triangle-ppw-inequality

Mathematica code for computations used in our paper proving the Ashbaugh-Benguria-PPW inequality for triangles.

Section 3

This is the code we used to compute the integrals necessary for our variational upper bounds on lambda_2 in section 3.

• Section3.wl defines all the eigenfunctions, affine transformations, test functions, and integrands that we need.
• Section3.nb checks that our eigenfunctions and affine transformations are correct.
• A30.nb, A45.nb etc. are notebooks for computing each of the integrals in equations (3.2) and (3.4) of the paper.

Section 4

This is the code we used for computations in our proofs in section 4. Section4-1.nb, Section4-2.nb, and Section4-3.nb respectively cover the calculations needed for sections 4.1, 4.2, and 4.3.