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import sympy
import gradio as gr
def taylor_series_expansion(expression_str: str, variable_str: str = 'x', point: float = 0, order: int = 5) -> str:
"""
Computes the Taylor series expansion of an expression around a point.
Args:
expression_str: The mathematical expression (e.g., "exp(x)").
variable_str: The variable (default 'x').
point: The point around which to expand (default 0).
order: The order of the Taylor polynomial (default 5).
Returns:
String representation of the Taylor series or an error message.
"""
try:
var = sympy.Symbol(variable_str)
expr = sympy.parse_expr(expression_str, local_dict={variable_str: var}, transformations='all')
series = expr.series(var, x0=point, n=order).removeO()
return str(series)
except Exception as e:
return f"Error calculating Taylor series: {e}"
taylor_series_interface = gr.Interface(
fn=taylor_series_expansion,
inputs=[
gr.Textbox(label="Expression (e.g., exp(x), cos(x))", value="exp(x)"),
gr.Textbox(label="Variable (e.g., x)", value="x"),
gr.Number(label="Point of Expansion (x0)", value=0),
gr.Number(label="Order of Taylor Polynomial", value=5, precision=0)
],
outputs="text",
title="Taylor Series Expansion",
description="Compute the Taylor series of a function around a point.\n\n**Description:**\nThis tool computes the Taylor series expansion of a function around a specified point and order.\n\n**Examples:**\n- Expression: exp(x), Variable: x, Point: 0, Order: 5 → Output: 1 + x + x**2/2 + x**3/6 + x**4/24 + x**5/120\n- Expression: cos(x), Variable: x, Point: 0, Order: 4 → Output: 1 - x**2/2 + x**4/24\n- Expression: sin(x), Variable: x, Point: 0, Order: 3 → Output: x - x**3/6",
examples=[["exp(x)", "x", 0, 5], ["cos(x)", "x", 0, 4], ["sin(x)", "x", 0, 3]],
)
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