Re: algebra problem, need help fast!!!

*To*: mathgroup at smc.vnet.net*Subject*: [mg14676] Re: [mg14645] algebra problem, need help fast!!!*From*: Ken Levasseur <Kenneth_Levasseur at uml.edu>*Date*: Sun, 8 Nov 1998 21:15:36 -0500*Organization*: UMass Lowell Mathematical Sciences*References*: <199811070709.CAA01816@smc.vnet.net.>*Sender*: owner-wri-mathgroup at wolfram.com

You should be able to get the subfields using AbstractAlgebra`, which is available at http://www.central.edu/homepages/hibbarda/EAAM/eaam.html. I am coauthor of these packages with Al Hibbard (Central College). You might also be able to do the same with the Standard package FiniteFields.m, but I don't think that any of its functions identifies subfields. With out packages, there is no single function that identifies subfields, but you could proceed as follows: In[1]:= <<AbstractAlgebra`Master` In[2]:= IrreduciblePolyOverZpQ[ x^5+x^2+1,2] (* Verify that the polynomial is irreducible *) In[3]:= F=GF[2^5,IrreduciblePolynomial-> x^5+x^2+1] In[4]:= G=GenerateGroupoid[{x},Multiplication[F],SizeLimit->31] In[5]:= subgroups=CyclicSubgroups[G] Since finite fields are cyclic, the subfields would be the subgroups that you get from Out[5] that are closed with respect to addition (other than sums that add to 0). However, for the example you cite, your answer is obvious from Out[5]. Your question for degree 4 or 6 (for example) yeilds more interesting results. Ken Levasseur UMass Lowell Base_D wrote: > Does anyone know how to use mathematica to find all the subfields the > following field: > > K = Z/2Z[X]/(f) where is an irreducible polynomial of degree 5. > > Any help would be greatly appreciated. Rick

**References**:**algebra problem, need help fast!!!***From:*bla@bloop.org (Base_D)