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Use polynomial indeterminate "x" for repr_table()
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@mhostetter
mhostetter committed Aug 8, 2021
1 parent 772d95e commit f1ba17d
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Showing 2 changed files with 53 additions and 43 deletions.
88 changes: 49 additions & 39 deletions galois/_field/_meta_class.py
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Original file line number Diff line number Diff line change
Expand Up @@ -183,7 +183,7 @@ def display(cls, mode="int"):
return context

def repr_table(cls, primitive_element=None, sort="power"):
"""
r"""
Generates a field element representation table comparing the power, polynomial, vector, and integer representations.
Parameters
Expand All @@ -207,13 +207,30 @@ def repr_table(cls, primitive_element=None, sort="power"):
.. ipython:: python
GF = galois.GF(2**4)
print(GF.properties)
Generate a representation table for :math:`\mathrm{GF}(2^4)`. Since :math:`x^4 + x + 1` is a primitive polynomial,
:math:`x` is a primitive element of the field. Notice, :math:`\textrm{ord}(x) = 15`.
.. ipython:: python
print(GF.repr_table())
print(GF.repr_table(sort="int"))
Generate a representation table for :math:`\mathrm{GF}(2^4)` using a different primitive element :math:`x^3 + x^2 + x`.
Notice, :math:`\textrm{ord}(x^3 + x^2 + x) = 15`.
.. ipython:: python
alpha = GF.primitive_elements[-1]
print(GF.repr_table(alpha))
Generate a representation table for :math:`\mathrm{GF}(2^4)` using a non-primitive element :math:`x^3 + x^2`. Notice,
:math:`\textrm{ord}(x^3 + x^2) = 5 \ne 15`.
.. ipython:: python
beta = GF("x^3 + x^2")
print(GF.repr_table(beta))
"""
if sort not in ["power", "poly", "vector", "int"]:
raise ValueError(f"Argument `sort` must be in ['power', 'poly', 'vector', 'int'], not {sort!r}.")
Expand All @@ -226,36 +243,36 @@ def repr_table(cls, primitive_element=None, sort="power"):
idxs = np.argsort(x)
degrees, x = degrees[idxs], x[idxs]
x = np.concatenate((np.atleast_1d(cls(0)), x)) # Add 0 = alpha**-Inf
prim = cls._print_poly(primitive_element)
prim = poly_to_str(integer_to_poly(primitive_element, cls.characteristic))

N_power = max(len("({})^{}".format(prim, str(cls.order - 1))), len("Power")) + 2
N_poly = max([len(cls._print_poly(e)) for e in x] + [len("Polynomial")]) + 2
N_vec = max([len(str(integer_to_poly(e, cls.characteristic, degree=cls.degree-1))) for e in x] + [len("Vector")]) + 2
N_int = max([len(cls._print_int(e)) for e in x] + [len("Integer")]) + 2
# Define print helper functions
if len(prim) > 1:
print_power = lambda power: "0" if power is None else f"({prim})^{power}"
else:
print_power = lambda power: "0" if power is None else f"{prim}^{power}"
print_poly = lambda x: poly_to_str(integer_to_poly(x, cls.characteristic))
print_vec = lambda x: str(integer_to_poly(x, cls.characteristic, degree=cls.degree-1))
print_int = lambda x: str(int(x))

# Determine column widths
N_power = max([len(print_power(max(degrees))), len("Power")]) + 2
N_poly = max([len(print_poly(e)) for e in x] + [len("Polynomial")]) + 2
N_vec = max([len(print_vec(e)) for e in x] + [len("Vector")]) + 2
N_int = max([len(print_int(e)) for e in x] + [len("Integer")]) + 2

