# jetMatrix -- construct the matrix of k-jets evaluated at a given point.

## Synopsis

• Usage:
jetMatrix(A,k,pt)
• Inputs:
• Outputs:
• ,

## Description

The function constructs the matrix of k-jets evaluated at the point pt for the polarized toric variety associated to the set of lattice points A.

 i1 : A=latticePoints(convexHull(matrix{{0,0,2},{0,2,0}})) o1 = {0, | 0 |, | 1 |, | 2 |, | 1 |, | 0 |} | 2 | | 1 | | 0 | | 0 | | 1 | o1 : List i2 : pt=matrix{{1},{1}} o2 = | 1 | | 1 | 2 1 o2 : Matrix ZZ <--- ZZ i3 : jetMatrix(A,2,pt) o3 = | 1 1 1 1 1 1 | | 0 0 1 2 1 0 | | 0 0 0 2 0 0 | | 0 0 1 0 0 0 | | 0 2 1 0 0 1 | | 0 2 0 0 0 0 | 6 6 o3 : Matrix ZZ <--- ZZ

If no point is provided the matrix of k-jets is provided as a matrix over a polynomial ring.

 i4 : A=latticePoints(convexHull(matrix{{0,0,2},{0,2,0}})) o4 = {0, | 0 |, | 1 |, | 2 |, | 1 |, | 0 |} | 2 | | 1 | | 0 | | 0 | | 1 | o4 : List i5 : jetMatrix(A,2) o5 = | 1 x_1^2 x_0x_1 x_0^2 x_0 x_1 | | 0 0 x_1 2x_0 1 0 | | 0 0 0 2 0 0 | | 0 0 1 0 0 0 | | 0 2x_1 x_0 0 0 1 | | 0 2 0 0 0 0 | 6 6 o5 : Matrix (ZZ[x ..x ]) <--- (ZZ[x ..x ]) 0 1 0 1