i1 : R = ZZ/101[x_0..x_3]; |
i2 : betti res (random hartshorneRaoModule)(0,{1},R) 0 1 2 3 4 o2 = total: 1 4 6 4 1 0: 1 4 6 4 1 o2 : BettiTally |
i3 : betti res (random hartshorneRaoModule)(0,{1,4},R) 0 1 2 3 4 o3 = total: 1 10 20 15 4 0: 1 . . . . 1: . 10 20 15 4 o3 : BettiTally |
i4 : betti res (random hartshorneRaoModule)(0,{1,4,1},R) 0 1 2 3 4 o4 = total: 1 9 16 9 1 0: 1 . . . . 1: . 9 16 9 . 2: . . . . 1 o4 : BettiTally |
i5 : betti res (random hartshorneRaoModule)(0,{1,4,2},R) 0 1 2 3 4 o5 = total: 1 8 12 7 2 0: 1 . . . . 1: . 8 12 3 . 2: . . . 4 2 o5 : BettiTally |
There are the following options:
* Attempts => ... a nonnegative integer or infinity (default) that limits the maximal number of attempts for the construction of the module
* Certify => ... true or false (default) checks whether the constructed module has the expected betti Table
i6 : betti res (random hartshorneRaoModule)(0,{1,3,2},R) 0 1 2 3 4 o6 = total: 1 5 9 7 2 0: 1 1 . . . 1: . 4 6 2 . 2: . . 3 5 2 o6 : BettiTally |
i7 : expectedBetti({1,3,2,0,0,0,0},3) 0 1 2 3 4 o7 = total: 1 5 7 5 2 0: 1 1 . . . 1: . 4 6 . . 2: . . 1 5 2 o7 : BettiTally |
i8 : null =!= (random hartshorneRaoModule)(0,{1,3,2},R) o8 = true |
i9 : null =!= (random hartshorneRaoModule)(0,{1,3,2},R,Certify=>true,Attempts=>1) o9 = false |
The object hartshorneRaoModule is an object of class RandomObject.