This method computes the ideal of critical equations of an SDP. This ideal can be used to solve the SDP symbolically.
i1 : A = (-matrix{{0,1,0},{1,0,0},{0,0,1}}, matrix{{0,0,1},{0,0,0},{1,0,0}}, -matrix{{0,0,0},{0,0,1},{0,1,0}}); |
i2 : (C, b) = (matrix{{1/1,0,3},{0,5,0},{3,0,9}}, matrix{{-1},{-1},{-1}}); |
i3 : P = sdp(C,A,b); |
i4 : (I,X,y,Z) = criticalIdeal P; |
i5 : degree I o5 = 6 |
We can restrict the rank of the primal matrix X.
i6 : rk = 1; |
i7 : (J,X,y,Z) = criticalIdeal(P, rk); |
i8 : degree J o8 = 4 |
The object criticalIdeal is a method function.