"""Transform a string with Python-like source code into SymPy expression. """ from tokenize import (generate_tokens, untokenize, TokenError, NUMBER, STRING, NAME, OP, ENDMARKER, ERRORTOKEN, NEWLINE) from keyword import iskeyword import ast import unicodedata from io import StringIO import builtins import types from typing import Tuple as tTuple, Dict as tDict, Any, Callable, \ List, Optional, Union as tUnion from sympy.assumptions.ask import AssumptionKeys from sympy.core.basic import Basic from sympy.core import Symbol from sympy.core.function import Function from sympy.utilities.misc import func_name from sympy.functions.elementary.miscellaneous import Max, Min null = '' TOKEN = tTuple[int, str] DICT = tDict[str, Any] TRANS = Callable[[List[TOKEN], DICT, DICT], List[TOKEN]] def _token_splittable(token_name: str) -> bool: """ Predicate for whether a token name can be split into multiple tokens. A token is splittable if it does not contain an underscore character and it is not the name of a Greek letter. This is used to implicitly convert expressions like 'xyz' into 'x*y*z'. """ if '_' in token_name: return False try: return not unicodedata.lookup('GREEK SMALL LETTER ' + token_name) except KeyError: return len(token_name) > 1 def _token_callable(token: TOKEN, local_dict: DICT, global_dict: DICT, nextToken=None): """ Predicate for whether a token name represents a callable function. Essentially wraps ``callable``, but looks up the token name in the locals and globals. """ func = local_dict.get(token[1]) if not func: func = global_dict.get(token[1]) return callable(func) and not isinstance(func, Symbol) def _add_factorial_tokens(name: str, result: List[TOKEN]) -> List[TOKEN]: if result == [] or result[-1][1] == '(': raise TokenError() beginning = [(NAME, name), (OP, '(')] end = [(OP, ')')] diff = 0 length = len(result) for index, token in enumerate(result[::-1]): toknum, tokval = token i = length - index - 1 if tokval == ')': diff += 1 elif tokval == '(': diff -= 1 if diff == 0: if i - 1 >= 0 and result[i - 1][0] == NAME: return result[:i - 1] + beginning + result[i - 1:] + end else: return result[:i] + beginning + result[i:] + end return result class ParenthesisGroup(List[TOKEN]): """List of tokens representing an expression in parentheses.""" pass class AppliedFunction: """ A group of tokens representing a function and its arguments. `exponent` is for handling the shorthand sin^2, ln^2, etc. """ def __init__(self, function: TOKEN, args: ParenthesisGroup, exponent=None): if exponent is None: exponent = [] self.function = function self.args = args self.exponent = exponent self.items = ['function', 'args', 'exponent'] def expand(self) -> List[TOKEN]: """Return a list of tokens representing the function""" return [self.function, *self.args] def __getitem__(self, index): return getattr(self, self.items[index]) def __repr__(self): return "AppliedFunction(%s, %s, %s)" % (self.function, self.args, self.exponent) def _flatten(result: List[tUnion[TOKEN, AppliedFunction]]): result2: List[TOKEN] = [] for tok in result: if isinstance(tok, AppliedFunction): result2.extend(tok.expand()) else: result2.append(tok) return result2 def _group_parentheses(recursor: TRANS): def _inner(tokens: List[TOKEN], local_dict: DICT, global_dict: DICT): """Group tokens between parentheses with ParenthesisGroup. Also processes those tokens recursively. """ result: List[tUnion[TOKEN, ParenthesisGroup]] = [] stacks: List[ParenthesisGroup] = [] stacklevel = 0 for token in tokens: if token[0] == OP: if token[1] == '(': stacks.append(ParenthesisGroup([])) stacklevel += 1 elif token[1] == ')': stacks[-1].append(token) stack = stacks.pop() if len(stacks) > 0: # We don't recurse here since the upper-level stack # would reprocess these tokens stacks[-1].extend(stack) else: # Recurse here to handle nested parentheses # Strip off the outer parentheses to avoid an infinite loop inner = stack[1:-1] inner = recursor(inner, local_dict, global_dict) parenGroup = [stack[0]] + inner + [stack[-1]] result.append(ParenthesisGroup(parenGroup)) stacklevel -= 1 continue if stacklevel: stacks[-1].append(token) else: result.append(token) if stacklevel: raise