I've recently started to use Singular, v. 3.1.0. The system I'm solving comes from the power flow analysis. I've computed "numerical" Groebner Basis in Mathematica and was very surprised by its very simple form, so I'm wondering if there is a way to find a symbolic form of the polynomial of one variable (Mathematica seems to be unable to do it). It's going to be a huge formula, but I'll deal with it.
The script I wrote:
ring R = 0,(y12,y13,y23,w12,w13,w23,s1,s2,s3,s4,u3,u1,u2,u4,u5),(ds(11), lp(4));
-(y12+y13)*u1*u4 + y12*u2*u4 + y13*u3*u4 - s1,
y12*u1*u5 - (y12+y23)*u2*u5 + y23*u3*u5 - s2,
-(w12+w13)*u1*u4 + w12*u1*u5 + w13*u3*u1 - s3,
w12*u2*u4 - (w12+w23)*u2*u5 + w23*u3*u2 - s4;
ideal Istd = simplify(std(I),1);
list L = facstd(Istd);
The result is the basis of 43 polynomials, but I cannot find any equivalent to numerical computation. My unknowns are u1,u2,u4,u5.
I'd appreciate any help!