17 мая 2013 г. · You sum the classes normally, and as to the product, you first take the product, and then take the remainder of Euclidean division by x4+1.

26 апр. 2015 г. · A polynomial q(x) is contained in the coset r(x)+I where I is the set of multiples of p(x). It is an expression in powers of x, where p(x)≡0 so ...

7 мар. 2014 г. · A quotient of rings is a structure where you add a new equation in the previous ring. For example, R[T]/(T2+1). is the ring of polynomials, ...

3 мар. 2022 г. · The notion of "size" we use when we quotient polynomial rings is not the absolute value, but the degree. So for instance, something like ...

25 февр. 2013 г. · The Quotient Ring is the set of additive cosets, so we have that R[x]/(x3)={f+(x3):f∈R[x]}. So we have the relation f−g≡0 ...

5 янв. 2014 г. · This normal form rewriting using the polynomial division algorithm generalizes to multivariate rings over nice coefficient rings (e.g. fields, ...

17 февр. 2017 г. · So the number of elements in the quotient rings is the number of linear polynomial with coefficient in F5 which is 5×5=25. as rings.

8 июл. 2018 г. · Since we are quotienting out by the ideal (Y−X2) we have the relation Y−X2=0⟺Y=X2 in our quotient ring. Then, working with this relation, we get ...

16 нояб. 2020 г. · I visualize elements of the polynomial ring R[x] as, well, polynomials, although perhaps it helps to keep one's focus on the 0 degree term: ...

16 окт. 2016 г. · 1) You can think of the quotient ring A=R[x]/(x2) as being like the polynomial ring R[x] but equipped with a new algebraic law saying that x2=0.