Implementing non-monic number fields would be hard, but not if the
leading coefficient is a unit :) Could a ticket be opened, mabshoff?
Nick
{{{
sage: NumberField(x^2 - 2, 'a')
Number Field in a with defining polynomial x^2 - 2
sage: NumberField(-x^2 - 2, 'a')
---------------------------------------------------------------------------
NotImplementedError Traceback (most recent call
last)
/Users/ncalexan/Devel/Squeak-3.10-1/platforms/unix/bld/<ipython
console> in <module>()
/Users/ncalexan/sage-3.0.6/local/lib/python2.5/site-packages/sage/
rings/number_field/number_field.py in NumberField(polynomial, name,
check, names, cache)
288
289 if polynomial.degree() == 2:
--> 290 K = NumberField_quadratic(polynomial, name, check)
291 else:
292 K = NumberField_absolute(polynomial, name, None, check)
/Users/ncalexan/sage-3.0.6/local/lib/python2.5/site-packages/sage/
rings/number_field/number_field.py in __init__(self, polynomial, name,
check)
6001 Number Field in a with defining polynomial x^2 - 4
6002 """
-> 6003 NumberField_absolute.__init__(self, polynomial,
name=name, check=check)
6004 self._element_class =
number_field_element_quadratic.NumberFieldElement_quadratic
6005 c, b, a = [rational.Rational(t) for t in
self.defining_polynomial().list()]
/Users/ncalexan/sage-3.0.6/local/lib/python2.5/site-packages/sage/
rings/number_field/number_field.py in __init__(self, polynomial, name,
latex_name, check)
3272
3273 def __init__(self, polynomial, name, latex_name=None,
check=True):
-> 3274 NumberField_generic.__init__(self, polynomial, name,
latex_name, check)
3275 self._element_class =
number_field_element.NumberFieldElement_absolute
3276
/Users/ncalexan/sage-3.0.6/local/lib/python2.5/site-packages/sage/
rings/number_field/number_field.py in __init__(self, polynomial, name,
latex_name, check)
668 raise TypeError, "polynomial must be defined
over rational field"
669 if not polynomial.is_monic():
--> 670 raise NotImplementedError, "number fields for
non-monic polynomials not yet implemented."
671 if not polynomial.is_irreducible():
672 raise ValueError, "defining polynomial (%s)
must be irreducible"%polynomial
NotImplementedError: number fields for non-monic polynomials not yet
implemented.
}}}
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