chore: 添加虚拟环境到仓库

- 添加 backend_service/venv 虚拟环境
- 包含所有Python依赖包
- 注意：虚拟环境约393MB，包含12655个文件

backend_service/venv/lib/python3.13/site-packages/sympy/parsing/tests/test_ast_parser.py

@@ -0,0 +1,25 @@
+from sympy.core.singleton import S
+from sympy.core.symbol import symbols
+from sympy.parsing.ast_parser import parse_expr
+from sympy.testing.pytest import raises
+from sympy.core.sympify import SympifyError
+import warnings
+
+def test_parse_expr():
+    a, b = symbols('a, b')
+    # tests issue_16393
+    assert parse_expr('a + b', {}) == a + b
+    raises(SympifyError, lambda: parse_expr('a + ', {}))
+
+    # tests Transform.visit_Constant
+    assert parse_expr('1 + 2', {}) == S(3)
+    assert parse_expr('1 + 2.0', {}) == S(3.0)
+
+    # tests Transform.visit_Name
+    assert parse_expr('Rational(1, 2)', {}) == S(1)/2
+    assert parse_expr('a', {'a': a}) == a
+
+    # tests issue_23092
+    with warnings.catch_warnings():
+        warnings.simplefilter('error')
+        assert parse_expr('6 * 7', {}) == S(42)

backend_service/venv/lib/python3.13/site-packages/sympy/parsing/tests/test_autolev.py

@@ -0,0 +1,178 @@
+import os
+
+from sympy.functions.elementary.trigonometric import (cos, sin)
+from sympy.external import import_module
+from sympy.testing.pytest import skip
+from sympy.parsing.autolev import parse_autolev
+
+antlr4 = import_module("antlr4")
+
+if not antlr4:
+    disabled = True
+
+FILE_DIR = os.path.dirname(
+    os.path.dirname(os.path.abspath(os.path.realpath(__file__))))
+
+
+def _test_examples(in_filename, out_filename, test_name=""):
+
+    in_file_path = os.path.join(FILE_DIR, 'autolev', 'test-examples',
+                                in_filename)
+    correct_file_path = os.path.join(FILE_DIR, 'autolev', 'test-examples',
+                                     out_filename)
+    with open(in_file_path) as f:
+        generated_code = parse_autolev(f, include_numeric=True)
+
+    with open(correct_file_path) as f:
+        for idx, line1 in enumerate(f):
+            if line1.startswith("#"):
+                break
+            try:
+                line2 = generated_code.split('\n')[idx]
+                assert line1.rstrip() == line2.rstrip()
+            except Exception:
+                msg = 'mismatch in ' + test_name + ' in line no: {0}'
+                raise AssertionError(msg.format(idx+1))
+
+
+def test_rule_tests():
+
+    l = ["ruletest1", "ruletest2", "ruletest3", "ruletest4", "ruletest5",
+         "ruletest6", "ruletest7", "ruletest8", "ruletest9", "ruletest10",
+         "ruletest11", "ruletest12"]
+
+    for i in l:
+        in_filepath = i + ".al"
+        out_filepath = i + ".py"
+        _test_examples(in_filepath, out_filepath, i)
+
+
+def test_pydy_examples():
+
+    l = ["mass_spring_damper", "chaos_pendulum", "double_pendulum",
+         "non_min_pendulum"]
+
+    for i in l:
+        in_filepath = os.path.join("pydy-example-repo", i + ".al")
+        out_filepath = os.path.join("pydy-example-repo", i + ".py")
+        _test_examples(in_filepath, out_filepath, i)
+
+
+def test_autolev_tutorial():
+
+    dir_path = os.path.join(FILE_DIR, 'autolev', 'test-examples',
+                            'autolev-tutorial')
+
+    if os.path.isdir(dir_path):
+        l = ["tutor1", "tutor2", "tutor3", "tutor4", "tutor5", "tutor6",
+             "tutor7"]
+        for i in l:
+            in_filepath = os.path.join("autolev-tutorial", i + ".al")
+            out_filepath = os.path.join("autolev-tutorial", i + ".py")
+            _test_examples(in_filepath, out_filepath, i)
+
+
+def test_dynamics_online():
+
+    dir_path = os.path.join(FILE_DIR, 'autolev', 'test-examples',
+                            'dynamics-online')
+
+    if os.path.isdir(dir_path):
+        ch1 = ["1-4", "1-5", "1-6", "1-7", "1-8", "1-9_1", "1-9_2", "1-9_3"]
+        ch2 = ["2-1", "2-2", "2-3", "2-4", "2-5", "2-6", "2-7", "2-8", "2-9",
+               "circular"]
+        ch3 = ["3-1_1", "3-1_2", "3-2_1", "3-2_2", "3-2_3", "3-2_4", "3-2_5",
+               "3-3"]
+        ch4 = ["4-1_1", "4-2_1", "4-4_1", "4-4_2", "4-5_1", "4-5_2"]
+        chapters = [(ch1, "ch1"), (ch2, "ch2"), (ch3, "ch3"), (ch4, "ch4")]
+        for ch, name in chapters:
+            for i in ch:
+                in_filepath = os.path.join("dynamics-online", name, i + ".al")
+                out_filepath = os.path.join("dynamics-online", name, i + ".py")
+                _test_examples(in_filepath, out_filepath, i)
+
+
+def test_output_01():
+    """Autolev example calculates the position, velocity, and acceleration of a
+    point and expresses in a single reference frame::
+
+          (1) FRAMES C,D,F
+          (2) VARIABLES FD'',DC''
+          (3) CONSTANTS R,L
+          (4) POINTS O,E
+          (5) SIMPROT(F,D,1,FD)
+       -> (6) F_D = [1, 0, 0; 0, COS(FD), -SIN(FD); 0, SIN(FD), COS(FD)]
+          (7) SIMPROT(D,C,2,DC)
+       -> (8) D_C = [COS(DC), 0, SIN(DC); 0, 1, 0; -SIN(DC), 0, COS(DC)]
+          (9) W_C_F> = EXPRESS(W_C_F>, F)
+       -> (10) W_C_F> = FD'*F1> + COS(FD)*DC'*F2> + SIN(FD)*DC'*F3>
+          (11) P_O_E>=R*D2>-L*C1>
+          (12) P_O_E>=EXPRESS(P_O_E>, D)
+       -> (13) P_O_E> = -L*COS(DC)*D1> + R*D2> + L*SIN(DC)*D3>
+          (14) V_E_F>=EXPRESS(DT(P_O_E>,F),D)
+       -> (15) V_E_F> = L*SIN(DC)*DC'*D1> - L*SIN(DC)*FD'*D2> + (R*FD'+L*COS(DC)*DC')*D3>
+          (16) A_E_F>=EXPRESS(DT(V_E_F>,F),D)
+       -> (17) A_E_F> = L*(COS(DC)*DC'^2+SIN(DC)*DC'')*D1> + (-R*FD'^2-2*L*COS(DC)*DC'*FD'-L*SIN(DC)*FD'')*D2> + (R*FD''+L*COS(DC)*DC''-L*SIN(DC)*DC'^2-L*SIN(DC)*FD'^2)*D3>
+
+    """
+
+    if not antlr4:
+        skip('Test skipped: antlr4 is not installed.')
+
+    autolev_input = """\
+FRAMES C,D,F
+VARIABLES FD'',DC''
+CONSTANTS R,L
+POINTS O,E
+SIMPROT(F,D,1,FD)
+SIMPROT(D,C,2,DC)
+W_C_F>=EXPRESS(W_C_F>,F)
+P_O_E>=R*D2>-L*C1>
+P_O_E>=EXPRESS(P_O_E>,D)
+V_E_F>=EXPRESS(DT(P_O_E>,F),D)
+A_E_F>=EXPRESS(DT(V_E_F>,F),D)\
+"""
+
+    sympy_input = parse_autolev(autolev_input)
+
+    g = {}
+    l = {}
+    exec(sympy_input, g, l)
+
+    w_c_f = l['frame_c'].ang_vel_in(l['frame_f'])
+    # P_O_E> means "the position of point E wrt to point O"
+    p_o_e = l['point_e'].pos_from(l['point_o'])
+    v_e_f = l['point_e'].vel(l['frame_f'])
+    a_e_f = l['point_e'].acc(l['frame_f'])
+
+    # NOTE : The Autolev outputs above were manually transformed into
+    # equivalent SymPy physics vector expressions. Would be nice to automate
+    # this transformation.
+    expected_w_c_f = (l['fd'].diff()*l['frame_f'].x +
+                      cos(l['fd'])*l['dc'].diff()*l['frame_f'].y +
+                      sin(l['fd'])*l['dc'].diff()*l['frame_f'].z)
+
+    assert (w_c_f - expected_w_c_f).simplify() == 0
+
+    expected_p_o_e = (-l['l']*cos(l['dc'])*l['frame_d'].x +
+                      l['r']*l['frame_d'].y +
+                      l['l']*sin(l['dc'])*l['frame_d'].z)
+
+    assert (p_o_e - expected_p_o_e).simplify() == 0
+
+    expected_v_e_f = (l['l']*sin(l['dc'])*l['dc'].diff()*l['frame_d'].x -
+                      l['l']*sin(l['dc'])*l['fd'].diff()*l['frame_d'].y +
+                      (l['r']*l['fd'].diff() +
+                       l['l']*cos(l['dc'])*l['dc'].diff())*l['frame_d'].z)
+    assert (v_e_f - expected_v_e_f).simplify() == 0
+
+    expected_a_e_f = (l['l']*(cos(l['dc'])*l['dc'].diff()**2 +
+                              sin(l['dc'])*l['dc'].diff().diff())*l['frame_d'].x +
+                      (-l['r']*l['fd'].diff()**2 -
+                       2*l['l']*cos(l['dc'])*l['dc'].diff()*l['fd'].diff() -
+                       l['l']*sin(l['dc'])*l['fd'].diff().diff())*l['frame_d'].y +
+                      (l['r']*l['fd'].diff().diff() +
+                       l['l']*cos(l['dc'])*l['dc'].diff().diff() -
+                       l['l']*sin(l['dc'])*l['dc'].diff()**2 -
+                       l['l']*sin(l['dc'])*l['fd'].diff()**2)*l['frame_d'].z)
+    assert (a_e_f - expected_a_e_f).simplify() == 0

backend_service/venv/lib/python3.13/site-packages/sympy/parsing/tests/test_custom_latex.py

@@ -0,0 +1,69 @@
+import os
+import tempfile
+from pathlib import Path
+
+import sympy
+from sympy.testing.pytest import raises
+from sympy.parsing.latex.lark import LarkLaTeXParser, TransformToSymPyExpr, parse_latex_lark
+from sympy.external import import_module
+
+lark = import_module("lark")
+
+# disable tests if lark is not present
+disabled = lark is None
+
+grammar_file = os.path.join(os.path.dirname(__file__), "../latex/lark/grammar/latex.lark")
+
+modification1 = """
+%override DIV_SYMBOL: DIV
+%override MUL_SYMBOL: MUL | CMD_TIMES
+"""
+
+modification2 = r"""
+%override number: /\d+(,\d*)?/
+"""
+
+def init_custom_parser(modification, transformer=None):
+    latex_grammar = Path(grammar_file).read_text(encoding="utf-8")
+    latex_grammar += modification
+
+    with tempfile.NamedTemporaryFile() as f:
+        f.write(bytes(latex_grammar, encoding="utf8"))
+        f.flush()
+
+        parser = LarkLaTeXParser(grammar_file=f.name, transformer=transformer)
+
+    return parser
+
+def test_custom1():
+    # Removes the parser's ability to understand \cdot and \div.
+
+    parser = init_custom_parser(modification1)
+
+    with raises(lark.exceptions.UnexpectedCharacters):
+        parser.doparse(r"a \cdot b")
+        parser.doparse(r"x \div y")
+
+class CustomTransformer(TransformToSymPyExpr):
+    def number(self, tokens):
+        if "," in tokens[0]:
+            # The Float constructor expects a dot as the decimal separator
+            return sympy.core.numbers.Float(tokens[0].replace(",", "."))
+        else:
+            return sympy.core.numbers.Integer(tokens[0])
+
+def test_custom2():
+    # Makes the parser parse commas as the decimal separator instead of dots
+
+    parser = init_custom_parser(modification2, CustomTransformer)
+
+    with raises(lark.exceptions.UnexpectedCharacters):
+        # Asserting that the default parser cannot parse numbers which have commas as
+        # the decimal separator
+        parse_latex_lark("100,1")
+        parse_latex_lark("0,009")
+
+    parser.doparse("100,1")
+    parser.doparse("0,009")
+    parser.doparse("2,71828")
+    parser.doparse("3,14159")

backend_service/venv/lib/python3.13/site-packages/sympy/parsing/tests/test_fortran_parser.py

