PolynomialMod[poly, m] gives the polynomial poly reduced modulo m.
PolynomialMod[poly, , , ... ] reduces modulo all of the .
PolynomialMod[poly, m] for integer m gives a polynomial in which all coefficients are reduced modulo m.
Example: PolynomialMod[3x^2 + 2x + 1, 2] .
When m is a polynomial, PolynomialMod[poly, m] reduces poly by subtracting polynomial multiples of m, to give a result with minimal degree and leading coefficient.
PolynomialMod gives results according to a definite convention; other conventions could yield results differing by multiples of m.
Unlike PolynomialRemainder, PolynomialMod never performs divisions in generating its results.
See The Mathematica Book: Section 3.3.4.
See also: PolynomialGCD, Mod, PolynomialRemainder, PolynomialReduce, GroebnerBasis.
Related package: Algebra`PolynomialPowerMod`.