# isLacunary -- Decides whether a polynomial system is lacunary

## Synopsis

• Usage:
isLacunary F
isLacunary A
• Inputs:
• F, a list, of (Laurent) polynomial equations.
• A, a list, of matrices whose column vectors are the support of a system of (Laurent) polynomial equations
• Outputs:
• , a boolean asserting whether or not the polynomial system (or set of supports) is lacunary

## 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

• isTriangular -- Decides whether a polynomial system is triangular
• isDecomposable -- Decides whether a polynomial system is decomposable

## Ways to use isLacunary :

• "isLacunary(List)"

## For the programmer

The object isLacunary is .