wgQMUdZddlmZddlmZmZddlmZddl m Z ddl Z ddl m Z ddlmZdd lmZGd d eZiZd ed <iZd ed<eZGddZdZdZ ddZdZdZddlmZy)z0sympify -- convert objects SymPy internal format) annotations)AnyCallableN)getmro)choice)global_parameters)iterableceZdZddZdZy) SympifyErrorNc ||_||_yN)exprbase_exc)selfrrs W/home/mcse/projects/flask/flask-venv/lib/python3.12/site-packages/sympy/core/sympify.py__init__zSympifyError.__init__s   c|jd|jSd|jd|jjjdt |jS)NzSympifyError: zSympify of expression 'z-' failed, because of exception being raised: z: )rr __class____name__str)rs r__str__zSympifyError.__str__sO == )-4 4 !"&DMM,C,C,L,L    !rr)r __module__ __qualname__rrrrr r s !!rr z'dict[type[Any], Callable[[Any], Basic]] converter_sympy_converterceZdZdZdZy) CantSympifya Mix in this trait to a class to disallow sympification of its instances. Examples ======== >>> from sympy import sympify >>> from sympy.core.sympify import CantSympify >>> class Something(dict): ... pass ... >>> sympify(Something()) {} >>> class Something(dict, CantSympify): ... pass ... >>> sympify(Something()) Traceback (most recent call last): ... SympifyError: SympifyError: {} rN)rrr__doc__ __slots__rrrr r 's2Irr cLtdt|jDS)zM Checks if an object is an instance of a type from the numpy module. c3:K|]}|jdk(yw)numpyN)r).0type_s r z%_is_numpy_instance..Js#-7*-s)anytype__mro__as r_is_numpy_instancer.Ds& - GOO- --rc |ddl}t||jsK|j|r t t |j St|j fi|Sddlm }|j|jdz}|j\}}tj|||}|||S)zG Converts a numpy datatype input to an appropriate SymPy type. rNr)Float) precision)r% isinstancefloating iscomplexrcomplexitemsympifynumbersr0finfonmantas_integer_ratiomlib from_rational)r- sympify_argsnpr0precpqs r_convert_numpy_typesrCNs a % <<?#G,QVVX6 616684|4 4"xx{  1$!!#1   q!T *Q$''rc t|dd}|dur|S||s|St|t|tr t|t|dd}t |D]:}t j |} | tj |} | 2| |cS|tdur|r t||S|tj}t|r&ddl } | j|rt||||||St|dd} | |jS|sAt|dd} | 2t|d d} | #dd lm}||j$|j&St|t(st|raddl } t|| j*rJt|| j,ro|j.dk(r` t1|j3|||||St5|d rt1t7|St5|d rt1t9|S|r t|t;|r. t||Dcgc]}t1||||| c}St|t(stdt|zddlm }m!}m"}ddlm#}ddlm$}|}|r||fz }|r||fz } |jKdd}|||||}|S#t$rYwxYwcc}w#t<$rYwxYw#|tLf$r}td|z|d}~wwxYw)a" Converts an arbitrary expression to a type that can be used inside SymPy. Explanation =========== It will convert Python ints into instances of :class:`~.Integer`, floats into instances of :class:`~.Float`, etc. It is also able to coerce symbolic expressions which inherit from :class:`~.Basic`. This can be useful in cooperation with SAGE. .. warning:: Note that this function uses ``eval``, and thus shouldn't be used on unsanitized input. If the argument is already a type that SymPy understands, it will do nothing but return that value. This can be used at the beginning of a function to ensure you are working with the correct type. Examples ======== >>> from sympy import sympify >>> sympify(2).is_integer True >>> sympify(2).is_real True >>> sympify(2.0).is_real True >>> sympify("2.0").is_real True >>> sympify("2e-45").is_real True If the expression could not be converted, a SympifyError is raised. >>> sympify("x***2") Traceback (most recent call last): ... SympifyError: SympifyError: "could not parse 'x***2'" When attempting to parse non-Python syntax using ``sympify``, it raises a ``SympifyError``: >>> sympify("2x+1") Traceback (most recent call last): ... SympifyError: Sympify of expression 'could not parse '2x+1'' failed To parse non-Python syntax, use ``parse_expr`` from ``sympy.parsing.sympy_parser``. >>> from sympy.parsing.sympy_parser import parse_expr >>> parse_expr("2x+1", transformations="all") 2*x + 1 For more details about ``transformations``: see :func:`~sympy.parsing.sympy_parser.parse_expr` Locals ------ The sympification happens with access to everything that is loaded by ``from sympy import *``; anything used in a string that is not defined by that import will be converted to a symbol. In the following, the ``bitcount`` function is treated as a symbol and the ``O`` is interpreted as the :class:`~.Order` object (used with series) and it raises an error when used improperly: >>> s = 'bitcount(42)' >>> sympify(s) bitcount(42) >>> sympify("O(x)") O(x) >>> sympify("O + 1") Traceback (most recent call last): ... TypeError: unbound method... In order to have ``bitcount`` be recognized it can