File size: 12,253 Bytes
6a86ad5
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
90
91
92
93
94
95
96
97
98
99
100
101
102
103
104
105
106
107
108
109
110
111
112
113
114
115
116
117
118
119
120
121
122
123
124
125
126
127
128
129
130
131
132
133
134
135
136
137
138
139
140
141
142
143
144
145
146
147
148
149
150
151
152
153
154
155
156
157
158
159
160
161
162
163
164
165
166
167
168
169
170
171
172
173
174
175
176
177
178
179
180
181
182
183
184
185
186
187
188
189
190
191
192
193
194
195
196
197
198
199
200
201
202
203
204
205
206
207
208
209
210
211
212
213
214
215
216
217
218
219
220
221
222
223
224
225
226
227
228
229
230
231
232
233
234
235
236
237
238
239
240
241
242
243
244
245
246
247
248
249
250
251
252
253
254
255
256
257
258
259
260
261
262
263
264
265
266
267
268
269
270
271
272
273
274
275
276
277
278
279
280
281
282
283
284
285
286
287
288
289
290
291
292
293
294
295
296
297
298
299
300
301
302
303
304
305
306
307
308
309
310
311
312
313
314
315
316
317
318
319
320
321
322
323
324
325
326
327
328
329
330
331
332
333
334
335
336
337
338
339
340
341
342
343
344
345
346
347
348
349
350
351
352
353
354
355
356
357
358
359
360
361
362
363
364
365
366
367
368
369
370
371
372
373
# -*- coding: utf-8 -*-


import sys
import builtins
import types

from sympy.assumptions import Q
from sympy.core import Symbol, Function, Float, Rational, Integer, I, Mul, Pow, Eq, Lt, Le, Gt, Ge, Ne
from sympy.functions import exp, factorial, factorial2, sin, Min, Max
from sympy.logic import And
from sympy.series import Limit
from sympy.testing.pytest import raises, skip

from sympy.parsing.sympy_parser import (
    parse_expr, standard_transformations, rationalize, TokenError,
    split_symbols, implicit_multiplication, convert_equals_signs,
    convert_xor, function_exponentiation, lambda_notation, auto_symbol,
    repeated_decimals, implicit_multiplication_application,
    auto_number, factorial_notation, implicit_application,
    _transformation, T
    )


def test_sympy_parser():
    x = Symbol('x')
    inputs = {
        '2*x': 2 * x,
        '3.00': Float(3),
        '22/7': Rational(22, 7),
        '2+3j': 2 + 3*I,
        'exp(x)': exp(x),
        'x!': factorial(x),
        'x!!': factorial2(x),
        '(x + 1)! - 1': factorial(x + 1) - 1,
        '3.[3]': Rational(10, 3),
        '.0[3]': Rational(1, 30),
        '3.2[3]': Rational(97, 30),
        '1.3[12]': Rational(433, 330),
        '1 + 3.[3]': Rational(13, 3),
        '1 + .0[3]': Rational(31, 30),
        '1 + 3.2[3]': Rational(127, 30),
        '.[0011]': Rational(1, 909),
        '0.1[00102] + 1': Rational(366697, 333330),
        '1.[0191]': Rational(10190, 9999),
        '10!': 3628800,
        '-(2)': -Integer(2),
        '[-1, -2, 3]': [Integer(-1), Integer(-2), Integer(3)],
        'Symbol("x").free_symbols': x.free_symbols,
        "S('S(3).n(n=3)')": Float(3, 3),
        'factorint(12, visual=True)': Mul(
            Pow(2, 2, evaluate=False),
            Pow(3, 1, evaluate=False),
            evaluate=False),
        'Limit(sin(x), x, 0, dir="-")': Limit(sin(x), x, 0, dir='-'),
        'Q.even(x)': Q.even(x),


    }
    for text, result in inputs.items():
        assert parse_expr(text) == result

    raises(TypeError, lambda:
        parse_expr('x', standard_transformations))
    raises(TypeError, lambda:
        parse_expr('x', transformations=lambda x,y: 1))
    raises(TypeError, lambda:
        parse_expr('x', transformations=(lambda x,y: 1,)))
    raises(TypeError, lambda: parse_expr('x', transformations=((),)))
    raises(TypeError, lambda: parse_expr('x', {}, [], []))
    raises(TypeError, lambda: parse_expr('x', [], [], {}))
    raises(TypeError, lambda: parse_expr('x', [], [], {}))


def test_rationalize():
    inputs = {
        '0.123': Rational(123, 1000)
    }
    transformations = standard_transformations + (rationalize,)
    for text, result in inputs.items():
        assert parse_expr(text, transformations=transformations) == result


def test_factorial_fail():
    inputs = ['x!!!', 'x!!!!', '(!)']


    for text in inputs:
        try:
            parse_expr(text)
            assert False
        except TokenError:
            assert True


def test_repeated_fail():
    inputs = ['1[1]', '.1e1[1]', '0x1[1]', '1.1j[1]', '1.1[1 + 1]',
        '0.1[[1]]', '0x1.1[1]']


