Macaulay2 » Documentation
Packages » CotangentSchubert :: doublePuzzle
next | previous | forward | backward | up | index | toc

# doublePuzzle -- Produces a rhombus puzzle

- Usage:
    `doublePuzzle (a,b,c,d)`
- Inputs:
  - a, a string,
  - b, a string,
  - c, a string,
  - d, a string,
- Optional inputs:
  - Equivariant (missing documentation) => ..., default value true,
  - Generic (missing documentation) => ..., default value true,
  - Ktheory (missing documentation) => ..., default value false,
  - Ktheory' (missing documentation) => ..., default value false,
  - Separation (missing documentation) => ..., default value null,
  - Steps (missing documentation) => ..., default value null,

## Description

Given 4 strings, computes the number of pairs of puzzles glued together to form a rhombus with boundaries a,b,c,d in clockwise order.

In WebApp mode, the output is interactive and allows to test associativity of puzzles.

    i1 : doublePuzzle("0101","0101","0101","0101",Equivariant=>false)

    o1 = {                   /\                   ,
                            /  \
                           1    0
                          /      \
                          ---10---
                        /\        /\
                       /  \      /  \
                      0    0    1    1
                     /      \  /      \
                     ---0----  ---1----
                   /\        /\        /\
                  /  \      /  \      /  \
                 1    1    10   1    1    0
                /      \  /      \  /      \
                ---1----  ---0----  ---10---
              /\        /\        /\        /\
             /  \      /  \      /  \      /  \
            0   10    0    0    0    0    1    1
           /      \  /      \  /      \  /      \
           ---1----  ---0----  ---0----  ---1----
           \      /  \      /  \      /  \      /
            1    1    0    0    0    0    10   0
             \  /      \  /      \  /      \  /
              \/        \/        \/        \/
                ---10---  ---0----  ---1----
                \      /  \      /  \      /
                 0    1    1   10    1    1
                  \  /      \  /      \  /
                   \/        \/        \/
                     ---1----  ---0----
                     \      /  \      /
                      1    1    0    0
                       \  /      \  /
                        \/        \/
                          ---10---
                          \      /
                           0    1
                            \  /
                             \/
         ------------------------------------------------------------------------
                           /\                   }
                          /  \
                         1    0
                        /      \
                        ---10---
                      /\        /\
                     /  \      /  \
                    0    0    1    1
                   /      \  /      \
                   ---0----  ---1----
                 /\        /\        /\
                /  \      /  \      /  \
               1    0    0   10    0    0
              /      \  /      \  /      \
              ---10---  ---1----  ---0----
            /\        /\        /\        /\
           /  \      /  \      /  \      /  \
          0    0    1    1    1    1    10   1
         /      \  /      \  /      \  /      \
         ---0----  ---1----  ---1----  ---0----
         \      /  \      /  \      /  \      /
          1   10    1    1    1    1    0    0
           \  /      \  /      \  /      \  /
            \/        \/        \/        \/
              ---0----  ---1----  ---10---
              \      /  \      /  \      /
               0    0    10   0    0    1
                \  /      \  /      \  /
                 \/        \/        \/
                   ---1----  ---0----
                   \      /  \      /
                    1    1    0    0
                     \  /      \  /
                      \/        \/
                        ---10---
                        \      /
                         0    1
                          \  /
                           \/

    o1 : List

## Caveat

At the moment, the interactive part only works on nonequivariant puzzles.

## For the programmer

The object doublePuzzle is a function closure.

The source of this document is in /build/macaulay2-88fgJW/macaulay2-1.25.11+ds/M2/Macaulay2/packages/CotangentSchubert.m2:398:0.