4.4.3 ideal operations

+

addition (concatenation of the generators and simplification)

*

multiplication (with ideal, poly, vector, module; simplification in case of multiplication with ideal)

^

exponentiation (by a non-negative integer)

ideal_expression [ intvec_expression ]

are polynomial generators of the ideal, index 1 gives the first generator.

Note: For simplification of an ideal, see also simplify.

Example:

ring r=0,(x,y,z),dp; ideal I = 0,x,0,1; I; ==> I[1]=0 ==> I[2]=x ==> I[3]=0 ==> I[4]=1 I + 0; // simplification ==> _[1]=1 ideal J = I,0,x,x-z;; J; ==> J[1]=0 ==> J[2]=x ==> J[3]=0 ==> J[4]=1 ==> J[5]=0 ==> J[6]=x ==> J[7]=x-z I * J; // multiplication with simplification ==> _[1]=1 I*x; ==> _[1]=0 ==> _[2]=x2 ==> _[3]=0 ==> _[4]=x vector V = [x,y,z]; print(V*I); ==> 0,x2,0,x, ==> 0,xy,0,y, ==> 0,xz,0,z ideal m = maxideal(1); m^2; ==> _[1]=x2 ==> _[2]=xy ==> _[3]=xz ==> _[4]=y2 ==> _[5]=yz ==> _[6]=z2 ideal II = I[2..4]; II; ==> II[1]=x ==> II[2]=0 ==> II[3]=1