@@ -0,0 +1,406 @@
+from sympy.testing.pytest import raises
+from sympy.parsing.sym_expr import SymPyExpression
+from sympy.external import import_module
+
+lfortran = import_module('lfortran')
+
+if lfortran:
+    from sympy.codegen.ast import (Variable, IntBaseType, FloatBaseType, String,
+                                   Return, FunctionDefinition, Assignment,
+                                   Declaration, CodeBlock)
+    from sympy.core import Integer, Float, Add
+    from sympy.core.symbol import Symbol
+
+
+    expr1 = SymPyExpression()
+    expr2 = SymPyExpression()
+    src = """\
+    integer :: a, b, c, d
+    real :: p, q, r, s
+    """
+
+
+    def test_sym_expr():
+        src1 = (
+            src +
+            """\
+            d = a + b -c
+            """
+        )
+        expr3 = SymPyExpression(src,'f')
+        expr4 = SymPyExpression(src1,'f')
+        ls1 = expr3.return_expr()
+        ls2 = expr4.return_expr()
+        for i in range(0, 7):
+            assert isinstance(ls1[i], Declaration)
+            assert isinstance(ls2[i], Declaration)
+        assert isinstance(ls2[8], Assignment)
+        assert ls1[0] == Declaration(
+            Variable(
+                Symbol('a'),
+                type = IntBaseType(String('integer')),
+                value = Integer(0)
+            )
+        )
+        assert ls1[1] == Declaration(
+            Variable(
+                Symbol('b'),
+                type = IntBaseType(String('integer')),
+                value = Integer(0)
+            )
+        )
+        assert ls1[2] == Declaration(
+            Variable(
+                Symbol('c'),
+                type = IntBaseType(String('integer')),
+                value = Integer(0)
+            )
+        )
+        assert ls1[3] == Declaration(
+            Variable(
+                Symbol('d'),
+                type = IntBaseType(String('integer')),
+                value = Integer(0)
+            )
+        )
+        assert ls1[4] == Declaration(
+            Variable(
+                Symbol('p'),
+                type = FloatBaseType(String('real')),
+                value = Float(0.0)
+            )
+        )
+        assert ls1[5] == Declaration(
+            Variable(
+                Symbol('q'),
+                type = FloatBaseType(String('real')),
+                value = Float(0.0)
+            )
+        )
+        assert ls1[6] == Declaration(
+            Variable(
+                Symbol('r'),
+                type = FloatBaseType(String('real')),
+                value = Float(0.0)
+            )
+        )
+        assert ls1[7] == Declaration(
+            Variable(
+                Symbol('s'),
+                type = FloatBaseType(String('real')),
+                value = Float(0.0)
+            )
+        )
+        assert ls2[8] == Assignment(
+            Variable(Symbol('d')),
+            Symbol('a') + Symbol('b') - Symbol('c')
+        )
+
+    def test_assignment():
+        src1 = (
+            src +
+            """\
+            a = b
+            c = d
+            p = q
+            r = s
+            """
+        )
+        expr1.convert_to_expr(src1, 'f')
+        ls1 = expr1.return_expr()
+        for iter in range(0, 12):
+            if iter < 8:
+                assert isinstance(ls1[iter], Declaration)
+            else:
+                assert isinstance(ls1[iter], Assignment)
+        assert ls1[8] == Assignment(
+            Variable(Symbol('a')),
+            Variable(Symbol('b'))
+        )
+        assert ls1[9] == Assignment(
+            Variable(Symbol('c')),
+            Variable(Symbol('d'))
+        )
+        assert ls1[10] == Assignment(
+            Variable(Symbol('p')),
+            Variable(Symbol('q'))
+        )
+        assert ls1[11] == Assignment(
+            Variable(Symbol('r')),
+            Variable(Symbol('s'))
+        )
+
+
+    def test_binop_add():
+        src1 = (
+            src +
+            """\
+            c = a + b
+            d = a + c
+            s = p + q + r
+            """
+        )
+        expr1.convert_to_expr(src1, 'f')
+        ls1 = expr1.return_expr()
+        for iter in range(8, 11):
+            assert isinstance(ls1[iter], Assignment)
+        assert ls1[8] == Assignment(
+            Variable(Symbol('c')),
+            Symbol('a') + Symbol('b')
+        )
+        assert ls1[9] == Assignment(
+            Variable(Symbol('d')),
+            Symbol('a') + Symbol('c')
+        )
+        assert ls1[10] == Assignment(
+            Variable(Symbol('s')),
+            Symbol('p') + Symbol('q') + Symbol('r')
+        )
+
+
+    def test_binop_sub():
+        src1 = (
+            src +
+            """\
+            c = a - b
+            d = a - c
+            s = p - q - r
+            """
+        )
+        expr1.convert_to_expr(src1, 'f')
+        ls1 = expr1.return_expr()
+        for iter in range(8, 11):
+            assert isinstance(ls1[iter], Assignment)
+        assert ls1[8] == Assignment(
+            Variable(Symbol('c')),
+            Symbol('a') - Symbol('b')
+        )
+        assert ls1[9] == Assignment(
+            Variable(Symbol('d')),
+            Symbol('a') - Symbol('c')
+        )
+        assert ls1[10] == Assignment(
+            Variable(Symbol('s')),
+            Symbol('p') - Symbol('q') - Symbol('r')
+        )
+
+
+    def test_binop_mul():
+        src1 = (
+            src +
+            """\
+            c = a * b
+            d = a * c
+            s = p * q * r
+            """
+        )
+        expr1.convert_to_expr(src1, 'f')
+        ls1 = expr1.return_expr()
+        for iter in range(8, 11):
+            assert isinstance(ls1[iter], Assignment)
+        assert ls1[8] == Assignment(
+            Variable(Symbol('c')),
+            Symbol('a') * Symbol('b')
+        )
+        assert ls1[9] == Assignment(
+            Variable(Symbol('d')),
+            Symbol('a') * Symbol('c')
+        )
+        assert ls1[10] == Assignment(
+            Variable(Symbol('s')),
+            Symbol('p') * Symbol('q') * Symbol('r')
+        )
+
+
+    def test_binop_div():
+        src1 = (
+            src +
+            """\
+            c = a / b
+            d = a / c
+            s = p / q
+            r = q / p
+            """
+        )
+        expr1.convert_to_expr(src1, 'f')
+        ls1 = expr1.return_expr()
+        for iter in range(8, 12):
+            assert isinstance(ls1[iter], Assignment)
+        assert ls1[8] == Assignment(
+            Variable(Symbol('c')),
+            Symbol('a') / Symbol('b')
+        )
+        assert ls1[9] == Assignment(
+            Variable(Symbol('d')),
+            Symbol('a') / Symbol('c')
+        )
+        assert ls1[10] == Assignment(
+            Variable(Symbol('s')),
+            Symbol('p') / Symbol('q')
+        )
+        assert ls1[11] == Assignment(
+            Variable(Symbol('r')),
+            Symbol('q') / Symbol('p')
+        )
+
+    def test_mul_binop():
+        src1 = (
+            src +
+            """\
+            d = a + b - c
+            c = a * b + d
+            s = p * q / r
+            r = p * s + q / p
+            """
+        )
+        expr1.convert_to_expr(src1, 'f')
+        ls1 = expr1.return_expr()
+        for iter in range(8, 12):
+            assert isinstance(ls1[iter], Assignment)
+        assert ls1[8] == Assignment(
+            Variable(Symbol('d')),
+            Symbol('a') + Symbol('b') - Symbol('c')
+        )
+        assert ls1[9] == Assignment(
+            Variable(Symbol('c')),
+            Symbol('a') * Symbol('b') + Symbol('d')
+        )
+        assert ls1[10] == Assignment(
+            Variable(Symbol('s')),
+            Symbol('p') * Symbol('q') / Symbol('r')
+        )
+        assert ls1[11] == Assignment(
+            Variable(Symbol('r')),
+            Symbol('p') * Symbol('s') + Symbol('q') / Symbol('p')
+        )
+
+
+    def test_function():
+        src1 = """\
+        integer function f(a,b)
+        integer :: x, y
+        f = x + y
+        end function
+        """
+        expr1.convert_to_expr(src1, 'f')
+        for iter in expr1.return_expr():
+            assert isinstance(iter, FunctionDefinition)
+            assert iter == FunctionDefinition(
+                IntBaseType(String('integer')),
+                name=String('f'),
+                parameters=(
+                    Variable(Symbol('a')),
+                    Variable(Symbol('b'))
+                ),
+                body=CodeBlock(
+                    Declaration(
+                        Variable(
+                            Symbol('a'),
+                            type=IntBaseType(String('integer')),
+                            value=Integer(0)
+                        )
+                    ),
+                    Declaration(
+                        Variable(
+                            Symbol('b'),
+                            type=IntBaseType(String('integer')),
+                            value=Integer(0)
+                        )
+                    ),
+                    Declaration(
+                        Variable(
+                            Symbol('f'),
+                            type=IntBaseType(String('integer')),
+                            value=Integer(0)
+                        )
+                    ),
+                    Declaration(
+                        Variable(
+                            Symbol('x'),
+                            type=IntBaseType(String('integer')),
+                            value=Integer(0)
+                        )
+                    ),
+                    Declaration(
+                        Variable(
+                            Symbol('y'),
+                            type=IntBaseType(String('integer')),
+                            value=Integer(0)
+                        )
+                    ),
+                    Assignment(
+                        Variable(Symbol('f')),
+                        Add(Symbol('x'), Symbol('y'))
+                    ),
+                    Return(Variable(Symbol('f')))
+                )
+            )
+
+
+    def test_var():
+        expr1.convert_to_expr(src, 'f')
+        ls = expr1.return_expr()
+        for iter in expr1.return_expr():
+            assert isinstance(iter, Declaration)
+        assert ls[0] == Declaration(
+            Variable(
+                Symbol('a'),
+                type = IntBaseType(String('integer')),
+                value = Integer(0)
+            )
+        )
+        assert ls[1] == Declaration(
+            Variable(
+                Symbol('b'),
+                type = IntBaseType(String('integer')),
+                value = Integer(0)
+            )
+        )
+        assert ls[2] == Declaration(
+            Variable(
+                Symbol('c'),
+                type = IntBaseType(String('integer')),
+                value = Integer(0)
+            )
+        )
+        assert ls[3] == Declaration(
+            Variable(
+                Symbol('d'),
+                type = IntBaseType(String('integer')),
+                value = Integer(0)
+            )
+        )
+        assert ls[4] == Declaration(
+            Variable(
+                Symbol('p'),
+                type = FloatBaseType(String('real')),
+                value = Float(0.0)
+            )
+        )
+        assert ls[5] == Declaration(
+            Variable(
+                Symbol('q'),
+                type = FloatBaseType(String('real')),
+                value = Float(0.0)
+            )
+        )
+        assert ls[6] == Declaration(
+            Variable(
+                Symbol('r'),
+                type = FloatBaseType(String('real')),
+                value = Float(0.0)
+            )
+        )
+        assert ls[7] == Declaration(
+            Variable(
+                Symbol('s'),
+                type = FloatBaseType(String('real')),
+                value = Float(0.0)
+            )
+        )
+
+else:
+    def test_raise():
+        from sympy.parsing.fortran.fortran_parser import ASR2PyVisitor
+        raises(ImportError, lambda: ASR2PyVisitor())
+        raises(ImportError, lambda: SymPyExpression(' ', mode = 'f'))

backend_service/venv/lib/python3.13/site-packages/sympy/parsing/tests/test_implicit_multiplication_application.py

@@ -0,0 +1,195 @@
+import sympy
+from sympy.parsing.sympy_parser import (
+    parse_expr,
+    standard_transformations,
+    convert_xor,
+    implicit_multiplication_application,
+    implicit_multiplication,
+    implicit_application,
+    function_exponentiation,
+    split_symbols,
+    split_symbols_custom,
+    _token_splittable
+)
+from sympy.testing.pytest import raises
+
+
+def test_implicit_multiplication():
+    cases = {
+        '5x': '5*x',
+        'abc': 'a*b*c',
+        '3sin(x)': '3*sin(x)',
+        '(x+1)(x+2)': '(x+1)*(x+2)',
+        '(5 x**2)sin(x)': '(5*x**2)*sin(x)',
+        '2 sin(x) cos(x)': '2*sin(x)*cos(x)',
+        'pi x': 'pi*x',
+        'x pi': 'x*pi',
+        'E x': 'E*x',
+        'EulerGamma y': 'EulerGamma*y',
+        'E pi': 'E*pi',
+        'pi (x + 2)': 'pi*(x+2)',
+        '(x + 2) pi': '(x+2)*pi',
+        'pi sin(x)': 'pi*sin(x)',
+    }
+    transformations = standard_transformations + (convert_xor,)
+    transformations2 = transformations + (split_symbols,
+                                          implicit_multiplication)
+    for case in cases:
+        implicit = parse_expr(case, transformations=transformations2)
+        normal = parse_expr(cases[case], transformations=transformations)
+        assert(implicit == normal)
+
+    application = ['sin x', 'cos 2*x', 'sin cos x']
+    for case in application:
+        raises(SyntaxError,
+               lambda: parse_expr(case, transformations=transformations2))
+    raises(TypeError,
+           lambda: parse_expr('sin**2(x)', transformations=transformations2))
+
+
+def test_implicit_application():
+    cases = {
+        'factorial': 'factorial',
+        'sin x': 'sin(x)',
+        'tan y**3': 'tan(y**3)',
+        'cos 2*x': 'cos(2*x)',
+        '(cot)': 'cot',
+        'sin cos tan x': 'sin(cos(tan(x)))'
+    }
+    transformations = standard_transformations + (convert_xor,)
+    transformations2 = transformations + (implicit_application,)
+    for case in cases:
+        implicit = parse_expr(case, transformations=transformations2)
+        normal = parse_expr(cases[case], transformations=transformations)
+        assert(implicit == normal), (implicit, normal)
+
+    multiplication = ['x y', 'x sin x', '2x']
+    for case in multiplication:
+        raises(SyntaxError,
+               lambda: parse_expr(case, transformations=transformations2))
+    raises(TypeError,
+           lambda: parse_expr('sin**2(x)', transformations=transformations2))
+
+
+def test_function_exponentiation():
+    cases = {
+        'sin**2(x)': 'sin(x)**2',
+        'exp^y(z)': 'exp(z)^y',
+        'sin**2(E^(x))': 'sin(E^(x))**2'
+    }
+    transformations = standard_transformations + (convert_xor,)
+    transformations2 = transformations + (function_exponentiation,)
+    for case in cases:
+        implicit = parse_expr(case, transformations=transformations2)
+        normal = parse_expr(cases[case], transformations=transformations)
+        assert(implicit == normal)
+
+    other_implicit = ['x y', 'x sin x', '2x', 'sin x',
+                      'cos 2*x', 'sin cos x']
+    for case in other_implicit:
+        raises(SyntaxError,
+               lambda: parse_expr(case, transformations=transformations2))
+
+    assert parse_expr('x**2', local_dict={ 'x': sympy.Symbol('x') },
+                      transformations=transformations2) == parse_expr('x**2')
+
+
+def test_symbol_splitting():
+    # By default Greek letter names should not be split (lambda is a keyword
+    # so skip it)
+    transformations = standard_transformations + (split_symbols,)
+    greek_letters = ('alpha', 'beta', 'gamma', 'delta', 'epsilon', 'zeta',
+                     'eta', 'theta', 'iota', 'kappa', 'mu', 'nu', 'xi',
+                     'omicron', 'pi', 'rho', 'sigma', 'tau', 'upsilon',
+                     'phi', 'chi', 'psi', 'omega')
+
+    for letter in greek_letters:
+        assert(parse_expr(letter, transformations=transformations) ==
+               parse_expr(letter))
+
+    # Make sure symbol splitting resolves names
+    transformations += (implicit_multiplication,)
+    local_dict = { 'e': sympy.E }
+    cases = {
+        'xe': 'E*x',
+        'Iy': 'I*y',
+        'ee': 'E*E',
+    }
+    for case, expected in cases.items():
+        assert(parse_expr(case, local_dict=local_dict,
+                          transformations=transformations) ==
+               parse_expr(expected))
+
+    # Make sure custom splitting works
+    def can_split(symbol):
+        if symbol not in ('unsplittable', 'names'):
+            return _token_splittable(symbol)
+        return False
+    transformations = standard_transformations
+    transformations += (split_symbols_custom(can_split),
+                        implicit_multiplication)
+
+    assert(parse_expr('unsplittable', transformations=transformations) ==
+           parse_expr('unsplittable'))
+    assert(parse_expr('names', transformations=transformations) ==
+           parse_expr('names'))
+    assert(parse_expr('xy', transformations=transformations) ==
+           parse_expr('x*y'))
+    for letter in greek_letters:
+        assert(parse_expr(letter, transformations=transformations) ==
+               parse_expr(letter))
+
+
+def test_all_implicit_steps():
+    cases = {
+        '2x': '2*x',  # implicit multiplication
+        'x y': 'x*y',
+        'xy': 'x*y',
+        'sin x': 'sin(x)',  # add parentheses
+        '2sin x': '2*sin(x)',
+        'x y z': 'x*y*z',
+        'sin(2 * 3x)': 'sin(2 * 3 * x)',
+        'sin(x) (1 + cos(x))': 'sin(x) * (1 + cos(x))',
+        '(x + 2) sin(x)': '(x + 2) * sin(x)',
+        '(x + 2) sin x': '(x + 2) * sin(x)',
+        'sin(sin x)': 'sin(sin(x))',
+        'sin x!': 'sin(factorial(x))',
+        'sin x!!': 'sin(factorial2(x))',
+        'factorial': 'factorial',  # don't apply a bare function
+        'x sin x': 'x * sin(x)',  # both application and multiplication
+        'xy sin x': 'x * y * sin(x)',
+        '(x+2)(x+3)': '(x + 2) * (x+3)',
+        'x**2 + 2xy + y**2': 'x**2 + 2 * x * y + y**2',  # split the xy
+        'pi': 'pi',  # don't mess with constants
+        'None': 'None',
+        'ln sin x': 'ln(sin(x))',  # multiple implicit function applications
+        'sin x**2': 'sin(x**2)',  # implicit application to an exponential
+        'alpha': 'Symbol("alpha")',  # don't split Greek letters/subscripts
+        'x_2': 'Symbol("x_2")',
+        'sin^2 x**2': 'sin(x**2)**2',  # function raised to a power
+        'sin**3(x)': 'sin(x)**3',
+        '(factorial)': 'factorial',
+        'tan 3x': 'tan(3*x)',
+        'sin^2(3*E^(x))': 'sin(3*E**(x))**2',
+        'sin**2(E^(3x))': 'sin(E**(3*x))**2',
+        'sin^2 (3x*E^(x))': 'sin(3*x*E^x)**2',
+        'pi sin x': 'pi*sin(x)',
+    }
+    transformations = standard_transformations + (convert_xor,)
+    transformations2 = transformations + (implicit_multiplication_application,)
+    for case in cases:
+        implicit = parse_expr(case, transformations=transformations2)
+        normal = parse_expr(cases[case], transformations=transformations)
+        assert(implicit == normal)
+
+
+def test_no_methods_implicit_multiplication():
+    # Issue 21020
+    u = sympy.Symbol('u')
+    transformations = standard_transformations + \
+                      (implicit_multiplication,)
+    expr = parse_expr('x.is_polynomial(x)', transformations=transformations)
+    assert expr == True
+    expr = parse_expr('(exp(x) / (1 + exp(2x))).subs(exp(x), u)',
+                      transformations=transformations)
+    assert expr == u/(u**2 + 1)

backend_service/venv/lib/python3.13/site-packages/sympy/parsing/tests/test_latex.py

