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

## Synopsis

• Function: rank
• Usage:
rank(L)
• Inputs:
• 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