Hi Daniel,
On 2017-07-14, Daniel Krenn <kr...@aon.at> wrote:
>>> R.<x,y> = PolynomialRing(QQ, 'lex')
>> That's not what you want.
>> [...]
>> Instead you have to do
>> sage: R.<x,y> = PolynomialRing(QQ, order='lex')
>> (i.e., specify what parameter is 'lex' being assigned to)
>
> What does the polynomial ring constructor do with the 'lex' in the first
> example? Why is no error raised?
The preparser translates it into
R = PolynomialRing(QQ, 'lex', names=('x', 'y',)); (x, y,) = R._first_ngens(2)
And we have the following function head:
def PolynomialRing(base_ring, arg1=None, arg2=None,
sparse=False, order='degrevlex',
names=None, name=None,
var_array=None,
implementation=None):
So, "lex" ends up in "arg1". Unfortunately, the documentation of
the PolynomialRing constructor is not very clear about what happens
with arg1. But in the source code, I find that arg1 is used to override the
parameter `name` (not `names`). However it seems that if both `name` and `names`
is present then the value of `name` has no effect. Let's try:
sage: PolynomialRing(QQ, name='lex', names=('x','y'))
Multivariate Polynomial Ring in x, y over Rational Field
sage: _.term_order()
Degree reverse lexicographic term order
Cheers,
Simon
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