ASKSAGE: Sage Q&A Forum - RSS feedhttps://ask.sagemath.org/questions/Q&A Forum for SageenCopyright Sage, 2010. Some rights reserved under creative commons license.Thu, 30 Aug 2018 05:59:52 +0200Power set with group operation as symmetric differencehttps://ask.sagemath.org/question/43507/power-set-with-group-operation-as-symmetric-difference/ 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. SamWed, 29 Aug 2018 01:36:14 +0200https://ask.sagemath.org/question/43507/power-set-with-group-operation-as-symmetric-difference/Answer by sam nazari for <p>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</p>
https://ask.sagemath.org/question/43507/power-set-with-group-operation-as-symmetric-difference/?answer=43526#post-id-43526Thank you!
Thu, 30 Aug 2018 05:59:52 +0200https://ask.sagemath.org/question/43507/power-set-with-group-operation-as-symmetric-difference/?answer=43526#post-id-43526Answer by vdelecroix for <p>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</p>
https://ask.sagemath.org/question/43507/power-set-with-group-operation-as-symmetric-difference/?answer=43508#post-id-43508What 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).Wed, 29 Aug 2018 07:06:17 +0200https://ask.sagemath.org/question/43507/power-set-with-group-operation-as-symmetric-difference/?answer=43508#post-id-43508