be imported into a namespace dictionary and passed as locals: >>> ns = {} >>> exec('from sympy.core.evalf import bitcount', ns) >>> sympify(s, locals=ns) 6 In order to have the ``O`` interpreted as a Symbol, identify it as such in the namespace dictionary. This can be done in a variety of ways; all three of the following are possibilities: >>> from sympy import Symbol >>> ns["O"] = Symbol("O") # method 1 >>> exec('from sympy.abc import O', ns) # method 2 >>> ns.update(dict(O=Symbol("O"))) # method 3 >>> sympify("O + 1", locals=ns) O + 1 If you want *all* single-letter and Greek-letter variables to be symbols then you can use the clashing-symbols dictionaries that have been defined there as private variables: ``_clash1`` (single-letter variables), ``_clash2`` (the multi-letter Greek names) or ``_clash`` (both single and multi-letter names that are defined in ``abc``). >>> from sympy.abc import _clash1 >>> set(_clash1) # if this fails, see issue #23903 {'E', 'I', 'N', 'O', 'Q', 'S'} >>> sympify('I & Q', _clash1) I & Q Strict ------ If the option ``strict`` is set to ``True``, only the types for which an explicit conversion has been defined are converted. In the other cases, a SympifyError is raised. >>> print(sympify(None)) None >>> sympify(None, strict=True) Traceback (most recent call last): ... SympifyError: SympifyError: None .. deprecated:: 1.6 ``sympify(obj)`` automatically falls back to ``str(obj)`` when all other conversion methods fail, but this is deprecated. ``strict=True`` will disable this deprecated behavior. See :ref:`deprecated-sympify-string-fallback`. Evaluation ---------- If the option ``evaluate`` is set to ``False``, then arithmetic and operators will be converted into their SymPy equivalents and the ``evaluate=False`` option will be added. Nested ``Add`` or ``Mul`` will be denested first. This is done via an AST transformation that replaces operators with their SymPy equivalents, so if an operand redefines any of those operations, the redefined operators will not be used. If argument a is not a string, the mathematical expression is evaluated before being passed to sympify, so adding ``evaluate=False`` will still return the evaluated result of expression. >>> sympify('2**2 / 3 + 5') 19/3 >>> sympify('2**2 / 3 + 5', evaluate=False) 2**2/3 + 5 >>> sympify('4/2+7', evaluate=True) 9 >>> sympify('4/2+7', evaluate=False) 4/2 + 7 >>> sympify(4/2+7, evaluate=False) 9.00000000000000 Extending --------- To extend ``sympify`` to convert custom objects (not derived from ``Basic``), just define a ``_sympy_`` method to your class. You can do that even to classes that you do not own by subclassing or adding the method at runtime. >>> from sympy import Matrix >>> class MyList1(object): ... def __iter__(self): ... yield 1 ... yield 2 ... return ... def __getitem__(self, i): return list(self)[i] ... def _sympy_(self): return Matrix(self) >>> sympify(MyList1()) Matrix([ [1], [2]]) If you do not have control over the class definition you could also use the ``converter`` global dictionary. The key is the class and the value is a function that takes a single argument and returns the desired SymPy object, e.g. ``converter[MyList] = lambda x: Matrix(x)``. >>> class MyList2(object): # XXX Do not do this if you control the class! ... def __iter__(self): # Use _sympy_! ... yield 1 ... yield 2 ... return ... def __getitem__(self, i): return list(self)[i] >>> from sympy.core.sympify import converter >>> converter[MyList2] = lambda x: Matrix(x) >>> sympify(MyList2()) Matrix([ [1], [2]]) Notes ===== The keywords ``rational`` and ``convert_xor`` are only used when the input is a string. convert_xor ----------- >>> sympify('x^y',convert_xor=True) x**y >>> sympify('x^y',convert_xor=False) x ^ y rational -------- >>> sympify('0.1',rational=False) 0.1 >>> sympify('0.1',rational=True) 1/10 Sometimes autosimplification during sympification results in expressions that are very different in structure than what was entered. Until such autosimplification is no longer done, the ``kernS`` function might be of some use. In the example below you can see how an expression reduces to $-1$ by autosimplification, but does not do so when ``kernS`` is used. >>> from