Update app.py via Colab one-block

app.py

@@ -1,68 +1,118 @@
-\
+
+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)"
 
+# ---------- 輸入正規化：隱式乘法 / ^→** / 全形→半形 / √→sqrt ----------
+def normalize_ascii(s: str) -> str:
+    table = str.maketrans({
+        '（':'(', '）':')', '，':',', '；':';', '：':':',
+        '＝':'=', '－':'-', '＋':'+', '＊':'*', '／':'/', '。':'.',
+        '×':'*', '√':'sqrt'
+    })
+    return s.translate(table)
+
+def auto_insert_stars(s: str) -> str:
+    # 3x -> 3*x； x(x+1) -> x*(x+1)；(x+1)x -> (x+1)*x； 2sqrt(x) -> 2*sqrt(x)
+    s = re.sub(r'(\d)([A-Za-z])', r'\1*\2', s)
+    s = re.sub(r'([A-Za-z0-9_])\(', r'\1*(', s)
+    s = re.sub(r'\)([A-Za-z0-9_])', r')*\1', s)
+    s = re.sub(r'(\d)\s*sqrt', r'\1*sqrt', s)
+    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 → 顯式
+    return s
+
+# 支援隱式乘法與 ^ 解析
+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))
+
+# ---------------- 主邏輯（保留原介面與輸出格式） ----------------
 def solve_math(q: str):
     q = (q or "").strip()
     if not q:
-        return "請輸入算式或方程，例如：2x+3=11；或：sin(x)**2 + cos(x)**2；或：factor(x**2-9)"
+        return "請輸入算式或方程，例如：2x+3=11；sin(x)^2 + cos(x)^2；factor(x^2-9)"
+
     try:
-        # 支援方程/聯立：可用分號或換行分隔
-        if "=" in q:
-            parts = [s.strip() for seg in q.split(";") for s in seg.split("\n")]
+        # 多題/聯立：分號 ; 或換行 \n 分隔
+        parts = [s.strip() for seg in q.split(";") for s in seg.split("\n")]
+        parts = [p for p in parts if p]
+
+        # 若任一行含 '='，啟用「解方程（可聯立）」模式
+        if any("=" in p for p in parts):
             eqs, syms = [], set()
             for s in parts:
-                if not s: 
-                    continue
-                if "=" not in s:
-                    continue
-                left, right = s.split("=", 1)
-                eq = sp.Eq(sp.sympify(left), sp.sympify(right))
-                eqs.append(eq)
-                syms |= eq.free_symbols
-                if hasattr(eq, "rhs"):
-                    syms |= eq.rhs.free_symbols
+                if "=" in s:
+                    e = to_sympy_eq(s)
+                    eqs.append(e)
+                    syms |= e.free_symbols | e.rhs.free_symbols
             if not syms:
-                x = sp.symbols("x")
-                syms = {x}
+                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。"
-            lines = []
-            for i, s in enumerate(sol, 1):
-                lines.append(f"解 {i}: " + ", ".join([f"{k} = {sp.simplify(v)}" for k, v in s.items()]))
-            return "\n".join(lines)
+            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)
+            )
 
-        # 非方程：做一輪常見操作
-        expr = sp.sympify(q)
-        tips = []
+        # 否則視為單一表達式：簡化 / 因式 / 微分 / 積分
+        expr = to_sympy_expr(q)
+        out = []
         try:
-            tips.append(f"簡化：{sp.simplify(expr)}")
+            out.append(f"簡化：{sp.simplify(expr)}")
         except Exception:
-            tips.append(f"簡化：{expr}")
+            out.append(f"簡化：{expr}")
         try:
             fact = sp.factor(expr)
             if fact != expr:
-                tips.append(f"因式分解：{fact}")
+                out.append(f"因式分解：{fact}")
         except Exception:
             pass
         try:
-            x = list(expr.free_symbols)[0] if expr.free_symbols else sp.symbols("x")
-            tips.append(f"對 {x} 微分：{sp.diff(expr, x)}")
-            tips.append(f"對 {x} 積分：{sp.integrate(expr, x)}")
+            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(tips) if tips else f"結果：{expr}"
+        return "\n".join(out) if out else f"結果：{expr}"
+
     except Exception as e:
         return f"解析失敗：{e}"
 
+# ---------------- 介面 ----------------
 with gr.Blocks(title=TITLE) as demo:
-    gr.Markdown(f"## {TITLE}\n貼上算式（可多行 / 用分號 `;` 分隔）：")
+    gr.Markdown(
+        "## " + TITLE + "\\n"
+        "貼上算式（可多行 / 用分號 `;` 分隔）。\\n\\n"
+        "**可直接輸入隱式乘法：** `3x`、`2(x+1)`、`(x)(x+1)`、`2sqrt(x)`；"
+        "也可用 `x^2`（自動轉為 `x**2`），`√(x)`（自動轉為 `sqrt(x)`）。"
+    )
     q = gr.Textbox(lines=6, label="題目 / 算式（可含聯立方程）")
-    out = gr.Textbox(lines=10, label="輸出")
+    out = gr.Textbox(lines=12, label="輸出")
     gr.Button("送出 🚀").click(fn=solve_math, inputs=q, outputs=out)
 
 if __name__ == "__main__":
+    # Space 環境不需要 share
     demo.launch()