Comment #52 on issue 1598 by mattpap: New polynomials manipulation module
http://code.google.com/p/sympy/issues/detail?id=1598
I was bored with what I was supposed to do today, so in the mean time I
implemented
factorization algorithm over algebraic number fields, e.g.:
In [1]: factor(x**4+1, extension=sqrt(2))
Out[1]:
⎛ ⎽⎽⎽ 2⎞ ⎛ ⎽⎽⎽ 2⎞
⎝1 + x⋅╲╱ 2 + x ⎠⋅⎝1 - x⋅╲╱ 2 + x ⎠
In [2]: expand(_)
Out[2]:
4
1 + x
In [3]: factor(x**4+1, extension=I)
Out[3]:
⎛ 2⎞ ⎛ 2⎞
⎝ⅈ + x ⎠⋅⎝-ⅈ + x ⎠
In [4]: expand(_)
Out[4]:
4
1 + x
You can also create Poly instances with algebraic coefficients, e.g.:
In [5]: f = Poly(2*I*x**2 + I/2, x, extension=I)
In [6]: f
Out[6]: Poly(2*I*x**2 + I/2, x, domain='QQ<I>')
or alternatively (for Gaussian integers):
In [7]: f = Poly(2*I*x**2 + I/2, x, gaussian=True)
In [8]: f
Out[8]: Poly(2*I*x**2 + I/2, x, domain='QQ<I>')
If you provide a wrong extension you will get:
In [9]: f = Poly(2*I*x**2 + I/2, x, extension=sqrt(2))
(...)
CoercionFailed: expected `Rational` object, got 2*I
Currently only univariate polynomials over a single extension of rationals
are
supported. However, soon I should have support for multivariate polynomials
and
multiple extensions.
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