A typical application is to find solutions for slices with real coefficients.
i1 : R=CC[a,b,c,d]; |
i2 : M=matrix for i to 2 list for j to 3 list random(1,R)+random(0,R); -- warning: experimental computation over inexact field begun -- results not reliable (one warning given per session) 3 4 o2 : Matrix R <--- R |
i3 : I=minors(3,M); o3 : Ideal of R |
i4 : f=flatten entries gens I; |
i5 : (w,ns) = topWitnessSet(f,2); *** variables in the ring : {a, b, c, d, zz1, zz2} *** |
i6 : slcmat = matrix applyTable (entries w.Slice, x->1_CC*realPart x); 2 7 o6 : Matrix CC <--- CC 53 53 |
i7 : Rtwo = ring w.Equations; |
i8 : X = transpose matrix {gens Rtwo | {1_CC}}; 7 1 o8 : Matrix Rtwo <--- Rtwo |
i9 : slcRR = flatten entries (promote(slcmat,Rtwo) * X); |
i10 : fsols = intersectSlice(w,slcRR) o10 = {{1.40406-.273197*ii, 1.85935-.233734*ii, -1.54647+.457338*ii, ----------------------------------------------------------------------- 1.13781-.347113*ii, 5.1446e-15+6.51162e-14*ii, ----------------------------------------------------------------------- -7.19684e-15+5.5108e-14*ii}, {-4.41658+5.54784*ii, -1.34961+.991832*ii, ----------------------------------------------------------------------- 4.92592-2.35104*ii, -.839952-4.43769*ii, 5.20926e-13-3.91506e-13*ii, ----------------------------------------------------------------------- -4.12899e-13+5.34275e-13*ii}, {.99884-3.40472*ii, -.485574-1.42614*ii, ----------------------------------------------------------------------- 2.82336+2.95296*ii, -5.49028+.222586*ii, 5.91162e-13-1.50415e-13*ii, ----------------------------------------------------------------------- -5.71879e-13-1.09968e-13*ii}, {1.13014+.051366*ii, 1.23215+.104164*ii, ----------------------------------------------------------------------- -.362187-.197232*ii, -.412066+.249488*ii, 7.78428e-15-5.55341e-15*ii, ----------------------------------------------------------------------- -3.97492e-15-9.34601e-15*ii}, {-2.38878-.549847*ii, ----------------------------------------------------------------------- -.132327+.197693*ii, 2.48754-.313798*ii, .152985+1.34536*ii, ----------------------------------------------------------------------- -3.54138e-14+8.7868e-16*ii, 1.63793e-14-2.22391e-14*ii}, ----------------------------------------------------------------------- {1.13528+2.30361*ii, 1.78765+1.08373*ii, -1.38888-2.21745*ii, ----------------------------------------------------------------------- 1.28046+.21289*ii, -1.06418e-14+4.07613e-14*ii, ----------------------------------------------------------------------- 2.30399e-14-4.07039e-14*ii}} o10 : List |