U L?h/@sddlmZddlmZddlmZddlmZddlm Z ddl m Z ddl m Z ddlmZdd lmZdd lmZdd lmZd d ZdddZddZdddZddZddZddZdS)Tuple)Basic)Expr) AppliedUndef) Relational)Dummy)sympify)BooleanFunction)ImageSet) FiniteSet)IndexedcCsrt|tttfs|g}tdd|Dr.tStjdd|D}|jdd|D}|pptjdd|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) css|]}t|VqdSNcallable.0erF/var/www/html/venv/lib/python3.8/site-packages/sympy/plotting/utils.py sz$_get_free_symbols..cSsg|]}|tqSr)atomsr rrrr sz%_get_free_symbols..cSsg|]}|tqSr)rrrrrrrscSsg|] }|jqSr free_symbolsrrrrrs) isinstancelisttuplesetallunion)exprsfreerrr_get_free_symbolss r# csH|t}|D]4}t|tfddtd|D}|||}q|S)aExtract numerical solutions from a set solution (computed by solveset, linsolve, nonlinsolve). Often, it is not trivial do get something useful out of them. Parameters ========== n : int, optional In order to replace ImageSet with FiniteSet, an iterator is created for each ImageSet contained in `set_sol`, starting from 0 up to `n`. Default value: 10. csg|] }tqSr)next)rnitrrr1sz$extract_solution..r)findr iterr rangesubs)Zset_solr&ZimagesZimsrr'rextract_solution!s r.cCst|tr|St|}t|D]f\}}t|ttfrLtt|ddi||<qt|ttfst |s|j j dkrxt|t rt |||<q|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 $, {, }, ... is used in the `label`, sympify will raise an error. r FZVector)rrr enumeraterr _plot_sympifystrdictr __class____name__rr )argsiarrrr06s  r0Nc CsZdd}t|}|dk r&||}t||krTtdd|dt||t||krttdt||ftdd |D}t|t|krtd t||kr||}|tkr|D]} ||| qt |t|D]} ||t qt||krVtd d |D}t||d krVtd d|d||S)aThis function does two things: 1. Check if the number of free symbols is in agreement with the type of plot chosen. For example, plot() requires 1 free symbol; plot3d() requires 2 free symbols. 2. Sometime users create plots without providing ranges for the variables. Here we create the necessary ranges. Parameters ========== exprs : iterable The expressions from which to extract the free symbols ranges : iterable The limiting ranges provided by the user npar : int The number of free symbols required by the plot functions. For example, npar=1 for plot, npar=2 for plot3d, ... params : dict A dictionary mapping symbols to parameters for interactive plot. cSs t|ddS)Nir$r)symbolrrrlz _create_ranges..NzToo many free symbols. zExpected {} free symbols. zReceived {}: {}z)Too many ranges. Received %s, expected %scSsg|] }|dqSrrrrrrrr~sz"_create_ranges..z$Multiple ranges with the same symbolcSsg|] }|dqSr<rr=rrrrsrz>Incompatible free symbols of the expressions with the ranges. z$Free symbols in the expressions: {} zFree symbols in the ranges: {}) r# differencekeyslen ValueErrorformatrr appendr+r) r!rangesnparlabelparamsZget_default_rangerZrfssymbolsr-r6rrr_create_rangesUsJ    rJcCsRt|toPt|dkoPt|jdt oP|jdjoPt|jdt oP|jdjS)zUA range is defined as (symbol, start, end). start and end should be numbers. )rrrAr5r1Z is_number)r>rrr _is_ranges    rNcGsxdd|D}dd|D}|s$dn|d}dd|D}|sBdn|d}dd|D}ddt||D}||||fS) aGiven a list/tuple of arguments previously processed by _plot_sympify() and/or _check_arguments(), separates and returns its components: expressions, ranges, label and rendering keywords. Examples ======== >>> from sympy import cos, sin, symbols >>> from sympy.plotting.utils import _plot_sympify, _unpack_args >>> x, y = symbols('x, y') >>> args = (sin(x), (x, -10, 10), "f1") >>> args = _plot_sympify(args) >>> _unpack_args(*args) ([sin(x)], [(x, -10, 10)], 'f1', None) >>> args = (sin(x**2 + y**2), (x, -2, 2), (y, -3, 3), "f2") >>> args = _plot_sympify(args) >>> _unpack_args(*args) ([sin(x**2 + y**2)], [(x, -2, 2), (y, -3, 3)], 'f2', None) >>> args = (sin(x + y), cos(x - y), x + y, (x, -2, 2), (y, -3, 3), "f3") >>> args = _plot_sympify(args) >>> _unpack_args(*args) ([sin(x + y), cos(x - y), x + y], [(x, -2, 2), (y, -3, 3)], 'f3', None) cSsg|]}t|r|qSrrNrtrrrrsz _unpack_args..cSsg|]}t|tr|qSrrr1rPrrrrs NrcSsg|]}t|tr|qSrrr2rPrrrrs cSs,g|]$}t|p$t|ttfp$|dk qSr)rNrr1r2rr7rrrrscSsg|]\}}|r|qSrr)rr7brrrrs)zip)r5rElabelsrG rendering_kwresultsr!rrr _unpack_argssrZc s6|sgSg}|dd}tdd|d|Drt|\}}}} tjdd|D} t|||||}|dkrt||krt|f}|D]6} t| t t t f} | r| fn| } | | ||| fqnlt|\}}}} |r|gng}t|t|| dk rt| nd}|dkr"|d| n|}t|dt ttfsB|g}|D]d dD}|sb|}d dD}|s~|}d dD}t|dkr| n|d}fd dt|Dt} td dDr| jddD} t||krt||d|}|sdn|d}| |||fqF|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)] rHNcss|]}t|tttfVqdSr)rrrr rTrrrrsz#_check_arguments..cSsg|] }|jqSrrrrrrr sz$_check_arguments..rLrcSsg|]}t|tr|qSrrRrTrrrr/s cSsg|]}t|r|qSrrOrTrrrr2scSsg|]}t|tr|qSrrSrTrrrr5s csg|] }|qSrr)rr6argrrr:scss|]}t| VqdSrrrTrrrr<scSsg|] }|jqSrrrTrrrr=sr8)getrrZrr rJrArrrrr rDrrcopyr+)r5ZnexprrFkwargsoutputrHr!rErGrXrexprZis_exprr_rWr&new_argslr>Zrend_kwrr[r_check_argumentssR0   re)r$)r8N)Zsympy.core.containersrZsympy.core.basicrZsympy.core.exprrZsympy.core.functionrZsympy.core.relationalrZsympy.core.symbolrZsympy.core.sympifyr Zsympy.logic.boolalgr Zsympy.sets.fancysetsr Zsympy.sets.setsr Zsympy.tensor.indexedr r#r.r0rJrNrZrerrrrs"             F &