@@ -0,0 +1,358 @@
+from sympy.testing.pytest import raises, XFAIL
+from sympy.external import import_module
+
+from sympy.concrete.products import Product
+from sympy.concrete.summations import Sum
+from sympy.core.add import Add
+from sympy.core.function import (Derivative, Function)
+from sympy.core.mul import Mul
+from sympy.core.numbers import (E, oo)
+from sympy.core.power import Pow
+from sympy.core.relational import (GreaterThan, LessThan, StrictGreaterThan, StrictLessThan, Unequality)
+from sympy.core.symbol import Symbol
+from sympy.functions.combinatorial.factorials import (binomial, factorial)
+from sympy.functions.elementary.complexes import (Abs, conjugate)
+from sympy.functions.elementary.exponential import (exp, log)
+from sympy.functions.elementary.integers import (ceiling, floor)
+from sympy.functions.elementary.miscellaneous import (root, sqrt)
+from sympy.functions.elementary.trigonometric import (asin, cos, csc, sec, sin, tan)
+from sympy.integrals.integrals import Integral
+from sympy.series.limits import Limit
+
+from sympy.core.relational import Eq, Ne, Lt, Le, Gt, Ge
+from sympy.physics.quantum.state import Bra, Ket
+from sympy.abc import x, y, z, a, b, c, t, k, n
+antlr4 = import_module("antlr4")
+
+# disable tests if antlr4-python3-runtime is not present
+disabled = antlr4 is None
+
+theta = Symbol('theta')
+f = Function('f')
+
+
+# shorthand definitions
+def _Add(a, b):
+    return Add(a, b, evaluate=False)
+
+
+def _Mul(a, b):
+    return Mul(a, b, evaluate=False)
+
+
+def _Pow(a, b):
+    return Pow(a, b, evaluate=False)
+
+
+def _Sqrt(a):
+    return sqrt(a, evaluate=False)
+
+
+def _Conjugate(a):
+    return conjugate(a, evaluate=False)
+
+
+def _Abs(a):
+    return Abs(a, evaluate=False)
+
+
+def _factorial(a):
+    return factorial(a, evaluate=False)
+
+
+def _exp(a):
+    return exp(a, evaluate=False)
+
+
+def _log(a, b):
+    return log(a, b, evaluate=False)
+
+
+def _binomial(n, k):
+    return binomial(n, k, evaluate=False)
+
+
+def test_import():
+    from sympy.parsing.latex._build_latex_antlr import (
+        build_parser,
+        check_antlr_version,
+        dir_latex_antlr
+    )
+    # XXX: It would be better to come up with a test for these...
+    del build_parser, check_antlr_version, dir_latex_antlr
+
+
+# These LaTeX strings should parse to the corresponding SymPy expression
+GOOD_PAIRS = [
+    (r"0", 0),
+    (r"1", 1),
+    (r"-3.14", -3.14),
+    (r"(-7.13)(1.5)", _Mul(-7.13, 1.5)),
+    (r"x", x),
+    (r"2x", 2*x),
+    (r"x^2", x**2),
+    (r"x^\frac{1}{2}", _Pow(x, _Pow(2, -1))),
+    (r"x^{3 + 1}", x**_Add(3, 1)),
+    (r"-c", -c),
+    (r"a \cdot b", a * b),
+    (r"a / b", a / b),
+    (r"a \div b", a / b),
+    (r"a + b", a + b),
+    (r"a + b - a", _Add(a+b, -a)),
+    (r"a^2 + b^2 = c^2", Eq(a**2 + b**2, c**2)),
+    (r"(x + y) z", _Mul(_Add(x, y), z)),
+    (r"a'b+ab'", _Add(_Mul(Symbol("a'"), b), _Mul(a, Symbol("b'")))),
+    (r"y''_1", Symbol("y_{1}''")),
+    (r"y_1''", Symbol("y_{1}''")),
+    (r"\left(x + y\right) z", _Mul(_Add(x, y), z)),
+    (r"\left( x + y\right ) z", _Mul(_Add(x, y), z)),
+    (r"\left(  x + y\right ) z", _Mul(_Add(x, y), z)),
+    (r"\left[x + y\right] z", _Mul(_Add(x, y), z)),
+    (r"\left\{x + y\right\} z", _Mul(_Add(x, y), z)),
+    (r"1+1", _Add(1, 1)),
+    (r"0+1", _Add(0, 1)),
+    (r"1*2", _Mul(1, 2)),
+    (r"0*1", _Mul(0, 1)),
+    (r"1 \times 2 ", _Mul(1, 2)),
+    (r"x = y", Eq(x, y)),
+    (r"x \neq y", Ne(x, y)),
+    (r"x < y", Lt(x, y)),
+    (r"x > y", Gt(x, y)),
+    (r"x \leq y", Le(x, y)),
+    (r"x \geq y", Ge(x, y)),
+    (r"x \le y", Le(x, y)),
+    (r"x \ge y", Ge(x, y)),
+    (r"\lfloor x \rfloor", floor(x)),
+    (r"\lceil x \rceil", ceiling(x)),
+    (r"\langle x |", Bra('x')),
+    (r"| x \rangle", Ket('x')),
+    (r"\sin \theta", sin(theta)),
+    (r"\sin(\theta)", sin(theta)),
+    (r"\sin^{-1} a", asin(a)),
+    (r"\sin a \cos b", _Mul(sin(a), cos(b))),
+    (r"\sin \cos \theta", sin(cos(theta))),
+    (r"\sin(\cos \theta)", sin(cos(theta))),
+    (r"\frac{a}{b}", a / b),
+    (r"\dfrac{a}{b}", a / b),
+    (r"\tfrac{a}{b}", a / b),
+    (r"\frac12", _Pow(2, -1)),
+    (r"\frac12y", _Mul(_Pow(2, -1), y)),
+    (r"\frac1234", _Mul(_Pow(2, -1), 34)),
+    (r"\frac2{3}", _Mul(2, _Pow(3, -1))),
+    (r"\frac{\sin{x}}2", _Mul(sin(x), _Pow(2, -1))),
+    (r"\frac{a + b}{c}", _Mul(a + b, _Pow(c, -1))),
+    (r"\frac{7}{3}", _Mul(7, _Pow(3, -1))),
+    (r"(\csc x)(\sec y)", csc(x)*sec(y)),
+    (r"\lim_{x \to 3} a", Limit(a, x, 3, dir='+-')),
+    (r"\lim_{x \rightarrow 3} a", Limit(a, x, 3, dir='+-')),
+    (r"\lim_{x \Rightarrow 3} a", Limit(a, x, 3, dir='+-')),
+    (r"\lim_{x \longrightarrow 3} a", Limit(a, x, 3, dir='+-')),
+    (r"\lim_{x \Longrightarrow 3} a", Limit(a, x, 3, dir='+-')),
+    (r"\lim_{x \to 3^{+}} a", Limit(a, x, 3, dir='+')),
+    (r"\lim_{x \to 3^{-}} a", Limit(a, x, 3, dir='-')),
+    (r"\lim_{x \to 3^+} a", Limit(a, x, 3, dir='+')),
+    (r"\lim_{x \to 3^-} a", Limit(a, x, 3, dir='-')),
+    (r"\infty", oo),
+    (r"\lim_{x \to \infty} \frac{1}{x}", Limit(_Pow(x, -1), x, oo)),
+    (r"\frac{d}{dx} x", Derivative(x, x)),
+    (r"\frac{d}{dt} x", Derivative(x, t)),
+    (r"f(x)", f(x)),
+    (r"f(x, y)", f(x, y)),
+    (r"f(x, y, z)", f(x, y, z)),
+    (r"f'_1(x)", Function("f_{1}'")(x)),
+    (r"f_{1}''(x+y)", Function("f_{1}''")(x+y)),
+    (r"\frac{d f(x)}{dx}", Derivative(f(x), x)),
+    (r"\frac{d\theta(x)}{dx}", Derivative(Function('theta')(x), x)),
+    (r"x \neq y", Unequality(x, y)),
+    (r"|x|", _Abs(x)),
+    (r"||x||", _Abs(Abs(x))),
+    (r"|x||y|", _Abs(x)*_Abs(y)),
+    (r"||x||y||", _Abs(_Abs(x)*_Abs(y))),
+    (r"\pi^{|xy|}", Symbol('pi')**_Abs(x*y)),
+    (r"\int x dx", Integral(x, x)),
+    (r"\int x d\theta", Integral(x, theta)),
+    (r"\int (x^2 - y)dx", Integral(x**2 - y, x)),
+    (r"\int x + a dx", Integral(_Add(x, a), x)),
+    (r"\int da", Integral(1, a)),
+    (r"\int_0^7 dx", Integral(1, (x, 0, 7))),
+    (r"\int\limits_{0}^{1} x dx", Integral(x, (x, 0, 1))),
+    (r"\int_a^b x dx", Integral(x, (x, a, b))),
+    (r"\int^b_a x dx", Integral(x, (x, a, b))),
+    (r"\int_{a}^b x dx", Integral(x, (x, a, b))),
+    (r"\int^{b}_a x dx", Integral(x, (x, a, b))),
+    (r"\int_{a}^{b} x dx", Integral(x, (x, a, b))),
+    (r"\int^{b}_{a} x dx", Integral(x, (x, a, b))),
+    (r"\int_{f(a)}^{f(b)} f(z) dz", Integral(f(z), (z, f(a), f(b)))),
+    (r"\int (x+a)", Integral(_Add(x, a), x)),
+    (r"\int a + b + c dx", Integral(_Add(_Add(a, b), c), x)),
+    (r"\int \frac{dz}{z}", Integral(Pow(z, -1), z)),
+    (r"\int \frac{3 dz}{z}", Integral(3*Pow(z, -1), z)),
+    (r"\int \frac{1}{x} dx", Integral(Pow(x, -1), x)),
+    (r"\int \frac{1}{a} + \frac{1}{b} dx",
+     Integral(_Add(_Pow(a, -1), Pow(b, -1)), x)),
+    (r"\int \frac{3 \cdot d\theta}{\theta}",
+     Integral(3*_Pow(theta, -1), theta)),
+    (r"\int \frac{1}{x} + 1 dx", Integral(_Add(_Pow(x, -1), 1), x)),
+    (r"x_0", Symbol('x_{0}')),
+    (r"x_{1}", Symbol('x_{1}')),
+    (r"x_a", Symbol('x_{a}')),
+    (r"x_{b}", Symbol('x_{b}')),
+    (r"h_\theta", Symbol('h_{theta}')),
+    (r"h_{\theta}", Symbol('h_{theta}')),
+    (r"h_{\theta}(x_0, x_1)",
+     Function('h_{theta}')(Symbol('x_{0}'), Symbol('x_{1}'))),
+    (r"x!", _factorial(x)),
+    (r"100!", _factorial(100)),
+    (r"\theta!", _factorial(theta)),
+    (r"(x + 1)!", _factorial(_Add(x, 1))),
+    (r"(x!)!", _factorial(_factorial(x))),
+    (r"x!!!", _factorial(_factorial(_factorial(x)))),
+    (r"5!7!", _Mul(_factorial(5), _factorial(7))),
+    (r"\sqrt{x}", sqrt(x)),
+    (r"\sqrt{x + b}", sqrt(_Add(x, b))),
+    (r"\sqrt[3]{\sin x}", root(sin(x), 3)),
+    (r"\sqrt[y]{\sin x}", root(sin(x), y)),
+    (r"\sqrt[\theta]{\sin x}", root(sin(x), theta)),
+    (r"\sqrt{\frac{12}{6}}", _Sqrt(_Mul(12, _Pow(6, -1)))),
+    (r"\overline{z}", _Conjugate(z)),
+    (r"\overline{\overline{z}}", _Conjugate(_Conjugate(z))),
+    (r"\overline{x + y}", _Conjugate(_Add(x, y))),
+    (r"\overline{x} + \overline{y}", _Conjugate(x) + _Conjugate(y)),
+    (r"x < y", StrictLessThan(x, y)),
+    (r"x \leq y", LessThan(x, y)),
+    (r"x > y", StrictGreaterThan(x, y)),
+    (r"x \geq y", GreaterThan(x, y)),
+    (r"\mathit{x}", Symbol('x')),
+    (r"\mathit{test}", Symbol('test')),
+    (r"\mathit{TEST}", Symbol('TEST')),
+    (r"\mathit{HELLO world}", Symbol('HELLO world')),
+    (r"\sum_{k = 1}^{3} c", Sum(c, (k, 1, 3))),
+    (r"\sum_{k = 1}^3 c", Sum(c, (k, 1, 3))),
+    (r"\sum^{3}_{k = 1} c", Sum(c, (k, 1, 3))),
+    (r"\sum^3_{k = 1} c", Sum(c, (k, 1, 3))),
+    (r"\sum_{k = 1}^{10} k^2", Sum(k**2, (k, 1, 10))),
+    (r"\sum_{n = 0}^{\infty} \frac{1}{n!}",
+     Sum(_Pow(_factorial(n), -1), (n, 0, oo))),
+    (r"\prod_{a = b}^{c} x", Product(x, (a, b, c))),
+    (r"\prod_{a = b}^c x", Product(x, (a, b, c))),
+    (r"\prod^{c}_{a = b} x", Product(x, (a, b, c))),
+    (r"\prod^c_{a = b} x", Product(x, (a, b, c))),
+    (r"\exp x", _exp(x)),
+    (r"\exp(x)", _exp(x)),
+    (r"\lg x", _log(x, 10)),
+    (r"\ln x", _log(x, E)),
+    (r"\ln xy", _log(x*y, E)),
+    (r"\log x", _log(x, E)),
+    (r"\log xy", _log(x*y, E)),
+    (r"\log_{2} x", _log(x, 2)),
+    (r"\log_{a} x", _log(x, a)),
+    (r"\log_{11} x", _log(x, 11)),
+    (r"\log_{a^2} x", _log(x, _Pow(a, 2))),
+    (r"[x]", x),
+    (r"[a + b]", _Add(a, b)),
+    (r"\frac{d}{dx} [ \tan x ]", Derivative(tan(x), x)),
+    (r"\binom{n}{k}", _binomial(n, k)),
+    (r"\tbinom{n}{k}", _binomial(n, k)),
+    (r"\dbinom{n}{k}", _binomial(n, k)),
+    (r"\binom{n}{0}", _binomial(n, 0)),
+    (r"x^\binom{n}{k}", _Pow(x, _binomial(n, k))),
+    (r"a \, b", _Mul(a, b)),
+    (r"a \thinspace b", _Mul(a, b)),
+    (r"a \: b", _Mul(a, b)),
+    (r"a \medspace b", _Mul(a, b)),
+    (r"a \; b", _Mul(a, b)),
+    (r"a \thickspace b", _Mul(a, b)),
+    (r"a \quad b", _Mul(a, b)),
+    (r"a \qquad b", _Mul(a, b)),
+    (r"a \! b", _Mul(a, b)),
+    (r"a \negthinspace b", _Mul(a, b)),
+    (r"a \negmedspace b", _Mul(a, b)),
+    (r"a \negthickspace b", _Mul(a, b)),
+    (r"\int x \, dx", Integral(x, x)),
+    (r"\log_2 x", _log(x, 2)),
+    (r"\log_a x", _log(x, a)),
+    (r"5^0 - 4^0", _Add(_Pow(5, 0), _Mul(-1, _Pow(4, 0)))),
+    (r"3x - 1", _Add(_Mul(3, x), -1))
+]
+
+
+def test_parseable():
+    from sympy.parsing.latex import parse_latex
+    for latex_str, sympy_expr in GOOD_PAIRS:
+        assert parse_latex(latex_str) == sympy_expr, latex_str
+
+# These bad LaTeX strings should raise a LaTeXParsingError when parsed
+BAD_STRINGS = [
+    r"(",
+    r")",
+    r"\frac{d}{dx}",
+    r"(\frac{d}{dx})",
+    r"\sqrt{}",
+    r"\sqrt",
+    r"\overline{}",
+    r"\overline",
+    r"{",
+    r"}",
+    r"\mathit{x + y}",
+    r"\mathit{21}",
+    r"\frac{2}{}",
+    r"\frac{}{2}",
+    r"\int",
+    r"!",
+    r"!0",
+    r"_",
+    r"^",
+    r"|",
+    r"||x|",
+    r"()",
+    r"((((((((((((((((()))))))))))))))))",
+    r"-",
+    r"\frac{d}{dx} + \frac{d}{dt}",
+    r"f(x,,y)",
+    r"f(x,y,",
+    r"\sin^x",
+    r"\cos^2",
+    r"@",
+    r"#",
+    r"$",
+    r"%",
+    r"&",
+    r"*",
+    r"" "\\",
+    r"~",
+    r"\frac{(2 + x}{1 - x)}",
+]
+
+def test_not_parseable():
+    from sympy.parsing.latex import parse_latex, LaTeXParsingError
+    for latex_str in BAD_STRINGS:
+        with raises(LaTeXParsingError):
+            parse_latex(latex_str)
+
+# At time of migration from latex2sympy, should fail but doesn't
+FAILING_BAD_STRINGS = [
+    r"\cos 1 \cos",
+    r"f(,",
+    r"f()",
+    r"a \div \div b",
+    r"a \cdot \cdot b",
+    r"a // b",
+    r"a +",
+    r"1.1.1",
+    r"1 +",
+    r"a / b /",
+]
+
+@XFAIL
+def test_failing_not_parseable():
+    from sympy.parsing.latex import parse_latex, LaTeXParsingError
+    for latex_str in FAILING_BAD_STRINGS:
+        with raises(LaTeXParsingError):
+            parse_latex(latex_str)
+
+# In strict mode, FAILING_BAD_STRINGS would fail
+def test_strict_mode():
+    from sympy.parsing.latex import parse_latex, LaTeXParsingError
+    for latex_str in FAILING_BAD_STRINGS:
+        with raises(LaTeXParsingError):
+            parse_latex(latex_str, strict=True)

backend_service/venv/lib/python3.13/site-packages/sympy/parsing/tests/test_latex_deps.py

@@ -0,0 +1,16 @@
+from sympy.external import import_module
+from sympy.testing.pytest import ignore_warnings, raises
+
+antlr4 = import_module("antlr4", warn_not_installed=False)
+
+# disable tests if antlr4-python3-runtime is not present
+if antlr4:
+    disabled = True
+
+
+def test_no_import():
+    from sympy.parsing.latex import parse_latex
+
+    with ignore_warnings(UserWarning):
+        with raises(ImportError):
+            parse_latex('1 + 1')

backend_service/venv/lib/python3.13/site-packages/sympy/parsing/tests/test_latex_lark.py

