*hlSSKJrJrJrJr SSKJr SSKJr SSK J r J r SSK J r SSKJrJr SrSrg ) )FunctionPowsympifyExpr) Relational)S)Poly decompose) func_name)MinMaxcv^[U5n[U[5(a[U[5(a[ S[ U5-5eTUR ;aU/$[U[[45(atUR(a+UR[R:Xa URnOURSnUT:XaU/$URUT5/[!UT5-$[U["[$45(a['UR5nSn[)U5H\upVUR+T5(dM[!UT5n[-U5S:XaT/U-nUcUSSnOUSSU:waT/n O USX5'M^ WST:XaU/$UR."U6/U-$[1U5n['[3U4SjUR455n [-U 5S:Xa3U ST:wa*URU ST5n U Sn U /[!U T5-$[7U5$![8a U/s$f=f)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`rNc">TUR;$)N) free_symbols)xsymbols U/home/mande/repo/quber/.venv/lib/python3.13/site-packages/sympy/solvers/decompogen.pydecompogen..Ms1>>!9)r isinstancerr TypeErrorr rrris_PowbaserExp1expargssubs decompogenr r list enumeratehas_freelenfuncr filtergensr ValueError) frargrd0iadfpr'f1f2s ` rr r s6  A a  *Q ";";61EFF Q^^#s !h_%% 88!&&(%%C&&)C &=3JsF#$z#v'>>>!c3Z  AFF| dODA::f%%1f%A1v{HqLzqrU12"HdDG$ Q46>3J ## aB 9277C DD 4yA~$q'V+ VVDGV $ !WtjV,,,| s s H(( H87H8c[U5S:XaUS$USRXS5n[U5S:XaU$[U/USS-U5$)a Returns the composition of functions. Given a list of functions ``g_s``, returns their composition ``f``, where: f = g_1 o g_2 o .. o g_n Note: This is a General composition function. It also composes Polynomials. For only Polynomial composition see ``compose`` in polys. Examples ======== >>> from sympy.solvers.decompogen import compogen >>> from sympy.abc import x >>> from sympy import sqrt, sin, cos >>> compogen([sin(x), cos(x)], x) sin(cos(x)) >>> compogen([x**2 + x + 1, sin(x)], x) sin(x)**2 + sin(x) + 1 >>> compogen([sqrt(x), 6*x**2 - 5], x) sqrt(6*x**2 - 5) >>> compogen([sin(x), sqrt(x), cos(x), x**2 + 1], x) sin(sqrt(cos(x**2 + 1))) >>> compogen([x**2 - x - 1, x**2 + x], x) -x**2 - x + (x**2 + x)**2 - 1 rrN)r$rcompogen)g_srfoos rr4r4[sW6 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