Is the following output for b.gens() correct?
sage: NumberField([x,x^2-3],'a')
Number Field in a0 with defining polynomial x over its base field
sage: b=NumberField([x,x^2-3],'a')
sage: b.gens()
(0, 0)
To contrast:
sage: c=NumberField([x^2-3, x^2-2],'a')
sage: c.gens()
(a0, a1)
Also, this blows up:
sage: c=NumberField([x^2-3, x],'a')
---------------------------------------------------------------------------
<class 'sage.libs.pari.gen.PariError'> Traceback (most recent call last)
/home/grout/sage/<ipython console> in <module>()
/home/grout/sage/local/lib/python2.5/site-packages/sage/rings/number_field/number_field.py
in NumberField(polynomial, name, check, names, cache)
243
244 if isinstance(polynomial, (list, tuple)):
--> 245 return NumberFieldTower(polynomial, name)
246
247 name = sage.structure.parent_gens.normalize_names(1, name)
/home/grout/sage/local/lib/python2.5/site-packages/sage/rings/number_field/number_field.py
in NumberFieldTower(v, names, check)
411 # return z
412 #else:
--> 413 return w.extension(f, name, check=check)
414
415
/home/grout/sage/local/lib/python2.5/site-packages/sage/rings/number_field/number_field.py
in extension(self, poly, name, names, check)
1813 if name is None:
1814 raise TypeError, "the variable name must be specified."
-> 1815 return NumberField_relative(self, poly, str(name),
check=check)
1816
1817 def factor_integer(self, n):
/home/grout/sage/local/lib/python2.5/site-packages/sage/rings/number_field/number_field.py
in __init__(self, base, polynomial, name, latex_name, names, check)
3110
3111 if check:
-> 3112 if not polynomial_y.is_irreducible():
3113 raise ValueError, "defining polynomial (%s)
must be irreducible"%polynomial
3114
/home/grout/sage/polynomial_element.pyx in
sage.rings.polynomial.polynomial_element.Polynomial.is_irreducible()
/home/grout/sage/polynomial_element.pyx in
sage.rings.polynomial.polynomial_element.Polynomial.factor()
/home/grout/sage/gen.pyx in sage.libs.pari.gen._pari_trap()
<class 'sage.libs.pari.gen.PariError'>: (8)
sage: c=NumberField([x^2-3, x-1],'a')
---------------------------------------------------------------------------
<class 'sage.libs.pari.gen.PariError'> Traceback (most recent call last)
/home/grout/sage/<ipython console> in <module>()
/home/grout/sage/local/lib/python2.5/site-packages/sage/rings/number_field/number_field.py
in NumberField(polynomial, name, check, names, cache)
243
244 if isinstance(polynomial, (list, tuple)):
--> 245 return NumberFieldTower(polynomial, name)
246
247 name = sage.structure.parent_gens.normalize_names(1, name)
/home/grout/sage/local/lib/python2.5/site-packages/sage/rings/number_field/number_field.py
in NumberFieldTower(v, names, check)
411 # return z
412 #else:
--> 413 return w.extension(f, name, check=check)
414
415
/home/grout/sage/local/lib/python2.5/site-packages/sage/rings/number_field/number_field.py
in extension(self, poly, name, names, check)
1813 if name is None:
1814 raise TypeError, "the variable name must be specified."
-> 1815 return NumberField_relative(self, poly, str(name),
check=check)
1816
1817 def factor_integer(self, n):
/home/grout/sage/local/lib/python2.5/site-packages/sage/rings/number_field/number_field.py
in __init__(self, base, polynomial, name, latex_name, names, check)
3110
3111 if check:
-> 3112 if not polynomial_y.is_irreducible():
3113 raise ValueError, "defining polynomial (%s)
must be irreducible"%polynomial
3114
/home/grout/sage/polynomial_element.pyx in
sage.rings.polynomial.polynomial_element.Polynomial.is_irreducible()
/home/grout/sage/polynomial_element.pyx in
sage.rings.polynomial.polynomial_element.Polynomial.factor()
/home/grout/sage/gen.pyx in sage.libs.pari.gen._pari_trap()
<class 'sage.libs.pari.gen.PariError'>: (8)
-Jason
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