Add tamagawa_numbers method for elliptic curves over number fields

[RalphieBoy]

Elliptic curves over the rationals have a method that returns a list of tamagawa numbers for the curve. There is no such method in the case of number fields.

Component: elliptic curves

Keywords: tamagawa number

Author: Justin Walker

Reviewer: David Loeffler

Merged: sage-4.5.2.alpha0

Issue created by migration from https://trac.sagemath.org/ticket/9387

[RalphieBoy]

comment:1

Added patch with the method tamagawa_numbers(), essentially a duplication of the code for the rational case.

[RalphieBoy]

comment:2

Updated the patch with a corrected doctest (run and passed).

[loefflerd]

comment:3

Just a suggestion: why duplicate the code? Since EllipticCurve_rational_field inherits from EllipticCurve_number_field, you could just move the code. Then we don't have the overhead of maintaining two routines doing exactly the same, and the likelihood of bugs is halved. Compare John's regulator patch at #9372.

[JohnCremona]

comment:4

That's a good idea. Justin, all that's needed is (a) delete the version in ell_rational_field, (b) make sure that the code in ell_number_field works over Q (say by moving the old doctest into the new function -- it should have examples over Q and over another field.

There might be other functions like this. If you notice any, make a ticket!

[loefflerd]

comment:6

sage -t  ell_number_field.py
**********************************************************************
File "/storage/masiao/sage-4.5.alpha1/devel/sage-reviewing/sage/schemes/elliptic_curves/ell_number_field.py", line 1049:
    sage: K=NumberField(x^2+3)
Exception raised:
    Traceback (most recent call last):
      File "/storage/masiao/sage-4.5.alpha1/local/bin/ncadoctest.py", line 1231, in run_one_test
        self.run_one_example(test, example, filename, compileflags)
      File "/storage/masiao/sage-4.5.alpha1/local/bin/sagedoctest.py", line 38, in run_one_example
        OrigDocTestRunner.run_one_example(self, test, example, filename, compileflags)
      File "/storage/masiao/sage-4.5.alpha1/local/bin/ncadoctest.py", line 1172, in run_one_example
        compileflags, 1) in test.globs
      File "<doctest __main__.example_22[5]>", line 1, in <module>
        K=NumberField(x**Integer(2)+Integer(3))###line 1049:
    sage: K=NumberField(x^2+3)
      File "/storage/masiao/sage-4.5.alpha1/local/lib/python/site-packages/sage/rings/number_field/number_field.py", line 431, in NumberField
        raise TypeError, "You must specify the name of the generator."
    TypeError: You must specify the name of the generator.
**********************************************************************                           

You should also probably delete, rather than comment out, the code in ell_rational_field.

[RalphieBoy]

comment:7

OK, that's weird. Turns out I popped when I should have pushed, so I was testing unmodified code. I'll be back.

[RalphieBoy]

Attachment: 9387.patch.gz

New version of patch following DavidL's suggestion

[RalphieBoy]

comment:8

New patch, replacing previous one. This time, with some luck, I verified the patch against both 4.4.4 and 4.5.a1.

Comments, brickbats, scotch all welcome.

[loefflerd]

Reviewer: David Loeffler

[loefflerd]

comment:9

Looks good to me.

[qed777]

Merged: sage-4.5.2.alpha0