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A simple question on modules.

asked 2011-12-23 01:44:13 +0200

updated 2011-12-23 01:48:45 +0200

Sorry to ask such simple question, but I am not able to find appropriate reference in the manual for this.

I have a power series ring (or polynomial ring) in multi-variables, say

R = k[X_1,\cdots, X_n] or k[[X_1,\cdots, X_n]].

I need to define a module over R, generated by


e.g. in Singular one can define it using

module M = f_1,\cdots,f_r.

(Of course not verbatim)

Also I would appreciate if one can redirect me to the corresponding section in the reference manual. Thanks in advance.

-- VInay

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answered 2011-12-23 16:15:40 +0200

benjaminfjones gravatar image

Here you go. It's a ways down in the reference manual.

There are good examples of constructing free modules and homomorphisms between modules in that chapter.

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answered 2011-12-24 02:25:42 +0200

Hi Benjamin,

Thanks for the reference. I had already gone through that, however it does not define the module when you know the generators. (The explicit way Singular does.)

The only workaround I could think within sage (mainly from the pages you mentioned), was to define the homomorphism into the free module. (Something like we do for computing resolution.) But that of course is very tedious as you know.

Do let me know if there is any better way!

Thanks and regards


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Asked: 2011-12-23 01:44:13 +0200

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Last updated: Dec 24 '11