Meta-ticket: Use new features from FLINT 2.x, 3.x

[mkoeppe]

As of Sage 10.4, Sage ships FLINT 3.0.1 (update to 3.1.3 in #37203), accepts system FLINT >= 3.0.

Many of the features added in the FLINT 2.x and 3.x series are so far unused in Sage.

Tickets/features:

• matrix classes for flint polynomials #8939
• Wrap flint's fast rational functions over QQ #16429
• Add a finite field implementation using FLINT's fq and fq_nmod modules #16664
• Implement power_sums and power_sums_to_poly #20004
• add minimal interface for using ZZ[x]-matrices from flint #29894
• Wrap FLINT 2.6 functions, drop support for system FLINT < 2.6 #31525
• Support FLINT 2.8.0 #32175
• Create matrix class for FLINT's nmod_mat module #31548 Use FLINT's nmod_mat_t for matrices mod n.
• Multivariate polynomials with FLINT #31666 very fast multi-variate polynomials - use them for Sage polynomial rings and perhaps in sage.tensor.modules
• Flint generic rings #36433

For creating the bindings to the new FLINT functions, there is a potential for synergy with https://github.com/fredrik-johansson/python-flint; the SymPy developers have announced (2021) that they plan to use python-flint.

CC: @slel @videlec @fredrik-johansson @isuruf

Component: algebra

Keywords: flint

Issue created by migration from https://trac.sagemath.org/ticket/31408

[mkoeppe]

Description changed:

--- 
+++ 
@@ -1,5 +1,10 @@
-https://github.com/wbhart/flint2/blob/trunk/NEWS (newest items at the end)
+Sage currently ships FLINT 2.6.3, accepts system FLINT 2.5.0; current release (as of Feb 2021) is 2.7.1
+
+Many of the features added in the FLINT 2.x series are so far unused in Sage. See https://github.com/wbhart/flint2/blob/trunk/NEWS (newest items at the end)
+
+Tickets/features:
+- #29894 minimal interface for using ZZ[x] matrices in Flint
+
+- very fast multi-variate polynomials
 
 
-
-

[mkoeppe]

Description changed:

--- 
+++ 
@@ -5,6 +5,6 @@
 Tickets/features:
 - #29894 minimal interface for using ZZ[x] matrices in Flint
 
-- very fast multi-variate polynomials
+- very fast multi-variate polynomials - use them for Sage polynomial rings and perhaps in sage.tensor.modules
 
 

[slel]

Description changed:

--- 
+++ 
@@ -1,10 +1,10 @@
-Sage currently ships FLINT 2.6.3, accepts system FLINT 2.5.0; current release (as of Feb 2021) is 2.7.1
+Sage currently ships FLINT 2.6.3, accepts system FLINT 2.5.0; current FLINT release (as of Feb 2021) is 2.7.1, see #31069 for upgrading FLINT in Sage.
 
 Many of the features added in the FLINT 2.x series are so far unused in Sage. See https://github.com/wbhart/flint2/blob/trunk/NEWS (newest items at the end)
 
 Tickets/features:
+
 - #29894 minimal interface for using ZZ[x] matrices in Flint
-
-- very fast multi-variate polynomials - use them for Sage polynomial rings and perhaps in sage.tensor.modules
+- very fast multi-variate polynomials - use them for Sage polynomial rings and perhaps in `sage.tensor.modules`
 
 

[slel]

Changed keywords from none to flint

[slel]

comment:4

Possibly related: #16812, #16664, #16429.

Older: #9541, #8939.

[mkoeppe]

Description changed:

--- 
+++ 
@@ -5,6 +5,7 @@
 Tickets/features:
 
 - #29894 minimal interface for using ZZ[x] matrices in Flint
+- #31525 Wrap FLINT 2.6 functions, drop support for system FLINT < 2.6
 - very fast multi-variate polynomials - use them for Sage polynomial rings and perhaps in `sage.tensor.modules`
 
 

[mkoeppe]

comment:6

Sage development has entered the release candidate phase for 9.3. Setting a new milestone for this ticket based on a cursory review of ticket status, priority, and last modification date.

[roed314]

Description changed:

--- 
+++ 
@@ -6,6 +6,7 @@
 
 - #29894 minimal interface for using ZZ[x] matrices in Flint
 - #31525 Wrap FLINT 2.6 functions, drop support for system FLINT < 2.6
+- #31548 Use FLINT's `nmod_mat_t` for matrices mod n.
 - very fast multi-variate polynomials - use them for Sage polynomial rings and perhaps in `sage.tensor.modules`
 
 

[mkoeppe]

Description changed:

--- 
+++ 
@@ -7,6 +7,6 @@
 - #29894 minimal interface for using ZZ[x] matrices in Flint
 - #31525 Wrap FLINT 2.6 functions, drop support for system FLINT < 2.6
 - #31548 Use FLINT's `nmod_mat_t` for matrices mod n.
-- very fast multi-variate polynomials - use them for Sage polynomial rings and perhaps in `sage.tensor.modules`
+- #31666 very fast multi-variate polynomials - use them for Sage polynomial rings and perhaps in `sage.tensor.modules`
 
 

[mkoeppe]

Description changed:

--- 
+++ 
@@ -1,4 +1,4 @@
-Sage currently ships FLINT 2.6.3, accepts system FLINT 2.5.0; current FLINT release (as of Feb 2021) is 2.7.1, see #31069 for upgrading FLINT in Sage.
+As of Sage 9.4, Sage ships FLINT 2.7.1 (#31069), accepts system FLINT >= 2.6.0, and is ready for FLINT 2.8.x.
 
 Many of the features added in the FLINT 2.x series are so far unused in Sage. See https://github.com/wbhart/flint2/blob/trunk/NEWS (newest items at the end)
 
@@ -6,7 +6,7 @@
 
 - #29894 minimal interface for using ZZ[x] matrices in Flint
 - #31525 Wrap FLINT 2.6 functions, drop support for system FLINT < 2.6
+- #32175 Support FLINT 2.8.0
 - #31548 Use FLINT's `nmod_mat_t` for matrices mod n.
 - #31666 very fast multi-variate polynomials - use them for Sage polynomial rings and perhaps in `sage.tensor.modules`
 
-

[mkoeppe]

Description changed:

--- 
+++ 
@@ -10,3 +10,6 @@
 - #31548 Use FLINT's `nmod_mat_t` for matrices mod n.
 - #31666 very fast multi-variate polynomials - use them for Sage polynomial rings and perhaps in `sage.tensor.modules`
 
+For creating the bindings to the new FLINT functions, there is a potential for synergy with https://github.com/fredrik-johansson/python-flint; the SymPy developers have [announced](https://groups.google.com/g/sympy/c/vYsavewGj1w/m/CQKTSznPAgAJ) (2021) that they plan to use `python-flint`.
+
+