Examples
Basic Examples (1)
Compute the Galois group of the polynomial x2+1:
Scope (7)
Compute the Galois group of the polynomial x4+2:
Return the CayleyGraph for the Galois group:
Find the group order:
Get the generators:
Find the group elements:
Display the group multiplication table:
Get all of the available properties as an Association:
Properties and Relations (2)
An irreducible polynomial of prime degree p larger than 4 with exactly 2 nonreal roots has Galois group SymmetricGroup[p]:
Verify that there are 3 real roots:
The Galois group for the irreducible polynomial of prime degree 5 with 2 nonreal roots is:
Publisher
Wolfram|Alpha Math Team
Version History
-
2.0.0
– 23 March 2023
-
1.0.0
– 25 August 2020
Related Resources
Author Notes
To view the full source code for GaloisGroupProperties, run the following code:
FileNameJoin[ReplacePart[FileNameSplit[FindFile["ResourceFunctionHelpers`"]], -1 →"GaloisGroupProperties.wl"]] // SystemOpen