sympy.core.sympify import kernS >>> from sympy.abc import x >>> -2*(-(-x + 1/x)/(x*(x - 1/x)**2) - 1/(x*(x - 1/x))) - 1 -1 >>> s = '-2*(-(-x + 1/x)/(x*(x - 1/x)**2) - 1/(x*(x - 1/x))) - 1' >>> sympify(s) -1 >>> kernS(s) -2*(-(-x + 1/x)/(x*(x - 1/x)**2) - 1/(x*(x - 1/x))) - 1 Parameters ========== a : - any object defined in SymPy - standard numeric Python types: ``int``, ``long``, ``float``, ``Decimal`` - strings (like ``"0.09"``, ``"2e-19"`` or ``'sin(x)'``) - booleans, including ``None`` (will leave ``None`` unchanged) - dicts, lists, sets or tuples containing any of the above convert_xor : bool, optional If true, treats ``^`` as exponentiation. If False, treats ``^`` as XOR itself. Used only when input is a string. locals : any object defined in SymPy, optional In order to have strings be recognized it can be imported into a namespace dictionary and passed as locals. strict : bool, optional If the option strict is set to ``True``, only the types for which an explicit conversion has been defined are converted. In the other cases, a SympifyError is raised. rational : bool, optional If ``True``, converts floats into :class:`~.Rational`. If ``False``, it lets floats remain as it is. Used only when input is a string. evaluate : bool, optional If False, then arithmetic and operators will be converted into their SymPy equivalents. If True the expression will be evaluated and the result will be returned. __sympy__NTrr)locals convert_xorstrictrationalevaluate_sympy_flatshape)Array __float____int__)rFrGrIrJz cannot sympify object of type %r) parse_expr TokenErrorstandard_transformations)rG) rationalize ) local_dicttransformationsrJzcould not parse %r)'getattrr r2r r_external_convertergetrr*r rJr.r%isscalarrCrKsympy.tensor.arrayrNrLrMrnumberndarrayndimr7r6hasattrfloatintr TypeErrorsympy.parsing.sympy_parserrQrRrSrGrTreplace SyntaxError)r-rFrGrHrIrJis_sympycls superclassconvr?rKrLrMrNxrQrRrS t_convert_xor t_rationalizerXrexcs rr7r7bs@hq+t,H4  Hq/ !![!1o ![$ 'CSk "&&z2 <#'' 3D  7N d4j q/ !H$--! ;;q>'&'!# #aD)Gyy{ q&$'  Aw-E 4QVVQWW-- a  a !!RYY/ //!RZZ(66Q;&qvvx.43>.40808  ::Q $58$ $ Q "3q6? " 1o{ 47?@B:;$Af+!H6BC C a =QGHHFFGG.OM++M++: IIdB !Zbc KS(B   ,  $:/!3S99:sN3K+K:KK(K+ KKK K('K(+ L 6LL ct|dS)a[ Short version of :func:`~.sympify` for internal usage for ``__add__`` and ``__eq__`` methods where it is ok to allow some things (like Python integers and floats) in the expression. This excludes things (like strings) that are unwise to allow into such an expression. >>> from sympy import Integer >>> Integer(1) == 1 True >>> Integer(1) == '1' False >>> from sympy.abc import x >>> x + 1 x + 1 >>> x + '1' Traceback (most recent call last): ... TypeError: unsupported operand type(s) for +: 'Symbol' and 'str' see: sympify T)rH)r7r,s r_sympifyrqs4 1T ""rc d}d|vxsd|v}d|vrp|sm|jd|jdk7r tddj|j}|}|j dd }|j d d }d }|j d |}dx}}|j dsJ |j ||}|dk(rna|t|dz z }t|t|D]$}||dk(r|dz }n ||dk(r|dz}|dk(s$n|d|dz||dz}|dz}yd|vrOd}||vr2|ttjtjzz }||vr2|j d|}||v}nd}tdD]} t|} n|s Sddlm} | di fd   } | S#t$r|r}d}YGt|} YTwxYw)aUse a hack to try keep autosimplification from distributing a a number into an Add; this modification does not prevent the 2-arg Mul from becoming an Add, however. Examples ======== >>> from sympy.core.sympify import kernS >>> from sympy.abc import x, y The 2-arg Mul distributes a number (or minus sign) across the terms of an expression, but kernS will prevent that: >>> 2*(x + y), -(x + 1) (2*x + 2*y, -x - 1) >>> kernS('2*(x + y)') 2*(x + y) >>> kernS('-(x + 1)') -(x + 1) If use of the hack fails, the un-hacked string will be passed to sympify... and you get what you get. XXX This hack should not be necessary once issue 4596 has been resolved. F"'()zunmatched left parenthesisrVz*(z* *(z** *z**z-( *(z-(rrN _)Symbolct|tttfr%t ||Dcgc] }| c}St |dr|j dS|Scc}w)NsubsT)hack2)r2listtuplesetr*rar})re_clearreps rrzkernS.._clear`s[ dT5#. /4:$7Qvay78 8 4 99S9- - 8sA#)countr joinsplitrfendswithfindlenrangerstring ascii_lettersdigitsr7rdsymbolr{) shitquotedoldstargetinestjkernrr{rrs @@rkernSrs74 C AX !F ax 773<1773< ';< < GGAGGI  IIdF # IIfd # IIdF # Ds###vq!ABw Vq A1c!f% Q43;AIDqTS[AID19  "1 ae#AAA !8D!)v33fmmCDD!) #t$A!)CC 1X  1:D     $< C $rs6"  $). !: !68 27=?9> :-((FKCL #:cNr