+ i/^RIHt^RIHt^RIHt^RIHt^RIH t ^RI H t ^RI H t ^RIHt^R IHt^R IHt^R IHtR tRR ltRtRRltRtRtRtR#)Tuple)Basic)Expr) AppliedUndef) Relational)Dummy)sympify)BooleanFunction)ImageSet) FiniteSet)Indexedc>\V\\\34'gV.p\;QJdRV4F 'dK RM RM !RV44'd \4#\4P !VUu.uFqP \4NK up!pVP !VUu.uFqP \4NK up!pT;'g2\4P !VUu.uFqPNK up!#uupiuupiuupi)zReturns the free symbols of a symbolic expression. If the expression contains any of these elements, assume that they are the "free symbols" of the expression: * indexed objects * applied undefined function (useful for sympy.physics.mechanics module) c38"TFp\V4xK R#5iNcallable).0es& t/Users/tonyclaw/.openclaw/workspace/skills/math-calculator/venv/lib/python3.14/site-packages/sympy/plotting/utils.py $_get_free_symbols..s &18A;;sFT) isinstancelisttuplesetallunionatomsrr free_symbols)exprsrfrees& r_get_free_symbolsr#s edE3/ 0 0 s & &sss & &&&u 5;;595a)59 :D ::u=u! -u= >D  @ @35;; ?A ?@@:= ?sD3D7Dc VP\4pVFKp\V4p\\ ^X4Uu.uFp\ V4NK up!pVP W54pKM V#uupi)aoExtract numerical solutions from a set solution (computed by solveset, linsolve, nonlinsolve). Often, it is not trivial do get something useful out of them. Parameters ========== n : int, optional In order to replace ImageSet with FiniteSet, an iterator is created for each ImageSet contained in `set_sol`, starting from 0 up to `n`. Default value: 10. )findr iterr rangenextsubs)set_solnimagesimitss&& rextract_solutionr0!sb\\( #F "X %1+6+QR+6 7,,r% N7sA) c\V\4'dV#\V4p\V4Fwr\V\\34'd\ \ V4RR/W&K9\V\\34'dKW\V4'dKjVPPR8Xd\V\4'gK\V4W&K V#)aThis function recursively loop over the arguments passed to the plot functions: the sympify function will be applied to all arguments except those of type string/dict. Generally, users can provide the following arguments to a plot function: expr, range1 [tuple, opt], ..., label [str, opt], rendering_kw [dict, opt] `expr, range1, ...` can be sympified, whereas `label, rendering_kw` can't. In particular, whenever a special character like $, {, }, ... is used in the `label`, sympify will raise an error. r FVector)rrr enumeraterr _plot_sympifystrdictr __class____name__rr )argsias& rr4r46s$ :D$ a$ ' ']1-=u=DGQd ,, %%1:a;O;OajDG  KNchRp\V4pVe VPVP44p\V4V8dB\ RRP V4,RP \V4V4,4h\V4V8d\ R\V4: RV: 24h\ 4PVUu.uF qw^,NK up4p\V4\V48wd \ R4h\V4V8dVPV4p V \ 48wd!V Fp VPV!V 44K \V\V4, 4F"p VPV!\444K$ \V4V8Xd\ 4PVUu.uF qw^,NK up4p\VPV44^8d8\ RR P V4,R P V4,4hV#uupiuupi) aThis function does two things: 1. Check if the number of free symbols is in agreement with the type of plot chosen. For example, plot() requires 1 free symbol; plot3d() requires 2 free symbols. 2. Sometime users create plots without providing ranges for the variables. Here we create the necessary ranges. Parameters ========== exprs : iterable The expressions from which to extract the free symbols ranges : iterable The limiting ranges provided by the user npar : int The number of free symbols required by the plot functions. For example, npar=1 for plot, npar=2 for plot3d, ... params : dict A dictionary mapping symbols to parameters for interactive plot. c\VR^ 4#) ir)symbols&r _create_ranges..ls uVS"'=r<zToo many free symbols. zExpected {} free symbols. zReceived {}: {}zToo many ranges. Received z , expected z$Multiple ranges with the same symbolz>Incompatible free symbols of the expressions with the ranges. z$Free symbols in the expressions: {} zFree symbols in the ranges: {}) r# differencekeyslen ValueErrorformatrrappendr'r ) r!rangesnparlabelparamsget_default_ranger rrfssymbolsr/r:s &&&&& r_create_rangesrQUs.>$U+L #..v{{}=  <4 &+2248 9&&s<'8,G H   6{T;>v; MO O %++V,VttV, -C 3x3v;?@@ 6{T))#. ce  /23tc&k)*A MM+EG4 5+ <D ekk0AQ4401 |&&s+ ,q 0 9@@NO399#>?  