lexIdeal -- compute the lex ideal with a given Hilbert function in an exterior algebra

Synopsis

• Usage:

  lexIdeal(hs,E) or lexIdeal I

• Inputs:
  • hs, a list of integers
  • E, an exterior algebra
  • I, an ideal of an exterior algebra
• Outputs:
  • an ideal, the lex ideal with Hilbert sequence hs or the lex ideal with the same Hilbert sequence of I

Description

Examples:

i1 : E=QQ[e_1..e_4,SkewCommutative=>true]

o1 = E

o1 : PolynomialRing, 4 skew commutative variable(s)

i2 : lexIdeal({1,4,3,1,0},E) 

o2 = ideal (e e , e e , e e )
             1 2   1 3   1 4

o2 : Ideal of E

i3 : Ilex=lexIdeal ideal {e_1*e_2,e_2*e_3}

o3 = ideal (e e , e e )
             1 2   1 3

o3 : Ideal of E

i4 : isLexIdeal Ilex

o4 = true

See also

• isLexIdeal -- whether an ideal is lex
• isHilbertSequence -- whether the given sequence is a Hilbert sequence