Betti numbers of modules over Noetherian rings with ... - IPM

Appendix A: Algorithms for our criterion for linear resolutions 94
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/*Rand(x,y) returns a random integer between x and y*/
Data: P of Rees ring R(I)
Result: a sparse upper triangular random bi-change of coordinates g
begin
end
/*the degree of sparsity, here 5 times product of random 0
and 1*/
DS ←− 5
for i ← 1 to r do
end
i−1
Xi ←− xi +
DS
( Rand(0, 1)xj)
j=1
for i ← 1 to m do
end
i−1
Ti ←− ti +
k=1
DS
( Rand(0, 1)tj)
j=1
k=1
if (X1, · · · , Xr, T1, · · · , Tm) = (x1, · · · , xr, t1, · · · , tm) then
else
endif
g := x1 ↦→ X1, · · · , xr ↦→ Xr, t1 ↦→ T1, · · · , tm ↦→ Tm
return g
Generate again
Algorithm 6: Algorithm for generating a sparse random upper triangular
bi-change of coordinates.