import sympy
import gradio as gr

def fourier_series_example(function_type: str = "sawtooth", n_terms: int = 5) -> str:
    """
    Provides an example of a Fourier series for a predefined function.

    Args:
        function_type: "sawtooth" or "square" wave.
        n_terms: Number of terms to compute in the series.

    Returns:
        String representation of the Fourier series.
    """
    try:
        L = sympy.pi
        x = sympy.Symbol('x')
        if function_type == "sawtooth":
            series = sympy.S(0)
            for i in range(1, n_terms + 1):
                bn_coeff = -2 * ((-1)**i) / i
                series += bn_coeff * sympy.sin(i * x)
            return f"Fourier series for sawtooth wave (f(x)=x on [-pi,pi]): {str(series)}"
        elif function_type == "square":
            series = sympy.S(0)
            for i in range(1, n_terms + 1):
                if i % 2 != 0:
                    bn_coeff = 4 / (i * sympy.pi)
                    series += bn_coeff * sympy.sin(i * x)
            return f"Fourier series for square wave (f(x)=1 on [0,pi], -1 on [-pi,0]): {str(series)}"
        else:
            return "Error: Unknown function type for Fourier series. Choose 'sawtooth' or 'square'."
    except Exception as e:
        return f"Error generating Fourier series: {e}"

fourier_series_interface = gr.Interface(
    fn=fourier_series_example,
    inputs=[
        gr.Radio(choices=["sawtooth", "square"], label="Function Type", value="sawtooth"),
        gr.Number(label="Number of Terms (n)", value=5, precision=0)
    ],
    outputs="text",
    title="Fourier Series Examples",
    description="Generate Fourier series for predefined periodic functions.\n\n**Description:**\nThis tool generates the Fourier series for a sawtooth or square wave with a specified number of terms.\n\n**Examples:**\n- Function Type: sawtooth, n=3 → Output: Fourier series for sawtooth wave (f(x)=x on [-pi,pi]): ...\n- Function Type: square, n=5 → Output: Fourier series for square wave (f(x)=1 on [0,pi], -1 on [-pi,0]): ...",
    examples=[["sawtooth", 3], ["square", 5]],
)