I need to find an online Finite Field calculator with the following operations: Inverse SqrRoot Mult Div I have found one a couple of days ago but lost the url, and cannot find it now. Any help would be highly appreciated.

  • $\begingroup$ thx but, I need something as the first one with SqrRoot and Inverses, online. Is for students, I cannot ask them to install anything $\endgroup$
    – DaWNFoRCe
    Commented Apr 20, 2014 at 19:14
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    $\begingroup$ Maybe wims.unice.fr/wims/en_tool~algebra~calcff.en.html ? More customisable solution could be SageMathCloud, and you may also use GAP there. $\endgroup$ Commented Apr 20, 2014 at 19:20
  • $\begingroup$ the first one does not work, and I do not know what u mean I could also use the GAP $\endgroup$
    – DaWNFoRCe
    Commented Apr 20, 2014 at 20:19
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    $\begingroup$ SageMathCloud gives you access to a virtual machine on which you may install GAP. Of course, you can use Sage there as well, and then either use GAP via Sage (the version which is included in Sage), or maybe use finite fields arithmetic provided by Sage - can not advice on the latter and compare it with GAP, though. Perhaps both systems will match your needs. $\endgroup$ Commented Apr 20, 2014 at 20:30
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    $\begingroup$ IMHO, might be helpful to post this question under tags (math-software) and (symbolic-computation), maybe replacing (finite-groups) and (galois-theory) ... $\endgroup$ Commented Apr 20, 2014 at 20:42

1 Answer 1


SageMathCloud (https://cloud.sagemath.com) can do absolutely everything you need online, for free. Tell your students to:

  1. Go to https://cloud.sagemath.com and create an account.
  2. Click "New Project" under projects.
  3. Open the project and click "+New" and click on "Sage Worksheet"
  4. In the worksheet that comes up they can do pretty much anything related to finite field calculations. Here is an image that shows how to do everything you requested in your question with a general finite field:

enter image description here

More comments:

k.<a> = GF(25)   # create the finite field of order 25 with generator a.  
                 # type a.minpoly() to find the poly that a satisfies

(3+a)*(5-2*a)    # do all standard arithmetic as usual

The implementation in Sage is extremely efficient for small-cardinality fields, and is built on top of Givaro and Pari.


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