**Overview:** The purpose of this package is to document the verification of a number of computational claims in the paper "The Variety of Polar Simplices" by Kristian Ranestad and Frank-Olaf Schreyer.

**Setup:** This package requires Macaulay2 version 1.4 or newer.

**Usage:** The verification of various formulas in the paper can be found in the documentation of several of the functions below.

1) The correctness of the set of equations printed in Lemma 5.5 and Lemma 5.8 checked with the functions

unfoldingEquations, flatteningRelations and equationsInThePaper.

The first two set up the computation of versal family by machine, the last makes the equation as printed in the paper. In the example section of the documentation of the function equationsInThePaper one can find the check of correctness.

2) Computations of the schemes *V _{h}^{aff}, V_{p}^{sec}, V_{p}^{loc}* and

3) Finally the degree of VSP(n) according to the formula from Theorem 6.2 is in the documentation of the function

- Functions and commands
- claimsOfTable1 -- check the claims of the paper
- computeVloc -- computete ideals of Vpsec and Vploc
- equationsInThePaper -- Write down the equations for $V_h^{aff}(n)$ of the paper
- flatteningRelations -- Compute the flattening relations in this special case
- formalDegreeComputation -- check the values for the degree of VSP
- symIndex -- sort the components of a Sequence
- symmetricUniversalFamily -- Build the miniversal deformation over V(n)
- symmetryMap -- define the map to the base space with symmetric indices
- unfoldingEquations -- setup the unfolding equations
- variableIndices -- make lists of desired indices

- Symbols
- Symmetric -- Option in the function variableIndices