gives the polynomial poly reduced modulo m.
reduces modulo all of the mi.
Details and Options
- PolynomialMod[poly,m] for integer m gives a polynomial in which all coefficients are reduced modulo m.
- 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.
Examplesopen allclose all
Reduce a polynomial modulo an integer:
Reduce a multivariate polynomial modulo an integer:
Reduce a polynomial modulo a polynomial:
The difference of the original polynomial and the result is divisible by the modulus:
Reduce a polynomial modulo a polynomial with complex coefficients:
Reduce a polynomial modulo a polynomial and an integer:
With the default CoefficientDomain->Rationals, integer coefficients can be inverted:
With CoefficientDomain->Integers, PolynomialMod does not invert integer coefficients:
Properties & Relations (5)
For univariate rational polynomials, PolynomialRemainder is the same as PolynomialMod:
PolynomialRemainder considers all polynomials to be univariate in the specified variable:
For multivariate polynomials, PolynomialMod picks its own variable order:
PolynomialRemainder considers parameters to be invertible:
PolynomialMod does not invert symbolic expressions:
Wolfram Research (1991), PolynomialMod, Wolfram Language function, https://reference.wolfram.com/language/ref/PolynomialMod.html.
Wolfram Language. 1991. "PolynomialMod." Wolfram Language & System Documentation Center. Wolfram Research. https://reference.wolfram.com/language/ref/PolynomialMod.html.
Wolfram Language. (1991). PolynomialMod. Wolfram Language & System Documentation Center. Retrieved from https://reference.wolfram.com/language/ref/PolynomialMod.html