Meta ticket: k-regular sequences

[dkrenn]

Implementation of k-regular sequences (https://en.wikipedia.org/wiki/K-regular_sequence).

---

Roadmap:

• basic:

  • 21295: recognizable series and the minimization algorithm

  • 21203: basic element and parent for k-regular sequences

• arithmetic:
  • enable coercions and functorial constructions

  • 21318: scalar multiplication

  • 21318: addition/subtraction

  • 21325: subsequences, shift

  • 21325: forward/backward differences, partial summation

  • 36001: regular sequences: use "positive" partial sums algorithm

  • conversion of automatic sequences to formal series via Christol's theorem and vice versa

  • 21319: hashing, equality testing, TestSuite

  • 35894: Regular sequences: implement convolution / ring structure

• 21204: guessing k-regular sequences from the first few values

• getting k-regular sequences from given recurrence relations:

  • 27940: basic methods, with symbolic equations as input

  • 32198, #31787: alternative input parameters (without symbolic ring)

  • 32921: deal with inhomogeneities

• 22964: boundedness

• other:

  • 21343: deal with mu[0]*right != right in k-regular sequences

• related tickets:

  • 21205: bounds for the joint spectral radius

Depends on #21203 Depends on #21204 Depends on #21295 Depends on #21318 Depends on #21319 Depends on #21325 Depends on #21343 Depends on #22964 Depends on #27940 Depends on #31787 Depends on #32198 Depends on #32921

CC: @behackl @cheuberg @galipnik

Component: combinatorics

Author: Daniel Krenn, Gabriel F. Lipnik

Branch/Commit: u/dkrenn/k-regular-trunk @ f3564a3

Issue created by migration from https://trac.sagemath.org/ticket/21202

[dkrenn]

comment:39

This is now on 9.3.

Dependency chain: #21295 #21203 #21318 #21325 #21319 #21204 #21343 #22964.

[galipnik]

Description changed:

--- 
+++ 
@@ -14,9 +14,10 @@
   - conversion of automatic sequences to formal series via Christol's theorem and vice versa
   - #21319: hashing, equality testing, TestSuite
 - #21204: guessing k-regular sequences from the first few values
-- getting k-regular sequences from given recurrence relations
-  - #27940: basic methods
-  - #31787: get sequences with different input parameters
+- getting k-regular sequences from given recurrence relations:
+  - #27940: basic methods, with symbolic equations as input
+  - #31787: alternative input parameters (without symbolic ring)
+  - deal with inhomogeneities
 - #22964: boundedness
 - other:
   - #21343: deal with mu[0]*right != right in k-regular sequences

[galipnik]

Description changed:

--- 
+++ 
@@ -16,7 +16,7 @@
 - #21204: guessing k-regular sequences from the first few values
 - getting k-regular sequences from given recurrence relations:
   - #27940: basic methods, with symbolic equations as input
-  - #31787: alternative input parameters (without symbolic ring)
+  - #32198, #31787: alternative input parameters (without symbolic ring)
   - deal with inhomogeneities
 - #22964: boundedness
 - other:

[galipnik]

Changed dependencies from #21203, #21204, #21295, #21318, #21319, #21325, #21343 to #21203, #21204, #21295, #21318, #21319, #21325, #21343, #22964, #27940, #31787, #32198, #32921

[galipnik]

Description changed:

--- 
+++ 
@@ -17,7 +17,7 @@
 - getting k-regular sequences from given recurrence relations:
   - #27940: basic methods, with symbolic equations as input
   - #32198, #31787: alternative input parameters (without symbolic ring)
-  - deal with inhomogeneities
+  - #32921: deal with inhomogeneities
 - #22964: boundedness
 - other:
   - #21343: deal with mu[0]*right != right in k-regular sequences

[galipnik]

Changed author from Daniel Krenn to Daniel Krenn, Gabriel F. Lipnik

[7ed8c4ca-6d56-4ae9-953a-41e42b4ed313]

Changed commit from 478b8b1 to f3564a3

[7ed8c4ca-6d56-4ae9-953a-41e42b4ed313]

Branch pushed to git repo; I updated commit sha1. Last 10 new commits:

3b7c431	Trac #21325 review comment 13: use .linear representation in examples partial_sum
33d4dae	Trac #21325 review comment 14+15: rewrite construction dict
ecb3663	Trac #21325 review comment 17: simpler (more readable) construction of block matrix
96df7b3	Trac #21325 review comment 18: deal with remaining block vectors
26e2d6f	Trac #21325 review comment 19: shift_left, shift_right
b4f83e4	Merge branch 'u/dkrenn/sequences/k-regular-subseq' into t/21319/sequences/rec-hash
9fefcce	Follow-up from Trac #21325 review comment 19: shift_left+right: test equality
3c634df	Merge branch 't/21319/sequences/rec-hash' into t/21204/sequences/k-regular-guess
4af416c	Merge branch 't/21204/sequences/k-regular-guess' into t/21343/k-regular-warning
f3564a3	Merge remote-tracking branch 'trac/u/dkrenn/k-regular-warning' into u/dkrenn/k-regular-trunk