Obtain the characteristic / minimal polynomial of an element over its prime field.
i1 : QQ[x]; F = splittingField((x^2+1)*(x^2-2)); |
i3 : minpoly a 4 2 o3 = x - 2x + 9 o3 : QQ[x] |
i4 : charpoly(a^2+1, Variable=>y) 4 3 2 o4 = y - 8y + 40y - 96y + 144 o4 : QQ[y] |
i5 : minpoly(a^2+1, Variable=>y) 2 o5 = y - 4y + 12 o5 : QQ[y] |
i6 : GF 81; minpoly(a+1) 4 3 o7 = x + x - x + 1 ZZ o7 : --[x] 3 |
The method minpoly can also be used on a field to recover the polynomial used in its definition.
i8 : minpoly F 4 2 o8 = a - 2a + 9 o8 : QQ[a] |
The object charpoly is a method function with options.