A polynomial system is lacunary when its support spans a proper sublattice of full rank of the integer lattice. This function checks whether a polynomial system is lacunary.
The function isLacunary accepts a list of polynomials forming a system.
i1 : R=QQ[x,y]; |
i2 : F={3+x^2*y^2-(17/3)*x^4*y^4,2-x^2+5*y^2-13*x^2*y^2}; |
i3 : isLacunary F o3 = true |
The function isLacunary also accepts a list of supports encoded as matrices.
i4 : A = {matrix{{0,2,4},{0,2,4}},matrix{{0,0,2,2},{0,2,0,2}}}; |
i5 : isLacunary A o5 = true |
i6 : B = {matrix{{0,2,4},{0,2,4}},matrix{{0,1,0},{0,0,1}}}; |
i7 : isLacunary B o7 = false |
The object isLacunary is a method function.