多项式环，其中发电机的数量是不同的

I'm trying to create a coordinate ring of an algebraic set (where the algebrais set is specified by some set of polynomials in arbitrary variables over a field).

我正在尝试创建一个代数集的坐标环（其中代数集由一个字段上的任意变量中的一些多项式集指定）。

So I'm using Sympy's poly_ring() function

所以我使用Sympy的poly_ring（）函数

It's usually used to create coordinate rings when you already know the generators of the ideal you want to define it for, for example;

例如，当您已经知道要为其定义理想的生成器时，它通常用于创建坐标环;

CoordinateRing = QQ.poly_ring(x,y,z) / [y**2 - z*x, xy*2 + z]

But I want to make no assumption on the number of variables used in the defining polynomials for my algebraic sets. So I wrote a function get_symbols() that extracts all the symbols used in the defining polynomials. Is there a way to set the generators for poly_ring() without having to list them as parameters?

但是我想对我的代数集的定义多项式中使用的变量数量没有假设。所以我编写了一个函数get_symbols（），它提取定义多项式中使用的所有符号。有没有办法为poly_ring（）设置生成器而不必将它们列为参数？

from sympy import * 

class AlgebraicSet(object):
    def __init__(self, polynomials,field):

        self.polynomials = polynomials
        self.field = field 

    def get_symbols(self):

        symbols = set()

        for f in self.polynomials:
            symbols = set(symbols | f.atoms(Symbol)) 

        return symbols

    def get_cooridinate_ring(self):
        return self.field.poly_ring(self.get_symbols(),order="ilex") / self.polynomials

1 个解决方案

#1

Your code wasn't working for me, but I found using old_poly_ring instead of poly_ring did the trick:

您的代码对我不起作用，但我发现使用old_poly_ring而不是poly_ring就可以了：

from sympy import * 

class AlgebraicSet(object):
    def __init__(self, polynomials,field):

        self.polynomials = polynomials
        self.field = field 

    def get_symbols(self):

        symbols = set()

        for f in self.polynomials:
            symbols = set(symbols | f.atoms(Symbol)) 

        return symbols

    def get_coordinate_ring(self):
        poly_ring = self.field.old_poly_ring(*self.get_symbols(),order="ilex")
        return poly_ring / poly_ring.ideal(*self.polynomials)

from sympy.abc import x, y, z

print AlgebraicSet([y**2 - z*x, x*y*2 + z], QQ).get_coordinate_ring()