# model -- creates a new model for random objects with a given list of parameters and generating function

## Synopsis

• Usage:
model(L,f,name)
• Inputs:
• L, a list, of parameter values chosen for the model
• f, , function that generates random elements in this model
• name, , of the model constructed
• Outputs:
• an instance of the type Model, with those fixed parameter values

## Description

To create your own model for random polynomials or other algebraic objects, use the model method as follows. Suppose you wish to construct a set of M random polynomials in 3 variables of degree 2. You may use Macaulay2's built-in random function:

 i1 : f=(D,n,M)->(R=QQ[x_1..x_n];apply(M,i->random(D,R))) o1 = f o1 : FunctionClosure

To formalize the study of these random polynomials, embed this function into an object of type Model:

 i2 : myModel = model({2,3,4},f,"rand(D,n,M): M random polynomials in n variables of degree D") o2 = Model{Generate => -*Function[/usr/share/Macaulay2/RandomMonomialIdeals.m2:116:24-116:40]*-} Name => rand(D,n,M): M random polynomials in n variables of degree D Parameters => {2, 3, 4} o2 : Model

Now obtain the data about such random polynomials from the sample (that is, the actual sample in the statistical sense) as follows:

 i3 : N=2; i4 : mySample = sample(myModel,N); i5 : peek mySample o5 = Sample{ModelName => rand(D,n,M): M random polynomials in n variables of degree D } Parameters => {2, 3, 4} SampleSize => 2 9 2 1 1 2 9 3 2 3 2 3 7 2 7 7 1 2 7 2 7 3 2 5 6 2 2 2 2 5 2 2 2 3 3 2 10 2 1 2 2 3 4 2 7 2 5 2 2 5 7 2 2 2 6 5 2 5 5 5 2 Data => {{-x + -x x + -x + -x x + x x + -x , -x + -x x + -x + -x x + --x x + -x , --x + -x x + -x + 7x x + -x x + -x , -x + x x + 6x + 2x x + -x x + -x }, {5x + --x x + -x + x x + 5x x + --x , -x + 10x x + 3x + 3x x + -x x + -x , -x + -x x + -x + 5x x + -x x + -x , -x + -x x + -x + -x x + -x x + -x }} 2 1 2 1 2 2 2 4 1 3 2 3 4 3 2 1 4 1 2 9 2 4 1 3 10 2 3 2 3 10 1 3 1 2 7 2 1 3 2 2 3 7 3 3 1 1 2 2 1 3 4 2 3 9 3 1 10 1 2 7 2 1 3 2 3 9 3 2 1 1 2 2 1 3 2 2 3 3 3 8 1 6 1 2 5 2 1 3 3 2 3 2 3 5 1 5 1 2 7 2 4 1 3 9 2 3 3 3