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I try to do the following in Magma:

P< x, y > := PolynomialRing(ComplexField(), 2);

I := ideal < P |

x + y>;

I got the error: "Runtime error in ideal<...>: Base ring must be an exact field or an Euclidean ring." I don't really understand what this is about. Could someone please explain?

Thanks!!!

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 Try P<x,y>:= .... but I'm voting to close as too localized. – Felipe Voloch Nov 23 2010 at 3:11
I second Felipe's suggestion. This sounds like something you should be able to find in the documentation. – Adam Hughes Nov 23 2010 at 3:16
Right, I tried that (and that was what I typed but for some reason, Mathoverflow ate my brackets). – Brian Nov 23 2010 at 3:18
@Brian: this is not really appropriate for this site. But I think I can tell you the problem. Probably magma wants to store ideals for polynomial rings internally in some sort of "canonical form", and this canonical form relies on the base field having some arithmetic properties. For example if you replace "ComplexField()" with "Rationals()" or "Integers()" then there is no problem. The problem is that the reals and the complexes are absolute minefields for computer algebra packages; the rationals are an "exact field" in the sense that every element can be encoded by a finite amount... – Kevin Buzzard Nov 23 2010 at 9:31
...of data. The complexes are very far from having this property. The worse your base field is, the less far you can expect general functions to be implemented: e.g. "ideal" doesn't seem to have been implemented for polynomials in several variables over the complexes. This does not mean that magma can't solve your problem! But it does mean that you're inputting your problem in not a good way. What do you want to do with these ideals? Why not work over a number field? Do you really need transcendentals? If you need one transcendental, then... – Kevin Buzzard Nov 23 2010 at 9:33
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closed as too localized by Felipe Voloch, Pete L. Clark, Andres Caicedo, Robin Chapman, Kevin Buzzard Nov 23 2010 at 9:34

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