Comment #88 on issue 1598 by mattpap: New polynomials manipulation module
http://code.google.com/p/sympy/issues/detail?id=1598
There is decompose() function which will do the job (up to constant terms),
e.g.:
In [1]: compose(x**3-3*x**2+1, x**3-2)
Out[1]:
3 6 9
-19 + 24⋅x - 9⋅x + x
In [2]: decompose(_)
Out[2]:
⎡ 2 3 3⎤
⎣-19 + 24⋅x - 9⋅x + x , x ⎦
In [3]: compose(x**3-3*x**2+1, x**6-x**3+2)
Out[3]:
6 9 12 15 18
-3 + 3⋅x - 7⋅x + 6⋅x - 3⋅x + x
In [4]: decompose(_)
Out[4]:
⎡ 2 3 2 3⎤
⎣-3 + 3⋅x + x , -x + x , x ⎦
Note that decompose() works only with univariate polynomials, so:
In [1]: compose(x**2 + 1, x**3-y, x)
Out[1]:
2 3 6
1 + y - 2⋅y⋅x + x
In [2]: decompose(_, x)
Out[2]:
⎡ 2 2 3⎤
⎣1 - 2⋅x⋅y + x + y , x ⎦
(actually in compose() you don't have to specify generators, because it
will do the
composition for the principal generator, assuming by default that x comes
before y,
but in decompose() this behavior is not yet implemented, so x is mandatory).
Also look into roots() and, especially, _try_decompose() where decompose()
is used
together with square-free factorization to compute roots the way you've
described.
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