Compute the Conway mass directly from the genus symbol.

[simonbrandhorst]

Conway and Sloane's formalism to compute the mass starts with their genus symbol.
Currently the quadratic forms code does this in a detour.

This ticket moves this functionality to the genus class where it really belongs. As a further advantage this allows to compute the mass of a genus without computing a representative first.

Component: quadratic forms

Author: Simon Brandhorst

Branch/Commit: 9b1bb8f

Reviewer: Frédéric Chapoton

Issue created by migration from https://trac.sagemath.org/ticket/29609

[simonbrandhorst]

Branch: u/sbrandhorst/compute_the_conway_mass_directly_from_the_genus_symbol_

[simonbrandhorst]

Commit: fff7fa5

[simonbrandhorst]

New commits:

fff7fa5

Mass formula for genus symbols

[fchapoton]

comment:3

patchbot's pyflakes plugin is not happy

[fchapoton]

comment:4

typo "are taken crom"

Better avoid unicode dash between pages numbers in the reference file

[simonbrandhorst]

comment:5

Note:
The mass computation should be correct. I compared mass computations for all genera of rank 3 and 4 and determinant < 1000 with magma.

[sagetrac-git]

Changed commit from fff7fa5 to fcb9a7a

[sagetrac-git]

Branch pushed to git repo; I updated commit sha1. New commits:

fcb9a7a

Pyflakes and docs

[simonbrandhorst]

comment:7

I guess in a follow up one could deprecate

conway_species_list_at_odd_prime, \
conway_species_list_at_2, \
conway_octane_of_this_unimodular_Jordan_block_at_2, \
conway_diagonal_factor, \
conway_cross_product_doubled_power, \
conway_type_factor, \
conway_p_mass, \
conway_standard_p_mass, \
conway_standard_mass, \

From my point of view the functions above have no value for themselves they are just intermediate results of the mass computation.

[fchapoton]

comment:8

a few more comments:

• Do you really need srange ?

• The comment "# By conway-sloane we have to compensate the missing euler factors" could use capitals for names.

• The 3 new raise statements must be doctested, for example raise ValueError("Genus must be definite.")

[sagetrac-git]

Changed commit from fcb9a7a to 1be5ffc

[sagetrac-git]

Branch pushed to git repo; I updated commit sha1. New commits:

1be5ffc

followed reviewers suggestions

[fchapoton]

comment:13

You need only a single colon after TESTS here

+        TESTS::
+
+        Check a random genus magma::

Why did you keep the import of srange ?

[sagetrac-git]

Changed commit from 1be5ffc to 9b1bb8f

[sagetrac-git]

Branch pushed to git repo; I updated commit sha1. New commits:

9b1bb8f

remove srange

[simonbrandhorst]

comment:15

Forgot to commit. Hope it is okay now.

[fchapoton]

comment:16

ok, let it be. Too bad that you need the symbolic ring.

[fchapoton]

Reviewer: Frédéric Chapoton

[simonbrandhorst]

comment:17

Do you think it slows down things a lot?
I guess one could get rid of SR when combining factors correctly. But it is more work.

[vbraun]

Changed branch from u/sbrandhorst/compute_the_conway_mass_directly_from_the_genus_symbol_ to 9b1bb8f