[with patch; positive review] Major Upgrade to QuadraticForm Local Density Routines

[jonhanke]

Completely rewritten and doctested Local densities routines according to a consistent interface (and algorithms) described in the attached PDF file.

[jonhanke]

Description of the inputs and algorithms used in QF local density routines

[jonhanke]

LaTeX file used to create the PDF writeup

[tornaria]

Looks nice. For the record, the following exported member functions (of QuadraticForm?) have been renamed/removed:

• reindex_vector_from_extraction was removed
• count_modp__by_gauss_sum was renamed to count_modp_solutions__by_Gauss_sum.
• local_good_density_congruence_even__experimental was removed.
• VecIncrement__deprecated was removed.
• local_solution_type__deprecated was removed.
• CountAllLocalTypesNaive__deprecated was removed.
• count_local_type was renamed to count_congruence_solutions.
• count_local_good_type was renamed to count_congruence_solutions__good_type.
• count_local_zero_type was renamed to count_congruence_solutions__zero_type.
• count_local_bad_type was renamed to count_congruence_solutions__bad_type.
• count_local_bad_typeI was renamed to count_congruence_solutions__bad_type_I.
• count_local_bad_typeII was renamed to count_congruence_solutions__bad_type_II.
• local_good_density was removed.
• local_zero_density was removed.
• local_bad_density was removed.
• local_badI_density was removed.
• local_badII_density was removed.

I think the __deprecated and __experimental functions need no comment. For the renamed functions, though, it may be nice to add a compatibility wrapper with deprecation warning... (where and how?)

Jon, internal routines should be using names starting with an underscore (that's the python convention).

[mabshoff]

Merged patch-2QF_local_densities3.4.1.patch in Sage 4.0.rc0.

Cheers,

Michael