@@ -0,0 +1,872 @@
+from sympy.testing.pytest import XFAIL
+from sympy.parsing.latex.lark import parse_latex_lark
+from sympy.external import import_module
+
+from sympy.concrete.products import Product
+from sympy.concrete.summations import Sum
+from sympy.core.function import Derivative, Function
+from sympy.core.numbers import E, oo, Rational
+from sympy.core.power import Pow
+from sympy.core.parameters import evaluate
+from sympy.core.relational import GreaterThan, LessThan, StrictGreaterThan, StrictLessThan, Unequality
+from sympy.core.symbol import Symbol
+from sympy.functions.combinatorial.factorials import binomial, factorial
+from sympy.functions.elementary.complexes import Abs, conjugate
+from sympy.functions.elementary.exponential import exp, log
+from sympy.functions.elementary.integers import ceiling, floor
+from sympy.functions.elementary.miscellaneous import root, sqrt, Min, Max
+from sympy.functions.elementary.trigonometric import asin, cos, csc, sec, sin, tan
+from sympy.integrals.integrals import Integral
+from sympy.series.limits import Limit
+from sympy import Matrix, MatAdd, MatMul, Transpose, Trace
+from sympy import I
+
+from sympy.core.relational import Eq, Ne, Lt, Le, Gt, Ge
+from sympy.physics.quantum import Bra, Ket, InnerProduct
+from sympy.abc import x, y, z, a, b, c, d, t, k, n
+
+from .test_latex import theta, f, _Add, _Mul, _Pow, _Sqrt, _Conjugate, _Abs, _factorial, _exp, _binomial
+
+lark = import_module("lark")
+
+# disable tests if lark is not present
+disabled = lark is None
+
+# shorthand definitions that are only needed for the Lark LaTeX parser
+def _Min(*args):
+    return Min(*args, evaluate=False)
+
+
+def _Max(*args):
+    return Max(*args, evaluate=False)
+
+
+def _log(a, b=E):
+    if b == E:
+        return log(a, evaluate=False)
+    else:
+        return log(a, b, evaluate=False)
+
+
+def _MatAdd(a, b):
+    return MatAdd(a, b, evaluate=False)
+
+
+def _MatMul(a, b):
+    return MatMul(a, b, evaluate=False)
+
+
+# These LaTeX strings should parse to the corresponding SymPy expression
+SYMBOL_EXPRESSION_PAIRS = [
+    (r"x_0", Symbol('x_{0}')),
+    (r"x_{1}", Symbol('x_{1}')),
+    (r"x_a", Symbol('x_{a}')),
+    (r"x_{b}", Symbol('x_{b}')),
+    (r"h_\theta", Symbol('h_{theta}')),
+    (r"h_{\theta}", Symbol('h_{theta}')),
+    (r"y''_1", Symbol("y''_{1}")),
+    (r"y_1''", Symbol("y_{1}''")),
+    (r"\mathit{x}", Symbol('x')),
+    (r"\mathit{test}", Symbol('test')),
+    (r"\mathit{TEST}", Symbol('TEST')),
+    (r"\mathit{HELLO world}", Symbol('HELLO world')),
+    (r"a'", Symbol("a'")),
+    (r"a''", Symbol("a''")),
+    (r"\alpha'", Symbol("alpha'")),
+    (r"\alpha''", Symbol("alpha''")),
+    (r"a_b", Symbol("a_{b}")),
+    (r"a_b'", Symbol("a_{b}'")),
+    (r"a'_b", Symbol("a'_{b}")),
+    (r"a'_b'", Symbol("a'_{b}'")),
+    (r"a_{b'}", Symbol("a_{b'}")),
+    (r"a_{b'}'", Symbol("a_{b'}'")),
+    (r"a'_{b'}", Symbol("a'_{b'}")),
+    (r"a'_{b'}'", Symbol("a'_{b'}'")),
+    (r"\mathit{foo}'", Symbol("foo'")),
+    (r"\mathit{foo'}", Symbol("foo'")),
+    (r"\mathit{foo'}'", Symbol("foo''")),
+    (r"a_b''", Symbol("a_{b}''")),
+    (r"a''_b", Symbol("a''_{b}")),
+    (r"a''_b'''", Symbol("a''_{b}'''")),
+    (r"a_{b''}", Symbol("a_{b''}")),
+    (r"a_{b''}''", Symbol("a_{b''}''")),
+    (r"a''_{b''}", Symbol("a''_{b''}")),
+    (r"a''_{b''}'''", Symbol("a''_{b''}'''")),
+    (r"\mathit{foo}''", Symbol("foo''")),
+    (r"\mathit{foo''}", Symbol("foo''")),
+    (r"\mathit{foo''}'''", Symbol("foo'''''")),
+    (r"a_\alpha", Symbol("a_{alpha}")),
+    (r"a_\alpha'", Symbol("a_{alpha}'")),
+    (r"a'_\alpha", Symbol("a'_{alpha}")),
+    (r"a'_\alpha'", Symbol("a'_{alpha}'")),
+    (r"a_{\alpha'}", Symbol("a_{alpha'}")),
+    (r"a_{\alpha'}'", Symbol("a_{alpha'}'")),
+    (r"a'_{\alpha'}", Symbol("a'_{alpha'}")),
+    (r"a'_{\alpha'}'", Symbol("a'_{alpha'}'")),
+    (r"a_\alpha''", Symbol("a_{alpha}''")),
+    (r"a''_\alpha", Symbol("a''_{alpha}")),
+    (r"a''_\alpha'''", Symbol("a''_{alpha}'''")),
+    (r"a_{\alpha''}", Symbol("a_{alpha''}")),
+    (r"a_{\alpha''}''", Symbol("a_{alpha''}''")),
+    (r"a''_{\alpha''}", Symbol("a''_{alpha''}")),
+    (r"a''_{\alpha''}'''", Symbol("a''_{alpha''}'''")),
+    (r"\alpha_b", Symbol("alpha_{b}")),
+    (r"\alpha_b'", Symbol("alpha_{b}'")),
+    (r"\alpha'_b", Symbol("alpha'_{b}")),
+    (r"\alpha'_b'", Symbol("alpha'_{b}'")),
+    (r"\alpha_{b'}", Symbol("alpha_{b'}")),
+    (r"\alpha_{b'}'", Symbol("alpha_{b'}'")),
+    (r"\alpha'_{b'}", Symbol("alpha'_{b'}")),
+    (r"\alpha'_{b'}'", Symbol("alpha'_{b'}'")),
+    (r"\alpha_b''", Symbol("alpha_{b}''")),
+    (r"\alpha''_b", Symbol("alpha''_{b}")),
+    (r"\alpha''_b'''", Symbol("alpha''_{b}'''")),
+    (r"\alpha_{b''}", Symbol("alpha_{b''}")),
+    (r"\alpha_{b''}''", Symbol("alpha_{b''}''")),
+    (r"\alpha''_{b''}", Symbol("alpha''_{b''}")),
+    (r"\alpha''_{b''}'''", Symbol("alpha''_{b''}'''")),
+    (r"\alpha_\beta", Symbol("alpha_{beta}")),
+    (r"\alpha_{\beta}", Symbol("alpha_{beta}")),
+    (r"\alpha_{\beta'}", Symbol("alpha_{beta'}")),
+    (r"\alpha_{\beta''}", Symbol("alpha_{beta''}")),
+    (r"\alpha'_\beta", Symbol("alpha'_{beta}")),
+    (r"\alpha'_{\beta}", Symbol("alpha'_{beta}")),
+    (r"\alpha'_{\beta'}", Symbol("alpha'_{beta'}")),
+    (r"\alpha'_{\beta''}", Symbol("alpha'_{beta''}")),
+    (r"\alpha''_\beta", Symbol("alpha''_{beta}")),
+    (r"\alpha''_{\beta}", Symbol("alpha''_{beta}")),
+    (r"\alpha''_{\beta'}", Symbol("alpha''_{beta'}")),
+    (r"\alpha''_{\beta''}", Symbol("alpha''_{beta''}")),
+    (r"\alpha_\beta'", Symbol("alpha_{beta}'")),
+    (r"\alpha_{\beta}'", Symbol("alpha_{beta}'")),
+    (r"\alpha_{\beta'}'", Symbol("alpha_{beta'}'")),
+    (r"\alpha_{\beta''}'", Symbol("alpha_{beta''}'")),
+    (r"\alpha'_\beta'", Symbol("alpha'_{beta}'")),
+    (r"\alpha'_{\beta}'", Symbol("alpha'_{beta}'")),
+    (r"\alpha'_{\beta'}'", Symbol("alpha'_{beta'}'")),
+    (r"\alpha'_{\beta''}'", Symbol("alpha'_{beta''}'")),
+    (r"\alpha''_\beta'", Symbol("alpha''_{beta}'")),
+    (r"\alpha''_{\beta}'", Symbol("alpha''_{beta}'")),
+    (r"\alpha''_{\beta'}'", Symbol("alpha''_{beta'}'")),
+    (r"\alpha''_{\beta''}'", Symbol("alpha''_{beta''}'")),
+    (r"\alpha_\beta''", Symbol("alpha_{beta}''")),
+    (r"\alpha_{\beta}''", Symbol("alpha_{beta}''")),
+    (r"\alpha_{\beta'}''", Symbol("alpha_{beta'}''")),
+    (r"\alpha_{\beta''}''", Symbol("alpha_{beta''}''")),
+    (r"\alpha'_\beta''", Symbol("alpha'_{beta}''")),
+    (r"\alpha'_{\beta}''", Symbol("alpha'_{beta}''")),
+    (r"\alpha'_{\beta'}''", Symbol("alpha'_{beta'}''")),
+    (r"\alpha'_{\beta''}''", Symbol("alpha'_{beta''}''")),
+    (r"\alpha''_\beta''", Symbol("alpha''_{beta}''")),
+    (r"\alpha''_{\beta}''", Symbol("alpha''_{beta}''")),
+    (r"\alpha''_{\beta'}''", Symbol("alpha''_{beta'}''")),
+    (r"\alpha''_{\beta''}''", Symbol("alpha''_{beta''}''"))
+
+]
+
+UNEVALUATED_SIMPLE_EXPRESSION_PAIRS = [
+    (r"0", 0),
+    (r"1", 1),
+    (r"-3.14", -3.14),
+    (r"(-7.13)(1.5)", _Mul(-7.13, 1.5)),
+    (r"1+1", _Add(1, 1)),
+    (r"0+1", _Add(0, 1)),
+    (r"1*2", _Mul(1, 2)),
+    (r"0*1", _Mul(0, 1)),
+    (r"x", x),
+    (r"2x", 2 * x),
+    (r"3x - 1", _Add(_Mul(3, x), -1)),
+    (r"-c", -c),
+    (r"\infty", oo),
+    (r"a \cdot b", a * b),
+    (r"1 \times 2 ", _Mul(1, 2)),
+    (r"a / b", a / b),
+    (r"a \div b", a / b),
+    (r"a + b", a + b),
+    (r"a + b - a", _Add(a + b, -a)),
+    (r"(x + y) z", _Mul(_Add(x, y), z)),
+    (r"a'b+ab'", _Add(_Mul(Symbol("a'"), b), _Mul(a, Symbol("b'"))))
+]
+
+EVALUATED_SIMPLE_EXPRESSION_PAIRS = [
+    (r"(-7.13)(1.5)", -10.695),
+    (r"1+1", 2),
+    (r"0+1", 1),
+    (r"1*2", 2),
+    (r"0*1", 0),
+    (r"2x", 2 * x),
+    (r"3x - 1", 3 * x - 1),
+    (r"-c", -c),
+    (r"a \cdot b", a * b),
+    (r"1 \times 2 ", 2),
+    (r"a / b", a / b),
+    (r"a \div b", a / b),
+    (r"a + b", a + b),
+    (r"a + b - a", b),
+    (r"(x + y) z", (x + y) * z),
+]
+
+UNEVALUATED_FRACTION_EXPRESSION_PAIRS = [
+    (r"\frac{a}{b}", a / b),
+    (r"\dfrac{a}{b}", a / b),
+    (r"\tfrac{a}{b}", a / b),
+    (r"\frac12", _Mul(1, _Pow(2, -1))),
+    (r"\frac12y", _Mul(_Mul(1, _Pow(2, -1)), y)),
+    (r"\frac1234", _Mul(_Mul(1, _Pow(2, -1)), 34)),
+    (r"\frac2{3}", _Mul(2, _Pow(3, -1))),
+    (r"\frac{a + b}{c}", _Mul(a + b, _Pow(c, -1))),
+    (r"\frac{7}{3}", _Mul(7, _Pow(3, -1)))
+]
+
+EVALUATED_FRACTION_EXPRESSION_PAIRS = [
+    (r"\frac{a}{b}", a / b),
+    (r"\dfrac{a}{b}", a / b),
+    (r"\tfrac{a}{b}", a / b),
+    (r"\frac12", Rational(1, 2)),
+    (r"\frac12y", y / 2),
+    (r"\frac1234", 17),
+    (r"\frac2{3}", Rational(2, 3)),
+    (r"\frac{a + b}{c}", (a + b) / c),
+    (r"\frac{7}{3}", Rational(7, 3))
+]
+
+RELATION_EXPRESSION_PAIRS = [
+    (r"x = y", Eq(x, y)),
+    (r"x \neq y", Ne(x, y)),
+    (r"x < y", Lt(x, y)),
+    (r"x > y", Gt(x, y)),
+    (r"x \leq y", Le(x, y)),
+    (r"x \geq y", Ge(x, y)),
+    (r"x \le y", Le(x, y)),
+    (r"x \ge y", Ge(x, y)),
+    (r"x < y", StrictLessThan(x, y)),
+    (r"x \leq y", LessThan(x, y)),
+    (r"x > y", StrictGreaterThan(x, y)),
+    (r"x \geq y", GreaterThan(x, y)),
+    (r"x \neq y", Unequality(x, y)), # same as 2nd one in the list
+    (r"a^2 + b^2 = c^2", Eq(a**2 + b**2, c**2))
+]
+
+UNEVALUATED_POWER_EXPRESSION_PAIRS = [
+    (r"x^2", x ** 2),
+    (r"x^\frac{1}{2}", _Pow(x, _Mul(1, _Pow(2, -1)))),
+    (r"x^{3 + 1}", x ** _Add(3, 1)),
+    (r"\pi^{|xy|}", Symbol('pi') ** _Abs(x * y)),
+    (r"5^0 - 4^0", _Add(_Pow(5, 0), _Mul(-1, _Pow(4, 0))))
+]
+
+EVALUATED_POWER_EXPRESSION_PAIRS = [
+    (r"x^2", x ** 2),
+    (r"x^\frac{1}{2}", sqrt(x)),
+    (r"x^{3 + 1}", x ** 4),
+    (r"\pi^{|xy|}", Symbol('pi') ** _Abs(x * y)),
+    (r"5^0 - 4^0", 0)
+]
+
+UNEVALUATED_INTEGRAL_EXPRESSION_PAIRS = [
+    (r"\int x dx", Integral(_Mul(1, x), x)),
+    (r"\int x \, dx", Integral(_Mul(1, x), x)),
+    (r"\int x d\theta", Integral(_Mul(1, x), theta)),
+    (r"\int (x^2 - y)dx", Integral(_Mul(1, x ** 2 - y), x)),
+    (r"\int x + a dx", Integral(_Mul(1, _Add(x, a)), x)),
+    (r"\int da", Integral(_Mul(1, 1), a)),
+    (r"\int_0^7 dx", Integral(_Mul(1, 1), (x, 0, 7))),
+    (r"\int\limits_{0}^{1} x dx", Integral(_Mul(1, x), (x, 0, 1))),
+    (r"\int_a^b x dx", Integral(_Mul(1, x), (x, a, b))),
+    (r"\int^b_a x dx", Integral(_Mul(1, x), (x, a, b))),
+    (r"\int_{a}^b x dx", Integral(_Mul(1, x), (x, a, b))),
+    (r"\int^{b}_a x dx", Integral(_Mul(1, x), (x, a, b))),
+    (r"\int_{a}^{b} x dx", Integral(_Mul(1, x), (x, a, b))),
+    (r"\int^{b}_{a} x dx", Integral(_Mul(1, x), (x, a, b))),
+    (r"\int_{f(a)}^{f(b)} f(z) dz", Integral(f(z), (z, f(a), f(b)))),
+    (r"\int a + b + c dx", Integral(_Mul(1, _Add(_Add(a, b), c)), x)),
+    (r"\int \frac{dz}{z}", Integral(_Mul(1, _Mul(1, Pow(z, -1))), z)),
+    (r"\int \frac{3 dz}{z}", Integral(_Mul(1, _Mul(3, _Pow(z, -1))), z)),
+    (r"\int \frac{1}{x} dx", Integral(_Mul(1, _Mul(1, Pow(x, -1))), x)),
+    (r"\int \frac{1}{a} + \frac{1}{b} dx",
+     Integral(_Mul(1, _Add(_Mul(1, _Pow(a, -1)), _Mul(1, Pow(b, -1)))), x)),
+    (r"\int \frac{1}{x} + 1 dx", Integral(_Mul(1, _Add(_Mul(1, _Pow(x, -1)), 1)), x))
+]
+
+EVALUATED_INTEGRAL_EXPRESSION_PAIRS = [
+    (r"\int x dx", Integral(x, x)),
+    (r"\int x \, dx", Integral(x, x)),
+    (r"\int x d\theta", Integral(x, theta)),
+    (r"\int (x^2 - y)dx", Integral(x ** 2 - y, x)),
+    (r"\int x + a dx", Integral(x + a, x)),
+    (r"\int da", Integral(1, a)),
+    (r"\int_0^7 dx", Integral(1, (x, 0, 7))),
+    (r"\int\limits_{0}^{1} x dx", Integral(x, (x, 0, 1))),
+    (r"\int_a^b x dx", Integral(x, (x, a, b))),
+    (r"\int^b_a x dx", Integral(x, (x, a, b))),
+    (r"\int_{a}^b x dx", Integral(x, (x, a, b))),
+    (r"\int^{b}_a x dx", Integral(x, (x, a, b))),
+    (r"\int_{a}^{b} x dx", Integral(x, (x, a, b))),
+    (r"\int^{b}_{a} x dx", Integral(x, (x, a, b))),
+    (r"\int_{f(a)}^{f(b)} f(z) dz", Integral(f(z), (z, f(a), f(b)))),
+    (r"\int a + b + c dx", Integral(a + b + c, x)),
+    (r"\int \frac{dz}{z}", Integral(Pow(z, -1), z)),
+    (r"\int \frac{3 dz}{z}", Integral(3 * Pow(z, -1), z)),
+    (r"\int \frac{1}{x} dx", Integral(1 / x, x)),
+    (r"\int \frac{1}{a} + \frac{1}{b} dx", Integral(1 / a + 1 / b, x)),
+    (r"\int \frac{1}{a} - \frac{1}{b} dx", Integral(1 / a - 1 / b, x)),
