next | previous | forward | backward | up | top | index | toc | Macaulay2 website
LatticePolytopes :: jetMatrix

jetMatrix -- construct the matrix of k-jets evaluated 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 |, | 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 polynomoial 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

See also

Ways to use jetMatrix :

For the programmer

The object jetMatrix is a method function.