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LatticePolytopes :: jetMatrix

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

Synopsis

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 |, | 0 |, | 1 |, | 1 |, | 2 |}
         | 1 |  | 2 |  | 0 |  | 1 |  | 0 |

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 0 1 1 2 |
     | 0 0 0 0 0 2 |
     | 0 0 0 0 1 0 |
     | 0 1 2 0 1 0 |
     | 0 0 2 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 polynomoial ring.

i4 : A=latticePoints(convexHull(matrix{{0,0,2},{0,2,0}}))

o4 = {0, | 0 |, | 0 |, | 1 |, | 1 |, | 2 |}
         | 1 |  | 2 |  | 0 |  | 1 |  | 0 |

o4 : List
i5 : jetMatrix(A,2)

o5 = | 1 x_1 x_1^2 x_0 x_0x_1 x_0^2 |
     | 0 0   0     1   x_1    2x_0  |
     | 0 0   0     0   0      2     |
     | 0 0   0     0   1      0     |
     | 0 1   2x_1  0   x_0    0     |
     | 0 0   2     0   0      0     |

                        6                  6
o5 : Matrix (ZZ[x , x ])  <--- (ZZ[x , x ])
                 0   1              0   1

See also

Ways to use jetMatrix :