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4.2.3 ideal operations
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+ addition (concatenation of the generators and simplification)
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* multiplication (with ideal, poly, vector, module; simplification in case of multiplication with ideal)
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^ 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 |