\h/SSKJr SSKJr SSKJr SSKJr SSKJ r SSK J r SSK J r SSKJr SS KJr SS KJr SS KJr S rSS jrSrSSjrSrSrSrg)Tuple)Basic)Expr) AppliedUndef) Relational)Dummy)sympify)BooleanFunction)ImageSet) FiniteSet)Indexedc[U[[[45(dU/n[ SU55(a [5$[5R "UVs/sHoR [5PM sn6nUR "UVs/sHoR [5PM sn6nU=(d1 [5R "UVs/sHoRPM sn6$s snfs snfs snf)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# UHn[U5v M g7fNcallable).0es L/var/www/auris/envauris/lib/python3.13/site-packages/sympy/plotting/utils.py $_get_free_symbols..s &18A;;s) isinstancelisttuplesetallunionatomsrr free_symbols)exprsrfrees r_get_free_symbolsr#s edE3/ 0 0 & &&&u 5;;595a)59 :D ::u=u! -u= >D  @35;; ?A ?@@:= ?sC+C0C5c UR[5nUHKn[U5n[[ SW5Vs/sHn[ U5PM sn6nUR X55nMM U$s snf)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. r)findr iterr rangenextsubs)set_solnimagesimitss rextract_solutionr0!sb\\( #F "X %1+6+QR+6 7,,r% N7sA) c[U[5(aU$[U5n[U5Hup[U[[45(a[ [ U5SS06X'M8[U[[45(aMU[U5(aMgURRS:Xa[U[5(dM[U5X'M U$)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  KNc$Sn[U5nUbURUR55n[U5U:a9[ SSR U5-SR [U5U5-5e[U5U:a[ S[U5<SU<35e[ 5RUVs/sHowSPM sn5n[U5[U5:wa [ S5e[U5U:a|URU5n U [ 5:wa U Hn URU"U 55 M [U[U5- 5H"n URU"[555 M$ [U5U:Xay[ 5RUVs/sHowSPM sn5n[URU55S:a/[ S S R U5-S R U5-5eU$s snfs snf) aThis function does two things: 1. Check if the number of free symbols is in agreement with the type of plot chosen. For example, plot() requires 1 free symbol; plot3d() requires 2 free symbols. 2. Sometime users create plots without providing ranges for the variables. Here we create the necessary ranges. Parameters ========== exprs : iterable The expressions from which to extract the free symbols ranges : iterable The limiting ranges provided by the user npar : int The number of free symbols required by the plot functions. For example, npar=1 for plot, npar=2 for plot3d, ... params : dict A dictionary mapping symbols to parameters for interactive plot. c[USS5$)Ni r)symbols r _create_ranges..ls uVS"'=r<zToo many free symbols. zExpected {} free symbols. zReceived {}: {}zToo many ranges. Received z , expected rz$Multiple ranges with the same symbolz>Incompatible free symbols of the expressions with the ranges. z$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,VtV, -C 3x3v;?@@ 6{T))#. ce  /23tc&k)*A MM+EG4 5+ <D ekk0AQ401 |&&s+ ,q 0 9@@NO399#>?  M5-$1s ;H$H cp[U[5=(a [U5S:H=(a [URS[5(+=(ab URSR =(aB [URS[5(+=(a URSR $)zMA range is defined as (symbol, start, end). start and end should be numbers. )rrrEr9r5 is_number)rNs r _is_rangerWs 1e E Vq[ EAFF1Is+ + E121D1D EAFF1Is+ + E231D1D r<cBUVs/sHn[U5(dMUPM nnUVs/sHn[U[5(dMUPM nnU(dSOUSnUVs/sHn[U[5(dMUPM nnU(dSOUSnUVs/sH;n[U5=(d! [U[[45=(d USL(+PM= nn[ X5VVs/sHuphU(dMUPM n nnXXE4$s snfs snfs snfs snfs snnf)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) Nr)rWrr5r6zip) r9trIlabelsrK rendering_kwr;resultsbr!s r _unpack_argsr_s4 .A1aF . 4AAs!3aF 4DF1IE#;t!z!T':AtL;+4aLY]]X\STIaLMJq3+$>M19NX\G]t- 3-41Q-E 3 % --/ 4;^ 3s4DDD D  D=DAD) D:Dc U(d/$/nURSS5n[SUSU55(a[U6upgp[5R"UV s/sHoR PM sn 6n [ XgX(U5nUS:a[U5U:Xa [U54nUHDn [U [[[45n U (aU 4OU n UR/U QUQUPU P75 MF U$[U6uppU(aU/O/n[U5[U5-U b [U 5OS-nUS:aUSU*OUn[US[[[45(dU/nUGH_nUVs/sHn[U[ 5(dMUPM nnU(dUnUVs/sHn[#U5(dMUPM nnU(dUR%5nUVs/sHn[U[&5(dMUPM nn[U5S:XaU OUSn[)U5Vs/sHnUUPM nn[5n [SU55(a*U R"UVs/sHnUR PM sn6n [U5U:wa[ UUUSU5nU(dSOUSnUR/UQUQUPUP75 GMb U$s sn fs snfs snfs snfs snfs snf)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# UH n[U[[[45v M" g7fr)rrrr rr;s rr#_check_arguments..s! T|!:a$ O< = =|s(*rTrc3B# UHn[U5(+v M g7frrrbs rrrc<s0Cqx{??Cs)getrr_rrr rQrErrrrr rHrrr5rWcopyr6r')r9nexprrJkwargsoutputrLr!rIrKr\rr expris_expr_r[r+new_argsargr;lrNrend_kwr:s r_check_argumentsrrs`  F ZZ$ 'F TtFU| TTT .:4-@*uu{{U$CU^^U$CD tFC 195zU"uD!j/'JKG"A MM 14Qs6K +KKK5KK5K K"K" )r?)reN)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#r0r4rQrWr_rrr<rrsN'" ,,#&/)%(A&*>CL #.Lur<