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
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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
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The object model is a method function.