intro
Introduces a variable with specified assumptions and stores it
intro_many
Introduces multiple variables with specified assumptions simultaneously
introduce_expression
Parses an expression string using available local variables and stores it
print_latex_expression
Prints a stored expression in LaTeX format, along with variable assumptions
solve_algebraically
Solves an equation algebraically for a given variable over a given domain
solve_linear_system
Solves a system of linear equations
solve_nonlinear_system
Solves a system of nonlinear equations
introduce_function
Introduces a function variable for use in differential equations
dsolve_ode
Solves an ordinary differential equation
pdsolve_pde
Solves a partial differential equation
create_predefined_metric
Creates a predefined spacetime metric (e.g. Schwarzschild, Kerr, Minkowski)
search_predefined_metrics
Searches available predefined metrics
calculate_tensor
Calculates tensors from a metric (Ricci, Einstein, Weyl tensors)
create_custom_metric
Creates a custom metric tensor from provided components and symbols
print_latex_tensor
Prints a stored tensor expression in LaTeX format
simplify_expression
Simplifies a mathematical expression using SymPy's canonicalize function
substitute_expression
Substitutes a variable with an expression in another expression
integrate_expression
Integrates an expression with respect to a variable
differentiate_expression
Differentiates an expression with respect to a variable
create_coordinate_system
Creates a 3D coordinate system for vector calculus operations
create_vector_field
Creates a vector field in the specified coordinate system
calculate_curl
Calculates the curl of a vector field
calculate_divergence
Calculates the divergence of a vector field
calculate_gradient
Calculates the gradient of a scalar field
convert_to_units
Converts a quantity to given target units
quantity_simplify_units
Simplifies a quantity with units
create_matrix
Creates a SymPy matrix from the provided data
matrix_determinant
Calculates the determinant of a matrix
matrix_inverse
Calculates the inverse of a matrix
matrix_eigenvalues
Calculates the eigenvalues of a matrix
matrix_eigenvectors
Calculates the eigenvectors of a matrix