app.py

\
import re
import gradio as gr
import sympy as sp
from sympy.parsing.sympy_parser import (
    parse_expr, standard_transformations,
    implicit_multiplication_application, convert_xor
)

TITLE = "LanguageBridge — Math Fast Agent (SymPy)"

# ---- 正規化：全形→半形、√→sqrt、^→**、自動補乘號（隱式→顯式） ----
def normalize_ascii(s: str) -> str:
    table = str.maketrans({
        '（':'(', '）':')', '，':',', '；':';', '：':':',
        '＝':'=', '－':'-', '＋':'+', '＊':'*', '／':'/', '。':'.',
        '×':'*', '√':'sqrt'
    })
    return s.translate(table)

def auto_insert_stars(s: str) -> str:
    s = re.sub(r'(\d)([A-Za-z])', r'\1*\2', s)      # 3x -> 3*x
    s = re.sub(r'([A-Za-z0-9_])\(', r'\1*(', s)      # x( -> x*(
    s = re.sub(r'\)([A-Za-z0-9_])', r')*\1', s)      # )x -> )*x
    s = re.sub(r'(\d)\s*sqrt', r'\1*sqrt', s)        # 2sqrt -> 2*sqrt
    return s

def preprocess(expr: str) -> str:
    s = (expr or "").strip()
    s = normalize_ascii(s)
    s = s.replace("^", "**")                         # 2^3 -> 2**3
    s = auto_insert_stars(s)                         # 隱式乘法補 *
    return s

TRANS = standard_transformations + (implicit_multiplication_application, convert_xor)

def to_sympy_expr(s: str):
    s = preprocess(s)
    return parse_expr(s, transformations=TRANS)

def to_sympy_eq(s: str):
    s = preprocess(s)
    if "=" not in s:
        raise ValueError("等式缺少 '='")
    L, R = s.split("=", 1)
    return sp.Eq(parse_expr(L, transformations=TRANS),
                 parse_expr(R, transformations=TRANS))

def solve_math(q: str):
    q = (q or "").strip()
    if not q:
        return "請輸入算式或方程，例如：3x+7=1；sin(x)^2 + cos(x)^2；factor(x^4-1)"

    try:
        # 允許多行或分號分隔
        parts = [s.strip() for seg in q.split(";") for s in seg.split("\n")]
        parts = [p for p in parts if p]

        # 有 '=' ：解方程（可聯立）
        if any("=" in p for p in parts):
            eqs, syms = [], set()
            for s in parts:
                if "=" in s:
                    e = to_sympy_eq(s)
                    eqs.append(e)
                    syms |= e.free_symbols | e.rhs.free_symbols
            if not syms:
                syms = {sp.symbols("x")}
            sol = sp.solve(eqs, list(syms), dict=True)
            if not sol:
                return "無解或需要更多條件。"
            return "\\n".join(
                f"解 {i}: " + ", ".join([f"{k} = {sp.simplify(v)}" for k, v in d.items()])
                for i, d in enumerate(sol, 1)
            )

        # 否則視為一般表達式：簡化/因式/微分/積分
        expr = to_sympy_expr(q)
        out = []
        try: out.append(f"簡化：{sp.simplify(expr)}")
        except Exception: out.append(f"簡化：{expr}")
        try:
            fact = sp.factor(expr)
            if fact != expr: out.append(f"因式分解：{fact}")
        except Exception: pass
        try:
            x = next(iter(expr.free_symbols)) if expr.free_symbols else sp.symbols("x")
            out.append(f"對 {x} 微分：{sp.diff(expr, x)}")
            out.append(f"對 {x} 積分：{sp.integrate(expr, x)}")
        except Exception: pass
        return "\\n".join(out) if out else f"結果：{expr}"

    except Exception as e:
        return f"解析失敗：{e}"

with gr.Blocks(title=TITLE) as demo:
    gr.Markdown(
        "## " + TITLE + "\\n"
        "貼上算式（可多行 / `;` 分隔）。支援：隱式乘法 `3x`, `2(x+1)`, `(x)(x+1)`, `2sqrt(x)`；"
        "`x^2` 自動轉 `x**2`，`√(x)` 自動轉 `sqrt(x)`。"
    )
    q = gr.Textbox(lines=6, label="題目 / 算式（可含聯立方程）")
    out = gr.Textbox(lines=12, label="輸出")
    gr.Button("送出 🚀").click(fn=solve_math, inputs=q, outputs=out)

if __name__ == "__main__":
    demo.launch()