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Conversions

func_to_op_const(expr)

Examples:

>>> e_1 = 'x_1*cubed(x_1*3-squared(c_1/x_1*2)-x_3)-squared(x)'
>>> func_to_op_const(e_1)
'x_1*(x_1*3-(c_1/x_1*2)**2-x_3)**3-(x)**2'
>>> func_to_op_const('cubed(x_1)')
'(x_1)**3'
Source code in src/equation_tree/util/conversions.py 
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def func_to_op_const(expr):
    """
    Examples:
        >>> e_1 = 'x_1*cubed(x_1*3-squared(c_1/x_1*2)-x_3)-squared(x)'
        >>> func_to_op_const(e_1)
        'x_1*(x_1*3-(c_1/x_1*2)**2-x_3)**3-(x)**2'
        >>> func_to_op_const('cubed(x_1)')
        '(x_1)**3'
    """
    for key, el in CONVERSIONS_FUNC_OP_CONST.items():
        expr = _func_op_const_rec(expr, key, el)
    return expr

infix_to_prefix(infix, function_test, operator_test)

Transforms prefix notation to infix notation

Example

is_function = lambda x: x in ['sin', 'cos'] is_operator = lambda x : x in ['+', '-', '*', '/'] infix_to_prefix('x_2-x_1', is_function, is_operator) ['-', 'x_2', 'x_1']

infix_to_prefix('x_1-(x_2+x_4)', is_function, is_operator) ['-', 'x_1', '+', 'x_2', 'x_4']

infix_to_prefix('x_1cos(c_1+x_2)', is_function, is_operator) ['', 'x_1', 'cos', '+', 'c_1', 'x_2']

is_function = lambda x: x in ['sin', 'cos', 'e'] is_operator = lambda x: x in ['+', '-', '', '^', 'max', '*', '/'] infix_to_prefix('x_1 + max(x_2, x_3)', is_function, is_operator) ['+', 'x_1', 'max', 'x_2', 'x_3']

infix_to_prefix('x_1-(x_2/(x_3-x_4))',is_function, is_operator) ['-', 'x_1', '/', 'x_2', '-', 'x_3', 'x_4']

infix_to_prefix('x_1^(sin(x_2)/x_3)', is_function, is_operator) ['^', 'x_1', '/', 'sin', 'x_2', 'x_3']

infix_to_prefix('sin(x_1)-x_2', is_function, is_operator) ['-', 'sin', 'x_1', 'x_2']

Source code in src/equation_tree/util/conversions.py 
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def infix_to_prefix(infix, function_test, operator_test):
    """
    Transforms prefix notation to infix notation

    Example:
        >>> is_function = lambda x: x in ['sin', 'cos']
        >>> is_operator = lambda x : x in ['+', '-', '*', '/']
        >>> infix_to_prefix('x_2-x_1', is_function, is_operator)
        ['-', 'x_2', 'x_1']

        >>> infix_to_prefix('x_1-(x_2+x_4)', is_function, is_operator)
        ['-', 'x_1', '+', 'x_2', 'x_4']

        >>> infix_to_prefix('x_1*cos(c_1+x_2)', is_function, is_operator)
        ['*', 'x_1', 'cos', '+', 'c_1', 'x_2']

        >>> is_function = lambda x: x in ['sin', 'cos', 'e']
        >>> is_operator = lambda x: x in ['+', '-', '*', '^', 'max', '**', '/']
        >>> infix_to_prefix('x_1 + max(x_2, x_3)', is_function, is_operator)
        ['+', 'x_1', 'max', 'x_2', 'x_3']

        >>> infix_to_prefix('x_1-(x_2/(x_3-x_4))',is_function, is_operator)
        ['-', 'x_1', '/', 'x_2', '-', 'x_3', 'x_4']

        >>> infix_to_prefix('x_1^(sin(x_2)/x_3)', is_function, is_operator)
        ['^', 'x_1', '/', 'sin', 'x_2', 'x_3']

