Compute Ext with Macaulay2

Question

I want to compute Ext with Macaulay2.

I see in the website they write how to do it, but I can not do it. Can anyone help me with an example?

For example, let $S=k[x,y,z,t]$. How to compute $\mathrm{Ext}^i_S (S/(xy^2,x^2z),S)$ for some $i$? How to interpret it?

Thanks.

Youngsu · Accepted Answer · 2016-04-13 21:02:16Z

4

S = QQ[x,y,z,t]

M = module S/ideal "xy2,x2z"

for i from 0 to 4 list Ext^i (M,S)

In general, if you have installed M2 property, viewHelp would direct you to a help page, and help would give you a short help message in M2.

answered Apr 13, 2016 at 21:02

Youngsu

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1

$\begingroup$ Many thanks. But im not able to interpret the answer.can you help $\endgroup$
– Sonii
Apr 14, 2016 at 13:53
1

$\begingroup$ What do you mean? $\endgroup$
– Youngsu
Apr 14, 2016 at 15:03
$\begingroup$ @Youngsu. The answer is : o4 = {image 0, cokernel {-1} | x |, cokernel {-5} | xz y2 |, 0, 0}. Here, what is $Ext^1$, what is$ Ext^2$,.., ? (probably OP wants to know this too.) $\endgroup$
– user 1
Apr 14, 2016 at 16:55
$\begingroup$ Yes user1. ,,,, $\endgroup$
– Sonii
Apr 14, 2016 at 18:02
$\begingroup$ The results are separated by commas. I recommend you to read the instruction for tutorial for Macualay2 which explains things like your question. For instance, if you only one a particular spot of the ext you can use $Ext^i (M,S)$. But in your example, all the other Exts are already zero. $\endgroup$
– Youngsu
Apr 14, 2016 at 19:17

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