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7.2.1.3 ideal operations (plural)

+
addition (concatenation of the generators and simplification)

*
multiplication (with ideal, poly, vector, module; in case of multiplication with ideal or module, the result will be simplified)

^
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;
matrix D[3][3];
D[1,2]=-z;  D[1,3]=y;  D[2,3]=x;
def R=nc_algebra(1,D); // this algebra is U(so_3)
setring R;
ideal I = 0,x,0,1;
I;
==> I[1]=0
==> I[2]=x
==> I[3]=0
==> I[4]=1
I + 0;    // simplification
==> _[1]=1
I*x;
==> _[1]=0
==> _[2]=x2
==> _[3]=0
==> _[4]=x
ideal J = I,0,x,x-z;
I * J;   //  multiplication with simplification
==> _[1]=1
vector V = [x,y,z];
print(I*V);
==> 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