isDecomposable -- Decides whether a polynomial system is decomposable

Synopsis

Usage:

isDecomposable F

isDecomposable 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 value, a boolean asserting whether the polynomial system (or set of supports) is decomposable

A polynomial system is decomposable if it is either lacunary or triangular. This function checks whether a polynomial system is decomposable.

The function isDecomposable 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 : isDecomposable F

o3 = true

The function isDecomposable 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 : isDecomposable A

o5 = true

i6 : B = {matrix{{0,2,4},{0,2,3}},matrix{{0,1,0},{0,0,1}}};

i7 : isDecomposable B

o7 = false