Separate Sage-specific components from generic C-interface in PariInstance

[defeo]

In preparation for #20238, take out of PariInstance all components specific to Sage.

CC: @jdemeyer

Component: interfaces

Author: Luca De Feo

Branch/Commit: 62f227e

Reviewer: Jeroen Demeyer

Issue created by migration from https://trac.sagemath.org/ticket/20241

[defeo]

Branch: u/defeo/trac/u/defeo/pari_instance

[defeo]

Commit: 799f255

[defeo]

Dependencies: #20217

[defeo]

comment:2

I'm pushing a failed attempt at splitting PariInstance into a generic PariInstance cython type, and a Sage-specific SagePariInstance.

This is problematic because of the global sage.libs.pari.pari_instance.pari variable: it is not clear where this variable should go.

Some concrete suggestions: PariInstance serves three main purposes:

• As a wrapper around the pari stack,
• As a collection of conversion methods to and from pari types,
• As a namespace for a handful of functions, for lack of a better place (e.g. primes, genus2_reduction, ...)

Of these, only the first one really needs a Cython type. I suggest:

• To make a proper abstraction PariStack around the pari stack. This should not be handled as a global variable, but rather as a singleton class (we cannot have more than one pari stack, because of global variables).
• Move conversion functions to a separate namespace, as Implement conversion PARI <-> Python int/long without GMP/MPIR #20226 started doing.
• Have PariInstance hold a pointer to a PariStack. Have gen's hold a pointer to a PariInstance. (Maybe this double wrapping is superfluous?)

I don't know quite well what to do with utility functions such as primes. They may stay as methods of PariInstance, or maybe go to a different namespace as pure functions (they should take a PariInstance or PariStack as parameter, then).

---

Last 10 new commits:

dce67fc	Move memory functions to cysignals
4bb8337	Rename sage_malloc -> sig_malloc and friends
5ab73c1	Get rid of factorint_withproof_sage in PARI interface
c0ed97a	Stop using deprecated PARI factoring features
edc5ce2	Merge branch 't/20205/get_rid_of_factorint_withproof_sage_in_pari_interface' into HEAD
5fb408d	Replace pari_catch_sig_on by sig_on
d5c934c	Deprecate PARI nth_prime and prime_list
d7d2d7d	Remove redundant functions from pari_instance.pyx
282b187	Failed attempt to split PariInstance
799f255	Split pxd file too

[kedlaya]

comment:3

Regarding the utility functions: I think primes belongs in sage.rings.fast_arith along with prime_range, while genus2red should be in sage.schemes.hyperelliptic_curves.HyperellipticCurve_g2_rational_field which is otherwise completely empty! The other functions don't provide any new functionality (factorials, Chebyshev polynomials, etc.).

[defeo]

comment:4

Replying to @kedlaya:

Regarding the utility functions: I think primes belongs in sage.rings.fast_arith along with prime_range, while genus2red should be in sage.schemes.hyperelliptic_curves.HyperellipticCurve_g2_rational_field which is otherwise completely empty! The other functions don't provide any new functionality (factorials, Chebyshev polynomials, etc.).

Good points. These would take a lengthy deprecation process, and are better handled after a successful separation of the interface (something we're still having a hard time with).

I think the best place for this comment is in #20238, hence I'm copying it there.

[jdemeyer]

comment:5

@kedlaya: I don't really understand your comment. This ticket is about the interface between Sage and PARI (which is a purely technical non-mathematical thing), not about how which PARI functions are used where.

[defeo]

Changed branch from u/defeo/trac/u/defeo/pari_instance to u/defeo/ticket/20241

[defeo]

Changed commit from 799f255 to 7ad5c61

[defeo]

Changed dependencies from #20217 to #20217, #21158

[defeo]

Last 10 new commits:

12d9d32	Implement unary operations in interfaces
aae48bd	Merge branch 'ticket/21152' into t/20767/move_coercion_to_element
0a44b08	Remove one doctest for __mul__
54b0fcd	Various minor fixes for the coercion model
2405dde	Merge commit '0a44b082f08c742fbe564c5afdd2f7309fabbb52'; commit '54b0fcdaf2fd69cd64978da526af6774b57a59a8' into t/20767/move_coercion_to_element
e1d2ba4	Move arithmetic using coercion model to Element
b3ea04f	Try reversed operation in richcmp if coercion fails
efc4fd0	Merge branch 't/21163/in_richcmp__fall_back_to_reversed_operation_if_coercion_fails' into t/21158/ticket/21158
71f31a4	Decouple PARI from the Sage coercion model
7ad5c61	Step 1: make the unique PariInstance private

[jdemeyer]

Changed dependencies from #20217, #21158 to #21158