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

Roadmap:

• basic:
  • recognizable series (a base for k-regular sequences) #21295: recognizable series and the minimization algorithm
  • basic element and parent for k-regular sequences #21203: basic element and parent for k-regular sequences
• arithmetic:
  • enable coercions and functorial constructions
  • recognizable series: basic arithmetic #21318: scalar multiplication
  • recognizable series: basic arithmetic #21318: addition/subtraction
  • k-regular sequences: subsequences, forward/backward difference, partial sums #21325: subsequences, shift
  • k-regular sequences: subsequences, forward/backward difference, partial sums #21325: forward/backward differences, partial summation
  • regular sequences: use "positive" partial sums algorithm #36001: regular sequences: use "positive" partial sums algorithm
  • conversion of automatic sequences to formal series via Christol's theorem and vice versa
  • recognizable series: hash, comparison, TestSuite #21319: hashing, equality testing, TestSuite
  • Regular sequences: implement convolution / ring structure #35894: Regular sequences: implement convolution / ring structure
• guessing k-regular sequences #21204: guessing k-regular sequences from the first few values
• getting k-regular sequences from given recurrence relations:
  • get k-regular sequence from certain recurrence relations #27940: basic methods, with symbolic equations as input
  • kRegularSequenceSpace.from_recurrence: make offset keyword-only #32198, Alternative parameters for generating a k-regular sequence from recurrence relations #31787: alternative input parameters (without symbolic ring)
  • k-recursive sequences with inhomogeneities #32921: deal with inhomogeneities
• k-regular sequences: boundedness #22964: boundedness
• other:
  • deal with bad chosen representations of k-regular sequences #21343: deal with mu[0]*right != right in k-regular sequences
• related tickets:
  • Compute bounds for the joint spectral radius #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