stdmathlib 0.1.10

A library to simplify mathematical computations.

stdmathlib

A Python library to simplify mathematical computations.

Installation

pip install stdmathlib

Functions

integrate_expression

Integrates a mathematical expression with respect to a variable.

Parameters:

• expression_str (str): The mathematical expression as a string.
• var (str): The variable to integrate with respect to (default is 'x').
• lower_limit (float, optional): The lower limit of integration.
• upper_limit (float, optional): The upper limit of integration.

Returns:

• integral_expr: The symbolic integral expression (indefinite integral).
• integral_value (optional): The numerical value of the definite integral.

Example Usage:

from stdmathlib import integrate_expression

# Indefinite integral
integral_expr = integrate_expression('x**2')
print(f"Indefinite integral: {integral_expr} + C")  # Output: x**3/3 + C

# Definite integral from x=0 to x=2
integral_expr, integral_value = integrate_expression('x**2', lower_limit=0, upper_limit=2)
print(f"Indefinite integral: {integral_expr} + C")          # Output: x**3/3 + C
print(f"Definite integral from 0 to 2: {integral_value}")  # Output: 2.66666666666667

derivative

Differentiates a mathematical expression with respect to a variable.

Parameters:

• expression_str (str): The mathematical expression as a string.
• var (str): The variable to differentiate with respect to (default is 'x').
• eval_point (float, optional): The point at which to evaluate the derivative.

Returns:

• derivative_expr: The symbolic derivative expression.
• derivative_value (optional): The numerical value of the derivative at eval_point.

Example Usage:

from stdmathlib import derivative

# Differentiate symbolically
derivative = derivative('x**2 + 3*x + 2')
print(derivative)  # Output: 2*x + 3

# Differentiate and evaluate at x = 2
derivative_expr, derivative_value = derivative('x**2 + 3*x + 2', eval_point=2)
print(derivative_expr)      # Output: 2*x + 3
print(derivative_value)     # Output: 7

partial_derivative_expression

Computes the partial derivative of a multivariable function with respect to specified variables.

Parameters:

• expression_str (str): The multivariable function as a string.
• variables (list of str): List of variable names in the function.
• differentiation_vars (list of str): List of variables to differentiate with respect to.
• eval_points (dict, optional): Dictionary of variable values for evaluation.

Returns:

• derivative_expr: The symbolic partial derivative expression.
• derivative_value (optional): The numerical value of the derivative at eval_points.

Example Usage:

from stdmathlib import partial_derivative_expression

# Compute ?f/?x
expression = 'x**2 * y + y**3'
variables = ['x', 'y']
differentiation_vars = ['x']
partial_derivative = partial_derivative_expression(expression, variables, differentiation_vars)
print(partial_derivative)  # Output: 2*x*y

plot

Plots a mathematical expression using matplotlib.

Parameters:

• expression_str (str): The mathematical expression as a string, e.g., 'sin(x)'.
• var (str): The variable in the expression (default is 'x').
• range_start (float): The start of the range for the variable (default is -10).
• range_end (float): The end of the range for the variable (default is 10).
• num_points (int): The number of points to compute for plotting (default is 1000).
• title (str): The title of the plot.
• xlabel (str): The label for the x-axis.
• ylabel (str): The label for the y-axis.
• line_style (str): The line style for the plot (e.g., '-', '--', '-.', ':').
• color (str): The color of the plot line (e.g., 'blue', 'red', '#FF5733').

Returns:

• None: Displays the plot.

Example Usage:

from stdmathlib import plot
import numpy as np

# Plot y = sin(x) from -2? to 2? with customizations
plot(
    expression_str='sin(x)',
    range_start=-2 * np.pi,
    range_end=2 * np.pi,
    title='Sine Function',
    xlabel='Angle (radians)',
    ylabel='Amplitude',
    line_style='--',
    color='red'
)

integrate_multivariable_expression

Computes the multivariable integral of an expression with respect to specified variables.

Parameters:

• expression_str (str): The mathematical expression as a string.
• variables (list of str): List of variable names to integrate with respect to.
• limits (list of tuples, optional): List of tuples specifying the limits for each variable. Each tuple should be (variable_name, lower_limit, upper_limit).

Returns:

• For indefinite integrals: The symbolic integral expression.
• For definite integrals: The numerical value of the integral.

Example Usage:

from stdmathlib import integrate_multivariable_expression

# Indefinite integral
integral_expr = integrate_multivariable_expression('x * y', ['x', 'y'])
print(f"Indefinite integral: {integral_expr} + C")

# Definite integral
limits = [('x', 0, 1), ('y', 0, 2)]
integral_value = integrate_multivariable_expression('x * y', ['x', 'y'], limits=limits)
print(f"Definite integral value: {integral_value}")

factorial

Computes the factorial of a non-negative integer.

Parameters:

• n (int): The number to compute the factorial of (n ? 0).

Returns:

• int: The factorial of n.

Example Usage:

from stdmathlib import factorial

result = factorial(5)
print(f"5! = {result}")  # Output: 5! = 120

combinations

Computes the number combinations of two non-negative integers.

Parameters:

• n (int): The number of items in the set (n ? 0).
• r (int): The number of spots that can be chosen from (n ? r ? 0).

Returns:

• int: The number of combinations possible given n and r.

Example Usage:

from stdmathlib import combinations

result = combinations(5, 3)
print(f"5C3 = {result}")  # Output: 5C3 = 10

permutations

Computes the number of arrangements that n can make with the length of r, where order is important.

Parameters:

• n (int): The number of items in the set (n ? 0).
• r (int): the number of selected objects arranged in a certain order (n ? r ? 0).

Returns:

• int: The number of permutations possible given n and r.

Example Usage:

from stdmathlib import permutations

result = permutations(5, 3)
print(f"5P3 = {result}")  # Output: 5P3 = 60