v0.3.3

Released February 1, 2023

Changes

  • Added a terms keyword argument to irreducible_poly(), irreducible_polys(), primitive_poly(), and primitive_polys() to find a polynomial with a desired number of non-zero terms. This may be set to an integer or to "min". (#463)

    >>> import galois
>>> galois.irreducible_poly(7, 9)
Poly(x^9 + 2, GF(7))
>>> galois.irreducible_poly(7, 9, terms=3)
Poly(x^9 + x + 1, GF(7))
>>> galois.primitive_poly(7, 9)
Poly(x^9 + x^2 + x + 2, GF(7))
>>> galois.primitive_poly(7, 9, terms="min")
Poly(x^9 + 3x^2 + 4, GF(7))

  • Added a database of binary irreducible polynomials with degrees less than 10,000. These polynomials are lexicographically-first and have the minimum number of non-zero terms. The database is accessed in irreducible_poly() when terms="min" and method="min". (#462)

    In [1]: import galois

# Manual search
In [2]: %time galois.irreducible_poly(2, 1001)
CPU times: user 6.8 s, sys: 0 ns, total: 6.8 s
Wall time: 6.81 s
Out[2]: Poly(x^1001 + x^5 + x^3 + x + 1, GF(2))

# With the database
In [3]: %time galois.irreducible_poly(2, 1001, terms="min")
CPU times: user 745 µs, sys: 0 ns, total: 745 µs
Wall time: 1.4 ms
Out[3]: Poly(x^1001 + x^17 + 1, GF(2))

  • Memoized expensive polynomial tests Poly.is_irreducible() and Poly.is_primitive(). Now, the expense of those calculations for a given polynomial is only incurred once. (#470)

    In [1]: import galois

In [2]: f = galois.Poly.Str("x^1001 + x^17 + 1"); f
Out[2]: Poly(x^1001 + x^17 + 1, GF(2))

In [3]: %time f.is_irreducible()
CPU times: user 1.05 s, sys: 3.47 ms, total: 1.05 s
Wall time: 1.06 s
Out[3]: True

In [4]: %time f.is_irreducible()
CPU times: user 57 µs, sys: 30 µs, total: 87 µs
Wall time: 68.2 µs
Out[4]: True

  • Added tests for Conway polynomials Poly.is_conway() and Poly.is_conway_consistent(). (#469)

  • Added the ability to manually search for a Conway polynomial if it is not found in Frank Luebeck’s database, using conway_poly(p, m, search=True). (#469)

  • Various documentation improvements.

Contributors

Last update: Feb 01, 2023