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3 added 206 characters in body

Occasionally, but more frequently lately, I would like to perform some hard computations. As an example, yesterday the following question came up:

What is the projective dimension of the edge ideal of the graph $G$ which is two complete bipartite graphs $K_{a,b}, K_{c,d}$ joined by another edge?

(I believe I can get the answer by hand, but a confirmation would be nice. Also, I wish to compute other similar examples).

For the above question, my personal computer crashed when $a=b=c=d=6$. I used Macaulay 2 with a special package for such situations: EdgeIdeals.

I have a few vague ideas on how to solve this: email people who are better at computations, try to find access to more powerful computers (a small fee is OK), or carefullly use MO (but may be that only works for people like Kevin Buzzard). Still:

What can one do in such situations?

I am looking for more generic answers (that can apply not only for the examples above, but in other situations). For example, a pointer to what powerful computers one can get access to would be helpful. Thank you!

2 added 3 characters in body

Occasionally, but more frequently lately, I would like to perform some hard computations. As an example, yesterday the following question came up:

What is the projective dimension of the edge ideal of the graph $G$ which is two complete bipartite graphs $K_{a,b}, K_{c,d}$ joined by another edge?

(I believe I can get the answer by hand, but a confirmation would be nice. Also, I wish to compute other similar examples).

For the above question, my personal computer crash crashed when $a=b=c=d=6$. I used Macaulay 2 with a special package for such situationsituations: EdgeIdeals.

I have a few vague ideas on how to solve this: email people who are better at computations, try to find access to more powerful computers (a small fee is OK). Still:

What can one do in such situations?

I am looking for more generic answers (that can apply not only for the examples above, but in other situations). For example, a pointer to what powerful computers one can get access to would be helpful. Thank you!

1

What to do when your research runs into a computationally challenging problem?

Occasionally, but more frequently lately, I would like to perform some hard computations. As an example, yesterday the following question came up:

What is the projective dimension of the edge ideal of the graph $G$ which is two complete bipartite graphs $K_{a,b}, K_{c,d}$ joined by another edge?

(I believe I can get the answer by hand, but a confirmation would be nice. Also, I wish to compute other similar examples).

For the above question, my personal computer crash when $a=b=c=d=6$. I used Macaulay 2 with a special package for such situation: EdgeIdeals.

I have a few vague ideas on how to solve this: email people who are better at computations, try to find access to more powerful computers (a small fee is OK). Still:

What can one do in such situations?

I am looking for more generic answers (that can apply not only for the examples above, but in other situations). For example, a pointer to what powerful computers one can get access to would be helpful. Thank you!