        >>> infix_to_prefix('sin(x_1)-x_2', is_function, is_operator)
        ['-', 'sin', 'x_1', 'x_2']
    """

    # n = len(infix)

    # infix = list(infix[::-1].lower())
    #
    # for i in range(n):
    #     if infix[i] == "(":
    #         infix[i] = ")"
    #     elif infix[i] == ")":
    #         infix[i] = "("
    #
    # infix = "".join(infix)
    postfix = _infix_to_postfix(infix, function_test, operator_test)
    prefix = postfix[::-1]

    return prefix

op_const_to_func(expr)

Known operators with constants to functions. For exampl, e2->squared Examples: >>> op_const_to_func('x_1(x_13-(c_1/x_1*2)2-x_3)3-(x)2') 'x_1cubed(x_13-squared(c_1/x_12)-x_3)-squared(x)' >>> op_const_to_func('(x_1)3') 'cubed(x_1)' >>> op_const_to_func('x2') 'squared(x)' >>> op_const_to_func('c_13') 'cubed(c_1)' >>> op_const_to_func('(x_2*2)') 'squared(x_2)'

Source code in src/equation_tree/util/conversions.py 
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def op_const_to_func(expr):
    """
    Known operators with constants to functions. For exampl, e**2->squared
    Examples:
        >>> op_const_to_func('x_1*(x_1*3-(c_1/x_1*2)**2-x_3)**3-(x)**2')
        'x_1*cubed(x_1*3-squared(c_1/x_1*2)-x_3)-squared(x)'
        >>> op_const_to_func('(x_1)**3')
        'cubed(x_1)'
        >>> op_const_to_func('x**2')
        'squared(x)'
        >>> op_const_to_func('c_1**3')
        'cubed(c_1)'
        >>> op_const_to_func('(x_2**2)')
        'squared(x_2)'
    """

    for key, el in CONVERSION_OP_CONST_FUNC.items():
        expr = _op_const_func_rec(expr, key, el)
    expr = _remove_unnecessary_parentheses(expr)

    return expr

prefix_to_infix(prefix, function_test=lambda : False, operator_test=lambda : False)

Transforms prefix notation to infix notation

Example

is_function = lambda x: x in ['sin', 'cos'] is_operator = lambda x : x in ['+', '-', '', 'max', '*'] prefix_to_infix(['-', 'x_1', 'x_2'], is_function, is_operator) '(x_1-x_2)'

prefix_to_infix( ... ['', 'x', 'cos', '+', 'y', 'z'], is_function, is_operator) '(xcos((y+z)))'

prefix_to_infix(['max', 'x_1', 'x_2'], is_function, is_operator) 'max(x_1,x_2)'

prefix_to_infix(['', 'x_1', 'x_2'], is_function, is_operator) '(x_1x_2)'

Source code in src/equation_tree/util/conversions.py 
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def prefix_to_infix(
    prefix, function_test=lambda _: False, operator_test=lambda _: False
):
    """
    Transforms prefix notation to infix notation

    Example:
        >>> is_function = lambda x: x in ['sin', 'cos']
        >>> is_operator = lambda x : x in ['+', '-', '*', 'max', '**']
        >>> prefix_to_infix(['-', 'x_1', 'x_2'], is_function, is_operator)
        '(x_1-x_2)'

        >>> prefix_to_infix(
        ...     ['*', 'x', 'cos', '+', 'y', 'z'], is_function, is_operator)
        '(x*cos((y+z)))'

        >>> prefix_to_infix(['max', 'x_1', 'x_2'], is_function, is_operator)
        'max(x_1,x_2)'

        >>> prefix_to_infix(['**', 'x_1', 'x_2'], is_function, is_operator)
        '(x_1**x_2)'

