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Power set with group operation as symmetric difference

asked 2018-08-28 18:36:14 -0600

sam nazari gravatar image

My apologies for the novice question but I know that for a set X the powerset P(X) along with the symmetric difference (denoted by D) forms a group (P(X), D). I would like to form this group with sage and then build up a module over F = {0,1}. I've googled everywhere on how to go about this but I am having trouble. I can show these by hand and I would love to be able to formulate them in Sage. Thanks for your help. Sam

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answered 2018-08-29 00:06:17 -0600

vdelecroix gravatar image

What you are looking for is isomorphic to the group ((Z / 2Z)^n, +) that you can build in Sage in many ways. For example

sage: Zmod(2) ^ 5
Vector space of dimension 5 over Ring of integers modulo 2

Concerning the module question, I don't see any link with the first part. You seem to want to use (Zmod(2), +, x) (this time as a ring).

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answered 2018-08-29 22:59:52 -0600

sam nazari gravatar image

Thank you!

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Asked: 2018-08-28 18:36:14 -0600

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Last updated: Aug 29 '18