14.1. Introduction🔗

HexGFqRing is the executable quotient ring Fₚ[x] / (f) over a fixed nonconstant polynomial modulus f of type Hex.FpPoly. Elements are reduced polynomial representatives: Hex.FpPoly values of degree strictly below Hex.FpPoly.degree of f. Every ring operation normalizes through Hex.GFqRing.reduceMod, so equality of quotient elements coincides with equality of canonical representatives.

The modulus f is not required to be irreducible: when f is reducible the quotient is still a ring, used downstream wherever a fixed-modulus polynomial ring is needed. When f is irreducible, the same underlying representation supports a field structure, supplied by HexGFqField. See Cross-references below.