    """
    stack = []
    for i in range(len(prefix) - 1, -1, -1):
        if function_test(prefix[i]):
            # symbol in unary operator
            stack.append(prefix[i] + "(" + stack.pop() + ")")
        elif (operator_test(prefix[i]) or prefix[i] == "**") and prefix[i] in [
            "+",
            "-",
            "/",
            "^",
            "*",
            "**",
        ]:
            # symbol is binary operator
            str = "(" + stack.pop() + prefix[i] + stack.pop() + ")"
            stack.append(str)
        elif operator_test(prefix[i]):
            str = prefix[i] + "(" + stack.pop() + "," + stack.pop() + ")"
            stack.append(str)
        else:
            # symbol is operand
            stack.append(prefix[i])
    return stack.pop()

standardize_sympy(sympy_expr, variable_test=lambda : False, constant_test=lambda : False)

replace all variables and constants with standards

Example

from sympy import sympify expr = sympify('x + A * cos(z+y)') expr A*cos(y + z) + x

is_variable = lambda x : x in ['x', 'y', 'z'] is_constant = lambda x : x in ['A'] standardize_sympy(expr, is_variable, is_constant) c_1*cos(x_2 + x_3) + x_1

expr = sympify('x_a+By') expr By + x_a is_variable = lambda x : '_' in x or x in ['y'] is_constant = lambda x : x == 'B' standardize_sympy(expr, is_variable, is_constant) c_1*x_2 + x_1

expr = sympify('x ** x') expr xx is_variable = lambda x: x in ['x'] standardize_sympy(expr, is_variable) x_1x_1

expr = sympify('sin(Cx) + cos(Cx)') expr sin(Cx) + cos(Cx)

is_variable = lambda x: x == 'x' is_constant = lambda x: x == 'C' standardize_sympy(expr, is_variable, is_constant) sin(c_1x_1) + cos(c_1x_1)

Source code in src/equation_tree/util/conversions.py 
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def standardize_sympy(
    sympy_expr, variable_test=lambda _: False, constant_test=lambda _: False
):
    """
    replace all variables and constants with standards

    Example:
        >>> from sympy import sympify
        >>> expr = sympify('x + A * cos(z+y)')
        >>> expr
        A*cos(y + z) + x

        >>> is_variable = lambda x : x in ['x', 'y', 'z']
        >>> is_constant = lambda x : x in ['A']
        >>> standardize_sympy(expr, is_variable, is_constant)
        c_1*cos(x_2 + x_3) + x_1

        >>> expr = sympify('x_a+B*y')
        >>> expr
        B*y + x_a
        >>> is_variable = lambda x : '_' in x or x in ['y']
        >>> is_constant = lambda x : x == 'B'
        >>> standardize_sympy(expr, is_variable, is_constant)
        c_1*x_2 + x_1

        >>> expr = sympify('x ** x')
        >>> expr
        x**x
        >>> is_variable = lambda x: x in ['x']
        >>> standardize_sympy(expr, is_variable)
        x_1**x_1

        >>> expr = sympify('sin(C*x) + cos(C*x)')
        >>> expr
        sin(C*x) + cos(C*x)

        >>> is_variable = lambda x: x == 'x'
        >>> is_constant = lambda x: x == 'C'
        >>> standardize_sympy(expr, is_variable, is_constant)
        sin(c_1*x_1) + cos(c_1*x_1)
    """
    variable_count = 0
    constant_count = 0
    variables = {}
    constants = {}

    def replace_symbols(node):
        nonlocal variable_count, constant_count, variables, constants
        if variable_test(str(node)):
            if is_variable_formatted(str(node)):
                new_symbol = symbols(str(node))
                variables[str(node)] = new_symbol
                return new_symbol
            if not str(node) in variables.keys() or str(node):
                variable_count += 1
                new_symbol = symbols(f"x_{variable_count}")
                variables[str(node)] = new_symbol
            else:
                new_symbol = variables[str(node)]
            return new_symbol
        elif constant_test(str(node)) and not is_numeric(str(node)):
            if is_constant_formatted(str(node)):
                new_symbol = symbols(str(node))
                constants[str(node)] = new_symbol
                return new_symbol
            if not str(node) in constants.keys():
                constant_count += 1
                new_symbol = symbols(f"c_{constant_count}")
                constants[str(node)] = new_symbol
            else:
                new_symbol = constants[str(node)]
            return new_symbol
        else:
            return node

