When you say "plot these values", do you mean as real or complex
values? To do so you need to choose an embedding, e.g.

sage: K.<a> = QQ[sqrt(5)]; K
 Number Field in sqrt5 with defining polynomial x^2 - 5

sage: K.embeddings(CC)
 [
Ring morphism:
  From: Number Field in sqrt5 with defining polynomial x^2 - 5
  To:   Complex Field with 53 bits of precision
  Defn: sqrt5 |--> -2.23606797749979,
Ring morphism:
  From: Number Field in sqrt5 with defining polynomial x^2 - 5
  To:   Complex Field with 53 bits of precision
  Defn: sqrt5 |--> 2.23606797749979
]

sage: f = K.embeddings(CC)[1]

sage: f(a)
 2.23606797749979

sage: f(1 + a)
 3.23606797749979

sage: f(a^2)
 5.00000000000000


If they are actually integral, you can do


sage: ZZ(a^2)
 5

sage: ZZ(a)
------------------------------------------------------------
Traceback (most recent call last):
  File "<ipython console>", line 1, in <module>
  File "parent.pyx", line 804, in
sage.structure.parent.Parent.__call__ (sage/structure/parent.c:7228)
  File "coerce_maps.pyx", line 156, in
sage.structure.coerce_maps.NamedConvertMap._call_
(sage/structure/coerce_maps.c:4557)
  File "number_field_element_quadratic.pyx", line 956, in
sage.rings.number_field.number_field_element_quadratic.NumberFieldElement_quadratic._integer_
(sage/rings/number_field/number_field_element_quadratic.cpp:8718)
TypeError: Unable to coerce sqrt5 to an integer


On Wed, Oct 17, 2012 at 10:45 AM, Eric Kangas <[email protected]> wrote:
> Hi,
>
> I am working with eigenvalues, and want to figure out a way to plot these
> values as a return map. I am using sage 4.7.2 on a ubuntu 10.10 on a Toshiba
> M200 tablet. Do I need to convert the algrbraic number to integers, or is
> there a way to plot these values?
>
> Eric
>
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