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SlackIdeals :: reconstructSlackMatrix

reconstructSlackMatrix -- a list of facet labels that make up a flag in a polytope

Synopsis

Description

Given a (column) reduced slack matrix S, a flag of columns and a list of facet columns F to refill, it extends S by the columns of F.

i1 : V = {{0,0,0},{0,0,1},{1,0,0},{1,0,1},{0,1,0},{0,1,1}};
i2 : S = slackMatrix V;

Order of vertices is 
{{0, 0, 0}, {1, 0, 0}, {0, 1, 0}, {0, 0, 1}, {1, 0, 1}, {0, 1, 1}}

              6        5
o2 : Matrix QQ  <--- QQ
i3 : redS = reducedSlackMatrix(3, S);

              6        4
o3 : Matrix QQ  <--- QQ
i4 : reconstructSlackMatrix(reducedSlackMatrix(S, Vars => {a,b,c,d,e,f,g,h,j,k,m,p}), {{0,1,2}})

o4 = | 0 0 a b 0     |
     | c 0 0 d 0     |
     | 0 e 0 f 0     |
     | 0 0 g 0 -bceg |
     | h 0 0 0 -adeh |
     | 0 j 0 0 -acfj |

                                                    6                                              5
o4 : Matrix (QQ[a, b, c, d, e, f, g, h, j, k, m, p])  <--- (QQ[a, b, c, d, e, f, g, h, j, k, m, p])
i5 : reconstructSlackMatrix(redS, {{0,1,2}})

o5 = | 0 0 1 1 0  |
     | 1 0 0 1 0  |
     | 0 1 0 1 0  |
     | 0 0 1 0 -1 |
     | 1 0 0 0 -1 |
     | 0 1 0 0 -1 |

              6        5
o5 : Matrix QQ  <--- QQ
i6 : reconstructSlackMatrix(redS, {{0,1,2}}, Vars => {x})
warning: clearing value of symbol x to allow access to subscripted variables based on it
       : debug with expression   debug 9868   or with command line option   --debug 9868

Not enough variables given. Making new ring for reconstructed matrix

o6 = | 0   0   x_0 x_1 0             |
     | x_2 0   0   x_3 0             |
     | 0   x_4 0   x_5 0             |
     | 0   0   x_6 0   -x_1x_2x_4x_6 |
     | x_7 0   0   0   -x_0x_3x_4x_7 |
     | 0   x_8 0   0   -x_0x_2x_5x_8 |

                                                    6                                              5
o6 : Matrix (QQ[x , x , x , x , x , x , x , x , x ])  <--- (QQ[x , x , x , x , x , x , x , x , x ])
                 0   1   2   3   4   5   6   7   8              0   1   2   3   4   5   6   7   8

See also

Ways to use reconstructSlackMatrix :