# gausskImage -- computes the image of the Gauss map of order k

## Synopsis

• Usage:
gausskImage(A,k)
• Inputs:
• A, , or a a list where the columns are lattice points
• k, an integer
• Outputs:
• a list, of monomials giving the torus embedding via the Plücker embedding of the image of the Gauss map of order k for generically k-jet spanned the toric variety X_A

## Description

gausskImage is a function. It computes the image of the Gauss map of order k embedded via the Plücker embedding as described in the paper A note on higher order Gauss maps

 i1 : P=hypercube(2,1); i2 : Q=convexHull(matrix{{0}}); i3 : A=latticePoints(P); i4 : B=latticePoints(cayley({Q,Q,Q},2)); i5 : gausskImage(A,2) -2 -2 -2 -1 -2 -1 -2 -1 -1 -1 -2 -1 -2 o5 = {x , x x , x x , x , x x , x x , x , x x , x , 1, x , 1 0 1 0 1 1 0 1 0 1 0 0 1 0 0 ------------------------------------------------------------------------ -1 -1 -2 2 2 -2 2 -1 2 2 2 2 2 x x , x x , x , x x , x , x x , x x , x x , x x , x x , x x , x , 0 1 0 1 1 0 1 0 0 1 0 1 0 1 0 1 0 1 0 1 1 ------------------------------------------------------------------------ -1 2 -2 2 x x , x x } 0 1 0 1 o5 : List i6 : gausskImage(B,2) 4 4 o6 = {x x } 0 1 o6 : List