# random(ZZ,Ring) -- get a random homogeneous element from a graded ring

## Synopsis

• Function: random
• Usage:
random(d, R)
• Inputs:
• Optional inputs:
• Density => ..., default value 1, get a random map of module
• Height => ..., default value 10
• MaximalRank => ..., default value false, get a random map of module
• UpperTriangular => ..., default value false, get a random map of module
• Outputs:
• , a random homogeneous element of the ring R of degree d

## Description

 i1 : R = ZZ[x,y] o1 = R o1 : PolynomialRing i2 : random(5, R) 5 4 3 2 2 3 4 5 o2 = 8x + x y + 3x y + 7x y + 8x*y + 3y o2 : R i3 : R = GF(25, Variable => a)[x, y]; i4 : VerticalList for i to 6 list random(3, R) { 3 2 2 3 } o4 = {(- 2a - 1)x - 2x y - 2a*x*y + 2a*y } { 3 2 2 3} {(- 2a - 2)x + 2a*x y + (- 2a + 1)x*y + (2a + 1)y } { 3 2 2 3 } {2a*x + (- 2a + 1)x y + (a - 2)x*y + (- a - 2)y } { 3 2 2 3 } {2x + (- 2a - 1)x y + (a - 2)x*y - 2a*y } { 3 2 2 3 } {(a + 1)x + (2a + 2)x y + (2a + 1)x*y - y } { 3 2 2 3 } {x + (- 2a - 2)x y + (- 2a - 2)x*y + y } { 3 2 2 3 } {(a - 1)x + 2a*x y + (a + 2)x*y + (- a - 1)y } o4 : VerticalList

The length of d, if it's a list, should be the same as degree rank of $R$.