Test for Lambda.ipynb

Kernel: SageMath 9.2

field = GF(3**2, 'g')
g = field.gen()
R = PolynomialRing(field, "x")
points = [(0, 1),(1, g), (g,g), (g+1, g)]
newpol = R.lagrange_polynomial(points)
newpol

2*x^3 + (2*g + 2)*x^2 + (2*g + 1)*x + 1

# from sage.crypto.sbox import SBox
# S = SBox(7, 0, 4, 12, 11, 8, 2, 1, 15, 3, 5, 6, 9, 10, 13, 14)
# pol = S.interpolation_polynomial()
# pol

from sympy import Eq
from sympy.abc import x,g
from sympy.utilities.lambdify import lambdify


f = lambdify([x,g], newpol)

/ext/sage/sage-9.2/local/lib/python3.8/site-packages/sympy/core/sympify.py:383: SymPyDeprecationWarning: 

String fallback in sympify has been deprecated since SymPy 1.6. Use
sympify(str(obj)) or sympy.core.sympify.converter or obj._sympy_
instead. See https://github.com/sympy/sympy/issues/18066 for more
info.

  SymPyDeprecationWarning(

f(g,g)

$\displaystyle 2 g^{3} + g^{2} \left(2 g + 2\right) + g \left(2 g + 1\right) + 1$

#Working Function Maker
from sympy.abc import x
from sympy.utilities.lambdify import lambdify, implemented_function
f = implemented_function('f', lambda x: newpol)
lam_f = lambdify(x, f(x))

lam_f(g)

$\displaystyle g x^{6} + g x^{4} + x^{5} + x^{3} \left(g^{2} + g + 1\right) + x^{2} \left(g + 1\right) + x \left(g + 1\right)$

#GF(2**N)
n = int(input())
p = 4
FF.<g> = GF(p**n)
FFlist = list(FF)
print(FFlist)

---------------------------------------------------------------------------
KeyboardInterrupt                         Traceback (most recent call last)
<ipython-input-3-4d0d8c5ed53a> in <module>
      1 #GF(2**N)
----> 2 n = int(input())
      3 p = Integer(4)
      4 FF = GF(p**n, names=('g',)); (g,) = FF._first_ngens(1)
      5 FFlist = list(FF)
/ext/sage/sage-9.2/local/lib/python3.8/site-packages/ipykernel/kernelbase.py in raw_input(self, prompt)
    858                 "raw_input was called, but this frontend does not support input requests."
    859             )
--> 860         return self._input_request(str(prompt),
    861             self._parent_ident,
    862             self._parent_header,
/ext/sage/sage-9.2/local/lib/python3.8/site-packages/ipykernel/kernelbase.py in _input_request(self, prompt, ident, parent, password)
    891             except KeyboardInterrupt:
    892                 # re-raise KeyboardInterrupt, to truncate traceback
--> 893                 raise KeyboardInterrupt("Interrupted by user") from None
    894             else:
    895                 break
KeyboardInterrupt: Interrupted by user

for x in FFlist:
    print (f(x,g))

1
g
g^3 + 1
g^3 + g + 1
g
1
g^2
g^2 + 1
0
g^2 + g + 1
g^3 + g + 1
g + 1
g^3 + g + 1
g^3 + g^2 + g + 1
g^3 + g
g