+ i^RIHt^RIHt^RIHtHt^RIHtH t ^RI H t ^RI H t Ht^RIHt^RIHtHtHtHtHtHtHtHtHtHtHtHtHt^R IH t RR R R RRR RR RRRRRR RR /Rllt!Rt"R R]!43RR /Rllt#R #))Tuple)oo)GtLt)DummySymbol)Abs)MinMax)And) AssignmentAddAugmentedAssignmentbreak_ CodeBlock DeclarationFunctionDefinitionPrintReturnScopeWhileVariablePointerreal)isnanNrtolgؗҼ<debugFitermaxcounterdelta_fnc4V)VPV4, #N)diff)exs&&x/Users/tonyclaw/.openclaw/workspace/skills/math-calculator/venv/lib/python3.14/site-packages/sympy/codegen/algorithms.pyr&saRq \cse handle_nanboundsc  Vf\4p\p Rp MRp VPp V!W4pV 'dX^RIHp V !VP 4.4wpwpVUUu.uFwpp\ VV4NK pppV\ VV4., pM \ W>4.pV e,V\\V4\V \44., pV\W4., pV e6V\ V\\W^,4V ^,44., pV'd2\W.RPVPV 44pVV., p\!\#V4W$\#V4,,4p\%\'V\(\*R74.pVexT;'g \RR7p\&P,!V^4pVP/\%V44VP/\V^44\1V\3Wv44p\V\V!4pTpV'd6VP/\V.RPVP444VV., pV !\V!4#uuppi) aGenerates an AST for Newton-Raphson method (a root-finding algorithm). Explanation =========== Returns an abstract syntax tree (AST) based on ``sympy.codegen.ast`` for Netwon's method of root-finding. Parameters ========== expr : expression wrt : Symbol With respect to, i.e. what is the variable. atol : number or expression Absolute tolerance (stopping criterion) rtol : number or expression Relative tolerance (stopping criterion) delta : Symbol Will be a ``Dummy`` if ``None``. debug : bool Whether to print convergence information during iterations itermax : number or expr Maximum number of iterations. counter : Symbol Will be a ``Dummy`` if ``None``. delta_fn: Callable[[Expr, Symbol], Expr] computes the step, default is newtons method. For e.g. Halley's method use delta_fn=lambda e, x: -2*e*e.diff(x)/(2*e.diff(x)**2 - e*e.diff(x, 2)) cse: bool Perform common sub-expression elimination on delta expression handle_nan: Token How to handle occurrence of not-a-number (NaN). bounds: Optional[tuple[Expr, Expr]] Perform optimization within bounds Examples ======== >>> from sympy import symbols, cos >>> from sympy.codegen.ast import Assignment >>> from sympy.codegen.algorithms import newtons_method >>> x, dx, atol = symbols('x dx atol') >>> expr = cos(x) - x**3 >>> algo = newtons_method(expr, x, atol=atol, delta=dx) >>> algo.has(Assignment(dx, -expr/expr.diff(x))) True References ========== .. [1] https://en.wikipedia.org/wiki/Newton%27s_method deltacV#r!)r$s&r%r& newtons_method..PsAr')r(z{}=%12.5g {}=%12.5g\n)typevalueT)integerz {}=%12.5g\n)rrnamesympy.simplify.cse_mainr(factorr rrrrrr r rformatrr rrrrdeducedappendr r)exprwrtatolr,rrrrrr(r)r*Wrappername_d delta_exprcsesreddumsub_ewhl_bdyprntreqdeclars v_counterwhlblcks&&&&$$$$$$$$ r%newtons_methodrJsv }$$J /J--/01 fs<@ADjc5:c5)DAJuc*++e01E%, *f(EFGG &s233G JsCC(;VAY$GHII c\#;#B#B388V#TUD6 SZSX - .C8EB?@AG00U40$$Wa0 {9-.-gq9:#r'+, Y( )C D  E3%!6!6sxx!@ABSEMD 9d# $$3BsI?c\V\4'dVPPpV#\V\4'd VPpV#r!) isinstancervariablesymbolr)args&r% _symbol_ofrPssB#{##ll!! J C " "jj Jr'newtonr,c @VfV3pVUu/uFLp\V\4'gKVP\RVPP,4bKN ppVf6\RVP,4pVP V4'dRp\ W3RV/VBPV4p \V \4'd V Pp VPPVUu0uFp\V4kK up4p V 'd0\RRP\\ V 44,4h\";QJd.RV4FNK 5M !RV44p \%V \'V44p \)\*W;WR7#uupiuupi) aYGenerates an AST for a function implementing the Newton-Raphson method. Parameters ========== expr : expression wrt : Symbol With respect to, i.e. what is the variable params : iterable of symbols Symbols appearing in expr that are taken as constants during the iterations (these will be accepted as parameters to the generated function). func_name : str Name of the generated function. attrs : Tuple Attribute instances passed as ``attrs`` to ``FunctionDefinition``. \*\*kwargs : Keyword arguments passed to :func:`sympy.codegen.algorithms.newtons_method`. Examples ======== >>> from sympy import symbols, cos >>> from sympy.codegen.algorithms import newtons_method_function >>> from sympy.codegen.pyutils import render_as_module >>> x = symbols('x') >>> expr = cos(x) - x**3 >>> func = newtons_method_function(expr, x) >>> py_mod = render_as_module(func) # source code as string >>> namespace = {} >>> exec(py_mod, namespace, namespace) >>> res = eval('newton(0.5)', namespace) >>> abs(res - 0.865474033102) < 1e-12 True See Also ======== sympy.codegen.algorithms.newtons_method Nz(*%s)d_r,zMissing symbols in params: %sz, c3B"TFp\V\4xK R#5ir!)rr).0ps& r% *newtons_method_function..s6v!HQ%%vs)attrs)rLrrNrr3hasrJxreplacerbody free_symbols differencerP ValueErrorjoinmapstrtuplerrrr) r9r:params func_namerYr,kwargsrV pointer_subsalgo not_in_paramsrFr\s &&&&&$, r%newtons_method_functionrj{sJR~#?#z!W'=>AHHfWqxx}}%<==#? }tchh' 88E??E $ ;5 ;F ; D D\ RD$yy%%001PA*Q-1PQM8499SmE\;]]^^e6v6ee6v66G T6#; 'D dI JJ?2QsF5F1F)g-q=N)$sympy.core.containersrsympy.core.numbersrsympy.core.relationalrrsympy.core.symbolrr$sympy.functions.elementary.complexesr (sympy.functions.elementary.miscellaneousr r sympy.logic.boolalgr sympy.codegen.astr rrrrrrrrrrrrsympy.codegen.cfunctionsrrJrPrjr.r'r%rts'!*-4=#+U`%e`%5`%`%)-`%8Q`%`%)-`%`%F/3heg9K`d9Kr'