Supplementary Materials for Oeding-Bates paper




multiplicity procedure : This Maple procedure computes the decomposition of the degree d polynomials on a tensor product space as Schur modules.

polnomial making procedure : This Maple procedure constructs the highest weight space of a Schur module.

deg_6_salmon (213493b) : This file contains a basis of the 10 dimensional Schur module S_{2,2,2}C^3 \otimes S_{2,2,2}C^3\otimes S_{3,1,1,1}C^4 of degree 6 polynomials in the ideal of the 4th secant variety to the Segre product of P^2 x P^2 x P^3.

main_data.txt (990403b) : This is the output from the Bertini run used for the decomposition of the zero set of the above degree 6 equations.

deg_9_salmon (23410546b) : This file contains a basis of the 20 dimensional Schur module S_{3,3,3}C^3 \otimes S_{3,3,3}C^3 \otimes S_{3,3,3}C^4 of degree 9 polynomials. These polynomials are in the ideal of the 4th secant variety to the Segre product of P^2 x P^2 x P^3.

deg_5_salmon (661388b) : This file contains a basis of the 4*6*4 dimensional Schur module S_{2,1,1,1}C^4 \otimes S_{3,1,1}C^3 \otimes S_{2,1,1,1}C^4 of degree 5 polynomials in the ideal of the 4th secant variety to the Segre product of P^3 x P^2 x P^3 (notice the dimension change!)