    # All are valid Python, so only raise TypeError for invalid indexing
    for text in inputs:
        raises(TypeError, lambda: parse_expr(text))


    inputs = ['0.1[', '0.1[1', '0.1[]']
    for text in inputs:
        raises((TokenError, SyntaxError), lambda: parse_expr(text))


def test_repeated_dot_only():
    assert parse_expr('.[1]') == Rational(1, 9)
    assert parse_expr('1 + .[1]') == Rational(10, 9)


def test_local_dict():
    local_dict = {
        'my_function': lambda x: x + 2
    }
    inputs = {
        'my_function(2)': Integer(4)
    }
    for text, result in inputs.items():
        assert parse_expr(text, local_dict=local_dict) == result


def test_local_dict_split_implmult():
    t = standard_transformations + (split_symbols, implicit_multiplication,)
    w = Symbol('w', real=True)
    y = Symbol('y')
    assert parse_expr('yx', local_dict={'x':w}, transformations=t) == y*w


def test_local_dict_symbol_to_fcn():
    x = Symbol('x')
    d = {'foo': Function('bar')}
    assert parse_expr('foo(x)', local_dict=d) == d['foo'](x)
    d = {'foo': Symbol('baz')}
    raises(TypeError, lambda: parse_expr('foo(x)', local_dict=d))


def test_global_dict():
    global_dict = {
        'Symbol': Symbol
    }
    inputs = {
        'Q & S': And(Symbol('Q'), Symbol('S'))
    }
    for text, result in inputs.items():
        assert parse_expr(text, global_dict=global_dict) == result


def test_no_globals():

    # Replicate creating the default global_dict:
    default_globals = {}
    exec('from sympy import *', default_globals)
    builtins_dict = vars(builtins)
    for name, obj in builtins_dict.items():
        if isinstance(obj, types.BuiltinFunctionType):
            default_globals[name] = obj
    default_globals['max'] = Max
    default_globals['min'] = Min

    # Need to include Symbol or parse_expr will not work:
    default_globals.pop('Symbol')
    global_dict = {'Symbol':Symbol}

    for name in default_globals:
        obj = parse_expr(name, global_dict=global_dict)
        assert obj == Symbol(name)


def test_issue_2515():
    raises(TokenError, lambda: parse_expr('(()'))
    raises(TokenError, lambda: parse_expr('"""'))


def test_issue_7663():
    x = Symbol('x')
    e = '2*(x+1)'
    assert parse_expr(e, evaluate=0) == parse_expr(e, evaluate=False)
    assert parse_expr(e, evaluate=0).equals(2*(x+1))

def test_recursive_evaluate_false_10560():
    inputs = {
        '4*-3' : '4*-3',
        '-4*3' : '(-4)*3',
        "-2*x*y": '(-2)*x*y',
        "x*-4*x": "x*(-4)*x"
    }
    for text, result in inputs.items():
        assert parse_expr(text, evaluate=False) == parse_expr(result, evaluate=False)


def test_function_evaluate_false():
    inputs = [
        'Abs(0)', 'im(0)', 're(0)', 'sign(0)', 'arg(0)', 'conjugate(0)',
        'acos(0)', 'acot(0)', 'acsc(0)', 'asec(0)', 'asin(0)', 'atan(0)',
        'acosh(0)', 'acoth(0)', 'acsch(0)', 'asech(0)', 'asinh(0)', 'atanh(0)',
        'cos(0)', 'cot(0)', 'csc(0)', 'sec(0)', 'sin(0)', 'tan(0)',
        'cosh(0)', 'coth(0)', 'csch(0)', 'sech(0)', 'sinh(0)', 'tanh(0)',
        'exp(0)', 'log(0)', 'sqrt(0)',
    ]
    for case in inputs:
        expr = parse_expr(case, evaluate=False)
        assert case == str(expr) != str(expr.doit())
    assert str(parse_expr('ln(0)', evaluate=False)) == 'log(0)'
    assert str(parse_expr('cbrt(0)', evaluate=False)) == '0**(1/3)'


def test_issue_10773():
    inputs = {
    '-10/5': '(-10)/5',
    '-10/-5' : '(-10)/(-5)',
    }
    for text, result in inputs.items():
        assert parse_expr(text, evaluate=False) == parse_expr(result, evaluate=False)


def test_split_symbols():
    transformations = standard_transformations + \
                      (split_symbols, implicit_multiplication,)
    x = Symbol('x')
    y = Symbol('y')
    xy = Symbol('xy')


    assert parse_expr("xy") == xy
    assert parse_expr("xy", transformations=transformations) == x*y


def test_split_symbols_function():
    transformations = standard_transformations + \
                      (split_symbols, implicit_multiplication,)
    x = Symbol('x')
    y = Symbol('y')
    a = Symbol('a')
    f = Function('f')


    assert parse_expr("ay(x+1)", transformations=transformations) == a*y*(x+1)
    assert parse_expr("af(x+1)", transformations=transformations,
                      local_dict={'f':f}) == a*f(x+1)


