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Tropical :: tropicalPrevariety

tropicalPrevariety -- the intersection of the tropical hypersurfaces

Synopsis

Description

This method intersects the tropical hypersurfaces coming from the tropicalizations of the polynomials in the list L.

i1 : QQ[x_1,x_2,x_3,x_4]

o1 = QQ[x , x , x , x ]
         1   2   3   4

o1 : PolynomialRing
i2 : L={x_1+x_2+x_3+x_4,x_1*x_2+x_2*x_3+x_3*x_4+x_4*x_1,x_1*x_2*x_3+x_2*x_3*x_4+x_3*x_4*x_1+x_4*x_1*x_2,x_1*x_2*x_3*x_4-1}

o2 = {x  + x  + x  + x , x x  + x x  + x x  + x x , x x x  + x x x  + x x x 
       1    2    3    4   1 2    2 3    1 4    3 4   1 2 3    1 2 4    1 3 4
     ------------------------------------------------------------------------
     + x x x , x x x x  - 1}
        2 3 4   1 2 3 4

o2 : List
i3 : tropicalPrevariety L

o3 = Fan{...1...}

o3 : Fan
i4 : QQ[x,y]

o4 = QQ[x, y]

o4 : PolynomialRing
i5 : tropicalPrevariety({x+y+1,x+y},Strategy => "gfan")

o5 = Fan{...1...}

o5 : Fan

Ways to use tropicalPrevariety :