Opened 13 years ago
Closed 13 years ago
#4041 closed defect (duplicate)
Implementing number fields defined by non-monic polynomials
Reported by: | mabshoff | Owned by: | was |
---|---|---|---|
Priority: | major | Milestone: | sage-duplicate/invalid/wontfix |
Component: | number theory | Keywords: | |
Cc: | Merged in: | ||
Authors: | Reviewers: | ||
Report Upstream: | Work issues: | ||
Branch: | Commit: | ||
Dependencies: | Stopgaps: |
Description
Implementing non-monic number fields would be hard, but not if the leading coefficient is a unit :)
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.
Change History (5)
comment:1 Changed 13 years ago by
- Summary changed from Implementing non-monic number fields to Implementing number fields defined by non-monic polynomials
comment:2 Changed 13 years ago by
This ticket seems to be a duplicate of #252. So I think this one can be deleted.
comment:3 Changed 13 years ago by
- Resolution set to fixed
- Status changed from new to closed
comment:4 Changed 13 years ago by
- Resolution fixed deleted
- Status changed from closed to reopened
comment:5 Changed 13 years ago by
- Milestone changed from sage-3.1.2 to sage-duplicate/invalid
- Resolution set to duplicate
- Status changed from reopened to closed
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It's not clear to me exactly what Nick means: defining polys in Z[x] with leading coefficient -1, or something more general over Q, or also relative number fields.