Better display of polynomials over fields with non-primitive polys

[mhostetter]

A field with a non-primitive polynomial with display="poly" will use the polynomial indeterminate x instead of α. When creating a polynomial over that field, these indeterminates get confused.

Primitive

In [1]: import galois

In [2]: GF = galois.GF(2**8, display="poly")

In [3]: print(GF)
Galois Field:
  name: GF(2^8)
  characteristic: 2
  degree: 8
  order: 256
  irreducible_poly: x^8 + x^4 + x^3 + x^2 + 1
  is_primitive_poly: True
  primitive_element: x

In [4]: f = galois.Poly([171, 0, 0, 53], field=GF); f
Out[4]: Poly((α^7 + α^5 + α^3 + α + 1)x^3 + (α^5 + α^4 + α^2 + 1), GF(2^8))

Non-primitive

In [1]: import galois

In [2]: GF = galois.GF(2**8, irreducible_poly="x^8 + x^4 + x^3 + x + 1", display="poly")

In [3]: print(GF)
Galois Field:
  name: GF(2^8)
  characteristic: 2
  degree: 8
  order: 256
  irreducible_poly: x^8 + x^4 + x^3 + x + 1
  is_primitive_poly: False
  primitive_element: x + 1

In [4]: f = galois.Poly([171, 0, 0, 53], field=GF); f
Out[4]: Poly((x^7 + x^5 + x^3 + x + 1)x^3 + (x^5 + x^4 + x^2 + 1), GF(2^8))  # Too confusing!