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SymPyToolkit

class SymPyToolkit(BaseToolkit):

A toolkit for performing symbolic computations using SymPy. This includes methods for Algebraic manipulation calculus and Linear Algebra.

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init

def __init__(
    self,
    default_variable: str = 'x',
    timeout: Optional[float] = None
):

Initializes the toolkit with a default variable and logging.

Parameters:

  • default_variable (str): The default variable for operations (default: :obj:x)

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simplify_expression

def simplify_expression(self, expression: str):

Simplifies a mathematical expression.

Parameters:

  • expression (str): The mathematical expression to simplify, provided as a string.

Returns:

str: JSON string containing the simplified mathematical expression in the "result" field. If an error occurs, the "status" field will be set to "error" with a corresponding "message".

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expand_expression

def expand_expression(self, expression: str):

Expands an algebraic expression.

Parameters:

  • expression (str): The algebraic expression to expand, provided as a string.

Returns:

str: JSON string containing the expanded algebraic expression in the "result" field. If an error occurs, the JSON string will include an "error" field with the corresponding error message.

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factor_expression

def factor_expression(self, expression: str):

Factors an algebraic expression.

Parameters:

  • expression (str): The algebraic expression to factor, provided as a string.

Returns:

str: JSON string containing the factored algebraic expression in the "result" field. If an error occurs, the JSON string will include an "error" field with the corresponding error message.

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solve_linear_system

def solve_linear_system(self, equations: List[str], variables: List[str]):

Solves a system of linear equations.

Parameters:

  • equations (List[str]): A list of strings representing the linear equations to be solved.
  • variables (List[str]): A list of strings representing the variables involved in the equations.

Returns:

str: JSON string containing the solution to the system of equations in the "result" field. Each solution is represented as a tuple of values corresponding to the variables. If an error occurs, the JSON string will include an "error" field with the corresponding error message.

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solve_nonlinear_system

def solve_nonlinear_system(self, sympy_equations: List[str], variables: List[str]):

Solves a system of nonlinear equations.

Parameters:

  • sympy_equations (List[str]): A list of strings representing the nonlinear equations to be solved. The equation to solve, must be compatible with SymPy, provided as a string.
  • variables (List[str]): A list of strings representing the variables involved in the equations.

Returns:

str: JSON string containing the solutions to the system of equations in the "result" field. Each solution is represented as a tuple of values corresponding to the variables. If an error occurs, the JSON string will include an "error" field with the corresponding error message.

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solve_univariate_inequality

def solve_univariate_inequality(self, inequality: str, variable: str):

Solves a single-variable inequality.

Parameters:

  • inequality (str): A string representing the inequality to be solved.
  • variable (str): The variable in the inequality.

Returns:

str: JSON string containing the solution to the inequality in the "result" field. The solution is represented in a symbolic format (e.g., intervals or expressions). If an error occurs, the JSON string will include an "error" field with the corresponding error message.

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reduce_inequalities

def reduce_inequalities(self, inequalities: List[str]):

Reduces a system of inequalities.

Parameters:

  • inequalities (List[str]): A list of strings representing the inequalities to be reduced.

Returns:

str: JSON string containing the reduced system of inequalities in the "result" field. The solution is represented in a symbolic format (e.g., combined intervals or expressions). If an error occurs, the JSON string will include an "error" field with the corresponding error message.

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polynomial_representation

def polynomial_representation(self, expression: str, variable: str):

Represents an expression as a polynomial.

Parameters:

  • expression (str): The mathematical expression to represent as a polynomial, provided as a string.
  • variable (str): The variable with respect to which the polynomial representation will be created.

Returns:

str: JSON string containing the polynomial representation of the expression in the "result" field. The polynomial is returned in a symbolic format. If an error occurs, the JSON string will include an "error" field with the corresponding error message.

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polynomial_degree

def polynomial_degree(self, expression: str, variable: str):

Returns the degree of a polynomial.

Parameters:

  • expression (str): The polynomial expression for which the degree is to be determined, provided as a string.
  • variable (str): The variable with respect to which the degree of the polynomial is calculated.

Returns:

str: JSON string containing the degree of the polynomial in the "result" field. If an error occurs, the JSON string will include an "error" field with the corresponding error message.

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polynomial_coefficients

def polynomial_coefficients(self, expression: str, variable: str):

Returns the coefficients of a polynomial.

