2 = ((x * d).numerator() for x in abc)
    for x in abc2:
        show (type(x))
        show (gcd (x.coefficients()))
    g = (gcd (x.coefficients()) for x in abc2)
    print ("g =", tuple(g))


def ECadd (P, E):
    (xP, yP) = P
    (a2,a1) = E

    # Get to short Weierstrass form  E': y^2 = x^2 + A x + B.
    k = -a2 / 3
    A = 3*k*k + 2*a2*k + a1
    # B = (k*k + a2*k + a1) * k

    (xS, yS) = (xP-k, yP)

    # Add S to itself on E'.
    s = (3 * xS*xS + A) / (2 * yS)
    xSS = s*s - xS - xS
    ySS = -yS - s * (xSS - xS)

    # Return P+P on E.
    (xPP, yPP) = (xSS+k, ySS)
    return (xPP, yPP)


E = (109, 224)

P = to_xy ((a,b,c), E)
P2 = ECadd (P, E)

to2_abc (P2, E)

Answer 1

当你遍历生成器时，当生成器耗尽时迭代停止，所以当你第二次遍历它时，没有剩下的元素。

如果您需要多次迭代数据，请先将其转换为另一种类型，例如列表，然后再对其进行迭代。

Sage / Python: 来自非空生成器的空元组

Sage / Python: Empty tuple from non-empty generator

python

python-3.x

sage