def test_functional_exponent():
    t = standard_transformations + (convert_xor, function_exponentiation)
    x = Symbol('x')
    y = Symbol('y')
    a = Symbol('a')
    yfcn = Function('y')
    assert parse_expr("sin^2(x)", transformations=t) == (sin(x))**2
    assert parse_expr("sin^y(x)", transformations=t) == (sin(x))**y
    assert parse_expr("exp^y(x)", transformations=t) == (exp(x))**y
    assert parse_expr("E^y(x)", transformations=t) == exp(yfcn(x))
    assert parse_expr("a^y(x)", transformations=t) == a**(yfcn(x))


def test_match_parentheses_implicit_multiplication():
    transformations = standard_transformations + \
                      (implicit_multiplication,)
    raises(TokenError, lambda: parse_expr('(1,2),(3,4]',transformations=transformations))


def test_convert_equals_signs():
    transformations = standard_transformations + \
                        (convert_equals_signs, )
    x = Symbol('x')
    y = Symbol('y')
    assert parse_expr("1*2=x", transformations=transformations) == Eq(2, x)
    assert parse_expr("y = x", transformations=transformations) == Eq(y, x)
    assert parse_expr("(2*y = x) = False",
        transformations=transformations) == Eq(Eq(2*y, x), False)


def test_parse_function_issue_3539():
    x = Symbol('x')
    f = Function('f')
    assert parse_expr('f(x)') == f(x)

def test_issue_24288():
    inputs = {
        "1 < 2": Lt(1, 2, evaluate=False),
        "1 <= 2": Le(1, 2, evaluate=False),
        "1 > 2": Gt(1, 2, evaluate=False),
        "1 >= 2": Ge(1, 2, evaluate=False),
        "1 != 2": Ne(1, 2, evaluate=False),
        "1 == 2": Eq(1, 2, evaluate=False)
    }
    for text, result in inputs.items():
        assert parse_expr(text, evaluate=False) == result

def test_split_symbols_numeric():
    transformations = (
        standard_transformations +
        (implicit_multiplication_application,))

    n = Symbol('n')
    expr1 = parse_expr('2**n * 3**n')
    expr2 = parse_expr('2**n3**n', transformations=transformations)
    assert expr1 == expr2 == 2**n*3**n

    expr1 = parse_expr('n12n34', transformations=transformations)
    assert expr1 == n*12*n*34


def test_unicode_names():
    assert parse_expr('α') == Symbol('α')


def test_python3_features():
    # Make sure the tokenizer can handle Python 3-only features
    if sys.version_info < (3, 8):
        skip("test_python3_features requires Python 3.8 or newer")


    assert parse_expr("123_456") == 123456
    assert parse_expr("1.2[3_4]") == parse_expr("1.2[34]") == Rational(611, 495)
    assert parse_expr("1.2[012_012]") == parse_expr("1.2[012012]") == Rational(400, 333)
    assert parse_expr('.[3_4]') == parse_expr('.[34]') == Rational(34, 99)
    assert parse_expr('.1[3_4]') == parse_expr('.1[34]') == Rational(133, 990)
    assert parse_expr('123_123.123_123[3_4]') == parse_expr('123123.123123[34]') == Rational(12189189189211, 99000000)


def test_issue_19501():
    x = Symbol('x')
    eq = parse_expr('E**x(1+x)', local_dict={'x': x}, transformations=(
        standard_transformations +
        (implicit_multiplication_application,)))
    assert eq.free_symbols == {x}


def test_parsing_definitions():
    from sympy.abc import x
    assert len(_transformation) == 12  # if this changes, extend below
    assert _transformation[0] == lambda_notation
    assert _transformation[1] == auto_symbol
    assert _transformation[2] == repeated_decimals
    assert _transformation[3] == auto_number
    assert _transformation[4] == factorial_notation
    assert _transformation[5] == implicit_multiplication_application
    assert _transformation[6] == convert_xor
    assert _transformation[7] == implicit_application
    assert _transformation[8] == implicit_multiplication
    assert _transformation[9] == convert_equals_signs
    assert _transformation[10] == function_exponentiation
    assert _transformation[11] == rationalize
    assert T[:5] == T[0,1,2,3,4] == standard_transformations
    t = _transformation
    assert T[-1, 0] == (t[len(t) - 1], t[0])
    assert T[:5, 8] == standard_transformations + (t[8],)
    assert parse_expr('0.3x^2', transformations='all') == 3*x**2/10
    assert parse_expr('sin 3x', transformations='implicit') == sin(3*x)


def test_builtins():
    cases = [
        ('abs(x)', 'Abs(x)'),
        ('max(x, y)', 'Max(x, y)'),
        ('min(x, y)', 'Min(x, y)'),
        ('pow(x, y)', 'Pow(x, y)'),
    ]
    for built_in_func_call, sympy_func_call in cases:
        assert parse_expr(built_in_func_call) == parse_expr(sympy_func_call)
    assert str(parse_expr('pow(38, -1, 97)')) == '23'


def test_issue_22822():
    raises(ValueError, lambda: parse_expr('x', {'': 1}))
    data = {'some_parameter': None}
    assert parse_expr('some_parameter is None', data) is True