U L?h@spddlmZmZmZmZddlmZddlmZddl m Z m Z ddl m Z ddlmZmZddZd d Zd S) )FunctionPowsympifyExpr) Relational)S)Poly decompose) func_name)MinMaxc st|}t|trt|tr,tdt||jkr<|gSt|ttfr|j rd|j t j krd|j }n |jd}|kr||gS||gt|St|ttfrVt|j}d}t|D]v\}}|sqt|}t|dkrg|}|dkr|dd}n|dd|kr$g}q2|d||<q|dkrF|gS|j|g|St|}ttfdd|j} t| dkr| dkr|| d} | d} | gt| Sz t|WStk r|gYSXdS)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`rNcs |jkS)N) free_symbols)xsymbolJ/var/www/html/venv/lib/python3.8/site-packages/sympy/solvers/decompogen.pyMzdecompogen..)r isinstancerr TypeErrorr rrrZis_PowbaserZExp1expargssubs decompogenr r list enumerateZhas_freelenfuncrfiltergensr ValueError) frargrZd0iadfpr"f1f2rrrr sP         rcCsPt|dkr|dS|d||d}t|dkr8|St|g|dd|S)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 r rN)rrcompogen)Zg_srZfoorrrr-[s   r-N)Z sympy.corerrrrZsympy.core.relationalrZsympy.core.singletonrZ sympy.polysrr Zsympy.utilities.miscr Z(sympy.functions.elementary.miscellaneousr r rr-rrrrs   R