4.11.1 Introduction to Ideals |
Example |
Use R ::= QQ[x,y]; I := Ideal(x,y^2,2+xy^2); |
I^N, I+J, E*F, P:Qwhere: I and J are ideals; N is a non-negative integer; E, F are either both ideals or one is an ideal and the other is a polynomial; and the pair (P, Q) has the form (IDEAL, POLY), (IDEAL, IDEAL), (MODULE, VECTOR), (MODULE, MODULE).
Example |
Use R ::= QQ[x,y]; I := Ideal(x,y^2,2+xy^2); I^2; Ideal(x^2, xy^2, x^2y^2 + 2x, y^4, xy^4 + 2y^2, x^2y^4 + 4xy^2 + 4) ------------------------------- J := Ideal(y); I+J; Ideal(x, y^2, xy^2 + 2, y) ------------------------------- I*J; Ideal(xy, y^3, xy^3 + 2y) ------------------------------- |