isLexCompatiblyGVD -- checks whether an ideal is <-compatibly geometrically vertex decomposable for a given order

Synopsis

• Usage:

  isLexCompatiblyGVD(I, L)

• Inputs:
  • I, an ideal,
  • L, a list,
• Optional inputs:
  • CheckCM => ..., default value "always", when to perform a Cohen-Macaulay check on the ideal
  • CheckUnmixed => ..., default value true, check whether ideals encountered are unmixed
  • IsIdealHomogeneous => ..., default value false, specify whether an ideal is homogeneous
  • IsIdealUnmixed => ..., default value false, specify whether an ideal is unmixed
  • UniversalGB => ..., default value false, whether the generators for an ideal form a universal Gröbner basis
  • Verbose => ..., default value false
• Outputs:
  • a Boolean value,

Description

i1 : R = QQ[x,y,z,w,r,s];

i2 : I = ideal(y*(z*s - x^2), y*w*r, w*r*(z^2 + z*x + w*r + s^2));

o2 : Ideal of R

i3 : isLexCompatiblyGVD(I, {x,y,z,w,r,s})

o3 = false

i4 : isLexCompatiblyGVD(I, {s,x,w,y,r,z}, Verbose=>true)
I = ideal(-x^2*y+y*z*s,y*w*r,x*z*w*r+z^2*w*r+w^2*r^2+w*r*s^2)
-- decomposing with respect to s
Warning: not a valid geometric vertex decomposition

o4 = false

References

See also

• CheckCM -- when to perform a Cohen-Macaulay check on the ideal
• CheckUnmixed -- check whether ideals encountered are unmixed
• isGeneratedByIndeterminates -- checks whether the ideal is generated by indeterminates
• isGVD -- checks whether an ideal is geometrically vertex decomposable
• IsIdealHomogeneous -- specify whether an ideal is homogeneous
• IsIdealUnmixed -- specify whether an ideal is unmixed
• isUnmixed -- checks whether an ideal is unmixed
• isWeaklyGVD -- checks whether an ideal is weakly geometrically vertex decomposable
• oneStepGVD -- computes a geometric vertex decomposition
• UniversalGB -- whether the generators for an ideal form a universal Gröbner basis
• Verbose -- request verbose feedback