polynomials over GF(2)

[Phillip M. Feldman]

I would like to perform operations on polynomials over GF(2), i.e., polynomials with binary coefficients.  Is there a way to do this with SymPy?

There is a sympy.polys.galoistools module, but I haven't found any user documentation for it

[Kalevi Suominen]

On Tuesday, May 24, 2016 at 3:37:42 AM UTC+3, Phillip M. Feldman wrote:

I would like to perform operations on polynomials over GF(2), i.e., polynomials with binary coefficients.  Is there a way to do this with SymPy?

There is a sympy.polys.galoistools module, but I haven't found any user documentation for it

galoistools is the low lever implementation module that is not intended for direct use. The user interface is the
same as with other polynomials. To define a polynomial ring  R  with generator (or 'unknown')  x  over  GF(2)  you write

R, x = ring('x', GF(2))

Polynomials are then constructed in the usual way: p = x**2 + x , etc. and all the standard operations are valid. (Note:  x  is also a polynomial, not a Symbol.)

[Phillip Feldman]

I tried the following:

In [1]: from sympy import *

In [2]: R, x= ring('x', GF(2))

In [3]: p= x**5 + 1

In [4]: q= x+1

In [5]: div(p, q)

The result is an exception: SympifyError: x**5 + 1 mod 2

Any advice will be appreciated.

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[Kalevi Suominen]

On Wednesday, May 25, 2016 at 3:31:23 AM UTC+3, Phillip M. Feldman wrote:

I tried the following:

In [1]: from sympy import *

In [2]: R, x= ring('x', GF(2))

In [3]: p= x**5 + 1

In [4]: q= x+1

In [5]: div(p, q)

The result is an exception: SympifyError: x**5 + 1 mod 2

Any advice will be appreciated.

div(p, q)  is intended for expressions. p and q  are polynomials, not expressions. Division of polynomials is defined as a method:
In [4]: p.div(q)
Out[4]: (x**4 + x**3 + x**2 + x + 1 mod 2, 0 mod 2)

[Kalevi Suominen]

On Wednesday, May 25, 2016 at 7:55:46 AM UTC+3, Kalevi Suominen wrote:

On Wednesday, May 25, 2016 at 3:31:23 AM UTC+3, Phillip M. Feldman wrote:

I tried the following:

In [1]: from sympy import *

In [2]: R, x= ring('x', GF(2))

In [3]: p= x**5 + 1

In [4]: q= x+1

In [5]: div(p, q)

The result is an exception: SympifyError: x**5 + 1 mod 2

Any advice will be appreciated.

div(p, q)  is intended for expressions. p and q  are polynomials, not expressions. Division of polynomials is defined as a method:
In [4]: p.div(q)
Out[4]: (x**4 + x**3 + x**2 + x + 1 mod 2, 0 mod 2)

PS: You can also write p/q, if the remainder 0 is not needed.