The ‘gamma trick’ refers to the following idea:
i1 : R = CC[x,y]; |
i2 : f = { x^3*y^5 + y^2 + x^2*y, x*y + x^2 - 1}; |
i3 : (m,q,qsols) = mixedVolume(f,startSystem=>true); using temporary files /tmp/M2-5187-1PHCinput and /tmp/M2-5187-1PHCoutput |
i4 : fsols = trackPaths(f,q,qsols,gamma => exp(ii*pi/3)) using temporary files /tmp/M2-5187-4PHCoutput and /tmp/M2-5187-6PHCtargetsols o4 = {{.742585-.425943*ii, .270685+1.00715*ii}, {-.894935-.624334*ii, ------------------------------------------------------------------------ .143333+1.14868*ii}, {1.33076-.335184*ii, -.62414+.513163*ii}, ------------------------------------------------------------------------ {-.894935+.624334*ii, .143333-1.14868*ii}, {-1.59272, .964857}, ------------------------------------------------------------------------ {1.33076+.335184*ii, -.62414-.513163*ii}, {.742585+.425943*ii, ------------------------------------------------------------------------ .270685-1.00715*ii}, {-.764107, -.544612}} o4 : List |