a  ¬t|ƒ}t|tƒrt|tƒr,tdt|ƒƒ‚ˆ|jvr<|gSg}t|ttfƒr |j rh|j t j krh|j }n |jd}|ˆkr€|gS|| |ˆ¡gt|ˆƒ7}|St|ƒ}tt‡fdd„|jƒƒ}t|ƒdkr |dˆkr | |dˆ¡}|d}||gt|ˆƒ7}|Sz|t|ƒ7}|WSty8|gYS0dS)a9 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] zexpecting Expr but got: `%s`rcs ˆ|jvS)N)Ú free_symbols)Úx©Úsymbol©úh/Users/vegardjervell/Documents/master/model/venv/lib/python3.9/site-packages/sympy/solvers/decompogen.pyÚ8ózdecompogen..éN)rÚ isinstancerrÚ TypeErrorr r rrZis_PowÚbaserZExp1ÚexpÚargsÚsubsÚ decompogenrÚlistÚfilterÚgensÚlenr Ú ValueError)ÚfrÚresultÚargÚfprÚf1Úf2rr rrs4   rcCsPt|ƒdkr|dS|d ||d¡}t|ƒdkr8|St|g|dd…|ƒS)a0 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 rréN)rrÚcompogen)Zg_srZfoorrrr'Hs   r'N)Z sympy.corerrrrZsympy.core.relationalrZsympy.core.singletonrZ sympy.polysrr Zsympy.utilities.miscr rr'rrrrÚs    @