ó ¡¼™\c@snddlmZmZmZmZddlmZddlmZm Z ddl m Z d„Z d„Z dS(iÿÿÿÿ(tFunctiontPowtsympifytExpr(t Relational(tPolyt decompose(t func_namecsˆt|ƒ}t|tƒ s+t|tƒrDtdt|ƒƒ‚nˆ|jkrZ|gSg}t|ttfƒrÇ|j dˆkr|gS||j |j dˆƒgt |j dˆƒ7}|St |ƒ}t t‡fd†|jƒƒ}t|ƒdkrT|dˆkrT|j |dˆƒ}|d}||gt |ˆƒ7}|Sy|t|ƒ7}|SWntk rƒ|gSXdS(se 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.solvers.decompogen import decompogen >>> from sympy.abc import x >>> from sympy import 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] sexpecting Expr but got: `%s`ics ˆ|jkS(N(t free_symbols(tx(tsymbol(s7lib/python2.7/site-packages/sympy/solvers/decompogen.pyt4tiN(Rt isinstanceRRt TypeErrorRRRRtargstsubst decompogenRtlisttfiltertgenstlenRt ValueError(tfR tresulttfpRtf1tf2((R s7lib/python2.7/site-packages/sympy/solvers/decompogen.pyRs. 4 !"  cCsbt|ƒdkr|dS|dj||dƒ}t|ƒdkrJ|St|g|d|ƒS(s0 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 iii(RRtcompogen(tg_sR tfoo((s7lib/python2.7/site-packages/sympy/solvers/decompogen.pyRDs N(t sympy.coreRRRRtsympy.core.relationalRt sympy.polysRRtsympy.utilities.miscRRR(((s7lib/python2.7/site-packages/sympy/solvers/decompogen.pyts " =