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README.md

@@ -9,4 +9,4 @@ app_file: app.py
 pinned: false
 ---
 
-純 SymPy 的數學推理代理（不依賴 LLM），支援一次貼上長式、簡化、解一元/聯立方程。
+純 **SymPy** 的數學推理代理（不依賴 LLM）。支援一次貼上長式、簡化、解一元/聯立方程與基本微積分。

app.py

@@ -8,61 +8,81 @@ 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)"
+
     try:
-        # 支援方程/聯立：可用分號或換行分隔
+        # 情境 A：含 '=' → 視為（可能多條）方程，支援分號/換行分隔
         if "=" in q:
-            parts = [s.strip() for seg in q.split(";") for s in seg.split("\n")]
-            eqs, syms = [], set()
+            # 將多行與分號斷開
+            parts = []
+            for seg in q.split(";"):
+                parts += [s.strip() for s in seg.split("\n")]
+            parts = [s for s in parts if s]
+
+            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))
+                L = sp.sympify(left)
+                R = sp.sympify(right)
+                eq = sp.Eq(L, R)
                 eqs.append(eq)
-                syms |= eq.free_symbols
-                if hasattr(eq, "rhs"):
-                    syms |= eq.rhs.free_symbols
+                syms |= L.free_symbols | R.free_symbols
+
+            if not eqs:
+                return "沒有可解析的方程式。"
             if not syms:
-                x = sp.symbols("x")
-                syms = {x}
+                syms = {sp.symbols("x")}
+
+            # 解聯立（回傳 dict 列表）
             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()]))
+                lines.append(
+                    "解 {}: ".format(i) + ", ".join(f"{k} = {sp.simplify(v)}" for k, v in s.items())
+                )
             return "\n".join(lines)
 
-        # 非方程：做一輪常見操作
+        # 情境 B：純表達式 → 嘗試簡化、因式、微分、積分
         expr = sp.sympify(q)
-        tips = []
+        out = []
+
         try:
-            tips.append(f"簡化：{sp.simplify(expr)}")
+            simp = sp.simplify(expr)
+            out.append(f"簡化：{simp}")
         except Exception:
-            tips.append(f"簡化：{expr}")
+            pass
+
         try:
-            fact = sp.factor(expr)
-            if fact != expr:
-                tips.append(f"因式分解：{fact}")
+            fac = sp.factor(expr)
+            if fac != expr:
+                out.append(f"因式分解：{fac}")
         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)}")
+            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}"
 
 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(f"## {TITLE}\n- 貼上**算式/方程**（可多行；或用分號 `;` 分隔聯立）\n- 範例：`2x+3=11`、`x+y=3; x-y=1`、`sin(x)**2 + cos(x)**2`、`factor(x**2-9)`")
     q = gr.Textbox(lines=6, label="題目 / 算式（可含聯立方程）")
-    out = gr.Textbox(lines=10, label="輸出")
-    gr.Button("送出 🚀").click(fn=solve_math, inputs=q, outputs=out)
+    out = gr.Textbox(lines=12, label="輸出")
+    btn = gr.Button("送出 🚀")
+    btn.click(solve_math, q, out)
 
 if __name__ == "__main__":
-    demo.launch()
+    # 在 Colab 預覽：一定要 share=True 才會印出 public URL
+    demo.launch(share=True)