SAGE：有限域上多项式的系数

Question

我需要一些帮助来获得多项式的系数。 如果尝试过

y = var('y')
q = y^3 -2*y + 1
coeff_list = [q(y=0)] + [q.coeff(y^k) for k in range(1, q.degree(y)+1)]

但在 GF(q) 中

S.<y> = PolynomialRing(GF(q),'y')  
q = y^3 -2*y + 1
coeff_list = [q(y=0)] + [q.coeff(y^k) for k in range(1, q.degree(y)+1)]
coeff_list

我收到了这个错误

Error in lines 1-1
Traceback (most recent call last):
  File "/projects/31b0bdd7-734b-4864-bf87-0b7cfafd06e9/.sagemathcloud/sage_server.py", line 733, in execute
    exec compile(block+'\n', '', 'single') in namespace, locals
  File "", line 1, in <module>
  File "factory.pyx", line 141, in sage.structure.factory.UniqueFactory.__call__ (sage/structure/factory.c:1157)
  File "/usr/local/sage/sage-5.12/local/lib/python2.7/site-packages/sage/rings/finite_rings/constructor.py", line 352, in create_key_and_extra_args
    order = int(order)
  File "expression.pyx", line 889, in sage.symbolic.expression.Expression.__int__ (sage/symbolic/expression.cpp:6157)
ValueError: cannot convert y^3 - 2*y + 1 to int

有没有人想得到系数。提前非常感谢。 约翰杜

Answer 1

首先，您的问题不是获取系数，而是构建环。我假设您想在GF(q) 上工作以获取素数q（比如7）。然后，当您在有限域 pol 上有多项式时，pol.list() 返回系数列表：

sage: q = 7
sage: S.<y> = PolynomialRing(GF(q),'y')
sage: pol = y^3 -2*y + 1  
sage: pol
y^3 + 5*y + 1
sage: pol.list()
[1, 5, 0, 1]