Computes the $k$th 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 3 o3 = ideal (b - 2a*b*c + a d + 2c - 2b*d, a*b - a c - b*c + a*d, a b - b - 2a*c + 2d, a - 3a*b + 2c) o3 : Ideal of R |
The object secant is a method function with options.