TokenError("Mismatched parentheses") return result return _inner def _apply_functions(tokens: List[tUnion[TOKEN, ParenthesisGroup]], local_dict: DICT, global_dict: DICT): """Convert a NAME token + ParenthesisGroup into an AppliedFunction. Note that ParenthesisGroups, if not applied to any function, are converted back into lists of tokens. """ result: List[tUnion[TOKEN, AppliedFunction]] = [] symbol = None for tok in tokens: if isinstance(tok, ParenthesisGroup): if symbol and _token_callable(symbol, local_dict, global_dict): result[-1] = AppliedFunction(symbol, tok) symbol = None else: result.extend(tok) elif tok[0] == NAME: symbol = tok result.append(tok) else: symbol = None result.append(tok) return result def _implicit_multiplication(tokens: List[tUnion[TOKEN, AppliedFunction]], local_dict: DICT, global_dict: DICT): """Implicitly adds '*' tokens. Cases: - Two AppliedFunctions next to each other ("sin(x)cos(x)") - AppliedFunction next to an open parenthesis ("sin x (cos x + 1)") - A close parenthesis next to an AppliedFunction ("(x+2)sin x")\ - A close parenthesis next to an open parenthesis ("(x+2)(x+3)") - AppliedFunction next to an implicitly applied function ("sin(x)cos x") """ result: List[tUnion[TOKEN, AppliedFunction]] = [] skip = False for tok, nextTok in zip(tokens, tokens[1:]): result.append(tok) if skip: skip = False continue if tok[0] == OP and tok[1] == '.' and nextTok[0] == NAME: # Dotted name. Do not do implicit multiplication skip = True continue if isinstance(tok, AppliedFunction): if isinstance(nextTok, AppliedFunction): result.append((OP, '*')) elif nextTok == (OP, '('): # Applied function followed by an open parenthesis if tok.function[1] == "Function": tok.function = (tok.function[0], 'Symbol') result.append((OP, '*')) elif nextTok[0] == NAME: # Applied function followed by implicitly applied function result.append((OP, '*')) else: if tok == (OP, ')'): if isinstance(nextTok, AppliedFunction): # Close parenthesis followed by an applied function result.append((OP, '*')) elif nextTok[0] == NAME: # Close parenthesis followed by an implicitly applied function result.append((OP, '*')) elif nextTok == (OP, '('): # Close parenthesis followed by an open parenthesis result.append((OP, '*')) elif tok[0] == NAME and not _token_callable(tok, local_dict, global_dict): if isinstance(nextTok, AppliedFunction) or \ (nextTok[0] == NAME and _token_callable(nextTok, local_dict, global_dict)): # Constant followed by (implicitly applied) function result.append((OP, '*')) elif nextTok == (OP, '('): # Constant followed by parenthesis result.append((OP, '*')) elif nextTok[0] == NAME: # Constant followed by constant result.append((OP, '*')) if tokens: result.append(tokens[-1]) return result def _implicit_application(tokens: List[tUnion[TOKEN, AppliedFunction]], local_dict: DICT, global_dict: DICT): """Adds parentheses as needed after functions.""" result: List[tUnion[TOKEN, AppliedFunction]] = [] appendParen = 0 # number of closing parentheses to add skip = 0 # number of tokens to delay before adding a ')' (to # capture **, ^, etc.) exponentSkip = False # skipping tokens before inserting parentheses to # work with function exponentiation for tok, nextTok in zip(tokens, tokens[1:]): result.append(tok) if (tok[0] == NAME and nextTok[0] not in [OP, ENDMARKER, NEWLINE]): if _token_callable(tok, local_dict, global_dict, nextTok): # type: ignore result.append((OP, '(')) appendParen += 1 # name followed by exponent - function exponentiation elif (tok[0] == NAME and nextTok[0] == OP and nextTok[1] == '**'): if _token_callable(tok, local_dict, global_dict): # type: ignore exponentSkip = True elif exponentSkip: # if the last token added was an applied function (i.e. the # power of the function exponent) OR a multiplication (as # implicit multiplication would have added an extraneous # multiplication) if (isinstance(tok, AppliedFunction) or (tok[0] == OP and tok[1] == '*')): # don't add anything if the next token is a multiplication # or if there's already a parenthesis (if parenthesis, still # stop skipping tokens) if not (nextTok[0] == OP and nextTok[1] == '*'): if not(nextTok[0] == OP and nextTok[1] == '('): result.append((OP, '(')) appendParen += 1 exponentSkip = False elif appendParen: if nextTok[0] == OP and nextTok[1] in ('^', '**', '*'): skip = 1 continue if skip: skip -= 1 continue result.append((OP, ')')) appendParen -= 1 if tokens: result.append(tokens[-1]) if appendParen: result.extend([(OP, ')')] * appendParen) return result def function_exponentiation(tokens: List[TOKEN], local_dict: DICT, global_dict: DICT): """Allows functions to be exponentiated, e.g. ``cos**2(x)``. Examples ======== >>> from sympy.parsing.sympy_parser import (parse_expr, ... standard_transformations, function_exponentiation) >>> transformations = standard_transformations + (function_exponentiation,) >>> parse_expr('sin**4(x)', transformations=transformations) sin(x)**4 """ result: List[TOKEN] = [] exponent: List[TOKEN] = [] consuming_exponent = False level = 0 for tok, nextTok in zip(tokens, tokens[1:]): if tok[0] == NAME and nextTok[0] == OP and nextTok[1] == '**': if _token_callable(tok, local_dict, global_dict): consuming_exponent = True elif consuming_exponent: if tok[0] == NAME and tok[1] == 'Function': tok = (NAME, 'Symbol') exponent.append(tok) # only want to stop after hitting ) if tok[0] == nextTok[0] == OP and tok[1] == ')' and nextTok[1] == '(': consuming_exponent = False # if implicit multiplication was used, we may have )*( instead if tok[0] == nextTok[0] == OP and tok[1] == '*' and nextTok[1] == '(': consuming_exponent = False del exponent[-1] continue elif exponent and not consuming_exponent: if tok[0] == OP: if tok[1] == '(': level += 1 elif tok[1] == ')': level -= 1 if level == 0: result.append(tok) result.extend(exponent) exponent = [] continue result.append(tok) if tokens: result.append(tokens[-1]) if exponent: result.extend(exponent) return result def split_symbols_custom(predicate: Callable[[str], bool]): """Creates a transformation that splits symbol names. ``predicate`` should return True if the symbol name is to be split. For instance, to retain the default behavior but avoid splitting certain symbol names, a predicate like this would work: >>> from sympy.parsing.sympy_parser import (parse_expr, _token_splittable, ... standard_transformations, implicit_multiplication, ... split_symbols_custom) >>> def can_split(symbol): ... if symbol not in ('list', 'of', 'unsplittable', 'names'): ... return _token_splittable(symbol) ... return False ... >>> transformation = split_symbols_custom(can_split) >>> parse_expr('unsplittable', transformations=standard_transformations + ... (transformation, implicit_multiplication)) unsplittable """ def _split_symbols(tokens: List[TOKEN], local_dict: DICT, global_dict: DICT): result: List[TOKEN] = [] split = False split_previous=False for tok in tokens: if split_previous: # throw out closing parenthesis of Symbol that was split split_previous=False continue split_previous=False if tok[0] == NAME and tok[1] in ['Symbol', 'Function']: split = True elif split and tok[0] == NAME: symbol = tok[1][1:-1] if predicate(symbol): tok_type = result[-2][1] # Symbol or Function del result[-2:] # Get rid of the call to Symbol i = 0 while i < len(symbol): char = symbol[i] if char in local_dict or char in global_dict: result.append((NAME, "%s" % char)) elif char.isdigit(): chars = [char] for i in range(i + 1, len(symbol)): if not symbol[i].isdigit(): i -= 1 break chars.append(symbol[i]) char = ''.join(chars) result.extend([(NAME, 'Number'), (OP, '('), (NAME, "'%s'" % char), (OP, ')')]) else: use = tok_type if i == len(symbol) else 'Symbol' result.extend([(NAME, use), (OP, '('), (NAME, "'%s'" % char), (OP, ')')]) i += 1 # Set split_previous=True so will skip # the closing parenthesis of the original Symbol split = False split_previous = True continue else: split = False result.append(tok) return result return _split_symbols #: Splits symbol names for implicit multiplication. #: #: Intended to let expressions like ``xyz`` be parsed as ``x*y*z``. Does not #: split Greek character names, so ``theta`` will *not* become #: ``t*h*e*t*a``. Generally this should be used with #: ``implicit_multiplication``. split_symbols = split_symbols_custom(_token_splittable) def implicit_multiplication(tokens: List[TOKEN], local_dict: