g/ddlmZddlmZddlmZddlmZddlm Z ddl m Z ddl m Z ddlmZdd lmZdd lmZdd lmZd ZddZdZddZdZdZdZdS)Tuple)Basic)Expr) AppliedUndef) Relational)Dummy)sympify)BooleanFunction)ImageSet) FiniteSet)IndexedcFt|tttfs|g}t d|DrtStjd|D}|jd|D}|ptjd|DS)aReturns 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) c34K|]}t|VdSNcallable.0es P/var/www/html/ai-engine/env/lib/python3.11/site-packages/sympy/plotting/utils.py z$_get_free_symbols..s( & &18A;; & & & & & &cBg|]}|tS)atomsrrs r z%_get_free_symbols..s$999a))999rcBg|]}|tSr)rrrs rrz%_get_free_symbols..s$===! --===rcg|] }|j Sr free_symbolsrs rrz%_get_free_symbols..s ? ? ?A ? ? ?r) isinstancelisttuplesetallunion)exprsfrees r_get_free_symbolsr*s edE3/ 0 0 & & & & &&&uu 355;995999 :D 4:==u=== >D  @;355; ? ? ? ? ?@@r c|t}|D]J}t|tfdt d|D}|||}K|S)aExtract 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. c.g|]}tSr)next)rnits rrz$extract_solution..1s666QR666rr)findr iterr rangesubs)set_solr/imagesimsr0s @rextract_solutionr9!sq\\( # #F&& "XX 6666%1++666 7,,r1%% Nrct|tr|St|}t|D]\}}t|ttfrt t |ddi||<>t|ttfsFt|s7|j j dkrt|trt|||<|S)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 $, {, }, ... is used in the `label`, sympify will raise an error. r FVector)r"rr# enumerater$r _plot_sympifystrdictr __class____name__rr )argsias rr=r=6s$ ::D$ ! !1 a$ ' ' !]1--=u==DGGQd ,, !  ! %11:a;O;O1ajjDG KrNcd}t|}|'||}t||krIt dd|zdt||zt||kr"t dt|d|t d|D}t|t|krt d t||kr||}|t kr#|D] } ||| !t|t|z D],} ||t-t||krt d |D}t||d kr;t d d |zd|z|S)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$t|ddS)Nir+r)symbols rz _create_ranges..lsuVS"'='=rNzToo many free symbols. zExpected {} free symbols. zReceived {}: {}zToo many ranges. Received z , expected cg|] }|d Srrrrs rrz"_create_ranges..~s,,,qt,,,rz$Multiple ranges with the same symbolcg|] }|d SrKrrLs rrz"_create_ranges..s000A1Q4000rrz>Incompatible free symbols of the expressions with the ranges. z$Free symbols in the expressions: {} zFree symbols in the ranges: {}) r* differencekeyslen ValueErrorformatr%r'appendr3r ) r(rangesnparlabelparamsget_default_ranger!rfssymbolsr8rCs r_create_rangesr\Usu.>=$U++L #..v{{}}==  <4 &+22488 9&&s<'8'8,GG H    6{{Tj;>v;;;; MOO O %%++,,V,,, - -C 3xx3v;;?@@@ 6{{T))#.. cee   4 4 //223333tc&kk)** 6 6A MM++EGG44 5 5 5 5 <D  eekk0000011 |&&s++ , ,q 0 0 9@@NNO399#>>?  Mrct|toxt|dkoet|jdt oD|jdjo2t|jdt o|jdjS)zUA range is defined as (symbol, start, end). start and end should be numbers. )r"rrQrBr> is_number)rMs r _is_rangerbs 1e E VVq[ EAF1Is++ + E121D EAF1Is++ + E231D rcd|D}d|D}|sdn|d}d|D}|sdn|d}d|D}dt||D}||||fS)aGiven 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) c0g|]}t||Srrbrts rrz _unpack_args..s# . . .A1 .a . . .rc<g|]}t|t|Srr"r>rfs rrz _unpack_args..s' 4 4 4AAs!3!3 4a 4 4 4rNrc<g|]}t|t|Srr"r?rfs rrz _unpack_args..s';;;!z!T':':;A;;;rcng|]2}t|pt|ttfp|du 3Sr)rbr"r>r?rrDs rrz _unpack_args..s>]]]STIaLLMJq3+$>$>M19N]]]rcg|] \}}|| Srr)rrDbs rrz _unpack_args..s! 3 3 341a 3Q 3 3 3r)zip)rBrUlabelsrW rendering_kwresultsr(s r _unpack_argsrts4/ . . . .F 4 4 4 4 4F -DDF1IE;;t;;;L+@44aL^]X\]]]G 3 33tW-- 3 3 3E &% --rc |sgSg}|dd}td|d|Drt|\}}}} tjd|D} t |||||}|dkr#t ||krt|f}|D]I} t| tttf} | r| fn| } | g| ||| RJnt|\}}}} |r|gng}t |t |z| t | ndz}|dkr |d| n|}t|dtttfs|g}|D]dD}|s|}dD}|s|}d D}t |dkr| n|d}fd t!|Dt} td Dr| jd D} t ||krt ||d |}|sdn|d}| g|||R|S)a,Checks 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)] rXNc3ZK|]&}t|tttfV'dSr)r"rrr rms rrz#_check_arguments..s3 T T!:a$ O< = = T T T T T Trcg|] }|j Srr rs rrz$_check_arguments.. s$C$C$CQ^$C$C$Crr_rc<g|]}t|t|Srrirms rrz$_check_arguments../s'666q:a#5#56666rc0g|]}t||Srrerms rrz$_check_arguments..2s#000q9Q<<0000rc<g|]}t|t|Srrkrms rrz$_check_arguments..5s'===QAt)<)<=q===rc g|] }| Srr)rrCargs rrz$_check_arguments..:s000a3q6000rc36K|]}t| VdSrrrms rrz#_check_arguments..<s*00qx{{?000000rcg|] }|j Srr rms rrz$_check_arguments..=s3P3P3PqAN3P3P3PrrE)getr&rtr%r'r\rQr$r"rrr rTr#rcopyr3)rBnexprrVkwargsoutputrXr(rUrWrrr!expris_exprr_rqr/new_argslrMrend_kwr|s @r_check_argumentsrs!`  F ZZ$ ' 'F T TtFUF| T T TTT?6 .:4-@*vul"suu{$C$CU$C$C$CD vtUFCC 1995zzU""u > >D!j/'JKKG",A MM+7*='66<#+&[[3v;; &".":S   C !A4!994 (1+eU';<< " zH 6 6C66C666A 00C000A "KKMM==#===G&)'lla&7&7llWQZG10005<<000C55L00C00000 R1|13P3PC3P3P3PQ 1vv~~"34V<< !+DDqtE MM4C4!4U4G44 5 5 5 5 Mr)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*r9r=r\rbrtrrrrrsV''''''"""""" ,,,,,,,,,,,,######&&&&&&//////))))))%%%%%%((((((AAA&*>CCCCL   #.#.#.Luuuuur