3. Solving equations

The simplest way to "solve" systems of polynomial equations via standard basis computation is the computation of a lexicographical standard basis.

Other Possibilities include the command eliminate or preprocessing etc.

SINGULAR example:

// consider a line and a plane:
ring R=0,(x,y,z),lp;
number a,b,c,d,e=0,1,1,1,1;
ideal L=a*x+b*y,z;
poly P=c*x+d*y+e*z;
ideal I=L,P;
// force the complete reduction of the  standard basis:
option(redSB);
std(I); 
eliminate(I,x);