+ in^RIHtHtHtHt^RIHt^RIHt^RI H t H t ^RI H t ^RIHtHtRtRtR #) )FunctionPowsympifyExpr) Relational)S)Poly decompose) func_name)MinMaxca\V4p\V\4'd\V\4'd\ R\ V4,4hSVP 9dV.#\V\\34'dVP'd-VP\P8XdVPpMVP^,pVS8XdV.#VPVS4.\!VS4,#\V\"\$34'd\'VP4pRp\)V4FpwrVVP+S4'gK\!VS4p\-V4^8Xd S.V,pVf VR,pMVR,V8wdS.pMV^,W5&Kr X^,S8XdV.#VP.!V!.V,#\1V4p\'\3V3RlVP444p \-V 4^8XdEV ^,S8wd7VPV ^,S4p V ^,p V .\!V S4,#\7V4# \8dT.u#i;i)a 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`N:NNc"<SVP9#)N) free_symbols)xsymbols&x/Users/tonyclaw/.openclaw/workspace/skills/math-calculator/venv/lib/python3.14/site-packages/sympy/solvers/decompogen.pydecompogen..Ms1>>!9)r isinstancerr TypeErrorr rrris_PowbaserExp1expargssubs decompogenr r list enumeratehas_freelenfuncr filtergensr ValueError) frargrd0iadfpr'f1f2s &f rr r s 6  A a  *Q ";";61EFF Q^^#s !h_%% 888!&&(%%C&&)C &=3JsF#$z#v'>>>!c3Z  AFF| dODA::f%%1f%A1v{HqLzrU2"HdDG$ Q46>3J ## aB 9277C DD 4yA~$q'V+ VVDGV $ !WtjV,,,| s s! I,,I=<I=c\V4^8Xd V^,#V^,PW^,4p\V4^8XdV#\V.VR,,V4#)a 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 :NN)r$rcompogen)g_srfoos&& rr4r4[sU6 3x1}1v a&++f!f %C 3x1} SECGOV ,,rN) sympy.corerrrrsympy.core.relationalrsympy.core.singletonr sympy.polysr r sympy.utilities.miscr (sympy.functions.elementary.miscellaneousr r r r4rrr>s&55,"'*=Od#-r