+    (r"\int \frac{1}{x} + 1 dx", Integral(1 / x + 1, x))
+]
+
+DERIVATIVE_EXPRESSION_PAIRS = [
+    (r"\frac{d}{dx} x", Derivative(x, x)),
+    (r"\frac{d}{dt} x", Derivative(x, t)),
+    (r"\frac{d}{dx} ( \tan x )", Derivative(tan(x), x)),
+    (r"\frac{d f(x)}{dx}", Derivative(f(x), x)),
+    (r"\frac{d\theta(x)}{dx}", Derivative(Function('theta')(x), x))
+]
+
+TRIGONOMETRIC_EXPRESSION_PAIRS = [
+    (r"\sin \theta", sin(theta)),
+    (r"\sin(\theta)", sin(theta)),
+    (r"\sin^{-1} a", asin(a)),
+    (r"\sin a \cos b", _Mul(sin(a), cos(b))),
+    (r"\sin \cos \theta", sin(cos(theta))),
+    (r"\sin(\cos \theta)", sin(cos(theta))),
+    (r"(\csc x)(\sec y)", csc(x) * sec(y)),
+    (r"\frac{\sin{x}}2", _Mul(sin(x), _Pow(2, -1)))
+]
+
+UNEVALUATED_LIMIT_EXPRESSION_PAIRS = [
+    (r"\lim_{x \to 3} a", Limit(a, x, 3, dir="+-")),
+    (r"\lim_{x \rightarrow 3} a", Limit(a, x, 3, dir="+-")),
+    (r"\lim_{x \Rightarrow 3} a", Limit(a, x, 3, dir="+-")),
+    (r"\lim_{x \longrightarrow 3} a", Limit(a, x, 3, dir="+-")),
+    (r"\lim_{x \Longrightarrow 3} a", Limit(a, x, 3, dir="+-")),
+    (r"\lim_{x \to 3^{+}} a", Limit(a, x, 3, dir="+")),
+    (r"\lim_{x \to 3^{-}} a", Limit(a, x, 3, dir="-")),
+    (r"\lim_{x \to 3^+} a", Limit(a, x, 3, dir="+")),
+    (r"\lim_{x \to 3^-} a", Limit(a, x, 3, dir="-")),
+    (r"\lim_{x \to \infty} \frac{1}{x}", Limit(_Mul(1, _Pow(x, -1)), x, oo))
+]
+
+EVALUATED_LIMIT_EXPRESSION_PAIRS = [
+    (r"\lim_{x \to \infty} \frac{1}{x}", Limit(1 / x, x, oo))
+]
+
+UNEVALUATED_SQRT_EXPRESSION_PAIRS = [
+    (r"\sqrt{x}", sqrt(x)),
+    (r"\sqrt{x + b}", sqrt(_Add(x, b))),
+    (r"\sqrt[3]{\sin x}", _Pow(sin(x), _Pow(3, -1))),
+    # the above test needed to be handled differently than the ones below because root
+    # acts differently if its second argument is a number
+    (r"\sqrt[y]{\sin x}", root(sin(x), y)),
+    (r"\sqrt[\theta]{\sin x}", root(sin(x), theta)),
+    (r"\sqrt{\frac{12}{6}}", _Sqrt(_Mul(12, _Pow(6, -1))))
+]
+
+EVALUATED_SQRT_EXPRESSION_PAIRS = [
+    (r"\sqrt{x}", sqrt(x)),
+    (r"\sqrt{x + b}", sqrt(x + b)),
+    (r"\sqrt[3]{\sin x}", root(sin(x), 3)),
+    (r"\sqrt[y]{\sin x}", root(sin(x), y)),
+    (r"\sqrt[\theta]{\sin x}", root(sin(x), theta)),
+    (r"\sqrt{\frac{12}{6}}", sqrt(2))
+]
+
+UNEVALUATED_FACTORIAL_EXPRESSION_PAIRS = [
+    (r"x!", _factorial(x)),
+    (r"100!", _factorial(100)),
+    (r"\theta!", _factorial(theta)),
+    (r"(x + 1)!", _factorial(_Add(x, 1))),
+    (r"(x!)!", _factorial(_factorial(x))),
+    (r"x!!!", _factorial(_factorial(_factorial(x)))),
+    (r"5!7!", _Mul(_factorial(5), _factorial(7)))
+]
+
+EVALUATED_FACTORIAL_EXPRESSION_PAIRS = [
+    (r"x!", factorial(x)),
+    (r"100!", factorial(100)),
+    (r"\theta!", factorial(theta)),
+    (r"(x + 1)!", factorial(x + 1)),
+    (r"(x!)!", factorial(factorial(x))),
+    (r"x!!!", factorial(factorial(factorial(x)))),
+    (r"5!7!", factorial(5) * factorial(7)),
+    (r"24! \times 24!", factorial(24) * factorial(24))
+]
+
+UNEVALUATED_SUM_EXPRESSION_PAIRS = [
+    (r"\sum_{k = 1}^{3} c", Sum(_Mul(1, c), (k, 1, 3))),
+    (r"\sum_{k = 1}^3 c", Sum(_Mul(1, c), (k, 1, 3))),
+    (r"\sum^{3}_{k = 1} c", Sum(_Mul(1, c), (k, 1, 3))),
+    (r"\sum^3_{k = 1} c", Sum(_Mul(1, c), (k, 1, 3))),
+    (r"\sum_{k = 1}^{10} k^2", Sum(_Mul(1, k ** 2), (k, 1, 10))),
+    (r"\sum_{n = 0}^{\infty} \frac{1}{n!}",
+     Sum(_Mul(1, _Mul(1, _Pow(_factorial(n), -1))), (n, 0, oo)))
+]
+
+EVALUATED_SUM_EXPRESSION_PAIRS = [
+    (r"\sum_{k = 1}^{3} c", Sum(c, (k, 1, 3))),
+    (r"\sum_{k = 1}^3 c", Sum(c, (k, 1, 3))),
+    (r"\sum^{3}_{k = 1} c", Sum(c, (k, 1, 3))),
+    (r"\sum^3_{k = 1} c", Sum(c, (k, 1, 3))),
+    (r"\sum_{k = 1}^{10} k^2", Sum(k ** 2, (k, 1, 10))),
+    (r"\sum_{n = 0}^{\infty} \frac{1}{n!}", Sum(1 / factorial(n), (n, 0, oo)))
+]
+
+UNEVALUATED_PRODUCT_EXPRESSION_PAIRS = [
+    (r"\prod_{a = b}^{c} x", Product(x, (a, b, c))),
+    (r"\prod_{a = b}^c x", Product(x, (a, b, c))),
+    (r"\prod^{c}_{a = b} x", Product(x, (a, b, c))),
+    (r"\prod^c_{a = b} x", Product(x, (a, b, c)))
+]
+
+APPLIED_FUNCTION_EXPRESSION_PAIRS = [
+    (r"f(x)", f(x)),
+    (r"f(x, y)", f(x, y)),
+    (r"f(x, y, z)", f(x, y, z)),
+    (r"f'_1(x)", Function("f_{1}'")(x)),
+    (r"f_{1}''(x+y)", Function("f_{1}''")(x + y)),
+    (r"h_{\theta}(x_0, x_1)",
+     Function('h_{theta}')(Symbol('x_{0}'), Symbol('x_{1}')))
+]
+
+UNEVALUATED_COMMON_FUNCTION_EXPRESSION_PAIRS = [
+    (r"|x|", _Abs(x)),
+    (r"||x||", _Abs(Abs(x))),
+    (r"|x||y|", _Abs(x) * _Abs(y)),
+    (r"||x||y||", _Abs(_Abs(x) * _Abs(y))),
+    (r"\lfloor x \rfloor", floor(x)),
+    (r"\lceil x \rceil", ceiling(x)),
+    (r"\exp x", _exp(x)),
+    (r"\exp(x)", _exp(x)),
+    (r"\lg x", _log(x, 10)),
+    (r"\ln x", _log(x)),
+    (r"\ln xy", _log(x * y)),
+    (r"\log x", _log(x)),
+    (r"\log xy", _log(x * y)),
+    (r"\log_{2} x", _log(x, 2)),
+    (r"\log_{a} x", _log(x, a)),
+    (r"\log_{11} x", _log(x, 11)),
+    (r"\log_{a^2} x", _log(x, _Pow(a, 2))),
+    (r"\log_2 x", _log(x, 2)),
+    (r"\log_a x", _log(x, a)),
+    (r"\overline{z}", _Conjugate(z)),
+    (r"\overline{\overline{z}}", _Conjugate(_Conjugate(z))),
+    (r"\overline{x + y}", _Conjugate(_Add(x, y))),
+    (r"\overline{x} + \overline{y}", _Conjugate(x) + _Conjugate(y)),
+    (r"\min(a, b)", _Min(a, b)),
+    (r"\min(a, b, c - d, xy)", _Min(a, b, c - d, x * y)),
+    (r"\max(a, b)", _Max(a, b)),
+    (r"\max(a, b, c - d, xy)", _Max(a, b, c - d, x * y)),
+    # physics things don't have an `evaluate=False` variant
+    (r"\langle x |", Bra('x')),
+    (r"| x \rangle", Ket('x')),
+    (r"\langle x | y \rangle", InnerProduct(Bra('x'), Ket('y'))),
+]
+
+EVALUATED_COMMON_FUNCTION_EXPRESSION_PAIRS = [
+    (r"|x|", Abs(x)),
+    (r"||x||", Abs(Abs(x))),
+    (r"|x||y|", Abs(x) * Abs(y)),
+    (r"||x||y||", Abs(Abs(x) * Abs(y))),
+    (r"\lfloor x \rfloor", floor(x)),
+    (r"\lceil x \rceil", ceiling(x)),
+    (r"\exp x", exp(x)),
+    (r"\exp(x)", exp(x)),
+    (r"\lg x", log(x, 10)),
+    (r"\ln x", log(x)),
+    (r"\ln xy", log(x * y)),
+    (r"\log x", log(x)),
+    (r"\log xy", log(x * y)),
+    (r"\log_{2} x", log(x, 2)),
+    (r"\log_{a} x", log(x, a)),
+    (r"\log_{11} x", log(x, 11)),
+    (r"\log_{a^2} x", log(x, _Pow(a, 2))),
+    (r"\log_2 x", log(x, 2)),
+    (r"\log_a x", log(x, a)),
+    (r"\overline{z}", conjugate(z)),
+    (r"\overline{\overline{z}}", conjugate(conjugate(z))),
+    (r"\overline{x + y}", conjugate(x + y)),
+    (r"\overline{x} + \overline{y}", conjugate(x) + conjugate(y)),
+    (r"\min(a, b)", Min(a, b)),
+    (r"\min(a, b, c - d, xy)", Min(a, b, c - d, x * y)),
+    (r"\max(a, b)", Max(a, b)),
+    (r"\max(a, b, c - d, xy)", Max(a, b, c - d, x * y)),
+    (r"\langle x |", Bra('x')),
+    (r"| x \rangle", Ket('x')),
+    (r"\langle x | y \rangle", InnerProduct(Bra('x'), Ket('y'))),
+]
+
+SPACING_RELATED_EXPRESSION_PAIRS = [
+    (r"a \, b", _Mul(a, b)),
+    (r"a \thinspace b", _Mul(a, b)),
+    (r"a \: b", _Mul(a, b)),
+    (r"a \medspace b", _Mul(a, b)),
+    (r"a \; b", _Mul(a, b)),
+    (r"a \thickspace b", _Mul(a, b)),
+    (r"a \quad b", _Mul(a, b)),
+    (r"a \qquad b", _Mul(a, b)),
+    (r"a \! b", _Mul(a, b)),
+    (r"a \negthinspace b", _Mul(a, b)),
+    (r"a \negmedspace b", _Mul(a, b)),
+    (r"a \negthickspace b", _Mul(a, b))
+]
+
+UNEVALUATED_BINOMIAL_EXPRESSION_PAIRS = [
+    (r"\binom{n}{k}", _binomial(n, k)),
+    (r"\tbinom{n}{k}", _binomial(n, k)),
+    (r"\dbinom{n}{k}", _binomial(n, k)),
+    (r"\binom{n}{0}", _binomial(n, 0)),
+    (r"x^\binom{n}{k}", _Pow(x, _binomial(n, k)))
+]
+
+EVALUATED_BINOMIAL_EXPRESSION_PAIRS = [
+    (r"\binom{n}{k}", binomial(n, k)),
+    (r"\tbinom{n}{k}", binomial(n, k)),
+    (r"\dbinom{n}{k}", binomial(n, k)),
+    (r"\binom{n}{0}", binomial(n, 0)),
+    (r"x^\binom{n}{k}", x ** binomial(n, k))
+]
+
+MISCELLANEOUS_EXPRESSION_PAIRS = [
+    (r"\left(x + y\right) z", _Mul(_Add(x, y), z)),
+    (r"\left( x + y\right ) z", _Mul(_Add(x, y), z)),
+    (r"\left(  x + y\right ) z", _Mul(_Add(x, y), z)),
+]
+
+UNEVALUATED_LITERAL_COMPLEX_NUMBER_EXPRESSION_PAIRS = [
+    (r"\imaginaryunit^2", _Pow(I, 2)),
+    (r"|\imaginaryunit|", _Abs(I)),
+    (r"\overline{\imaginaryunit}", _Conjugate(I)),
+    (r"\imaginaryunit+\imaginaryunit", _Add(I, I)),
+    (r"\imaginaryunit-\imaginaryunit", _Add(I, -I)),
+    (r"\imaginaryunit*\imaginaryunit", _Mul(I, I)),
+    (r"\imaginaryunit/\imaginaryunit", _Mul(I, _Pow(I, -1))),
+    (r"(1+\imaginaryunit)/|1+\imaginaryunit|", _Mul(_Add(1, I), _Pow(_Abs(_Add(1, I)), -1)))
+]
+
+UNEVALUATED_MATRIX_EXPRESSION_PAIRS = [
+    (r"\begin{pmatrix}a & b \\x & y\end{pmatrix}",
+     Matrix([[a, b], [x, y]])),
+    (r"\begin{pmatrix}a & b \\x & y\\\end{pmatrix}",
+     Matrix([[a, b], [x, y]])),
+    (r"\begin{bmatrix}a & b \\x & y\end{bmatrix}",
+     Matrix([[a, b], [x, y]])),
+    (r"\left(\begin{matrix}a & b \\x & y\end{matrix}\right)",
+     Matrix([[a, b], [x, y]])),
+    (r"\left[\begin{matrix}a & b \\x & y\end{matrix}\right]",
+     Matrix([[a, b], [x, y]])),
+    (r"\left[\begin{array}{cc}a & b \\x & y\end{array}\right]",
+     Matrix([[a, b], [x, y]])),
+    (r"\left(\begin{array}{cc}a & b \\x & y\end{array}\right)",
+     Matrix([[a, b], [x, y]])),
+    (r"\left( { \begin{array}{cc}a & b \\x & y\end{array} } \right)",
+     Matrix([[a, b], [x, y]])),
+    (r"+\begin{pmatrix}a & b \\x & y\end{pmatrix}",
+     Matrix([[a, b], [x, y]])),
+    ((r"\begin{pmatrix}x & y \\a & b\end{pmatrix}+"
+      r"\begin{pmatrix}a & b \\x & y\end{pmatrix}"),
+     _MatAdd(Matrix([[x, y], [a, b]]), Matrix([[a, b], [x, y]]))),
+    (r"-\begin{pmatrix}a & b \\x & y\end{pmatrix}",
+     _MatMul(-1, Matrix([[a, b], [x, y]]))),
+    ((r"\begin{pmatrix}x & y \\a & b\end{pmatrix}-"
+      r"\begin{pmatrix}a & b \\x & y\end{pmatrix}"),
+     _MatAdd(Matrix([[x, y], [a, b]]), _MatMul(-1, Matrix([[a, b], [x, y]])))),
+    ((r"\begin{pmatrix}a & b & c \\x & y & z \\a & b & c \end{pmatrix}*"
+      r"\begin{pmatrix}x & y & z \\a & b & c \\a & b & c \end{pmatrix}*"
+      r"\begin{pmatrix}a & b & c \\x & y & z \\x & y & z \end{pmatrix}"),
+     _MatMul(_MatMul(Matrix([[a, b, c], [x, y, z], [a, b, c]]),
+                     Matrix([[x, y, z], [a, b, c], [a, b, c]])),
+             Matrix([[a, b, c], [x, y, z], [x, y, z]]))),
+    (r"\begin{pmatrix}a & b \\x & y\end{pmatrix}/2",
+     _MatMul(Matrix([[a, b], [x, y]]), _Pow(2, -1))),
+    (r"\begin{pmatrix}a & b \\x & y\end{pmatrix}^2",
+     _Pow(Matrix([[a, b], [x, y]]), 2)),
+    (r"\begin{pmatrix}a & b \\x & y\end{pmatrix}^{-1}",
+     _Pow(Matrix([[a, b], [x, y]]), -1)),
+    (r"\begin{pmatrix}a & b \\x & y\end{pmatrix}^T",
+     Transpose(Matrix([[a, b], [x, y]]))),
+    (r"\begin{pmatrix}a & b \\x & y\end{pmatrix}^{T}",
+     Transpose(Matrix([[a, b], [x, y]]))),
+    (r"\begin{pmatrix}a & b \\x & y\end{pmatrix}^\mathit{T}",
+     Transpose(Matrix([[a, b], [x, y]]))),
+    (r"\begin{pmatrix}1 & 2 \\3 & 4\end{pmatrix}^T",
+     Transpose(Matrix([[1, 2], [3, 4]]))),
+    ((r"(\begin{pmatrix}1 & 2 \\3 & 4\end{pmatrix}+"
+      r"\begin{pmatrix}1 & 2 \\3 & 4\end{pmatrix}^T)*"
+      r"\begin{bmatrix}1\\0\end{bmatrix}"),
+     _MatMul(_MatAdd(Matrix([[1, 2], [3, 4]]),
+                     Transpose(Matrix([[1, 2], [3, 4]]))),
+                Matrix([[1], [0]]))),
+    ((r"(\begin{pmatrix}a & b \\x & y\end{pmatrix}+"
+      r"\begin{pmatrix}x & y \\a & b\end{pmatrix})^2"),
+    _Pow(_MatAdd(Matrix([[a, b], [x, y]]),
+                 Matrix([[x, y], [a, b]])), 2)),
+    ((r"(\begin{pmatrix}a & b \\x & y\end{pmatrix}+"
+      r"\begin{pmatrix}x & y \\a & b\end{pmatrix})^T"),
+    Transpose(_MatAdd(Matrix([[a, b], [x, y]]),
+                      Matrix([[x, y], [a, b]])))),
+    (r"\overline{\begin{pmatrix}\imaginaryunit&2\\3&4\end{pmatrix}+\begin{pmatrix}\imaginaryunit&2\\3&4\end{pmatrix}}",
+     _Conjugate(_MatAdd(Matrix([[I, 2], [3, 4]]),
+                        Matrix([[I, 2], [3, 4]]))))
+]
+
+EVALUATED_MATRIX_EXPRESSION_PAIRS = [
+    (r"\det\left(\left[   { \begin{array}{cc}a&b\\x&y\end{array} } \right]\right)",
+     Matrix([[a, b], [x, y]]).det()),
+    (r"\det \begin{pmatrix}1&2\\3&4\end{pmatrix}", -2),
+    (r"\det{\begin{pmatrix}1&2\\3&4\end{pmatrix}}", -2),
+    (r"\det(\begin{pmatrix}1&2\\3&4\end{pmatrix})", -2),
