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joinIdeal -- compute the join of several ideals

Synopsis

Usage:

joinIdeal(I,J)

joinIdeal L
Inputs:
- I, an ideal,
- J, an ideal,
- L, a list, of ideals in the same ring
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

See also

secant -- compute the secant of an ideal

Ways to use joinIdeal :

joinIdeal(Ideal,Ideal)
joinIdeal(List)

For the programmer

The object joinIdeal is a method function with options.