On Dec 22, 2008, at 6:20 AM, John Cremona wrote: > You can do K(r.lift()), but it would be nicer if this was handled by > coercion magic.
This isn't really a coercion issue per se, it's a question of adding another case to the _element_constructor_ method of number fields. Do we want coercion here, i.e. should someone be able to write r + K.gen ()? If so, would it be the most natural to put the result into K or the quotient ring? > I don't know how that could be done in Sage, but > mathematically it would make sense whenever the defining polynomial of > K divided that of R. > > John > > 2008/12/22 Alex Ghitza <aghi...@gmail.com>: >> Hi, >> >> While working with number fields, I've run into this: >> >> sage: K.<a> = NumberField(x^8+1) >> sage: R = K.polynomial_quotient_ring() >> sage: r = R.random_element() >> >> And now the point of this: I would like to think of r as an >> element of K. >> However: >> >> sage: K(r) >> --------------------------------------------------------------------- >> ------ >> TypeError Traceback (most recent >> call last) >> >> /opt/sage-3.2.1/devel/sage-main/sage/<ipython console> in <module>() >> >> /opt/sage-3.2.1/local/lib/python2.5/site-packages/sage/structure/ >> parent.so >> in sage.structure.parent.Parent.__call__ (sage/structure/parent.c: >> 3645)() >> >> /opt/sage-3.2.1/local/lib/python2.5/site-packages/sage/structure/ >> coerce_maps.so >> in sage.structure.coerce_maps.DefaultConvertMap_unique._call_ >> (sage/structure/coerce_maps.c:2778)() >> >> /opt/sage-3.2.1/local/lib/python2.5/site-packages/sage/structure/ >> coerce_maps.so >> in sage.structure.coerce_maps._call_ (sage/structure/coerce_maps.c: >> 2685)() >> >> /opt/sage-3.2.1/local/lib/python2.5/site-packages/sage/rings/ >> number_field/number_field.pyc >> in _element_constructor_(self, x) >> 1422 raise ValueError, "vector must be of >> length equal to >> the degree of this number field" >> 1423 return sum([ x[i]*self.gen(0)**i for i in >> range(self.degree()) ]) >> -> 1424 return self._coerce_non_number_field_element_in(x) >> 1425 >> 1426 def _coerce_from_str(self, x): >> >> /opt/sage-3.2.1/local/lib/python2.5/site-packages/sage/rings/ >> number_field/number_field.pyc >> in _coerce_non_number_field_element_in(self, x) >> 1520 except (TypeError, AttributeError), msg: >> 1521 pass >> -> 1522 raise TypeError, type(x) >> 1523 >> 1524 def _coerce_map_from_(self, R): >> >> TypeError: <class >> 'sage.rings.polynomial.polynomial_quotient_ring_element.PolynomialQuo >> tientRingElement'> >> >> >> >> Since K and R are canonically isomorphic, it seems to me that K(r) >> should >> really work. Any thoughts? Is there another way I can get r into K? >> >> Best, >> Alex >> >> >> -- >> Alex Ghitza -- Lecturer in Mathematics -- The University of >> Melbourne -- >> Australia -- http://www.ms.unimelb.edu.au/~aghitza/ >> >>> >> > > > --~--~---------~--~----~------------~-------~--~----~ To post to this group, send email to sage-devel@googlegroups.com To unsubscribe from this group, send email to sage-devel-unsubscr...@googlegroups.com For more options, visit this group at http://groups.google.com/group/sage-devel URLs: http://www.sagemath.org -~----------~----~----~----~------~----~------~--~---
