Dear all,
1. In number fields, some elements are considered as prime, which is
not mathematically correct:
|
sage:S.<x>=NumberField(x^2+5)
sage:S(11).is_prime()
True
|
|
In the field of rational number, the answer is correct:
|
sage:QQ(11).is_prime()
False
|
Is that a bug?
|
2. When one defines a number field as above, one cannot define a new
number field anymore:
|
sage:S.<x>=NumberField(x^2+5)
sage:R.<y>=NumberField(x^2+7)
Traceback(most recent call last):
...
ValueError:variable names must be alphanumeric,but one is'Rational
Field'which isnot.
sage:NumberField(x^2+7,'x')
|Traceback(most recent call last):
...
ValueError:variable names must be alphanumeric,but one is'Rational
Field'which isnot.
|
|
Note that this does not happen if the first number field S has be
defined as follows:
|
sage: S = NumberField(x^2+5, 'x')
sage: NumberField(x^2+7,'x')
Number Field in x with defining polynomial x^2 + 7
sage: R.<t> = NumberField(x^2+7)
sage: R
Number Field in t with defining polynomial x^2 + 7
|
How may this be corrected?
Thanks in advance!
Bruno
P.S.: I encounter these bugs while reading this question
<http://ask.sagemath.org/question/26695/check-if-element-is-irreducible-in-algebraic-number-field/>
on ask.sagemath.org which asks for an "is_irreducible()" method in
number field (or maybe in their rings of integers).
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