sagemathgh-38952: adding the ring of quantum-valued polynomials
    
This is a q-analogue of the ring of integer-valued polynomials. The
elements are polynomials in x such that their evaluation at every
q-integer is a polynomial in q.

### 📝 Checklist

- [x] The title is concise and informative.
- [x] The description explains in detail what this PR is about.
- [ ] I have linked a relevant issue or discussion.
- [x] I have created tests covering the changes.
- [x] I have updated the documentation and checked the documentation
preview.
    
URL: sagemath#38952
Reported by: Frédéric Chapoton
Reviewer(s): Frédéric Chapoton, Travis Scrimshaw

Author: Release Manager

src/doc/en/reference/polynomial_rings/polynomial_rings_univar.rst

@@ -45,3 +45,4 @@ whereas others have multiple bases.
    sage/rings/polynomial/polynomial_fateman
 
    sage/rings/polynomial/integer_valued_polynomials
+   sage/rings/polynomial/q_integer_valued_polynomials

src/doc/en/reference/references/index.rst

@@ -3214,6 +3214,10 @@ REFERENCES:
              The Electronic Journal of Combinatorics 11 (2004), #R77.
              http://www.combinatorics.org/Volume_11/PDF/v11i1r77.pdf
 
+.. [HaHo2017] Nate Harman and Sam Hopkins,
+              *Quantum integer-valued polynomials*,
+              J. Alg. Comb. 2017, :doi:`10.1007/s10801-016-0717-3`
+
 .. [Hai1989] M.D. Haiman, *On mixed insertion, symmetry, and shifted
              Young tableaux*. Journal of Combinatorial Theory, Series
              A Volume 50, Number 2 (1989), pp. 196-225.
@@ -3227,7 +3231,7 @@ REFERENCES:
              http://www-math.mit.edu/~hajiagha/pp11.ps
 
 .. [Han1960] Haim Hanani,
-             On quadruple systems,
+             *On quadruple systems*,
              pages 145--157, vol. 12,
              Canadian Journal of Mathematics,
              1960

src/sage/rings/polynomial/all.py

@@ -54,3 +54,5 @@
 # Integer-valued Univariate Polynomial Ring
 lazy_import('sage.rings.polynomial.integer_valued_polynomials',
             'IntegerValuedPolynomialRing')
+lazy_import('sage.rings.polynomial.q_integer_valued_polynomials',
+            'QuantumValuedPolynomialRing')

src/sage/rings/polynomial/meson.build

@@ -52,6 +52,7 @@ py.install_sources(
   'polynomial_singular_interface.py',
   'polynomial_zmod_flint.pxd',
   'polynomial_zz_pex.pxd',
+  'q_integer_valued_polynomials.py',
   'real_roots.pxd',
   'skew_polynomial_element.pxd',
   'skew_polynomial_finite_field.pxd',