# Useful characters: https://www.utf8-chartable.de/unicode-utf8-table.pl?start=9472
string = "╔" + "═"*N_power + "╤" + "═"*N_poly + "╤" + "═"*N_vec + "╤" + "═"*N_int + "╗"

labels = "║" + "Power".center(N_power) + "│" + "Polynomial".center(N_poly) + "│" + "Vector".center(N_vec) + "│" + "Integer".center(N_int) + "║"
string += "\n" + labels

divider = "║" + "═"*N_power + "╪" + "═"*N_poly + "╪" + "═"*N_vec + "╪" + "═"*N_int + "║"
string += "\n" + divider
string += "\n║" + "Power".center(N_power) + "│" + "Polynomial".center(N_poly) + "│" + "Vector".center(N_vec) + "│" + "Integer".center(N_int) + "║"
string += "\n║" + "═"*N_power + "╪" + "═"*N_poly + "╪" + "═"*N_vec + "╪" + "═"*N_int + "║"

for i in range(x.size):
if i == 0:
power = "0"
else:
power = "({})^{}".format(prim, degrees[i - 1]) if len(prim) > 1 else "{}^{}".format(prim, degrees[i - 1])
line = "║" + power.center(N_power) + "│" + cls._print_poly(x[i]).center(N_poly) + "│" + str(integer_to_poly(x[i], cls.characteristic, degree=cls.degree-1)).center(N_vec) + "│" + cls._print_int(x[i]).center(N_int) + "║"
string += "\n" + line
d = None if i == 0 else degrees[i - 1]
string += "\n║" + print_power(d).center(N_power) + "│" + poly_to_str(integer_to_poly(x[i], cls.characteristic)).center(N_poly) + "│" + str(integer_to_poly(x[i], cls.characteristic, degree=cls.degree-1)).center(N_vec) + "│" + cls._print_int(x[i]).center(N_int) + "║"

if i < x.size - 1:
divider = "╟" + "─"*N_power + "┼" + "─"*N_poly + "┼" + "─"*N_vec + "┼" + "─"*N_int + "╢"
string += "\n" + divider
string += "\n╟" + "─"*N_power + "┼" + "─"*N_poly + "┼" + "─"*N_vec + "┼" + "─"*N_int + "╢"

bottom = "╚" + "═"*N_power + "╧" + "═"*N_poly + "╧"+ "═"*N_vec + "╧" + "═"*N_int + "╝"
string += "\n" + bottom
string += "\n╚" + "═"*N_power + "╧" + "═"*N_poly + "╧"+ "═"*N_vec + "╧" + "═"*N_int + "╝"

return string

Expand Down Expand Up @@ -343,29 +360,22 @@ def arithmetic_table(cls, operation, x=None, y=None):

# Useful characters: https://www.utf8-chartable.de/unicode-utf8-table.pl?start=9472
string = "╔" + "═"*N_left + "╦" + ("═"*N + "╤")*(y.size - 1) + "═"*N + "╗"

line = "║" + operation_str.rjust(N_left - 1) + " ║"
string += "\n║" + operation_str.rjust(N_left - 1) + " ║"
for j in range(y.size):
line += print_element(y[j]).center(N)
line += "│" if j < y.size - 1 else "║"
string += "\n" + line

divider = "╠" + "═"*N_left + "╬" + ("═"*N + "╪")*(y.size - 1) + "═"*N + "╣"
string += "\n" + divider
string += print_element(y[j]).center(N)
string += "│" if j < y.size - 1 else "║"
string += "\n╠" + "═"*N_left + "╬" + ("═"*N + "╪")*(y.size - 1) + "═"*N + "╣"

for i in range(x.size):
line = "║" + print_element(x[i]).rjust(N_left - 1) + " ║"
string += "\n║" + print_element(x[i]).rjust(N_left - 1) + " ║"
for j in range(y.size):
line += print_element(Z[i,j]).center(N)
line += "│" if j < y.size - 1 else "║"
string += "\n" + line
string += print_element(Z[i,j]).center(N)
string += "│" if j < y.size - 1 else "║"

if i < x.size - 1:
divider = "╟" + "─"*N_left + "╫" + ("─"*N + "┼")*(y.size - 1) + "─"*N + "╢"
string += "\n" + divider
string += "\n╟" + "─"*N_left + "╫" + ("─"*N + "┼")*(y.size - 1) + "─"*N + "╢"

bottom = "╚" + "═"*N_left + "╩" + ("═"*N + "╧")*(y.size - 1) + "═"*N + "╝"
string += "\n" + bottom
string += "\n╚" + "═"*N_left + "╩" + ("═"*N + "╧")*(y.size - 1) + "═"*N + "╝"

return string

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