DICT, global_dict: DICT) -> List[TOKEN]: """Makes the multiplication operator optional in most cases. Use this before :func:`implicit_application`, otherwise expressions like ``sin 2x`` will be parsed as ``x * sin(2)`` rather than ``sin(2*x)``. Examples ======== >>> from sympy.parsing.sympy_parser import (parse_expr, ... standard_transformations, implicit_multiplication) >>> transformations = standard_transformations + (implicit_multiplication,) >>> parse_expr('3 x y', transformations=transformations) 3*x*y """ # These are interdependent steps, so we don't expose them separately res1 = _group_parentheses(implicit_multiplication)(tokens, local_dict, global_dict) res2 = _apply_functions(res1, local_dict, global_dict) res3 = _implicit_multiplication(res2, local_dict, global_dict) result = _flatten(res3) return result def implicit_application(tokens: List[TOKEN], local_dict: DICT, global_dict: DICT) -> List[TOKEN]: """Makes parentheses optional in some cases for function calls. Use this after :func:`implicit_multiplication`, otherwise expressions like ``sin 2x`` will be parsed as ``x * sin(2)`` rather than ``sin(2*x)``. Examples ======== >>> from sympy.parsing.sympy_parser import (parse_expr, ... standard_transformations, implicit_application) >>> transformations = standard_transformations + (implicit_application,) >>> parse_expr('cot z + csc z', transformations=transformations) cot(z) + csc(z) """ res1 = _group_parentheses(implicit_application)(tokens, local_dict, global_dict) res2 = _apply_functions(res1, local_dict, global_dict) res3 = _implicit_application(res2, local_dict, global_dict) result = _flatten(res3) return result def implicit_multiplication_application(result: List[TOKEN], local_dict: DICT, global_dict: DICT) -> List[TOKEN]: """Allows a slightly relaxed syntax. - Parentheses for single-argument method calls are optional. - Multiplication is implicit. - Symbol names can be split (i.e. spaces are not needed between symbols). - Functions can be exponentiated. Examples ======== >>> from sympy.parsing.sympy_parser import (parse_expr, ... standard_transformations, implicit_multiplication_application) >>> parse_expr("10sin**2 x**2 + 3xyz + tan theta", ... transformations=(standard_transformations + ... (implicit_multiplication_application,))) 3*x*y*z + 10*sin(x**2)**2 + tan(theta) """ for step in (split_symbols, implicit_multiplication, implicit_application, function_exponentiation): result = step(result, local_dict, global_dict) return result def auto_symbol(tokens: List[TOKEN], local_dict: DICT, global_dict: DICT): """Inserts calls to ``Symbol``/``Function`` for undefined variables.""" result: List[TOKEN] = [] prevTok = (-1, '') tokens.append((-1, '')) # so zip traverses all tokens for tok, nextTok in zip(tokens, tokens[1:]): tokNum, tokVal = tok nextTokNum, nextTokVal = nextTok if tokNum == NAME: name = tokVal if (name in ['True', 'False', 'None'] or iskeyword(name) # Don't convert attribute access or (prevTok[0] == OP and prevTok[1] == '.') # Don't convert keyword arguments or (prevTok[0] == OP and prevTok[1] in ('(', ',') and nextTokNum == OP and nextTokVal == '=') # the name has already been defined or name in local_dict and local_dict[name] is not null): result.append((NAME, name)) continue elif name in local_dict: local_dict.setdefault(null, set()).add(name) if nextTokVal == '(': local_dict[name] = Function(name) else: local_dict[name] = Symbol(name) result.append((NAME, name)) continue elif name in global_dict: obj = global_dict[name] if isinstance(obj, (AssumptionKeys, Basic, type)) or callable(obj): result.append((NAME, name)) continue result.extend([ (NAME, 'Symbol' if nextTokVal != '(' else 'Function'), (OP, '('), (NAME, repr(str(name))), (OP, ')'), ]) else: result.append((tokNum, tokVal)) prevTok = (tokNum, tokVal) return result def lambda_notation(tokens: List[TOKEN], local_dict: DICT, global_dict: DICT): """Substitutes "lambda" with its SymPy equivalent Lambda(). However, the conversion does not take place if only "lambda" is passed because that is a syntax error. """ result: List[TOKEN] = [] flag = False toknum, tokval = tokens[0] tokLen = len(tokens) if toknum == NAME and tokval == 'lambda': if