M5-$1s H*:H/c\V\4;'d\V4^8H;'d\VP^,\4'*;'dqVP^,P ;'dL\VP^,\4'*;'dVP^,P #)zMA range is defined as (symbol, start, end). start and end should be numbers. )rrrEr9r5 is_number)rNs&r _is_rangerTs 1e E E Vq[ E EAFF1Is+ + E E121D1D E EAFF1Is+ + E E231D1D r<cXVUu.uFp\V4'gKVNK ppVUu.uFp\V\4'gKVNK ppV'gRMV^,pVUu.uFp\V\4'gKVNK ppV'gRMV^,pVUu.uF=p\V4;'g#\V\\34;'gVRJ'*NK? pp\ W4UUu.uFwrhV'gKVNK p ppWWE3#uupiuupiuupiuupiuuppi)aRGiven a list/tuple of arguments previously processed by _plot_sympify() and/or _check_arguments(), separates and returns its components: expressions, ranges, label and rendering keywords. Examples ======== >>> from sympy import cos, sin, symbols >>> from sympy.plotting.utils import _plot_sympify, _unpack_args >>> x, y = symbols('x, y') >>> args = (sin(x), (x, -10, 10), "f1") >>> args = _plot_sympify(args) >>> _unpack_args(*args) ([sin(x)], [(x, -10, 10)], 'f1', None) >>> args = (sin(x**2 + y**2), (x, -2, 2), (y, -3, 3), "f2") >>> args = _plot_sympify(args) >>> _unpack_args(*args) ([sin(x**2 + y**2)], [(x, -2, 2), (y, -3, 3)], 'f2', None) >>> args = (sin(x + y), cos(x - y), x + y, (x, -2, 2), (y, -3, 3), "f3") >>> args = _plot_sympify(args) >>> _unpack_args(*args) ([sin(x + y), cos(x - y), x + y], [(x, -2, 2), (y, -3, 3)], 'f3', None) N)rTrr5r6zip) r9trIlabelsrK rendering_kwr;resultsbr!s * r _unpack_argsr\s4 .A1aaF . 4AAs!3aaF 4DF1IE#;t!z!T':AAtL;+4aLY]]X\STIaLMMJq3+$>MM19NX\G]t- 3-41QQ-E 3 % --/ 4;^ 3s?DDDD%DD!D!8D!D!4 D&D&c V'g.#.pVPRR4p\;QJdRVRV4F 'dK RM RM!RVRV44'd\V!wrgr\4P!VU u.uFqP NK up !p \ WgW(V4pV^8d\V4V8Xd \V43pVFEp \V \\\34p V 'dV 3MT p VP.V OVOVNV N54KG V#\V!wrrV'dV.M.p\V4\V4,V e \V 4M^,pV^8dVRV)MTp\V^,\\\34'gV.pVEFpVUu.uFp\V\ 4'gKVNK ppV'gTpVUu.uFp\#V4'gKVNK ppV'gVP%4pVUu.uFp\V\&4'gKVNK pp\V4^8XdT MV^,p\)V4Uu.uF pVV,NK pp\4p \;QJdRV4F 'dK RM RM !RV44'd+V P!VUu.uFpVP NK up!p \V4V8wd\ VVVRV4pV'gRMV^,pVP.VOVOVNVN54EK V#uup iuupiuupiuupiuupiuupi)aChecks the arguments and converts into tuples of the form (exprs, ranges, label, rendering_kw). Parameters ========== args The arguments provided to the plot functions nexpr The number of sub-expression forming an expression to be plotted. For example: nexpr=1 for plot. nexpr=2 for plot_parametric: a curve is represented by a tuple of two elements. nexpr=1 for plot3d. nexpr=3 for plot3d_parametric_line: a curve is represented by a tuple of three elements. npar The number of free symbols required by the plot functions. For example, npar=1 for plot, npar=2 for plot3d, ... **kwargs : keyword arguments passed to the plotting function. It will be used to verify if ``params`` has ben provided. Examples ======== .. plot:: :context: reset :format: doctest :include-source: True >>> from sympy import cos, sin, symbols >>> from sympy.plotting.plot import _check_arguments >>> x = symbols('x') >>> _check_arguments([cos(x), sin(x)], 2, 1) [(cos(x), sin(x), (x, -10, 10), None, None)] >>> _check_arguments([cos(x), sin(x), "test"], 2, 1) [(cos(x), sin(x), (x, -10, 10), 'test', None)] >>> _check_arguments([cos(x), sin(x), "test", {"a": 0, "b": 1}], 2, 1) [(cos(x), sin(x), (x, -10, 10), 'test', {'a': 0, 'b': 1})] >>> _check_arguments([x, x**2], 1, 1) [(x, (x, -10, 10), None, None), (x**2, (x, -10, 10), None, None)] rLNc3X"TF p\V\\\34xK" R#5ir)rrrr rr;s& rr#_check_arguments..s! T|!:a$ O< = =|s(*FTc3B"TFp\V4'*xK R#5irrr_s& rrr`<s0Cqx{??Cs)getrr\rrr rQrErrrrr rHrrr5rTcopyr6r')r9nexprrJkwargsoutputrLr!rIrKrYrr expris_expr_rXr+new_argsargr;lrNrend_kwr:s&&&, r_check_argumentsros`  F ZZ$ 'F s TtFU| Tsss TtFU| TTT .:4-@*uu{{U$CU^^U$CD tFC 195zU"uD!j/'JKG"A MM 14Qs6L8'L=L=M2MM3M#M  M )r?)rbN)sympy.core.containersrsympy.core.basicrsympy.core.exprrsympy.core.functionrsympy.core.relationalrsympy.core.symbolr sympy.core.sympifyr sympy.logic.boolalgr sympy.sets.fancysetsr sympy.sets.setsr sympy.tensor.indexedrr#r0r4rQrTr\ror<rr|sN'" ,,#&/)%(A&*>CL #.Lur<