    def recursive_replace(node):
        if node.is_Function or node.is_Add or node.is_Mul or node.is_Pow:
            return node.func(*[recursive_replace(arg) for arg in node.args])
        return replace_symbols(node)

    new_expression = recursive_replace(sympy_expr)
    return new_expression

unary_minus_to_binary(expr, operator_test)

replace unary minus with binary

Examples:

>>> o = lambda x: x in ['+', '-', '*', '/', '^']
>>> o_ = lambda x : x in ['+', '-', '*', '/', '**']
>>> unary_minus_to_binary('-x_1+x_2', o)
'x_2-x_1'

>>> unary_minus_to_binary('x_1-x_2', o)
'x_1-x_2'

>>> unary_minus_to_binary('x_1+(-x_2+x_3)', o)
'x_1+(x_3-x_2)'

>>> unary_minus_to_binary('-tan(x_1-exp(x_2))', o)
'(0-tan(x_1-exp(x_2)))'

>>> unary_minus_to_binary('-x_2', o)
'(0-x_2)'

>>> unary_minus_to_binary('exp(-x_1)*log(x_2)', o)
'exp((0-x_1))*log(x_2)'

>>> unary_minus_to_binary('(c_1 + x_2)*(-c_2 + x_3)', o)
'(c_1+x_2)*(x_3-c_2)'

>>> unary_minus_to_binary('-(c_1 - x_1)^2', o)
'(0-(c_1-x_1))^2'

>>> unary_minus_to_binary('-(c_1 - x_2)*(x_1 + x_2)', o)
'(0-(c_1-x_2))*(x_1+x_2)'

>>> unary_minus_to_binary('x_1**2 + x_2', o_)
'x_1**2+x_2'
Source code in src/equation_tree/util/conversions.py 
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def unary_minus_to_binary(expr, operator_test):
    """
    replace unary minus with binary

    Examples:
        >>> o = lambda x: x in ['+', '-', '*', '/', '^']
        >>> o_ = lambda x : x in ['+', '-', '*', '/', '**']
        >>> unary_minus_to_binary('-x_1+x_2', o)
        'x_2-x_1'

        >>> unary_minus_to_binary('x_1-x_2', o)
        'x_1-x_2'

        >>> unary_minus_to_binary('x_1+(-x_2+x_3)', o)
        'x_1+(x_3-x_2)'

        >>> unary_minus_to_binary('-tan(x_1-exp(x_2))', o)
        '(0-tan(x_1-exp(x_2)))'

        >>> unary_minus_to_binary('-x_2', o)
        '(0-x_2)'

        >>> unary_minus_to_binary('exp(-x_1)*log(x_2)', o)
        'exp((0-x_1))*log(x_2)'

        >>> unary_minus_to_binary('(c_1 + x_2)*(-c_2 + x_3)', o)
        '(c_1+x_2)*(x_3-c_2)'

        >>> unary_minus_to_binary('-(c_1 - x_1)^2', o)
        '(0-(c_1-x_1))^2'

        >>> unary_minus_to_binary('-(c_1 - x_2)*(x_1 + x_2)', o)
        '(0-(c_1-x_2))*(x_1+x_2)'

        >>> unary_minus_to_binary('x_1**2 + x_2', o_)
        'x_1**2+x_2'

    """
    _temp = _find_unary("-", str(expr), operator_test)
    while "#" in _temp:
        _temp = _move_placeholder(_temp, operator_test)
    _temp = _find_unary("+", _temp, operator_test)
    _temp = __remove_character_from_string(_temp, "#")
    _temp = _find_unary("-", _temp, operator_test)
    while "#" in _temp:
        _temp = _replace_with_zero_minus(_temp, operator_test)
    return _temp