+    (r"\det\left(\begin{pmatrix}1&2\\3&4\end{pmatrix}\right)", -2),
+    (r"\begin{pmatrix}a & b \\x & y\end{pmatrix}/\begin{vmatrix}a & b \\x & y\end{vmatrix}",
+     _MatMul(Matrix([[a, b], [x, y]]), _Pow(Matrix([[a, b], [x, y]]).det(), -1))),
+    (r"\begin{pmatrix}a & b \\x & y\end{pmatrix}/|\begin{matrix}a & b \\x & y\end{matrix}|",
+     _MatMul(Matrix([[a, b], [x, y]]), _Pow(Matrix([[a, b], [x, y]]).det(), -1))),
+    (r"\frac{\begin{pmatrix}a & b \\x & y\end{pmatrix}}{| { \begin{matrix}a & b \\x & y\end{matrix} } |}",
+     _MatMul(Matrix([[a, b], [x, y]]), _Pow(Matrix([[a, b], [x, y]]).det(), -1))),
+    (r"\overline{\begin{pmatrix}\imaginaryunit & 1+\imaginaryunit \\-\imaginaryunit & 4\end{pmatrix}}",
+     Matrix([[-I, 1-I], [I, 4]])),
+    (r"\begin{pmatrix}\imaginaryunit & 1+\imaginaryunit \\-\imaginaryunit & 4\end{pmatrix}^H",
+     Matrix([[-I, I], [1-I, 4]])),
+    (r"\trace(\begin{pmatrix}\imaginaryunit & 1+\imaginaryunit \\-\imaginaryunit & 4\end{pmatrix})",
+     Trace(Matrix([[I, 1+I], [-I, 4]]))),
+    (r"\adjugate(\begin{pmatrix}1 & 2 \\3 & 4\end{pmatrix})",
+     Matrix([[4, -2], [-3, 1]])),
+    (r"(\begin{pmatrix}\imaginaryunit&2\\3&4\end{pmatrix}+\begin{pmatrix}\imaginaryunit&2\\3&4\end{pmatrix})^\ast",
+     Matrix([[-2*I, 6], [4, 8]])),
+    (r"(\begin{pmatrix}\imaginaryunit&2\\3&4\end{pmatrix}+\begin{pmatrix}\imaginaryunit&2\\3&4\end{pmatrix})^{\ast}",
+     Matrix([[-2*I, 6], [4, 8]])),
+    (r"(\begin{pmatrix}\imaginaryunit&2\\3&4\end{pmatrix}+\begin{pmatrix}\imaginaryunit&2\\3&4\end{pmatrix})^{\ast\ast}",
+     Matrix([[2*I, 4], [6, 8]])),
+    (r"(\begin{pmatrix}\imaginaryunit&2\\3&4\end{pmatrix}+\begin{pmatrix}\imaginaryunit&2\\3&4\end{pmatrix})^{\ast\ast\ast}",
+     Matrix([[-2*I, 6], [4, 8]])),
+    (r"(\begin{pmatrix}\imaginaryunit&2\\3&4\end{pmatrix}+\begin{pmatrix}\imaginaryunit&2\\3&4\end{pmatrix})^{*}",
+     Matrix([[-2*I, 6], [4, 8]])),
+    (r"(\begin{pmatrix}\imaginaryunit&2\\3&4\end{pmatrix}+\begin{pmatrix}\imaginaryunit&2\\3&4\end{pmatrix})^{**}",
+     Matrix([[2*I, 4], [6, 8]])),
+    (r"(\begin{pmatrix}\imaginaryunit&2\\3&4\end{pmatrix}+\begin{pmatrix}\imaginaryunit&2\\3&4\end{pmatrix})^{***}",
+     Matrix([[-2*I, 6], [4, 8]])),
+    (r"(\begin{pmatrix}\imaginaryunit&2\\3&4\end{pmatrix}+\begin{pmatrix}\imaginaryunit&2\\3&4\end{pmatrix})^\prime",
+     Transpose(_MatAdd(Matrix([[I, 2], [3, 4]]),
+                       Matrix([[I, 2], [3, 4]])))),
+    (r"(\begin{pmatrix}\imaginaryunit&2\\3&4\end{pmatrix}+\begin{pmatrix}\imaginaryunit&2\\3&4\end{pmatrix})^{\prime}",
+     Transpose(_MatAdd(Matrix([[I, 2], [3, 4]]),
+                       Matrix([[I, 2], [3, 4]])))),
+    (r"(\begin{pmatrix}\imaginaryunit&2\\3&4\end{pmatrix}+\begin{pmatrix}\imaginaryunit&2\\3&4\end{pmatrix})^{\prime\prime}",
+     _MatAdd(Matrix([[I, 2], [3, 4]]),
+             Matrix([[I, 2], [3, 4]]))),
+    (r"(\begin{pmatrix}\imaginaryunit&2\\3&4\end{pmatrix}+\begin{pmatrix}\imaginaryunit&2\\3&4\end{pmatrix})^{\prime\prime\prime}",
+     Transpose(_MatAdd(Matrix([[I, 2], [3, 4]]),
+                       Matrix([[I, 2], [3, 4]])))),
+    (r"(\begin{pmatrix}\imaginaryunit&2\\3&4\end{pmatrix}+\begin{pmatrix}\imaginaryunit&2\\3&4\end{pmatrix})^{'}",
+     Transpose(_MatAdd(Matrix([[I, 2], [3, 4]]),
+                       Matrix([[I, 2], [3, 4]])))),
+    (r"(\begin{pmatrix}\imaginaryunit&2\\3&4\end{pmatrix}+\begin{pmatrix}\imaginaryunit&2\\3&4\end{pmatrix})^{''}",
+     _MatAdd(Matrix([[I, 2], [3, 4]]),
+             Matrix([[I, 2], [3, 4]]))),
+    (r"(\begin{pmatrix}\imaginaryunit&2\\3&4\end{pmatrix}+\begin{pmatrix}\imaginaryunit&2\\3&4\end{pmatrix})^{'''}",
+     Transpose(_MatAdd(Matrix([[I, 2], [3, 4]]),
+                       Matrix([[I, 2], [3, 4]])))),
+    (r"(\begin{pmatrix}\imaginaryunit&2\\3&4\end{pmatrix}+\begin{pmatrix}\imaginaryunit&2\\3&4\end{pmatrix})'",
+     Transpose(_MatAdd(Matrix([[I, 2], [3, 4]]),
+                       Matrix([[I, 2], [3, 4]])))),
+    (r"(\begin{pmatrix}\imaginaryunit&2\\3&4\end{pmatrix}+\begin{pmatrix}\imaginaryunit&2\\3&4\end{pmatrix})''",
+     _MatAdd(Matrix([[I, 2], [3, 4]]),
+             Matrix([[I, 2], [3, 4]]))),
+    (r"(\begin{pmatrix}\imaginaryunit&2\\3&4\end{pmatrix}+\begin{pmatrix}\imaginaryunit&2\\3&4\end{pmatrix})'''",
+     Transpose(_MatAdd(Matrix([[I, 2], [3, 4]]),
+                       Matrix([[I, 2], [3, 4]])))),
+    (r"\det(\begin{pmatrix}\imaginaryunit&2\\3&4\end{pmatrix}+\begin{pmatrix}\imaginaryunit&2\\3&4\end{pmatrix})",
+     (_MatAdd(Matrix([[I, 2], [3, 4]]),
+              Matrix([[I, 2], [3, 4]]))).det()),
+    (r"\trace(\begin{pmatrix}\imaginaryunit&2\\3&4\end{pmatrix}+\begin{pmatrix}\imaginaryunit&2\\3&4\end{pmatrix})",
+     Trace(_MatAdd(Matrix([[I, 2], [3, 4]]),
+                   Matrix([[I, 2], [3, 4]])))),
+    (r"\adjugate(\begin{pmatrix}\imaginaryunit&2\\3&4\end{pmatrix}+\begin{pmatrix}\imaginaryunit&2\\3&4\end{pmatrix})",
+     (Matrix([[8, -4], [-6, 2*I]]))),
+    (r"(\begin{pmatrix}\imaginaryunit&2\\3&4\end{pmatrix}+\begin{pmatrix}\imaginaryunit&2\\3&4\end{pmatrix})^T",
+     Transpose(_MatAdd(Matrix([[I, 2], [3, 4]]),
+                       Matrix([[I, 2], [3, 4]])))),
+    (r"(\begin{pmatrix}\imaginaryunit&2\\3&4\end{pmatrix}+\begin{pmatrix}\imaginaryunit&2\\3&4\end{pmatrix})^H",
+     (Matrix([[-2*I, 6], [4, 8]])))
+]
+
+
+def test_symbol_expressions():
+    expected_failures = {6, 7}
+    for i, (latex_str, sympy_expr) in enumerate(SYMBOL_EXPRESSION_PAIRS):
+        if i in expected_failures:
+            continue
+        with evaluate(False):
+            assert parse_latex_lark(latex_str) == sympy_expr, latex_str
+
+
+def test_simple_expressions():
+    expected_failures = {20}
+    for i, (latex_str, sympy_expr) in enumerate(UNEVALUATED_SIMPLE_EXPRESSION_PAIRS):
+        if i in expected_failures:
+            continue
+        with evaluate(False):
+            assert parse_latex_lark(latex_str) == sympy_expr, latex_str
+
+    for i, (latex_str, sympy_expr) in enumerate(EVALUATED_SIMPLE_EXPRESSION_PAIRS):
+        if i in expected_failures:
+            continue
+        assert parse_latex_lark(latex_str) == sympy_expr, latex_str
+
+
+def test_fraction_expressions():
+    for latex_str, sympy_expr in UNEVALUATED_FRACTION_EXPRESSION_PAIRS:
+        with evaluate(False):
+            assert parse_latex_lark(latex_str) == sympy_expr, latex_str
+
+    for latex_str, sympy_expr in EVALUATED_FRACTION_EXPRESSION_PAIRS:
+        assert parse_latex_lark(latex_str) == sympy_expr, latex_str
+
+
+def test_relation_expressions():
+    for latex_str, sympy_expr in RELATION_EXPRESSION_PAIRS:
+        with evaluate(False):
+            assert parse_latex_lark(latex_str) == sympy_expr, latex_str
+
+def test_power_expressions():
+    expected_failures = {3}
+    for i, (latex_str, sympy_expr) in enumerate(UNEVALUATED_POWER_EXPRESSION_PAIRS):
+        if i in expected_failures:
+            continue
+        with evaluate(False):
+            assert parse_latex_lark(latex_str) == sympy_expr, latex_str
+
+    for i, (latex_str, sympy_expr) in enumerate(EVALUATED_POWER_EXPRESSION_PAIRS):
+        if i in expected_failures:
+            continue
+        assert parse_latex_lark(latex_str) == sympy_expr, latex_str
+
+
+def test_integral_expressions():
+    expected_failures = {14}
+    for i, (latex_str, sympy_expr) in enumerate(UNEVALUATED_INTEGRAL_EXPRESSION_PAIRS):
+        if i in expected_failures:
+            continue
+        with evaluate(False):
+            assert parse_latex_lark(latex_str) == sympy_expr, i
+
+    for i, (latex_str, sympy_expr) in enumerate(EVALUATED_INTEGRAL_EXPRESSION_PAIRS):
+        if i in expected_failures:
+            continue
+        assert parse_latex_lark(latex_str) == sympy_expr, latex_str
+
+
+def test_derivative_expressions():
+    expected_failures = {3, 4}
+    for i, (latex_str, sympy_expr) in enumerate(DERIVATIVE_EXPRESSION_PAIRS):
+        if i in expected_failures:
+            continue
+        with evaluate(False):
+            assert parse_latex_lark(latex_str) == sympy_expr, latex_str
+
+    for i, (latex_str, sympy_expr) in enumerate(DERIVATIVE_EXPRESSION_PAIRS):
+        if i in expected_failures:
+            continue
+        assert parse_latex_lark(latex_str) == sympy_expr, latex_str
+
+
+def test_trigonometric_expressions():
+    expected_failures = {3}
+    for i, (latex_str, sympy_expr) in enumerate(TRIGONOMETRIC_EXPRESSION_PAIRS):
+        if i in expected_failures:
+            continue
+        with evaluate(False):
+            assert parse_latex_lark(latex_str) == sympy_expr, latex_str
+
+
+def test_limit_expressions():
+    for latex_str, sympy_expr in UNEVALUATED_LIMIT_EXPRESSION_PAIRS:
+        with evaluate(False):
+            assert parse_latex_lark(latex_str) == sympy_expr, latex_str
+
+
+def test_square_root_expressions():
+    for latex_str, sympy_expr in UNEVALUATED_SQRT_EXPRESSION_PAIRS:
+        with evaluate(False):
+            assert parse_latex_lark(latex_str) == sympy_expr, latex_str
+
+    for latex_str, sympy_expr in EVALUATED_SQRT_EXPRESSION_PAIRS:
+        assert parse_latex_lark(latex_str) == sympy_expr, latex_str
+
+
+def test_factorial_expressions():
+    for latex_str, sympy_expr in UNEVALUATED_FACTORIAL_EXPRESSION_PAIRS:
+        with evaluate(False):
+            assert parse_latex_lark(latex_str) == sympy_expr, latex_str
+
+    for latex_str, sympy_expr in EVALUATED_FACTORIAL_EXPRESSION_PAIRS:
+        assert parse_latex_lark(latex_str) == sympy_expr, latex_str
+
+
+def test_sum_expressions():
+    for latex_str, sympy_expr in UNEVALUATED_SUM_EXPRESSION_PAIRS:
+        with evaluate(False):
+            assert parse_latex_lark(latex_str) == sympy_expr, latex_str
+
+    for latex_str, sympy_expr in EVALUATED_SUM_EXPRESSION_PAIRS:
+        assert parse_latex_lark(latex_str) == sympy_expr, latex_str
+
+
+def test_product_expressions():
+    for latex_str, sympy_expr in UNEVALUATED_PRODUCT_EXPRESSION_PAIRS:
+        with evaluate(False):
+            assert parse_latex_lark(latex_str) == sympy_expr, latex_str
+
+@XFAIL
+def test_applied_function_expressions():
+    expected_failures = {0, 3, 4}  # 0 is ambiguous, and the others require not-yet-added features
+    # not sure why 1, and 2 are failing
+    for i, (latex_str, sympy_expr) in enumerate(APPLIED_FUNCTION_EXPRESSION_PAIRS):
+        if i in expected_failures:
+            continue
+        with evaluate(False):
+            assert parse_latex_lark(latex_str) == sympy_expr, latex_str
+
+
+def test_common_function_expressions():
+    for latex_str, sympy_expr in UNEVALUATED_COMMON_FUNCTION_EXPRESSION_PAIRS:
+        with evaluate(False):
+            assert parse_latex_lark(latex_str) == sympy_expr, latex_str
+
+    for latex_str, sympy_expr in EVALUATED_COMMON_FUNCTION_EXPRESSION_PAIRS:
+        assert parse_latex_lark(latex_str) == sympy_expr, latex_str
+
+
+# unhandled bug causing these to fail
+@XFAIL
+def test_spacing():
+    for latex_str, sympy_expr in SPACING_RELATED_EXPRESSION_PAIRS:
+        with evaluate(False):
+            assert parse_latex_lark(latex_str) == sympy_expr, latex_str
+
+
+def test_binomial_expressions():
+    for latex_str, sympy_expr in UNEVALUATED_BINOMIAL_EXPRESSION_PAIRS:
+        with evaluate(False):
+            assert parse_latex_lark(latex_str) == sympy_expr, latex_str
+
+    for latex_str, sympy_expr in EVALUATED_BINOMIAL_EXPRESSION_PAIRS:
+        assert parse_latex_lark(latex_str) == sympy_expr, latex_str
+
+
+def test_miscellaneous_expressions():
+    for latex_str, sympy_expr in MISCELLANEOUS_EXPRESSION_PAIRS:
+        with evaluate(False):
+            assert parse_latex_lark(latex_str) == sympy_expr, latex_str
+
+
+def test_literal_complex_number_expressions():
+    for latex_str, sympy_expr in UNEVALUATED_LITERAL_COMPLEX_NUMBER_EXPRESSION_PAIRS:
+        with evaluate(False):
+            assert parse_latex_lark(latex_str) == sympy_expr, latex_str
+
+
+def test_matrix_expressions():
+    for latex_str, sympy_expr in UNEVALUATED_MATRIX_EXPRESSION_PAIRS:
+        with evaluate(False):
+            assert parse_latex_lark(latex_str) == sympy_expr, latex_str
+
+    for latex_str, sympy_expr in EVALUATED_MATRIX_EXPRESSION_PAIRS:
+        assert parse_latex_lark(latex_str) == sympy_expr, latex_str