Parameters:

  • expression (str): The polynomial expression from which the coefficients are to be extracted, provided as a string.
  • variable (str): The variable with respect to which the polynomial coefficients are determined.

Returns:

str: JSON string containing the list of coefficients of the polynomial in the "result" field. The coefficients are ordered from the highest degree term to the constant term. If an error occurs, the JSON string will include an `“error” field with the corresponding error message.

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solve_equation

def solve_equation(self, sympy_equation: str, variable: Optional[str] = None):

Solves an equation for a specific variable.

Parameters:

  • sympy_equation (str): The equation to solve, must be compatible with SymPy, provided as a string.
  • variable (str, optional): The variable to solve for. If not specified, the function will use the default variable.

Returns:

str: JSON string containing the solutions to the equation in the "result" field. Each solution is represented as a string. If an error occurs, the JSON string will include an "error" field with the corresponding error message.

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find_roots

def find_roots(self, expression: str):

Finds the roots of a polynomial or algebraic equation.

Parameters:

  • expression (str): The polynomial or algebraic equation for which the roots are to be found, provided as a string.

Returns:

str: JSON string containing the roots of the expression in the "result" field. The roots are represented as a list of solutions. If an error occurs, the JSON string will include a "status" field set to "error" and a "message" field with the corresponding error description.

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differentiate

def differentiate(self, expression: str, variable: Optional[str] = None):

Differentiates an expression with respect to a variable.

Parameters:

  • expression (str): The mathematical expression to differentiate, provided as a string.
  • variable (str, optional): The variable with respect to which the differentiation is performed. If not specified, the default variable is used.

Returns:

str: JSON string containing the derivative of the expression in the "result" field. If an error occurs, the JSON string will include an "error" field with the corresponding error message.

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integrate

def integrate(self, expression: str, variable: Optional[str] = None):

Integrates an expression with respect to a variable.

Parameters:

  • expression (str): The mathematical expression to integrate, provided as a string.
  • variable (str, optional): The variable with respect to which the integration is performed. If not specified, the default variable is used.

Returns:

str: JSON string containing the integral of the expression in the "result" field. If an error occurs, the JSON string will include an "error" field with the corresponding error message.

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definite_integral

def definite_integral(
    self,
    expression: str,
    variable: str,
    lower: float,
    upper: float
):

Computes the definite integral of an expression within given bounds.

Parameters:

  • expression (str): The mathematical expression to integrate, provided as a string.
  • variable (str): The variable with respect to which the definite integration is performed.
  • lower (float): The lower limit of the integration.
  • upper (float): The upper limit of the integration.

Returns:

str: JSON string containing the result of the definite integral in the "result" field. If an error occurs, the JSON string will include an "error" field with the corresponding error message.

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series_expansion

def series_expansion(
    self,
    expression: str,
    variable: str,
    point: float,
    order: int
):

Expands an expression into a Taylor series around a given point up to a specified order.

Parameters:

  • expression (str): The mathematical expression to expand, provided as a string.
  • variable (str): The variable with respect to which the series expansion is performed.
  • point (float): The point around which the Taylor series is expanded.
  • order (int): The order up to which the series expansion is computed.

Returns:

str: JSON string containing the Taylor series expansion of the expression in the "result" field. If an error occurs, the JSON string will include an "error" field with the corresponding error message.

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compute_limit

def compute_limit(
    self,
    expression: str,
    variable: str,
    point: float
):

Computes the limit of an expression as a variable approaches a point.

Parameters:

  • expression (str): The mathematical expression for which the limit is to be computed, provided as a string.
  • variable (str): The variable with respect to which the limit is computed.
  • point (float): The point that the variable approaches.

Returns:

str: JSON string containing the computed limit of the expression in the "result" field. If an error occurs, the JSON string will include an "error" field with the corresponding error message.

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find_critical_points

def find_critical_points(self, expression: str, variable: str):

Finds the critical points of an expression by setting its derivative to zero.

Parameters:

  • expression (str): The mathematical expression for which critical points are to be found, provided as a string.
  • variable (str): The variable with respect to which the critical points are determined.

Returns:

str: JSON string containing the critical points of the expression in the "result" field. The critical points are returned as a list of values corresponding to the variable. If an error occurs, the JSON string will include an "error" field with the corresponding error message.

