If we adjoin a root a of an irreducible polynomial f Î K[x] to the field K we get an algebraic extension K(a), which is again a field. We call K the base field of K(a).
By Kronecker's construction, we may identify K(a) with the factor ring K[x]/(f), an identification that also provides a method for computing in these extension fields.
It is important to note that different extensions of the same field are entirely different (and its elements lie in different families), even if mathematically one could be embedded in the other one.
Currently sf GAP only allows extension fields of fields K, when K itself is not an extension field.
[Top] [Previous] [Up] [Next] [Index]
GAP 4 manual