Macaulay2 Does Nothing
I've been trying to run Macaulay2 in Sage to generate some examples for a project I have.
I used cloud.sagemath.com and everything worked fine for a while, but some inputs just wouldn't evaluate. There was no error, and it wouldn't freeze- it's just that nothing would happen. I figured there was a calculation limit, so I downloaded sage and Macaulay2, but the same problem occurs. Sage and Macaulay2 appear to be properly installed.
An example of code which doesn't do anything is:
R = ZZ[O1,O2,O3,O4,O5,In1,In2,In3,In4,In5];
I = ideal(O1*O2,O2*O3,O3*O4,O4*O5,O5*O1,In1*In3,In3*In5,In5*In2,In2*In4,In4*In1,O1*In1,O2*In2,O3*In3,O4*In4,O5*In5);
J = ideal(O1,O2,O3,O4,O5,In1,In2,In3,In4,In5);
v = flatten entries mingens J;
e = flatten entries mingens I;
m = table(e,e,(a,b)->a*b);
s = unique flatten m;
for i when i<length e do s=delete(e#i^2,s);
dvds = (a,b) -> if b%(a*a)==0 then true else false;
f = x -> any(v, a -> dvds(a,x));
i = 0; while i<#s do if f(s#i)==false then s=delete(s#i,s) else i=i+1;
F = ideal(s);
betti F
betti I
Meanwhile, similar code which returns correct-looking output is
%macaulay2
R = ZZ[x1,x2,x3,x4];
I = ideal(x1*x2, x2*x3, x3*x4, x4*x1);
J = ideal (x1,x2,x3,x4);
v = flatten entries mingens J;
e = flatten entries mingens I;
m = table(e,e,(a,b)->a*b);
s = unique flatten m;
for i when i<length e do s=delete(e#i^2,s);
dvds = (a,b) -> if b%(a*a)==0 then true else false;
f = x -> any(v, a -> dvds(a,x));
i = 0; while i<#s do if f(s#i)==false then s=delete(s#i,s) else i=i+1;
F = ideal(s);
betti F
betti I
The output is
Ideal of R
Ideal of R
2 2 2 2
{x1*x3*x4 , x2*x3 x4, x1 x2*x4, x1*x2 x3}
List
Ideal of R
0 1
total: 1 4
0: 1 .
1: . .
2: . .
3: . 4
BettiTally
0 1
total: 1 4
0: 1 .
1: . 4
BettiTally
The only real difference seems to be the number of calculations made, and this idea is confirmed in that the calculations always seem to fail around ZZ[x1..xn] for n>8. There must be some way to fix this. Can anyone help?