tokLen == 2 or tokLen == 3 and tokens[1][0] == NEWLINE: # In Python 3.6.7+, inputs without a newline get NEWLINE added to # the tokens result.extend(tokens) elif tokLen > 2: result.extend([ (NAME, 'Lambda'), (OP, '('), (OP, '('), (OP, ')'), (OP, ')'), ]) for tokNum, tokVal in tokens[1:]: if tokNum == OP and tokVal == ':': tokVal = ',' flag = True if not flag and tokNum == OP and tokVal in ('*', '**'): raise TokenError("Starred arguments in lambda not supported") if flag: result.insert(-1, (tokNum, tokVal)) else: result.insert(-2, (tokNum, tokVal)) else: result.extend(tokens) return result def factorial_notation(tokens: List[TOKEN], local_dict: DICT, global_dict: DICT): """Allows standard notation for factorial.""" result: List[TOKEN] = [] nfactorial = 0 for toknum, tokval in tokens: if toknum == OP and tokval == "!": # In Python 3.12 "!" are OP instead of ERRORTOKEN nfactorial += 1 elif toknum == ERRORTOKEN: op = tokval if op == '!': nfactorial += 1 else: nfactorial = 0 result.append((OP, op)) else: if nfactorial == 1: result = _add_factorial_tokens('factorial', result) elif nfactorial == 2: result = _add_factorial_tokens('factorial2', result) elif nfactorial > 2: raise TokenError nfactorial = 0 result.append((toknum, tokval)) return result def convert_xor(tokens: List[TOKEN], local_dict: DICT, global_dict: DICT): """Treats XOR, ``^``, as exponentiation, ``**``.""" result: List[TOKEN] = [] for toknum, tokval in tokens: if toknum == OP: if tokval == '^': result.append((OP, '**')) else: result.append((toknum, tokval)) else: result.append((toknum, tokval)) return result def repeated_decimals(tokens: List[TOKEN], local_dict: DICT, global_dict: DICT): """ Allows 0.2[1] notation to represent the repeated decimal 0.2111... (19/90) Run this before auto_number. """ result: List[TOKEN] = [] def is_digit(s): return all(i in '0123456789_' for i in s) # num will running match any DECIMAL [ INTEGER ] num: List[TOKEN] = [] for toknum, tokval in tokens: if toknum == NUMBER: if (not num and '.' in tokval and 'e' not in tokval.lower() and 'j' not in tokval.lower()): num.append((toknum, tokval)) elif is_digit(tokval)and len(num) == 2: num.append((toknum, tokval)) elif is_digit(tokval) and len(num) == 3 and is_digit(num[-1][1]): # Python 2 tokenizes 00123 as '00', '123' # Python 3 tokenizes 01289 as '012', '89' num.append((toknum, tokval)) else: num = [] elif toknum == OP: if tokval == '[' and len(num) == 1: num.append((OP, tokval)) elif tokval == ']' and len(num) >= 3: num.append((OP, tokval)) elif tokval == '.' and not num: # handle .[1] num.append((NUMBER, '0.')) else: num = [] else: num = [] result.append((toknum, tokval)) if num and num[-1][1] == ']': # pre.post[repetend] = a + b/c + d/e where a = pre, b/c = post, # and d/e = repetend result = result[:-len(num)] pre, post = num[0][1].split('.') repetend = num[2][1] if len(num) == 5: repetend += num[3][1] pre = pre.replace('_', '') post = post.replace('_', '') repetend = repetend.replace('_', '') zeros = '0'*len(post) post, repetends = [w.lstrip('0') for w in [post, repetend]] # or else interpreted as octal a = pre or '0' b, c = post or '0', '1' + zeros d, e = repetends, ('9'*len(repetend)) + zeros seq = [ (OP, '('), (NAME, 'Integer'), (OP, '('), (NUMBER, a), (OP, ')'), (OP, '+'), (NAME, 'Rational'), (OP, '('), (NUMBER, b), (OP, ','), (NUMBER, c), (OP, ')'), (OP, '+'), (NAME, 'Rational'), (OP, '('), (NUMBER, d), (OP, ','), (NUMBER, e), (OP, ')'), (OP, ')'), ] result.extend(seq) num = [] return result def auto_number(tokens: List[TOKEN], local_dict: DICT, global_dict: DICT): """ Converts numeric literals to use SymPy equivalents. Complex numbers use ``I``, integer literals use ``Integer``, and float literals use ``Float``. """ result: List[TOKEN] = [] for toknum, tokval in tokens: if toknum == NUMBER: number = tokval postfix = [] if number.endswith('j') or number.endswith('J'): number = number[:-1] postfix = [(OP, '*'), (NAME, 'I')] if '.' in number or (('e' in number or 'E' in number) and not (number.startswith('0x') or number.startswith('0X'))): seq = [(NAME, 'Float'), (OP, '('), (NUMBER, repr(str(number))), (OP, ')')] else: seq = [(NAME, 