backend_service/venv/lib/python3.13/site-packages/sympy/parsing/tests/test_mathematica.py

@@ -0,0 +1,280 @@
+from sympy import sin, Function, symbols, Dummy, Lambda, cos
+from sympy.parsing.mathematica import parse_mathematica, MathematicaParser
+from sympy.core.sympify import sympify
+from sympy.abc import n, w, x, y, z
+from sympy.testing.pytest import raises
+
+
+def test_mathematica():
+    d = {
+        '- 6x': '-6*x',
+        'Sin[x]^2': 'sin(x)**2',
+        '2(x-1)': '2*(x-1)',
+        '3y+8': '3*y+8',
+        'ArcSin[2x+9(4-x)^2]/x': 'asin(2*x+9*(4-x)**2)/x',
+        'x+y': 'x+y',
+        '355/113': '355/113',
+        '2.718281828': '2.718281828',
+        'Cos(1/2 * π)': 'Cos(π/2)',
+        'Sin[12]': 'sin(12)',
+        'Exp[Log[4]]': 'exp(log(4))',
+        '(x+1)(x+3)': '(x+1)*(x+3)',
+        'Cos[ArcCos[3.6]]': 'cos(acos(3.6))',
+        'Cos[x]==Sin[y]': 'Eq(cos(x), sin(y))',
+        '2*Sin[x+y]': '2*sin(x+y)',
+        'Sin[x]+Cos[y]': 'sin(x)+cos(y)',
+        'Sin[Cos[x]]': 'sin(cos(x))',
+        '2*Sqrt[x+y]': '2*sqrt(x+y)',   # Test case from the issue 4259
+        '+Sqrt[2]': 'sqrt(2)',
+        '-Sqrt[2]': '-sqrt(2)',
+        '-1/Sqrt[2]': '-1/sqrt(2)',
+        '-(1/Sqrt[3])': '-(1/sqrt(3))',
+        '1/(2*Sqrt[5])': '1/(2*sqrt(5))',
+        'Mod[5,3]': 'Mod(5,3)',
+        '-Mod[5,3]': '-Mod(5,3)',
+        '(x+1)y': '(x+1)*y',
+        'x(y+1)': 'x*(y+1)',
+        'Sin[x]Cos[y]': 'sin(x)*cos(y)',
+        'Sin[x]^2Cos[y]^2': 'sin(x)**2*cos(y)**2',
+        'Cos[x]^2(1 - Cos[y]^2)': 'cos(x)**2*(1-cos(y)**2)',
+        'x y': 'x*y',
+        'x  y': 'x*y',
+        '2 x': '2*x',
+        'x 8': 'x*8',
+        '2 8': '2*8',
+        '4.x': '4.*x',
+        '4. 3': '4.*3',
+        '4. 3.': '4.*3.',
+        '1 2 3': '1*2*3',
+        ' -  2 *  Sqrt[  2 3 *   ( 1   +  5 ) ]  ': '-2*sqrt(2*3*(1+5))',
+        'Log[2,4]': 'log(4,2)',
+        'Log[Log[2,4],4]': 'log(4,log(4,2))',
+        'Exp[Sqrt[2]^2Log[2, 8]]': 'exp(sqrt(2)**2*log(8,2))',
+        'ArcSin[Cos[0]]': 'asin(cos(0))',
+        'Log2[16]': 'log(16,2)',
+        'Max[1,-2,3,-4]': 'Max(1,-2,3,-4)',
+        'Min[1,-2,3]': 'Min(1,-2,3)',
+        'Exp[I Pi/2]': 'exp(I*pi/2)',
+        'ArcTan[x,y]': 'atan2(y,x)',
+        'Pochhammer[x,y]': 'rf(x,y)',
+        'ExpIntegralEi[x]': 'Ei(x)',
+        'SinIntegral[x]': 'Si(x)',
+        'CosIntegral[x]': 'Ci(x)',
+        'AiryAi[x]': 'airyai(x)',
+        'AiryAiPrime[5]': 'airyaiprime(5)',
+        'AiryBi[x]': 'airybi(x)',
+        'AiryBiPrime[7]': 'airybiprime(7)',
+        'LogIntegral[4]': ' li(4)',
+        'PrimePi[7]': 'primepi(7)',
+        'Prime[5]': 'prime(5)',
+        'PrimeQ[5]': 'isprime(5)',
+        'Rational[2,19]': 'Rational(2,19)',    # test case for issue 25716
+        }
+
+    for e in d:
+        assert parse_mathematica(e) == sympify(d[e])
+
+    # The parsed form of this expression should not evaluate the Lambda object:
+    assert parse_mathematica("Sin[#]^2 + Cos[#]^2 &[x]") == sin(x)**2 + cos(x)**2
+
+    d1, d2, d3 = symbols("d1:4", cls=Dummy)
+    assert parse_mathematica("Sin[#] + Cos[#3] &").dummy_eq(Lambda((d1, d2, d3), sin(d1) + cos(d3)))
+    assert parse_mathematica("Sin[#^2] &").dummy_eq(Lambda(d1, sin(d1**2)))
+    assert parse_mathematica("Function[x, x^3]") == Lambda(x, x**3)
+    assert parse_mathematica("Function[{x, y}, x^2 + y^2]") == Lambda((x, y), x**2 + y**2)
+
+
+def test_parser_mathematica_tokenizer():
+    parser = MathematicaParser()
+
+    chain = lambda expr: parser._from_tokens_to_fullformlist(parser._from_mathematica_to_tokens(expr))
+
+    # Basic patterns
+    assert chain("x") == "x"
+    assert chain("42") == "42"
+    assert chain(".2") == ".2"
+    assert chain("+x") == "x"
+    assert chain("-1") == "-1"
+    assert chain("- 3") == "-3"
+    assert chain("α") == "α"
+    assert chain("+Sin[x]") == ["Sin", "x"]
+    assert chain("-Sin[x]") == ["Times", "-1", ["Sin", "x"]]
+    assert chain("x(a+1)") == ["Times", "x", ["Plus", "a", "1"]]
+    assert chain("(x)") == "x"
+    assert chain("(+x)") == "x"
+    assert chain("-a") == ["Times", "-1", "a"]
+    assert chain("(-x)") == ["Times", "-1", "x"]
+    assert chain("(x + y)") == ["Plus", "x", "y"]
+    assert chain("3 + 4") == ["Plus", "3", "4"]
+    assert chain("a - 3") == ["Plus", "a", "-3"]
+    assert chain("a - b") == ["Plus", "a", ["Times", "-1", "b"]]
+    assert chain("7 * 8") == ["Times", "7", "8"]
+    assert chain("a + b*c") == ["Plus", "a", ["Times", "b", "c"]]
+    assert chain("a + b* c* d + 2 * e") == ["Plus", "a", ["Times", "b", "c", "d"], ["Times", "2", "e"]]
+    assert chain("a / b") == ["Times", "a", ["Power", "b", "-1"]]
+
+    # Missing asterisk (*) patterns:
+    assert chain("x y") == ["Times", "x", "y"]
+    assert chain("3 4") == ["Times", "3", "4"]
+    assert chain("a[b] c") == ["Times", ["a", "b"], "c"]
+    assert chain("(x) (y)") == ["Times", "x", "y"]
+    assert chain("3 (a)") == ["Times", "3", "a"]
+    assert chain("(a) b") == ["Times", "a", "b"]
+    assert chain("4.2") == "4.2"
+    assert chain("4 2") == ["Times", "4", "2"]
+    assert chain("4  2") == ["Times", "4", "2"]
+    assert chain("3 . 4") == ["Dot", "3", "4"]
+    assert chain("4. 2") == ["Times", "4.", "2"]
+    assert chain("x.y") == ["Dot", "x", "y"]
+    assert chain("4.y") == ["Times", "4.", "y"]
+    assert chain("4 .y") == ["Dot", "4", "y"]
+    assert chain("x.4") == ["Times", "x", ".4"]
+    assert chain("x0.3") == ["Times", "x0", ".3"]
+    assert chain("x. 4") == ["Dot", "x", "4"]
+
+    # Comments
+    assert chain("a (* +b *) + c") == ["Plus", "a", "c"]
+    assert chain("a (* + b *) + (**)c (* +d *) + e") == ["Plus", "a", "c", "e"]
+    assert chain("""a + (*
+    + b
+    *) c + (* d
+    *) e
+    """) == ["Plus", "a", "c", "e"]
+
+    # Operators couples + and -, * and / are mutually associative:
+    # (i.e. expression gets flattened when mixing these operators)
+    assert chain("a*b/c") == ["Times", "a", "b", ["Power", "c", "-1"]]
+    assert chain("a/b*c") == ["Times", "a", ["Power", "b", "-1"], "c"]
+    assert chain("a+b-c") == ["Plus", "a", "b", ["Times", "-1", "c"]]
+    assert chain("a-b+c") == ["Plus", "a", ["Times", "-1", "b"], "c"]
+    assert chain("-a + b -c ") == ["Plus", ["Times", "-1", "a"], "b", ["Times", "-1", "c"]]
+    assert chain("a/b/c*d") == ["Times", "a", ["Power", "b", "-1"], ["Power", "c", "-1"], "d"]
+    assert chain("a/b/c") == ["Times", "a", ["Power", "b", "-1"], ["Power", "c", "-1"]]
+    assert chain("a-b-c") == ["Plus", "a", ["Times", "-1", "b"], ["Times", "-1", "c"]]
+    assert chain("1/a") == ["Times", "1", ["Power", "a", "-1"]]
+    assert chain("1/a/b") == ["Times", "1", ["Power", "a", "-1"], ["Power", "b", "-1"]]
+    assert chain("-1/a*b") == ["Times", "-1", ["Power", "a", "-1"], "b"]
+
+    # Enclosures of various kinds, i.e. ( )  [ ]  [[ ]]  { }
+    assert chain("(a + b) + c") == ["Plus", ["Plus", "a", "b"], "c"]
+    assert chain(" a + (b + c) + d ") == ["Plus", "a", ["Plus", "b", "c"], "d"]
+    assert chain("a * (b + c)") == ["Times", "a", ["Plus", "b", "c"]]
+    assert chain("a b (c d)") == ["Times", "a", "b", ["Times", "c", "d"]]
+    assert chain("{a, b, 2, c}") == ["List", "a", "b", "2", "c"]
+    assert chain("{a, {b, c}}") == ["List", "a", ["List", "b", "c"]]
+    assert chain("{{a}}") == ["List", ["List", "a"]]
+    assert chain("a[b, c]") == ["a", "b", "c"]
+    assert chain("a[[b, c]]") == ["Part", "a", "b", "c"]
+    assert chain("a[b[c]]") == ["a", ["b", "c"]]
+    assert chain("a[[b, c[[d, {e,f}]]]]") == ["Part", "a", "b", ["Part", "c", "d", ["List", "e", "f"]]]
+    assert chain("a[b[[c,d]]]") == ["a", ["Part", "b", "c", "d"]]
+    assert chain("a[[b[c]]]") == ["Part", "a", ["b", "c"]]
+    assert chain("a[[b[[c]]]]") == ["Part", "a", ["Part", "b", "c"]]
+    assert chain("a[[b[c[[d]]]]]") == ["Part", "a", ["b", ["Part", "c", "d"]]]
+    assert chain("a[b[[c[d]]]]") == ["a", ["Part", "b", ["c", "d"]]]
+    assert chain("x[[a+1, b+2, c+3]]") == ["Part", "x", ["Plus", "a", "1"], ["Plus", "b", "2"], ["Plus", "c", "3"]]
+    assert chain("x[a+1, b+2, c+3]") == ["x", ["Plus", "a", "1"], ["Plus", "b", "2"], ["Plus", "c", "3"]]
+    assert chain("{a+1, b+2, c+3}") == ["List", ["Plus", "a", "1"], ["Plus", "b", "2"], ["Plus", "c", "3"]]
+
+    # Flat operator:
+    assert chain("a*b*c*d*e") == ["Times", "a", "b", "c", "d", "e"]
+    assert chain("a +b + c+ d+e") == ["Plus", "a", "b", "c", "d", "e"]
+
+    # Right priority operator:
+    assert chain("a^b") == ["Power", "a", "b"]
+    assert chain("a^b^c") == ["Power", "a", ["Power", "b", "c"]]
+    assert chain("a^b^c^d") == ["Power", "a", ["Power", "b", ["Power", "c", "d"]]]
+
+    # Left priority operator:
+    assert chain("a/.b") == ["ReplaceAll", "a", "b"]
+    assert chain("a/.b/.c/.d") == ["ReplaceAll", ["ReplaceAll", ["ReplaceAll", "a", "b"], "c"], "d"]
+
+    assert chain("a//b") == ["a", "b"]
+    assert chain("a//b//c") == [["a", "b"], "c"]
+    assert chain("a//b//c//d") == [[["a", "b"], "c"], "d"]
+
+    # Compound expressions
+    assert chain("a;b") == ["CompoundExpression", "a", "b"]
+    assert chain("a;") == ["CompoundExpression", "a", "Null"]
+    assert chain("a;b;") == ["CompoundExpression", "a", "b", "Null"]
+    assert chain("a[b;c]") == ["a", ["CompoundExpression", "b", "c"]]
+    assert chain("a[b,c;d,e]") == ["a", "b", ["CompoundExpression", "c", "d"], "e"]
+    assert chain("a[b,c;,d]") == ["a", "b", ["CompoundExpression", "c", "Null"], "d"]
+
+    # New lines
+    assert chain("a\nb\n") == ["CompoundExpression", "a", "b"]
+    assert chain("a\n\nb\n (c \nd)  \n") == ["CompoundExpression", "a", "b", ["Times", "c", "d"]]
+    assert chain("\na; b\nc") == ["CompoundExpression", "a", "b", "c"]
+    assert chain("a + \nb\n") == ["Plus", "a", "b"]
+    assert chain("a\nb; c; d\n e; (f \n g); h + \n i") == ["CompoundExpression", "a", "b", "c", "d", "e", ["Times", "f", "g"], ["Plus", "h", "i"]]
+    assert chain("\n{\na\nb; c; d\n e (f \n g); h + \n i\n\n}\n") == ["List", ["CompoundExpression", ["Times", "a", "b"], "c", ["Times", "d", "e", ["Times", "f", "g"]], ["Plus", "h", "i"]]]
+
+    # Patterns
+    assert chain("y_") == ["Pattern", "y", ["Blank"]]
+    assert chain("y_.") == ["Optional", ["Pattern", "y", ["Blank"]]]
+    assert chain("y__") == ["Pattern", "y", ["BlankSequence"]]
+    assert chain("y___") == ["Pattern", "y", ["BlankNullSequence"]]
+    assert chain("a[b_.,c_]") == ["a", ["Optional", ["Pattern", "b", ["Blank"]]], ["Pattern", "c", ["Blank"]]]
+    assert chain("b_. c") == ["Times", ["Optional", ["Pattern", "b", ["Blank"]]], "c"]
+
+    # Slots for lambda functions
+    assert chain("#") == ["Slot", "1"]
+    assert chain("#3") == ["Slot", "3"]
+    assert chain("#n") == ["Slot", "n"]
+    assert chain("##") == ["SlotSequence", "1"]
+    assert chain("##a") == ["SlotSequence", "a"]
+
+    # Lambda functions
+    assert chain("x&") == ["Function", "x"]
+    assert chain("#&") == ["Function", ["Slot", "1"]]
+    assert chain("#+3&") == ["Function", ["Plus", ["Slot", "1"], "3"]]
+    assert chain("#1 + #2&") == ["Function", ["Plus", ["Slot", "1"], ["Slot", "2"]]]
+    assert chain("# + #&") == ["Function", ["Plus", ["Slot", "1"], ["Slot", "1"]]]
+    assert chain("#&[x]") == [["Function", ["Slot", "1"]], "x"]
+    assert chain("#1 + #2 & [x, y]") == [["Function", ["Plus", ["Slot", "1"], ["Slot", "2"]]], "x", "y"]
+    assert chain("#1^2#2^3&") == ["Function", ["Times", ["Power", ["Slot", "1"], "2"], ["Power", ["Slot", "2"], "3"]]]
+
+    # Strings inside Mathematica expressions:
+    assert chain('"abc"') == ["_Str", "abc"]
+    assert chain('"a\\"b"') == ["_Str", 'a"b']
+    # This expression does not make sense mathematically, it's just testing the parser:
+    assert chain('x + "abc" ^ 3') == ["Plus", "x", ["Power", ["_Str", "abc"], "3"]]
+    assert chain('"a (* b *) c"') == ["_Str", "a (* b *) c"]
+    assert chain('"a" (* b *) ') == ["_Str", "a"]
+    assert chain('"a [ b] "') == ["_Str", "a [ b] "]
+    raises(SyntaxError, lambda: chain('"'))
+    raises(SyntaxError, lambda: chain('"\\"'))
+    raises(SyntaxError, lambda: chain('"abc'))
+    raises(SyntaxError, lambda: chain('"abc\\"def'))
+
+    # Invalid expressions:
+    raises(SyntaxError, lambda: chain("(,"))
+    raises(SyntaxError, lambda: chain("()"))
+    raises(SyntaxError, lambda: chain("a (* b"))
+
+
+def test_parser_mathematica_exp_alt():
+    parser = MathematicaParser()
+
+    convert_chain2 = lambda expr: parser._from_fullformlist_to_fullformsympy(parser._from_fullform_to_fullformlist(expr))
+    convert_chain3 = lambda expr: parser._from_fullformsympy_to_sympy(convert_chain2(expr))
+
+    Sin, Times, Plus, Power = symbols("Sin Times Plus Power", cls=Function)
+
+    full_form1 = "Sin[Times[x, y]]"
+    full_form2 = "Plus[Times[x, y], z]"
+    full_form3 = "Sin[Times[x, Plus[y, z], Power[w, n]]]]"
+    full_form4 = "Rational[Rational[x, y], z]"
+
+    assert parser._from_fullform_to_fullformlist(full_form1) == ["Sin", ["Times", "x", "y"]]
+    assert parser._from_fullform_to_fullformlist(full_form2) == ["Plus", ["Times", "x", "y"], "z"]
+    assert parser._from_fullform_to_fullformlist(full_form3) == ["Sin", ["Times", "x", ["Plus", "y", "z"], ["Power", "w", "n"]]]
+    assert parser._from_fullform_to_fullformlist(full_form4) == ["Rational", ["Rational", "x", "y"], "z"]
+
+    assert convert_chain2(full_form1) == Sin(Times(x, y))
+    assert convert_chain2(full_form2) == Plus(Times(x, y), z)
+    assert convert_chain2(full_form3) == Sin(Times(x, Plus(y, z), Power(w, n)))
+
+    assert convert_chain3(full_form1) == sin(x*y)
+    assert convert_chain3(full_form2) == x*y + z
+    assert convert_chain3(full_form3) == sin(x*(y + z)*w**n)

