Let me give some more details about my question: i have a number field
K, and a ring of polynomials over it, R1. I also have a ring
homomorphism from K to QQbar (which actually makes all sense from a
mathematical point of view), and a ring of polynomials R2 over QQbar.
All this should give a map from R1 to R2, but when i try to construct
it in sage, i can't:
sage: alpha=symbolic_expression(x^2+x+1).roots
(ring=QQbar,multiplicities=False)
sage: K.<a>=NumberField(x^2+x+1)
sage: R1.<x,y>=K[]
sage: f=R1(x*y-a*y+x)
sage: H=K.hom([alpha[0]],QQbar)
sage: H(a)
-0.500000000000000? - 0.866025403784439?*I
sage: R2.<x,y>=QQbar[]
sage: H(f)
ERROR: An unexpected error occurred while tokenizing input
The following traceback may be corrupted or invalid
The error message is: ('EOF in multi-line statement', (920, 0))
---------------------------------------------------------------------------
TypeError Traceback (most recent call
last)
/home/mmarco/<ipython console> in <module>()
/home/mmarco/sage/local/lib/python2.5/site-packages/sage/categories/
map.so in sage.categories.map.Map.__call__ (sage/categories/map.c:3227)
()
TypeError: x*y + x + (-a)*y must be coercible into Number Field in a
with defining polynomial x^2 + x + 1
sage: R1.hom([x,y],R2)
---------------------------------------------------------------------------
TypeError Traceback (most recent call
last)
/home/mmarco/<ipython console> in <module>()
/home/mmarco/sage/local/lib/python2.5/site-packages/sage/structure/
parent_gens.so in sage.structure.parent_gens.ParentWithGens.hom (sage/
structure/parent_gens.c:3785)()
/home/mmarco/sage/local/lib/python2.5/site-packages/sage/rings/
homset.pyc in __call__(self, im_gens, check)
79 return self._coerce_impl(im_gens)
80 except TypeError:
---> 81 raise TypeError, "images do not define a valid
homomorphism"
82
83
TypeError: images do not define a valid homomorphism
Actually, both error messages are correct (H is not defined in R1, and
there is no natural coercion from K to QQbar), but i have not found
any other way to build a homomorphism that involves the variables AND
the base ring.
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