'Integer'), (OP, '('), ( NUMBER, number), (OP, ')')] result.extend(seq + postfix) else: result.append((toknum, tokval)) return result def rationalize(tokens: List[TOKEN], local_dict: DICT, global_dict: DICT): """Converts floats into ``Rational``. Run AFTER ``auto_number``.""" result: List[TOKEN] = [] passed_float = False for toknum, tokval in tokens: if toknum == NAME: if tokval == 'Float': passed_float = True tokval = 'Rational' result.append((toknum, tokval)) elif passed_float == True and toknum == NUMBER: passed_float = False result.append((STRING, tokval)) else: result.append((toknum, tokval)) return result def _transform_equals_sign(tokens: List[TOKEN], local_dict: DICT, global_dict: DICT): """Transforms the equals sign ``=`` to instances of Eq. This is a helper function for ``convert_equals_signs``. Works with expressions containing one equals sign and no nesting. Expressions like ``(1=2)=False`` will not work with this and should be used with ``convert_equals_signs``. Examples: 1=2 to Eq(1,2) 1*2=x to Eq(1*2, x) This does not deal with function arguments yet. """ result: List[TOKEN] = [] if (OP, "=") in tokens: result.append((NAME, "Eq")) result.append((OP, "(")) for token in tokens: if token == (OP, "="): result.append((OP, ",")) continue result.append(token) result.append((OP, ")")) else: result = tokens return result def convert_equals_signs(tokens: List[TOKEN], local_dict: DICT, global_dict: DICT) -> List[TOKEN]: """ Transforms all the equals signs ``=`` to instances of Eq. Parses the equals signs in the expression and replaces them with appropriate Eq instances. Also works with nested equals signs. Does not yet play well with function arguments. For example, the expression ``(x=y)`` is ambiguous and can be interpreted as x being an argument to a function and ``convert_equals_signs`` will not work for this. See also ======== convert_equality_operators Examples ======== >>> from sympy.parsing.sympy_parser import (parse_expr, ... standard_transformations, convert_equals_signs) >>> parse_expr("1*2=x", transformations=( ... standard_transformations + (convert_equals_signs,))) Eq(2, x) >>> parse_expr("(1*2=x)=False", transformations=( ... standard_transformations + (convert_equals_signs,))) Eq(Eq(2, x), False) """ res1 = _group_parentheses(convert_equals_signs)(tokens, local_dict, global_dict) res2 = _apply_functions(res1, local_dict, global_dict) res3 = _transform_equals_sign(res2, local_dict, global_dict) result = _flatten(res3) return result #: Standard transformations for :func:`parse_expr`. #: Inserts calls to :class:`~.Symbol`, :class:`~.Integer`, and other SymPy #: datatypes and allows the use of standard factorial notation (e.g. ``x!``). standard_transformations: tTuple[TRANS, ...] \ = (lambda_notation, auto_symbol, repeated_decimals, auto_number, factorial_notation) def stringify_expr(s: str, local_dict: DICT, global_dict: DICT, transformations: tTuple[TRANS, ...]) -> str: """ Converts the string ``s`` to Python code, in ``local_dict`` Generally, ``parse_expr`` should be used. """ tokens = [] input_code = StringIO(s.strip()) for toknum, tokval, _, _, _ in generate_tokens(input_code.readline): tokens.append((toknum, tokval)) for transform in transformations: tokens = transform(tokens, local_dict, global_dict) return untokenize(tokens) def eval_expr(code, local_dict: DICT, global_dict: DICT): """ Evaluate Python code generated by ``stringify_expr``. Generally, ``parse_expr`` should be used. """ expr = eval( code, global_dict, local_dict) # take local objects in preference return expr def parse_expr(s: str, local_dict: Optional[DICT] = None, transformations: tUnion[tTuple[TRANS, ...], str] \ = standard_transformations, global_dict: Optional[DICT] = None, evaluate=True): """Converts the string ``s`` to a SymPy expression, in ``local_dict``. Parameters ========== s : str The string to parse. local_dict : dict, optional A dictionary of local variables to use when parsing. global_dict : dict, optional A dictionary of global variables. By default, this is initialized with ``from sympy import *``; provide this parameter to override this behavior (for instance, to parse ``"Q & S"``). transformations : tuple or str A tuple of transformation functions used to modify the tokens of the parsed expression before evaluation. The default transformations convert numeric literals into their SymPy equivalents, convert undefined variables into SymPy symbols, and allow the use of standard mathematical factorial notation (e.g. ``x!