Comment #27 on issue 51 by mattpap: RootOf for polynomial equations
http://code.google.com/p/sympy/issues/detail?id=51
Regarding #25, I slightly improved RooOf's API, so now we have:
1. Just a single root:
In [1]: RootOf(x**3 + x + 1, 0)
Out[1]:
⎛ 3 ⎞
RootOf⎝x + x + 1, 0⎠
2. Collection of roots:
In [2]: RootOf(x**3 + x + 1, (0,1,2))
Out[2]:
⎡ ⎛ 3 ⎞ ⎛ 3 ⎞ ⎛ 3 ⎞⎤
⎣RootOf⎝x + x + 1, 0⎠, RootOf⎝x + x + 1, 1⎠, RootOf⎝x + x + 1, 2⎠⎦
3. Only real roots:
In [3]: RootOf(x**3 + x + 1)
Out[3]:
⎡ ⎛ 3 ⎞⎤
⎣RootOf⎝x + x + 1, 0⎠⎦
4. All roots:
In [4]: RootOf(x**3 + x + 1, True)
Out[4]:
⎡ ⎛ 3 ⎞ ⎛ 3 ⎞ ⎛ 3 ⎞⎤
⎣RootOf⎝x + x + 1, 0⎠, RootOf⎝x + x + 1, 1⎠, RootOf⎝x + x + 1, 2⎠⎦
5. A generator can be specified as the second argument to RootOf. If
specified, then indices are moved to the third argument and work exactly
the same as above:
In [5]: RootOf(y*x**3 + y*x + y, x, 0)
Out[5]:
⎛ 3 ⎞
RootOf⎝x + x + 1, 0⎠
Note that a polynomial must be univariate a prior:
In [6]: RootOf(y*x**3 + y*x + y, 0)
---------------------------------------------------------------------------
PolynomialError Traceback (most recent call last)
/home/matt/repo/git/sympy/<ipython console> in <module>()
/home/matt/repo/git/sympy/sympy/polys/rootoftools.pyc in __new__(cls, f, x,
indices, radicals, expand)
390
391 if not poly.is_univariate:
--> 392 raise PolynomialError("only univariate polynomials are
supported")
393
394 degree = poly.degree()
PolynomialError: only univariate polynomials are supported
(this limitation will be removed in future).
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