# isTriangular -- Decides whether a polynomial system is triangular

## Synopsis

• Usage:
isTriangular F
isTriangular 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 the polynomial system (or set of supports) is triangular

## Description

A polynomial system is triangular if, after a monomial change of coordinates, there is a proper subset of $k$ equations which involve only the first $k$ variables. This function checks whether a polynomial system (or set of supports) is triangular.

The function isTriangular 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 : isTriangular F o3 = true

The function isTriangular 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 : isTriangular A o5 = true i6 : B = {matrix{{0,2,4},{0,2,3}},matrix{{0,1,0},{0,0,1}}}; i7 : isTriangular B o7 = false