intersectSlice -- intersects a witness set by a slice

Usage:

fSols = intersectSlice(w, slice)
Inputs:
- w, a witness set, a witness set for a solution set
- slice, a list, a list of linear equations
Outputs:
- fSols, a list, solutions that satisfy w.Equations and the equations in the slice

Description

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);

             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);

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 = {{1.16626-.105934*ii, .496544-.889818*ii, -1.53284+1.25196*ii,
      -----------------------------------------------------------------------
      -.890403+.003468*ii, -1.41254e-14+9.81678e-15*ii,
      -----------------------------------------------------------------------
      2.32647e-14-2.38814e-15*ii}, {1.57184-10.2689*ii, -5.76995+13.6093*ii,
      -----------------------------------------------------------------------
      5.51841-.920151*ii, -1.09813+2.34365*ii, 3.91646e-12+1.8113e-12*ii,
      -----------------------------------------------------------------------
      -2.40749e-12-3.74632e-12*ii}, {.417509-.780358*ii, .368317+.591548*ii,
      -----------------------------------------------------------------------
      -.227864+.472091*ii, -.742041+.169201*ii, -9.35238e-16+1.34365e-15*ii,
      -----------------------------------------------------------------------
      -1.2834e-15-1.76545e-15*ii}, {.696183+.387534*ii, .404198-.069945*ii,
      -----------------------------------------------------------------------
      -.699053-.508509*ii, -.797497-.079528*ii, -3.99082e-16-9.25094e-17*ii,
      -----------------------------------------------------------------------
      -2.32799e-15-9.15055e-16*ii}, {-1.63065-.257888*ii,
      -----------------------------------------------------------------------
      -2.32709-2.84506*ii, 6.21272+3.87904*ii, -.38334-.0052031*ii,
      -----------------------------------------------------------------------
      -1.26369e-13-5.19308e-13*ii, -2.62201e-13+5.57671e-13*ii},
      -----------------------------------------------------------------------
      {-.161616-.365942*ii, .535477+1.0178*ii, .455351-.685211*ii,
      -----------------------------------------------------------------------
      -.621937+.094229*ii, -1.98164e-15-3.45829e-15*ii,
      -----------------------------------------------------------------------
      5.06719e-16+6.23699e-15*ii}}

o10 : List

Ways to use intersectSlice:

intersectSlice(WitnessSet,List)

For the programmer

The object intersectSlice is a method function.

The source of this document is in PHCpack/PHCpackDoc.m2:1670:0.

intersectSlice -- intersects a witness set by a slice

Description

See also

Ways to use intersectSlice:

For the programmer