Plucker Manual

Edition : auto generated by oxgentexi on 31 August 2017

OpenXM.org

1 Plucker Relations

1.0.1 plucker

Consider (m + 1) × n matrix. The subsquare matrix consisting of i_{1}, …, i_{m}, j_{k} columns is denoted by p_{i_{1}···i_{m}j_{k}}. The Plucker relation is

∑_{k=0}^{m+1}(−1)^{k}p_{i_{1}···i_{m}j_{k}}p_{j_{0}···ˆ j_{k}···j_{m+1}} = 0.

This package provides functions for Plucker relations.

1.0.2 plucker_relation
plucker_relation(L,M)

:: Returns the plucker relation defined by the index sets L and M.

return quote

L List

M List

• L is the index set i_{1}, …, i_{m} of the plucker relations and M is the index set j_{0}, …, j_{m+1} of the plucker relations.

     [297] A = plucker_relation([1,2],[3,4,5,6]);
     quote(y_1_2_3*y_4_5_6-y_1_2_4*y_3_5_6+y_1_2_5*y_3_4_6-y_1_2_6*y_3_4_5)
     [298] eval_str(print_terminal_form(A));
     y_4_5_6*y_1_2_3-y_3_5_6*y_1_2_4+y_3_4_6*y_1_2_5-y_3_4_5*y_1_2_6

1.0.3 plucker_y
plucker_y(L)

:: Returns the variable standing for the index L.

return Variable

L List

• Index set L is sorted and the sign is evaluated by the sorting.

     [297] plucker_y([1,2,3]);
     y_1_2_3
     [298] plucker_y([2,1,3]);
     -y_1_2_3

1.0.4 plucker_index
plucker_index(V)

: It gets the index of the variable V.

Example:

      plucker_index(plucker_y([1,2,3]));

Index 2

Index

(Index is nonexistent) (Index is nonexistent)

Short Contents

1 Plucker Relations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 Index. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2

Table of Contents

1 Plucker Relations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1

1.0.1 plucker . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 1.0.2 plucker_relation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 1.0.3 plucker_y . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 1.0.4 plucker_index . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1

Index . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2