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# Sets -- sets of a Cartesian code

- Usage:
    `C.Sets`
- Inputs:
  - C, an instance of the type EvaluationCode,
- Outputs:
  - a list,

## Description

This key stores a list of subsets of a field that are used for constructing a cartesianCode.

This symbol is provided by the package CodingTheory.

    i1 : F=GF(4);

    i2 : R=F[x,y];

    i3 : C=cartesianCode(F,{{0,1,a},{0,1,a}},{1+x+y,x*y})

    o3 = EvaluationCode{cache => CacheTable{}                                                                                                                                                                                                                                               }
                                                                   9
                        LinearCode => LinearCode{AmbientModule => F                                                                                                                                                                                                                        }
                                                 BaseField => F
                                                 cache => CacheTable{}
                                                 Code => image | 1   a+1 |
                                                               | a+1 0   |
                                                               | a+1 0   |
                                                               | a   a   |
                                                               | a   a   |
                                                               | 1   0   |
                                                               | 0   0   |
                                                               | 0   0   |
                                                               | 1   1   |
                                                 GeneratorMatrix => | 1   a+1 a+1 a a 1 0 0 1 |
                                                                    | a+1 0   0   a a 0 0 0 1 |
                                                 Generators => {{1, a + 1, a + 1, a, a, 1, 0, 0, 1}, {a + 1, 0, 0, a, a, 0, 0, 0, 1}}
                                                 ParityCheckMatrix => | 1 0 0 0 0 a   0 0 a+1 |
                                                                      | 0 1 0 0 0 a+1 0 0 0   |
                                                                      | 0 0 1 0 0 a+1 0 0 0   |
                                                                      | 0 0 0 1 0 0   0 0 a   |
                                                                      | 0 0 0 0 1 0   0 0 a   |
                                                                      | 0 0 0 0 0 0   1 0 0   |
                                                                      | 0 0 0 0 0 0   0 1 0   |
                                                 ParityCheckRows => {{1, 0, 0, 0, 0, a, 0, 0, a + 1}, {0, 1, 0, 0, 0, a + 1, 0, 0, 0}, {0, 0, 1, 0, 0, a + 1, 0, 0, 0}, {0, 0, 0, 1, 0, 0, 0, 0, a}, {0, 0, 0, 0, 1, 0, 0, 0, a}, {0, 0, 0, 0, 0, 0, 1, 0, 0}, {0, 0, 0, 0, 0, 0, 0, 1, 0}}
                        Points => {{a, a}, {0, a}, {a, 0}, {1, a}, {a, 1}, {0, 0}, {0, 1}, {1, 0}, {1, 1}}
                        PolynomialSet => {x + y + 1, x*y}
                        Sets => {{0, 1, a}, {0, 1, a}}
                                                  3           2         3           2
                        VanishingIdeal => ideal (x  + (a + 1)x  + a*x, y  + (a + 1)y  + a*y)

    o3 : EvaluationCode

    i4 : C.Sets

    o4 = {{0, 1, a}, {0, 1, a}}

    o4 : List

## For the programmer

The object Sets is a symbol.

The source of this document is in /build/macaulay2-88fgJW/macaulay2-1.25.11+ds/M2/Macaulay2/packages/CodingTheory.m2:5130:0.