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Computes General functional decomposition of ``f``.
Given an expression ``f``, returns a list ``[f_1, f_2, ..., f_n]``,
where::
f = f_1 o f_2 o ... f_n = f_1(f_2(... f_n))
Note: This is a General decomposition function. It also decomposes
Polynomials. For only Polynomial decomposition see ``decompose`` in polys.
Examples
========
>>> from sympy.abc import x
>>> from sympy import decompogen, sqrt, sin, cos
>>> decompogen(sin(cos(x)), x)
[sin(x), cos(x)]
>>> decompogen(sin(x)**2 + sin(x) + 1, x)
[x**2 + x + 1, sin(x)]
>>> decompogen(sqrt(6*x**2 - 5), x)
[sqrt(x), 6*x**2 - 5]
>>> decompogen(sin(sqrt(cos(x**2 + 1))), x)
[sin(x), sqrt(x), cos(x), x**2 + 1]
>>> decompogen(x**4 + 2*x**3 - x - 1, x)
[x**2 - x - 1, x**2 + x]
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Returns the composition of functions.
Given a list of functions ``g_s``, returns their composition ``f``,
where:
f = g_1 o g_2 o .. o g_n
Note: This is a General composition function. It also composes Polynomials.
For only Polynomial composition see ``compose`` in polys.
Examples
========
>>> from sympy.solvers.decompogen import compogen
>>> from sympy.abc import x
>>> from sympy import sqrt, sin, cos
>>> compogen([sin(x), cos(x)], x)
sin(cos(x))
>>> compogen([x**2 + x + 1, sin(x)], x)
sin(x)**2 + sin(x) + 1
>>> compogen([sqrt(x), 6*x**2 - 5], x)
sqrt(6*x**2 - 5)
>>> compogen([sin(x), sqrt(x), cos(x), x**2 + 1], x)
sin(sqrt(cos(x**2 + 1)))
>>> compogen([x**2 - x - 1, x**2 + x], x)
-x**2 - x + (x**2 + x)**2 - 1
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