i1 : R=CC[u1,u2,u3,x,y]; |
i2 : f1=u1*(y-1)+u2*(y-2)+u3*(y-3); --parameters are u1, u2, and u3 |
i3 : f2=(x-11)*(x-12)*(x-13)-u1; |
i4 : paramValues0={{1,0,0}}; |
i5 : paramValues1={{0,1+2*ii,0}}; |
i6 : bPH=bertiniParameterHomotopy( {f1,f2}, {u1,u2,u3},{paramValues0 ,paramValues1 }) Temporary directory for input and output files:/var/folders/46/9b86vqxj4hjcngvy7kd7sb140000gn/T/M2-66055-0/0 The version of Bertini you have installed on your computer was used for this run. Bertini is under ongoing development by D. Bates, J. Hauenstein, A. Sommese, and C. Wampler. o6 = {{{11.3376+.56228*ii, 1}, {13.3247, 1}, {11.3376-.56228*ii, 1}}, {{12, ------------------------------------------------------------------------ 2}, {13, 2}, {11, 2}}} o6 : List |
i7 : bPH_0--the solutions to the system with parameters set equal to paramValues0 o7 = {{11.3376+.56228*ii, 1}, {13.3247, 1}, {11.3376-.56228*ii, 1}} o7 : List |
i8 : R=CC[x,y,z,u1,u2] o8 = R o8 : PolynomialRing |
i9 : f1=x^2+y^2-z^2 2 2 2 o9 = x + y - z o9 : R |
i10 : f2=u1*x+u2*y o10 = x*u1 + y*u2 o10 : R |
i11 : finalParameters0={{0,1}} o11 = {{0, 1}} o11 : List |
i12 : finalParameters1={{1,0}} o12 = {{1, 0}} o12 : List |
i13 : bPH=bertiniParameterHomotopy( {f1,f2}, {u1,u2},{finalParameters0 ,finalParameters1 },ISPROJECTIVE=>1) Temporary directory for input and output files:/var/folders/46/9b86vqxj4hjcngvy7kd7sb140000gn/T/M2-66055-0/2 The version of Bertini you have installed on your computer was used for this run. Bertini is under ongoing development by D. Bates, J. Hauenstein, A. Sommese, and C. Wampler. o13 = {{{.231211+.490643*ii, -1.04639e-16-7.6165e-18*ii, .231211+.490643*ii}, ----------------------------------------------------------------------- {-.972753+.285112*ii, -2.82435e-17+1.87567e-17*ii, ----------------------------------------------------------------------- .972753-.285112*ii}}, {{-2.1684e-18+6.85487e-16*ii, 1.04288-.251215*ii, ----------------------------------------------------------------------- 1.04288-.251215*ii}, {4.62683e-17+5.48064e-17*ii, -.252659-.491864*ii, ----------------------------------------------------------------------- .252659+.491864*ii}}} o13 : List |
i14 : bPH_0--The two solutions for finalParameters0 o14 = {{.231211+.490643*ii, -1.04639e-16-7.6165e-18*ii, .231211+.490643*ii}, ----------------------------------------------------------------------- {-.972753+.285112*ii, -2.82435e-17+1.87567e-17*ii, .972753-.285112*ii}} o14 : List |