``). Selection via string is available (see below). evaluate : bool, optional When False, the order of the arguments will remain as they were in the string and automatic simplification that would normally occur is suppressed. (see examples) Examples ======== >>> from sympy.parsing.sympy_parser import parse_expr >>> parse_expr("1/2") 1/2 >>> type(_) >>> from sympy.parsing.sympy_parser import standard_transformations,\\ ... implicit_multiplication_application >>> transformations = (standard_transformations + ... (implicit_multiplication_application,)) >>> parse_expr("2x", transformations=transformations) 2*x When evaluate=False, some automatic simplifications will not occur: >>> parse_expr("2**3"), parse_expr("2**3", evaluate=False) (8, 2**3) In addition the order of the arguments will not be made canonical. This feature allows one to tell exactly how the expression was entered: >>> a = parse_expr('1 + x', evaluate=False) >>> b = parse_expr('x + 1', evaluate=0) >>> a == b False >>> a.args (1, x) >>> b.args (x, 1) Note, however, that when these expressions are printed they will appear the same: >>> assert str(a) == str(b) As a convenience, transformations can be seen by printing ``transformations``: >>> from sympy.parsing.sympy_parser import transformations >>> print(transformations) 0: lambda_notation 1: auto_symbol 2: repeated_decimals 3: auto_number 4: factorial_notation 5: implicit_multiplication_application 6: convert_xor 7: implicit_application 8: implicit_multiplication 9: convert_equals_signs 10: function_exponentiation 11: rationalize The ``T`` object provides a way to select these transformations: >>> from sympy.parsing.sympy_parser import T If you print it, you will see the same list as shown above. >>> str(T) == str(transformations) True Standard slicing will return a tuple of transformations: >>> T[:5] == standard_transformations True So ``T`` can be used to specify the parsing transformations: >>> parse_expr("2x", transformations=T[:5]) Traceback (most recent call last): ... SyntaxError: invalid syntax >>> parse_expr("2x", transformations=T[:6]) 2*x >>> parse_expr('.3', transformations=T[3, 11]) 3/10 >>> parse_expr('.3x', transformations=T[:]) 3*x/10 As a further convenience, strings 'implicit' and 'all' can be used to select 0-5 and all the transformations, respectively. >>> parse_expr('.3x', transformations='all') 3*x/10 See Also ======== stringify_expr, eval_expr, standard_transformations, implicit_multiplication_application """ if local_dict is None: local_dict = {} elif not isinstance(local_dict, dict): raise TypeError('expecting local_dict to be a dict') elif null in local_dict: raise ValueError('cannot use "" in local_dict') if global_dict is None: global_dict = {} exec('from sympy import *', global_dict) builtins_dict = vars(builtins) for name, obj in builtins_dict.items(): if isinstance(obj, types.BuiltinFunctionType): global_dict[name] = obj global_dict['max'] = Max global_dict['min'] = Min elif not isinstance(global_dict, dict): raise TypeError('expecting global_dict to be a dict') transformations = transformations or () if isinstance(transformations, str): if transformations == 'all': _transformations = T[:] elif transformations == 'implicit': _transformations = T[:6] else: raise ValueError('unknown transformation group name') else: _transformations = transformations code = stringify_expr(s, local_dict, global_dict, _transformations) if not evaluate: code = compile(evaluateFalse(code), '', 'eval') # type: ignore try: rv = eval_expr(code, local_dict, global_dict) # restore neutral definitions for names for i in local_dict.pop(null, ()): local_dict[i] = null return rv except Exception as e: # restore neutral definitions for names for i in local_dict.pop(null, ()): local_dict[i] = null raise e from ValueError(f"Error from parse_expr with transformed code: {code!r}") def evaluateFalse(s: str): """ Replaces