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# rank(DiffAlgDistribution) -- rank of the given distribution

- Function: rank
- Usage:
    `rank(L)`
- Inputs:
  - L, an instance of the type DiffAlgDistribution, list of vector fields, see dist
- Outputs:
  - an integer, the rank of the distribution generated by L

## Description

This routine returns the rank of the distribution L.

In this example we generate two random vector fields in three variables with polynomial coefficients of degree 2. Then we compute the rank of some distributions generated with them.

    i1 : X = random newField(2,2,"a")

            2             2                            2            2
    o1 = (2x  - 2x x  + 6x  - 3x x  + 6x x )ax  + (- 7x  + 5x x  - x  - 2x x  -
            0     0 1     1     0 2     1 2   0        0     0 1    1     0 2
         ------------------------------------------------------------------------
                 2            2             2                     2
         x x  + x )ax  + (- 3x  - 4x x  + 7x  + 2x x  - 7x x  - 3x )ax
          1 2    2   1        0     0 1     1     0 2     1 2     2   2

    o1 : DiffAlgField

    i2 : Y = random newField(2,2,"a")

           2             2                    2           2     2
    o2 = (x  + 7x x  + 3x  + 2x x  + x x  + 8x )ax  + (- x  - 4x  - 7x x  - x x
           0     0 1     1     0 2    1 2     2   0       0     1     0 2    1 2
         ------------------------------------------------------------------------
            2          2             2            2
         - x )ax  + (3x  - 4x x  + 7x  - 5x x  + x )ax
            2   1      0     0 1     1     0 2    2   2

    o2 : DiffAlgField

    i3 : rank dist {X,Y}

    o3 = 2

    i4 : rank dist {X,Y,X+Y,X-Y}

    o4 = 2

    i5 : rank dist {X,Y,X|Y}

    o5 = 3

## See also

- newField -- constructor of a vector field
- radial -- defines the radial vector field
- isInvolutive -- tests if a distribution is involutive

## Ways to use this method:

- rank(DiffAlgDistribution) -- rank of the given distribution

The source of this document is in /build/macaulay2-88fgJW/macaulay2-1.25.11+ds/M2/Macaulay2/packages/DiffAlg.m2:832:0.