[with patch, needs review] Factory and pickling framework (part of coercion branch)

Code documented and works great/passes tests. Just need some doctests in factory.pyx (perhaps via a fake test class?)

Needs to be rebased against 3.1.2.alpha4:

sage: hg_sage.apply('http://trac.sagemath.org/sage_trac/attachment/ticket/3623/3623-factory-2.patch')
Attempting to load remote file: http://trac.sagemath.org/sage_trac/attachment/ticket/3623/3623-factory-2.patch?format=raw
Loading: [....]
cd "/Volumes/Place/anakha/sage-3.1.2.alpha4/devel/sage" && hg status
cd "/Volumes/Place/anakha/sage-3.1.2.alpha4/devel/sage" && hg status
cd "/Volumes/Place/anakha/sage-3.1.2.alpha4/devel/sage" && hg import   "/Users/anakha/.sage/temp/fullmetal.umn/58245/tmp_1.patch"
applying /Users/anakha/.sage/temp/fullmetal.umn/58245/tmp_1.patch
patching file sage/modules/free_module.py
Hunk #1 FAILED at 157
Hunk #2 FAILED at 261
2 out of 2 hunks FAILED -- saving rejects to file sage/modules/free_module.py.rej
abort: patch failed to apply

Otherwise, I like this very much after having gone through the pain of implementing a unique factory for a parent already, I would have wasted a week less if this had already been in sage.

Thanks. I'll rebase this as soon as 3.1.2 comes out (as I doubt this ticket will make it into there).

All four patches rebased.

Hi Robert,

This bitrotted again. Sorry!

was@sage:~/build/sage-3.2.1.alpha1$ ./sage
----------------------------------------------------------------------
| Sage Version 3.2.1.alpha1, Release Date: 2008-11-26                |
| Type notebook() for the GUI, and license() for information.        |
----------------------------------------------------------------------
sage: hg_sage.apply('http://trac.sagemath.org/sage_trac/attachment/ticket/3623/3623-factory-1.patch')
Attempting to load remote file: http://trac.sagemath.org/sage_trac/attachment/ticket/3623/3623-factory-1.patch?format=raw
Loading: [.]
cd "/home/was/build/sage-3.2.1.alpha1/devel/sage" && hg status
cd "/home/was/build/sage-3.2.1.alpha1/devel/sage" && hg status
cd "/home/was/build/sage-3.2.1.alpha1/devel/sage" && hg import   "/home/was/.sage/temp/sage/14985/tmp_0.patch"
applying /home/was/.sage/temp/sage/14985/tmp_0.patch
patching file setup.py
Hunk #1 FAILED at 533
1 out of 1 hunk FAILED -- saving rejects to file setup.py.rej
abort: patch failed to apply
sage: 

Can you rebase it an email me asap so this can get properly refereed and *not* bitrot again.

patches 1-5 folded and rebased onto 3.2.1

OK, this is once again rebased.

The patch applies cleanly against 3.2.1 and together with #4276 I am seeing two doctest failures:

sage -t -long "devel/sage/sage/structure/coerce.pyx"        
**********************************************************************
File "/scratch/mabshoff/release-cycle/sage-3.2.2.alpha0/devel/sage/sage/structure/coerce.pyx", line 862:
    sage: V is W
Expected:
    False
Got:
    True
**********************************************************************
File "/scratch/mabshoff/release-cycle/sage-3.2.2.alpha0/devel/sage/sage/structure/coerce.pyx", line 865:
    sage: cm.coercion_maps(V, W)
Expected:
    (None,
     Call morphism:
      From: Vector space of dimension 3 over Rational Field
      To:   Vector space of dimension 3 over Rational Field)
Got:
    (None, None)
**********************************************************************
File "/scratch/mabshoff/release-cycle/sage-3.2.2.alpha0/devel/sage/sage/structure/coerce.pyx", line 870:
    sage: cm.coercion_maps(W, V)
Expected:
    (None,
     Call morphism:
      From: Vector space of dimension 3 over Rational Field
      To:   Vector space of dimension 3 over Rational Field)
Got:
    (None, Free module morphism defined by the matrix
    [1 0 0]
    [0 1 0]
    [0 0 1]
    Domain: Vector space of dimension 3 over Rational Field
    Codomain: Vector space of dimension 3 over Rational Field)
**********************************************************************
1 items had failures:
   3 of  21 in __main__.example_15
***Test Failed*** 3 failures.

I guess the first one is worrying while the rest is mostly a printing issue.

The other failure is:

sage -t -long "devel/sage/sage/schemes/elliptic_curves/ell_number_field.py"
**********************************************************************
File "/scratch/mabshoff/release-cycle/sage-3.2.2.alpha0/devel/sage/sage/schemes/elliptic_curves/ell_number_field.py", line 667:
    sage: [E.tamagawa_exponent(P) for P in K(11).support()]
Exception raised:
    Traceback (most recent call last):
      File "/scratch/mabshoff/release-cycle/sage-3.2.2.alpha0/local/bin/ncadoctest.py", line 1231, in run_one_test
        self.run_one_example(test, example, filename, compileflags)
      File "/scratch/mabshoff/release-cycle/sage-3.2.2.alpha0/local/bin/sagedoctest.py", line 38, in run_one_example
        OrigDocTestRunner.run_one_example(self, test, example, filename, compileflags)
      File "/scratch/mabshoff/release-cycle/sage-3.2.2.alpha0/local/bin/ncadoctest.py", line 1172, in run_one_example
        compileflags, 1) in test.globs
      File "<doctest __main__.example_20[7]>", line 1, in <module>
        [E.tamagawa_exponent(P) for P in K(Integer(11)).support()]###line 667:
    sage: [E.tamagawa_exponent(P) for P in K(11).support()]
      File "/scratch/mabshoff/release-cycle/sage-3.2.2.alpha0/local/lib/python2.5/site-packages/sage/schemes/elliptic_curves/ell_number_field.py", line 675, in tamagawa_exponent
        return self.local_data(P, proof).tamagawa_exponent()
      File "/scratch/mabshoff/release-cycle/sage-3.2.2.alpha0/local/lib/python2.5/site-packages/sage/schemes/elliptic_curves/ell_number_field.py", line 401, in local_data
        return self._get_local_data(P,proof)
      File "/scratch/mabshoff/release-cycle/sage-3.2.2.alpha0/local/lib/python2.5/site-packages/sage/schemes/elliptic_curves/ell_number_field.py", line 418, in _get_local_data
        self._local_data[P] = EllipticCurveLocalData(self, P, proof)
      File "/scratch/mabshoff/release-cycle/sage-3.2.2.alpha0/local/lib/python2.5/site-packages/sage/schemes/elliptic_curves/ell_local_data.py", line 140, in __init__
        self._Emin, ch, self._val_disc, self._fp, self._KS, self._cp, self._split = self._tate(proof)
      File "/scratch/mabshoff/release-cycle/sage-3.2.2.alpha0/local/lib/python2.5/site-packages/sage/schemes/elliptic_curves/ell_local_data.py", line 528, in _tate
        r = -pinv(12*c4) * (c6 + b2 * c4)
      File "element.pyx", line 1074, in sage.structure.element.RingElement.__mul__ (sage/structure/element.c:8580)
      File "coerce.pyx", line 697, in sage.structure.coerce.CoercionModel_cache_maps.bin_op (sage/structure/coerce.c:5808)
    TypeError: unsupported operand parent(s) for '*': 'Maximal Order in Number Field in a with defining polynomial x^2 + 11' and 'Number Field in a with defining polynomial x^2 + 11'
**********************************************************************

Cheers,

Michael