backend_service/venv/lib/python3.13/site-packages/sympy/parsing/tests/test_maxima.py

@@ -0,0 +1,50 @@
+from sympy.parsing.maxima import parse_maxima
+from sympy.core.numbers import (E, Rational, oo)
+from sympy.core.symbol import Symbol
+from sympy.functions.combinatorial.factorials import factorial
+from sympy.functions.elementary.complexes import Abs
+from sympy.functions.elementary.exponential import log
+from sympy.functions.elementary.trigonometric import (cos, sin)
+from sympy.abc import x
+
+n = Symbol('n', integer=True)
+
+
+def test_parser():
+    assert Abs(parse_maxima('float(1/3)') - 0.333333333) < 10**(-5)
+    assert parse_maxima('13^26') == 91733330193268616658399616009
+    assert parse_maxima('sin(%pi/2) + cos(%pi/3)') == Rational(3, 2)
+    assert parse_maxima('log(%e)') == 1
+
+
+def test_injection():
+    parse_maxima('c: x+1', globals=globals())
+    # c created by parse_maxima
+    assert c == x + 1 # noqa:F821
+
+    parse_maxima('g: sqrt(81)', globals=globals())
+    # g created by parse_maxima
+    assert g == 9 # noqa:F821
+
+
+def test_maxima_functions():
+    assert parse_maxima('expand( (x+1)^2)') == x**2 + 2*x + 1
+    assert parse_maxima('factor( x**2 + 2*x + 1)') == (x + 1)**2
+    assert parse_maxima('2*cos(x)^2 + sin(x)^2') == 2*cos(x)**2 + sin(x)**2
+    assert parse_maxima('trigexpand(sin(2*x)+cos(2*x))') == \
+        -1 + 2*cos(x)**2 + 2*cos(x)*sin(x)
+    assert parse_maxima('solve(x^2-4,x)') == [-2, 2]
+    assert parse_maxima('limit((1+1/x)^x,x,inf)') == E
+    assert parse_maxima('limit(sqrt(-x)/x,x,0,minus)') is -oo
+    assert parse_maxima('diff(x^x, x)') == x**x*(1 + log(x))
+    assert parse_maxima('sum(k, k, 1, n)', name_dict={
+        "n": Symbol('n', integer=True),
+        "k": Symbol('k', integer=True)
+    }) == (n**2 + n)/2
+    assert parse_maxima('product(k, k, 1, n)', name_dict={
+        "n": Symbol('n', integer=True),
+        "k": Symbol('k', integer=True)
+    }) == factorial(n)
+    assert parse_maxima('ratsimp((x^2-1)/(x+1))') == x - 1
+    assert Abs( parse_maxima(
+        'float(sec(%pi/3) + csc(%pi/3))') - 3.154700538379252) < 10**(-5)

backend_service/venv/lib/python3.13/site-packages/sympy/parsing/tests/test_sym_expr.py

@@ -0,0 +1,209 @@
+from sympy.parsing.sym_expr import SymPyExpression
+from sympy.testing.pytest import raises
+from sympy.external import import_module
+
+lfortran = import_module('lfortran')
+cin = import_module('clang.cindex', import_kwargs = {'fromlist': ['cindex']})
+
+if lfortran and cin:
+    from sympy.codegen.ast import (Variable, IntBaseType, FloatBaseType, String,
+                                   Declaration, FloatType)
+    from sympy.core import Integer, Float
+    from sympy.core.symbol import Symbol
+
+    expr1 = SymPyExpression()
+    src = """\
+    integer :: a, b, c, d
+    real :: p, q, r, s
+    """
+
+    def test_c_parse():
+        src1 = """\
+        int a, b = 4;
+        float c, d = 2.4;
+        """
+        expr1.convert_to_expr(src1, 'c')
+        ls = expr1.return_expr()
+
+        assert ls[0] == Declaration(
+            Variable(
+                Symbol('a'),
+                type=IntBaseType(String('intc'))
+            )
+        )
+        assert ls[1] == Declaration(
+            Variable(
+                Symbol('b'),
+                type=IntBaseType(String('intc')),
+                value=Integer(4)
+            )
+        )
+        assert ls[2] == Declaration(
+            Variable(
+                Symbol('c'),
+                type=FloatType(
+                    String('float32'),
+                    nbits=Integer(32),
+                    nmant=Integer(23),
+                    nexp=Integer(8)
+                    )
+            )
+        )
+        assert ls[3] == Declaration(
+            Variable(
+                Symbol('d'),
+                type=FloatType(
+                    String('float32'),
+                    nbits=Integer(32),
+                    nmant=Integer(23),
+                    nexp=Integer(8)
+                    ),
+                value=Float('2.3999999999999999', precision=53)
+            )
+        )
+
+
+    def test_fortran_parse():
+        expr = SymPyExpression(src, 'f')
+        ls = expr.return_expr()
+
+        assert ls[0] == Declaration(
+            Variable(
+                Symbol('a'),
+                type=IntBaseType(String('integer')),
+                value=Integer(0)
+            )
+        )
+        assert ls[1] == Declaration(
+            Variable(
+                Symbol('b'),
+                type=IntBaseType(String('integer')),
+                value=Integer(0)
+            )
+        )
+        assert ls[2] == Declaration(
+            Variable(
+                Symbol('c'),
+                type=IntBaseType(String('integer')),
+                value=Integer(0)
+            )
+        )
+        assert ls[3] == Declaration(
+            Variable(
+                Symbol('d'),
+                type=IntBaseType(String('integer')),
+                value=Integer(0)
+            )
+        )
+        assert ls[4] == Declaration(
+            Variable(
+                Symbol('p'),
+                type=FloatBaseType(String('real')),
+                value=Float('0.0', precision=53)
+            )
+        )
+        assert ls[5] == Declaration(
+            Variable(
+                Symbol('q'),
+                type=FloatBaseType(String('real')),
+                value=Float('0.0', precision=53)
+            )
+        )
+        assert ls[6] == Declaration(
+            Variable(
+                Symbol('r'),
+                type=FloatBaseType(String('real')),
+                value=Float('0.0', precision=53)
+            )
+        )
+        assert ls[7] == Declaration(
+            Variable(
+                Symbol('s'),
+                type=FloatBaseType(String('real')),
+                value=Float('0.0', precision=53)
+            )
+        )
+
+
+    def test_convert_py():
+        src1 = (
+            src +
+            """\
+            a = b + c
+            s = p * q / r
+            """
+        )
+        expr1.convert_to_expr(src1, 'f')
+        exp_py = expr1.convert_to_python()
+        assert exp_py == [
+            'a = 0',
+            'b = 0',
+            'c = 0',
+            'd = 0',
+            'p = 0.0',
+            'q = 0.0',
+            'r = 0.0',
+            's = 0.0',
+            'a = b + c',
+            's = p*q/r'
+        ]
+
+
+    def test_convert_fort():
+        src1 = (
+            src +
+            """\
+            a = b + c
+            s = p * q / r
+            """
+        )
+        expr1.convert_to_expr(src1, 'f')
+        exp_fort = expr1.convert_to_fortran()
+        assert exp_fort == [
+            '      integer*4 a',
+            '      integer*4 b',
+            '      integer*4 c',
+            '      integer*4 d',
+            '      real*8 p',
+            '      real*8 q',
+            '      real*8 r',
+            '      real*8 s',
+            '      a = b + c',
+            '      s = p*q/r'
+        ]
+
+
+    def test_convert_c():
+        src1 = (
+            src +
+            """\
+            a = b + c
+            s = p * q / r
+            """
+        )
+        expr1.convert_to_expr(src1, 'f')
+        exp_c = expr1.convert_to_c()
+        assert exp_c == [
+            'int a = 0',
+            'int b = 0',
+            'int c = 0',
+            'int d = 0',
+            'double p = 0.0',
+            'double q = 0.0',
+            'double r = 0.0',
+            'double s = 0.0',
+            'a = b + c;',
+            's = p*q/r;'
+        ]
+
+
+    def test_exceptions():
+        src = 'int a;'
+        raises(ValueError, lambda: SymPyExpression(src))
+        raises(ValueError, lambda: SymPyExpression(mode = 'c'))
+        raises(NotImplementedError, lambda: SymPyExpression(src, mode = 'd'))
+
+elif not lfortran and not cin:
+    def test_raise():
+        raises(ImportError, lambda: SymPyExpression('int a;', 'c'))
+        raises(ImportError, lambda: SymPyExpression('integer :: a', 'f'))

backend_service/venv/lib/python3.13/site-packages/sympy/parsing/tests/test_sympy_parser.py

@@ -0,0 +1,371 @@
+# -*- coding: utf-8 -*-
+
+
+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
+
+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=False) == parse_expr(e, evaluate=False)
+    assert parse_expr(e, evaluate=False).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():
+    assert parse_expr("1 < 2", evaluate=False) == Lt(1, 2, evaluate=False)
+    assert parse_expr("1 <= 2", evaluate=False) == Le(1, 2, evaluate=False)
+    assert parse_expr("1 > 2", evaluate=False) == Gt(1, 2, evaluate=False)
+    assert parse_expr("1 >= 2", evaluate=False) == Ge(1, 2, evaluate=False)
+    assert parse_expr("1 != 2", evaluate=False) == Ne(1, 2, evaluate=False)
+    assert parse_expr("1 == 2", evaluate=False) == Eq(1, 2, evaluate=False)
+    assert parse_expr("1 < 2 < 3", evaluate=False) == And(Lt(1, 2, evaluate=False), Lt(2, 3, evaluate=False), evaluate=False)
+    assert parse_expr("1 <= 2 <= 3", evaluate=False) == And(Le(1, 2, evaluate=False), Le(2, 3, evaluate=False), evaluate=False)
+    assert parse_expr("1 < 2 <= 3 < 4", evaluate=False) == \
+        And(Lt(1, 2, evaluate=False), Le(2, 3, evaluate=False), Lt(3, 4, evaluate=False), evaluate=False)
+    # Valid Python relational operators that SymPy does not decide how to handle them yet
+    raises(ValueError, lambda: parse_expr("1 in 2", evaluate=False))
+    raises(ValueError, lambda: parse_expr("1 is 2", evaluate=False))
+    raises(ValueError, lambda: parse_expr("1 not in 2", evaluate=False))
+    raises(ValueError, lambda: parse_expr("1 is not 2", evaluate=False))
+
+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():
+    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