load("../../General/settingsAndPermutations.sage")
load("../../General/orbit.sage")
load("../../General/removeDoubles.sage")

# Start with one equation from Proposition 2.2 of the paper "Tropicalization of Del Pezzo Surfaces" by Ren, Shaw and Sturmfels.

# equations = set([expand((d3-d4)*(d1+d3+d4)*E2*F12 - (d2-d4)*(d1+d2+d4)*E3*F13 + (d2-d3)*(d1+d2+d3)*E4*F14)])
# we obtain a linear equation in terms of the anticanonical coordinates by multiplying by G1
linear = set([expand((d3-d4)*(d1+d3+d4)*X21 - (d2-d4)*(d1+d2+d4)*X31 + (d2-d3)*(d1+d2+d3)*X41)])

linears = computeOrbit(linear, homsStd)

linearsNoDoubles = removeDoubles(linears)
#save(linearsNoDoubles,"../Output/270AnticanonicalLinearEquations.sobj")
#save(linears, "../Output/540AnticanonicalLinearEquations.sobj")