在sympy be中，为什么get_field因有限场GF（9）而失败（定义为GF（3）的有限扩展）？

发布于 2025-02-04 02:54:55 字数 1603 浏览 3 评论 0原文

我正在尝试使用Sympy中的groebner函数来求解GF（9）= GF（3）[G]/（G ** 2 + 1）中的多元多项式系统。当我这样做时，我会得到错误

文件 “/applications/spyder.app/contents/resources/lib/python3.9/sympy/polys/groebnertools.py”，第37行，格罗布纳 orig，ring = ring，ring.clone（domain = domain.get_field（））
文件 “/applications/spyder.app/contents/resources/lib/python3.9/sympy/polys/domains/domains/domain.py”，第846行，在get_field 提高域名（'没有与％s'％self相关的字段）
domainerror：没有与gf（3）[g]/（g ** 2 + 1）
没有的字段

我将代码减少到最低限度get_field（）失败。我还看了IS_FIELD ...这是真的！我知道非prime有限字段的GF和类似机制失败了，但是如果我使用有限的扩展定义了自己的GF（9），我认为一切都会很好。我是否缺少某些内容，或者Get_field（）没有意识到GF9是一个领域？

我的最小代码

from sympy import Symbol, Poly
from sympy.polys.agca.extensions import FiniteExtension


g = Symbol('g')
gf9 = FiniteExtension(Poly(g**2 + 1, g, modulus=3))  # correct GF(9)
print('gf9 = ', gf9, 'type =', type(gf9), 'is_field?', gf9.is_Field)
print()
print('field associated with', gf9, '=', gf9.get_field())

响应

gf9 = gf（3）[g]/（g ** 2 + 1）is_field？ true
追溯（最近的最新电话）：
文件 “/applications/spyder.app/contents/resources/lib/python3.9/spyder_kernels/py3compat.py”，第356行，在compat_exec中 exec（代码，全球，当地人）
file“/users/rick/.spyder-py3/temp.py”，第17行，in print（与'，gf9，'='相关的'字段
文件 “/applications/spyder.app/contents/resources/lib/python3.9/sympy/polys/domains/domains/domain.py”，第846行，在get_field 提高域名（'没有与％s'％self相关的字段）
domainerror：没有与gf（3）[g]/（g ** 2 + 1）
没有的字段

任何

domainerror：与gf（3）[g] / 领域我从未问过我的真正问题：如何将Sympy的Groebner函数与GF（3）[G]/（G ** 2 + 1）一起使用？

原文

I'm trying to use the groebner function in Sympy to solve a system of multivariate polynomials in GF(9) = GF(3)[g]/(g**2 + 1). When I do this I get the error

File
"/Applications/Spyder.app/Contents/Resources/lib/python3.9/sympy/polys/groebnertools.py",
line 37, in groebner
orig, ring = ring, ring.clone(domain=domain.get_field())
File
"/Applications/Spyder.app/Contents/Resources/lib/python3.9/sympy/polys/domains/domain.py",
line 846, in get_field
raise DomainError('there is no field associated with %s' % self)
DomainError: there is no field associated with GF(3)[g]/(g**2 + 1)

I reduced the code to the minimum that gives this get_field() failure. I also looked at is_field ... which was True!?
I know that GF and similar mechanisms fail for non-prime finite fields, but I thought that all would be well, if I defined my own GF(9) using a finite extension.
Am I missing something, or does get_field() not realize that gf9 is a field?

My minimal code

from sympy import Symbol, Poly
from sympy.polys.agca.extensions import FiniteExtension


g = Symbol('g')
gf9 = FiniteExtension(Poly(g**2 + 1, g, modulus=3))  # correct GF(9)
print('gf9 = ', gf9, 'type =', type(gf9), 'is_field?', gf9.is_Field)
print()
print('field associated with', gf9, '=', gf9.get_field())

Response

gf9 = GF(3)[g]/(g**2 + 1) is_field? True
Traceback (most recent call last):
File
"/Applications/Spyder.app/Contents/Resources/lib/python3.9/spyder_kernels/py3compat.py",
line 356, in compat_exec
exec(code, globals, locals)
File "/Users/rick/.spyder-py3/temp.py", line 17, in
print('field associated with', gf9, '=', gf9.get_field())
File
"/Applications/Spyder.app/Contents/Resources/lib/python3.9/sympy/polys/domains/domain.py",
line 846, in get_field
raise DomainError('there is no field associated with %s' % self)
DomainError: there is no field associated with GF(3)[g]/(g**2 + 1)

Any help appreciated :)

Addendum: I just noticed that I never asked my real question: How can I use Sympy's groebner function with GF(3)[g]/(g**2 + 1)?

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