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

Description

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

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