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Bertini :: Variable groups

Variable groups -- an option to group variables and use multihomogeneous homotopies

Grouping the variables has Bertini solve zero dimensional systems using multihomogeneous homotopies.

i1 : R = CC[x,y];
i2 : F1 = {x*y+1,2*x*y+3*x+4*y+5};
i3 : bertiniZeroDimSolve(F1, AffVariableGroup=>{{x},{y}});
i4 : hR =CC[x0,x1,y0,y1]

o4 = hR

o4 : PolynomialRing
i5 : F2 = {x1*y1+x0*y0,2*x1*y1+3*x1*y0+4*x0*y1+5*x0*y0};
i6 : bertiniZeroDimSolve(F2,HomVariableGroup=>{{x0,x1},{y0,y1}});