Comment #89 on issue 1598 by mattpap: New polynomials manipulation module
http://code.google.com/p/sympy/issues/detail?id=1598
A little update:
1. Implemented continued fraction real root isolation algorithm. Now you
can compute
the following:
In [1]: intervals((x**2-2)*(x**2-3))
Out[1]: [((-2, -3/2), 1), ((-3/2, -1), 1), ((1, 3/2), 1), ((3/2, 2), 1)]
In [2]: intervals((x**2-2)*(x**2-3), eps=QQ(1,1000000))
Out[2]:
⎡⎛⎛ 1351 2340⎞ ⎞ ⎛⎛ 1970 1393⎞ ⎞ ⎛⎛1393 1970⎞ ⎞ ⎛⎛2340
1351⎞ ⎞⎤
⎢⎜⎜- ────, - ────⎟, 1⎟, ⎜⎜- ────, - ────⎟, 1⎟, ⎜⎜────, ────⎟, 1⎟, ⎜⎜────,
────⎟, 1⎟⎥
⎣⎝⎝ 780 1351⎠ ⎠ ⎝⎝ 1393 985 ⎠ ⎠ ⎝⎝985 1393⎠ ⎠ ⎝⎝1351
780 ⎠ ⎠⎦
By default large but disjoint open intervals (or points) are computed. If
narrow
intervals are needed then specify 'eps' keyword argument which tells how
long (at
most) can be the resulting intervals. Non-squarefree polynomials are
supported
natively. Only integer and rational coefficients are supported.
2. Implemented complex root isolation algorithm. This is preliminary, slow
and
annoying. Works only with floating-point coefficients. Not exposed to the
toplevel. I
need to implement another algorithm, which doesn't use Sturm sequences.
Should be
faster and purely symbolic.
3. Started work on new RootOf.
4. (a bit off-topic) Written bibliography for SymPy (mostly polys) in
BibTeX format.
For now there are 150+ items (books, articles, proceedings) which were used
directly
to implement some algorithms or influenced my view on symbolic manipulation
systems
and algebraic computations. This is preliminary result, more items will be
added.
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