operators with the SymPy equivalent and sets evaluate=False. """ node = ast.parse(s) transformed_node = EvaluateFalseTransformer().visit(node) # node is a Module, we want an Expression transformed_node = ast.Expression(transformed_node.body[0].value) return ast.fix_missing_locations(transformed_node) class EvaluateFalseTransformer(ast.NodeTransformer): operators = { ast.Add: 'Add', ast.Mult: 'Mul', ast.Pow: 'Pow', ast.Sub: 'Add', ast.Div: 'Mul', ast.BitOr: 'Or', ast.BitAnd: 'And', ast.BitXor: 'Not', } functions = ( 'Abs', 'im', 're', 'sign', 'arg', 'conjugate', 'acos', 'acot', 'acsc', 'asec', 'asin', 'atan', 'acosh', 'acoth', 'acsch', 'asech', 'asinh', 'atanh', 'cos', 'cot', 'csc', 'sec', 'sin', 'tan', 'cosh', 'coth', 'csch', 'sech', 'sinh', 'tanh', 'exp', 'ln', 'log', 'sqrt', 'cbrt', ) relational_operators = { ast.NotEq: 'Ne', ast.Lt: 'Lt', ast.LtE: 'Le', ast.Gt: 'Gt', ast.GtE: 'Ge', ast.Eq: 'Eq' } def visit_Compare(self, node): if node.ops[0].__class__ in self.relational_operators: sympy_class = self.relational_operators[node.ops[0].__class__] right = self.visit(node.comparators[0]) left = self.visit(node.left) new_node = ast.Call( func=ast.Name(id=sympy_class, ctx=ast.Load()), args=[left, right], keywords=[ast.keyword(arg='evaluate', value=ast.Constant(value=False))] ) return new_node return node def flatten(self, args, func): result = [] for arg in args: if isinstance(arg, ast.Call): arg_func = arg.func if isinstance(arg_func, ast.Call): arg_func = arg_func.func if arg_func.id == func: result.extend(self.flatten(arg.args, func)) else: result.append(arg) else: result.append(arg) return result def visit_BinOp(self, node): if node.op.__class__ in self.operators: sympy_class = self.operators[node.op.__class__] right = self.visit(node.right) left = self.visit(node.left) rev = False if isinstance(node.op, ast.Sub): right = ast.Call( func=ast.Name(id='Mul', ctx=ast.Load()), args=[ast.UnaryOp(op=ast.USub(), operand=ast.Constant(1)), right], keywords=[ast.keyword(arg='evaluate', value=ast.Constant(value=False))] ) elif isinstance(node.op, ast.Div): if isinstance(node.left, ast.UnaryOp): left, right = right, left rev = True left = ast.Call( func=ast.Name(id='Pow', ctx=ast.Load()), args=[left, ast.UnaryOp(op=ast.USub(), operand=ast.Constant(1))], keywords=[ast.keyword(arg='evaluate', value=ast.Constant(value=False))] ) else: right = ast.Call( func=ast.Name(id='Pow', ctx=ast.Load()), args=[right, ast.UnaryOp(op=ast.USub(), operand=ast.Constant(1))], keywords=[ast.keyword(arg='evaluate', value=ast.Constant(value=False))] ) if rev: # undo reversal left, right = right, left new_node = ast.Call( func=ast.Name(id=sympy_class, ctx=ast.Load()), args=[left, right], keywords=[ast.keyword(arg='evaluate', value=ast.Constant(value=False))] ) if sympy_class in ('Add', 'Mul'): # Denest Add or Mul as appropriate new_node.args = self.flatten(new_node.args, sympy_class) return new_node return node def visit_Call(self, node): new_node = self.generic_visit(node) if isinstance(node.func, ast.Name) and node.func.id in self.functions: new_node.keywords.append(ast.keyword(arg='evaluate', value=ast.Constant(value=False))) return new_node _transformation = { # items can be added but never re-ordered 0: lambda_notation, 1: auto_symbol, 2: repeated_decimals, 3: auto_number, 4: factorial_notation, 5: implicit_multiplication_application, 6: convert_xor, 7: implicit_application, 8: implicit_multiplication, 9: convert_equals_signs, 10: function_exponentiation, 11: rationalize} transformations = '\n'.join('%s: %s' % (i, func_name(f)) for i, f in _transformation.items()) class _T(): """class to retrieve transformations from a given slice EXAMPLES ======== >>> from sympy.parsing.sympy_parser import T, standard_transformations >>> assert T[:5] == standard_transformations """ def __init__(self): self.N = len(_transformation) def __str__(self): return transformations def __getitem__(self, t): if not type(t) is tuple: t = (t,) i = [] for ti in t: if type(ti) is int: i.append(range(self.N)[ti]) elif type(ti) is slice: i.extend(range(*ti.indices(self.N))) else: raise TypeError('unexpected slice arg') return tuple([_transformation[_] for _ in i]) T = _T()