# joinIdeal -- compute the join of several ideals

## Synopsis

• Usage:
joinIdeal(I,J)
joinIdeal L
• Inputs:
• Optional inputs:
• DegreeLimit => ..., default value {}
• Outputs:
• an ideal, the join of the input ideals

## Description

This function computes the ideal of the join by constructing the abstract join and then projecting with elimination.

Setting the optional argument DegreeLimit to \{d\} will produce only the generators of the join ideal up to degree d.

This method is general and will work for arbitrary polynomial ideals, not just phylogenetic ideals.

 i1 : R = QQ[a,b,c,d] o1 = R o1 : PolynomialRing i2 : I = ideal {a-d,b^2-c*d} 2 o2 = ideal (a - d, b - c*d) o2 : Ideal of R i3 : J = ideal {a,b,c} o3 = ideal (a, b, c) o3 : Ideal of R i4 : joinIdeal(I,J) 2 o4 = ideal(b - a*c) o4 : Ideal of R