5 citations · 17 across the 11 of their papers we have counts for
12 papers
Terracini loci of tangential varieties of Veroneseans
Douglas A. Torrance
The Terracini locus of a projective variety tells us the sets of points at which Terracini's lemma will fail to recover the dimension of the corresponding secant variety. We study…
Implementing p-adic numbers in Macaulay2 using its foreign function interface and FLINT
Douglas A. Torrance
Macaulay2 is a computer algebra platform widely used by researchers in algebraic geometry and commutative algebra. Using the ForeignFunctions package, it is possible to make calls…
Properties of regular Tangles
Rebecca M. Bowen, Sadie Pruitt, Douglas A. Torrance
A Tangle is a smooth simple closed curve formed from arcs (or ``links'') of circles with fixed radius. Most previous study of Tangles has dealt with the case where these arcs are q…
ForeignFunctions package for Macaulay2
Douglas A. Torrance
We introduce the ForeignFunctions package for Macaulay2, which uses libffi to provide the ability to call functions from external libraries without needing to link against them at…
Geometry of first nonempty Terracini loci
Francesco Galuppi, Pierpaola Santarsiero, Douglas A. Torrance +1
After a few results on curves, we characterize the smallest nonempty Terracini loci of Veronese and Segre-Veronese varieties. For del Pezzo surfaces, we give a full description of…
Probability package for Macaulay2
Douglas A. Torrance
We introduce the Probability package for Macaulay2, which provides an interface for users to compute probabilities and generate random variates from a wide variety of univariate pr…
Almost all subgeneric third-order Chow decompositions are identifiable
Douglas A. Torrance, Nick Vannieuwenhoven
For real and complex homogeneous cubic polyomials in variables, we prove that the Chow variety of products of linear forms is generically complex identifiable for all ranks u…
All secant varieties of the Chow variety are nondefective for cubics and quaternary forms
Douglas A. Torrance, Nick Vannieuwenhoven
The Chow rank of a form is the length of its smallest decomposition into a sum of products of linear forms. For a generic form, this corresponds to finding the smallest secant vari…
Enumeration of planar Tangles
Douglas A. Torrance
A planar Tangle is a smooth simple closed curve piecewise defined by quadrants of circles with constant curvature. We can enumerate Tangles by counting their dual graphs, which con…
Generic forms of low Chow rank
Douglas A. Torrance
The least number of products of linear forms that may be added together to obtain a given form is the Chow rank of this form. The Chow rank of a generic form corresponds to the sma…
Nondefective secant varieties of varieties of completely decomposable forms
Douglas A. Torrance
A variation of Waring's problem from classical number theory is the question, ``What is the smallest number such that any generic homogeneous polynomial of degree in …
Castelnuovo-Mumford regularity and arithmetic Cohen-Macaulayness of complete bipartite subspace arrangements
Zach Teitler, Douglas A. Torrance
We give the Castelnuovo-Mumford regularity of arrangements of (n-2)-planes in P^n whose incidence graph is a sufficiently large complete bipartite graph, and determine when such ar…