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DecomposableSparseSystems :: isLacunary

isLacunary -- Decides whether a polynomial system is lacunary

Synopsis

Description

A polynomial system is lacunary when its support spans a proper sublattice of full rank of the integer lattice. This function checks whether or not a polynomial system is lacunary.

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

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

See also

Ways to use isLacunary :

For the programmer

The object isLacunary is a method function.