What does it mean to reduce one polynomial "modulo" another polynomial?

Question

I'm familiar with the concept of modular arithmetic, but only with constants. I've never seen it with polynomials before. How would I reduce $q(x)$ modulo $p(x)$? Do polynomial long division and take the remainder?

More or less, yes. It's the same as with integers in that regard. — Arthur, Apr 13 '17 at 16:43
It's explained here pretty clearly -- https://en.wikipedia.org/wiki/Polynomial_long_division — Zz'Rot, Apr 13 '17 at 16:49

score 1 · Answer 1 · answered Apr 13 '17 at 16:52

1

Exactly as you said, if $q(x)$ can be divided with remainder by $p(x)$, you can keep $r(x)$ instead of $q(x)$.

answered Apr 13 '17 at 16:52

Reb

367

score 1 · Answer 2 · answered Apr 13 '17 at 16:55

1

It means to calculate the remainer when dividing $q(x)$ by $p(x)$ using long division.

answered Apr 13 '17 at 16:55

Asinomás

105,651

What does it mean to reduce one polynomial "modulo" another polynomial?

2 Answers2