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check_continuity

def check_continuity(
    self,
    expression: str,
    variable: str,
    point: float
):

Checks if an expression is continuous at a given point.

Parameters:

  • expression (str): The mathematical expression to check for continuity, provided as a string.
  • variable (str): The variable with respect to which continuity is checked.
  • point (float): The point at which the continuity of the expression is checked.

Returns:

str: JSON string containing the result of the continuity check in the "result" field. The result will be "True" if the expression is continuous at the given point, otherwise "False". If an error occurs, the JSON string will include an "error" field with the corresponding error message.

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compute_determinant

def compute_determinant(self, matrix: List[List[float]]):

Computes the determinant of a matrix.

Parameters:

  • matrix (List[List[float]]): A two-dimensional list representing the matrix for which the determinant is to be computed.

Returns:

str: JSON string containing the determinant of the matrix in the "result" field. If an error occurs, the JSON string will include an "error" field with the corresponding error message.

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compute_inverse

def compute_inverse(self, matrix: List[List[float]]):

Computes the inverse of a matrix.

Parameters:

  • matrix (List[List[float]]): A two-dimensional list representing the matrix for which the inverse is to be computed.

Returns:

str: JSON string containing the inverse of the matrix in the "result" field. The inverse is represented in a symbolic matrix format. If an error occurs, the JSON string will include an "error" field with the corresponding error message.

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compute_eigenvalues

def compute_eigenvalues(self, matrix: List[List[float]]):

Computes the eigenvalues of a matrix.

Parameters:

  • matrix (List[List[float]]): A two-dimensional list representing the matrix for which the eigenvalues are to be computed.

Returns:

str: JSON string containing the eigenvalues of the matrix in the "result" field. The eigenvalues are represented as a dictionary where keys are the eigenvalues (as strings) and values are their multiplicities (as strings). If an error occurs, the JSON string will include an "error" field with the corresponding error message.

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compute_eigenvectors

def compute_eigenvectors(self, matrix: List[List[float]]):

Computes the eigenvectors of a matrix.

Parameters:

  • matrix (List[List[float]]): A two-dimensional list representing the matrix for which the eigenvectors are to be computed.

Returns:

str: JSON string containing the eigenvectors of the matrix in the "result" field. Each eigenvalue is represented as a dictionary with the following keys:

  • "eigenvalue": The eigenvalue (as a string).
  • "multiplicity": The multiplicity of the eigenvalue (as an integer).
  • "eigenvectors": A list of eigenvectors (each represented as a string).

If an error occurs, the JSON string will include an "error" field with the corresponding error message.

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compute_nullspace

def compute_nullspace(self, matrix: List[List[float]]):

Computes the null space of a matrix.

Parameters:

  • matrix (List[List[float]]): A two-dimensional list representing the matrix for which the null space is to be computed.

Returns:

str: JSON string containing the null space of the matrix in the "result" field. The null space is represented as a list of basis vectors, where each vector is given as a string in symbolic format. If an error occurs, the JSON string will include an "error" field with the corresponding error message.

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compute_rank

def compute_rank(self, matrix: List[List[float]]):

Computes the rank of a matrix.

Parameters:

  • matrix (List[List[float]]): A two-dimensional list representing the matrix for which the rank is to be computed.

Returns:

str: JSON string containing the rank of the matrix in the "result" field. The rank is represented as an integer. If an error occurs,the JSON string will include an "error" field with the corresponding error message.

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compute_inner_product

def compute_inner_product(self, vector1: List[float], vector2: List[float]):

Computes the inner (dot) product of two vectors.

Parameters:

  • vector1 (List[float]): The first vector as a list of floats.
  • vector2 (List[float]): The second vector as a list of floats.

Returns:

str: JSON string containing the inner product in the "result" field. If an error occurs, the JSON string will include an "error" field with the corresponding error message.

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handle_exception

def handle_exception(self, func_name: str, error: Exception):

Handles exceptions by logging and returning error details.

Parameters:

  • func_name (str): The name of the function where the exception occurred.
  • error (Exception): The exception object containing details about the error.

Returns:

str: JSON string containing the error details. The JSON includes:

  • "status": Always set to "error".
  • "message": A string representation of the exception message.

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get_tools

def get_tools(self):

Returns:

List[FunctionTool]: A list of FunctionTool objects representing the toolkit’s methods, making them accessible to the agent.