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PhylogeneticTrees :: secant

secant -- Computes the secant of an ideal

Synopsis

Description

Computes the kth secant of I by constructing the abstract secant and then projecting with elimination.

Setting k to 1 gives the dimension of the ideal, while 2 is the usual secant, and higher values correspond to higher order secants.

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

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

i1 : R = QQ[a..d]

o1 = R

o1 : PolynomialRing
i2 : I = ideal {a^2-b,a^3-c,a^4-d}

             2       3       4
o2 = ideal (a  - b, a  - c, a  - d)

o2 : Ideal of R
i3 : secant(I,2)

             3             2      2            2    2                2     2
o3 = ideal (b  - 2a*b*c + a d + 2c  - 2b*d, a*b  - a c - b*c + a*d, a b - b 
     ------------------------------------------------------------------------
                   3
     - 2a*c + 2d, a  - 3a*b + 2c)

o3 : Ideal of R

See also

Ways to use secant :