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Bracket

Description

In a BracketRing, a Bracket represents a maximal minor of the matrix of coordinates of a configuration of points in a projective space. The example below illustrates this for a configuration of 5 points in the projective space $\mathbb{P}^2$.

i1 : B = bracketRing(5,3)

o1 = B
      5,3

o1 : BracketRing
i2 : [1 2 3]_B

o2 = [123]

o2 : Bracket
i3 : X = matrix B

o3 = {-1} | x_(1,1) x_(1,2) x_(1,3) |
     {-1} | x_(2,1) x_(2,2) x_(2,3) |
     {-1} | x_(3,1) x_(3,2) x_(3,3) |
     {-1} | x_(4,1) x_(4,2) x_(4,3) |
     {-1} | x_(5,1) x_(5,2) x_(5,3) |

                                                                                                            5                                                                                                     3
o3 : Matrix (QQ[x   ..x   , y     , y     , y     , y     , y     , y     , y     , y     , y     , y     ])  <-- (QQ[x   ..x   , y     , y     , y     , y     , y     , y     , y     , y     , y     , y     ])
                 1,1   5,3   [345]   [245]   [235]   [234]   [145]   [135]   [134]   [125]   [124]   [123]             1,1   5,3   [345]   [245]   [235]   [234]   [145]   [135]   [134]   [125]   [124]   [123]
i4 : toBracketPolynomial(det X^{0,1,2},B)

o4 = [123]

o4 : GCExpression

See also BracketRing and toBracketPolynomial.

For the programmer

The object Bracket is a type, with ancestor classes GCExpression < HashTable < Thing.


The source of this document is in /build/reproducible-path/macaulay2-1.25.05+ds/M2/Macaulay2/packages/Brackets.m2:518:0.