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README.md

@@ -1,5 +1,5 @@
 ---
-title: LanguageBridge — Math Fast Agent (SymPy, Safe)
+title: LanguageBridge — Math Fast Agent (SymPy)
 emoji: 🧮
 colorFrom: yellow
 colorTo: blue
@@ -9,9 +9,4 @@ app_file: app.py
 pinned: false
 ---
 
-A lightweight SymPy-based math agent. No torch needed.
-
-Usage examples:
-- 2*x + 5 = 11
-- sin(theta) = sqrt(3)/2, 0 <= theta < 2*pi
-- factor(x**4 - 1)
+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

@@ -1,131 +1,88 @@
-
+\
 import gradio as gr
 import sympy as sp
 
-def default_symbols():
-    names = ["x","y","z","t","theta","a","b","c","n","m"]
-    d = {name: sp.symbols(name, real=True) for name in names}
-    d["pi"] = sp.pi
-    d["e"]  = sp.E
-    d["sqrt"] = sp.sqrt
-    return d
+TITLE = "LanguageBridge — Math Fast Agent (SymPy)"
 
-def parse_constraints(parts, syms):
-    cons = []
-    for p in parts:
-        s = p.strip()
-        if not s:
-            continue
-        try:
-            rel = sp.sympify(s, locals=syms)
-            cons.append(rel)
-        except Exception:
-            pass
-    return cons
+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)"
 
-def solve_line(txt):
-    syms = default_symbols()
+    try:
+        # 情境 A：含 '=' → 視為（可能多條）方程，支援分號/換行分隔
+        if "=" in q:
+            # 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 in s:
+                    continue
+                left, right = s.split("=", 1)
+                L = sp.sympify(left)
+                R = sp.sympify(right)
+                eq = sp.Eq(L, R)
+                eqs.append(eq)
+                syms |= L.free_symbols | R.free_symbols
+
+            if not eqs:
+                return "沒有可解析的方程式。"
+            if not syms:
+                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。"
 
-    # constraints after comma: "eq, 0 <= theta < 2*pi"
-    if "," in txt:
-        main = txt.split(",", 1)[0].strip()
-        cons = parse_constraints(txt.split(",")[1:].copy(), syms)
-    else:
-        main = txt.strip()
-        cons = []
+            lines = []
+            for i, s in enumerate(sol, 1):
+                lines.append(
+                    "解 {}: ".format(i) + ", ".join(f"{k} = {sp.simplify(v)}" for k, v in s.items())
+                )
+            return "\n".join(lines)
 
-    if not main:
-        return "Empty input."
+        # 情境 B：純表達式 → 嘗試簡化、因式、微分、積分
+        expr = sp.sympify(q)
+        out = []
 
-    if "=" in main:
-        left, right = main.split("=", 1)
         try:
-            eq = sp.Eq(sp.sympify(left, locals=syms), sp.sympify(right, locals=syms))
-        except Exception as e:
-            return f"Parse equation failed: {e}"
-
-        vars_set = set(eq.free_symbols)
-        if not vars_set:
-            vars_set = {sp.symbols("x", real=True)}
-        vars_list = list(vars_set)
-
-        # try solveset on first var with simple real-domain extraction
-        if cons:
-            v = vars_list[0]
-            domain = sp.S.Reals
-            try:
-                # If constraints form an And of relationals, keep as boolean condition.
-                cond = cons[0]
-                for c in cons[1:]:
-                    cond = sp.And(cond, c)
-                # best-effort: do not over-process; pass domain=Reals
-                sol = sp.solveset(eq, v, domain=domain)
-                return f"solveset({v} in Reals): {sp.simplify(sol)}"
-            except Exception:
-                pass
+            simp = sp.simplify(expr)
+            out.append(f"簡化：{simp}")
+        except Exception:
+            pass
 
         try:
-            sols = sp.solve([eq], vars_list, dict=True)
-            if not sols:
-                return "No solution or need more conditions."
-            lines = []
-            for i, s in enumerate(sols, 1):
-                parts = []
-                for k, v in s.items():
-                    parts.append(f"{k} = {sp.simplify(v)}")
-                lines.append("Solution " + str(i) + ": " + ", ".join(parts))
-            return "\n".join(lines)
-        except Exception as e:
-            return f"Solve failed: {e}"
-
-    # pure expression branch
-    try:
-        expr = sp.sympify(main, locals=syms)
-    except Exception as e:
-        return f"Parse failed: {e}"
+            fac = sp.factor(expr)
+            if fac != expr:
+                out.append(f"因式分解：{fac}")
+        except Exception:
+            pass
 
-    out = []
-    try:
-        out.append("Simplify: " + str(sp.simplify(expr)))
-    except Exception:
-        pass
-    try:
-        fact = sp.factor(expr)
-        if fact != expr:
-            out.append("Factor: " + str(fact))
-    except Exception:
-        pass
-    try:
-        v = list(expr.free_symbols)[0] if expr.free_symbols else sp.symbols("x", real=True)
-        out.append("d/d" + str(v) + ": " + str(sp.diff(expr, v)))
-        out.append("Integral d" + str(v) + ": " + str(sp.integrate(expr, v)))
-    except Exception:
-        pass
+        try:
+            x = list(expr.free_symbols)[0] 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
 
-    if out:
-        return "\n".join(out)
-    return "Result: " + str(expr)
+        return "\n".join(out) if out else f"結果：{expr}"
 
-def solve_math(q):
-    q = (q or "").strip()
-    if not q:
-        return "Enter expression(s) or equation(s). Use semicolons or newlines to separate.\nExamples:\n 2*x + 5 = 11\n sin(theta) = sqrt(3)/2, 0 <= theta < 2*pi\n factor(x**4 - 1)"
-    segs = []
-    for line in q.splitlines():
-        segs.extend([p for p in line.split(";")])
-    segs = [s.strip() for s in segs if s.strip()]
-    outputs = []
-    for s in segs:
-        outputs.append(">>> " + s + "\n" + solve_line(s))
-    return "\n\n".join(outputs)
+    except Exception as e:
+        return f"解析失敗：{e}"
 
-with gr.Blocks(title="LanguageBridge — Math Fast Agent (SymPy)") as demo:
-    gr.Markdown("# LanguageBridge — Math Fast Agent (SymPy)")
-    gr.Markdown("Paste expressions or equations. Add constraints after a comma. Examples:\n- 2*x + 5 = 11\n- sin(theta) = sqrt(3)/2, 0 <= theta < 2*pi\n- factor(x**4 - 1)")
-    q = gr.Textbox(lines=6, label="Problem / Expression (semicolon or newline for systems)")
-    out = gr.Textbox(lines=12, label="Output")
-    btn = gr.Button("Solve")
-    btn.click(fn=solve_math, inputs=q, outputs=out)
+with gr.Blocks(title=TITLE) as demo:
+    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=12, label="輸出")
+    btn = gr.Button("送出 🚀")
+    btn.click(solve_math, q, out)
 
 if __name__ == "__main__":
+    # 在 Colab 預覽：一定要 share=True 才會印出 public URL
     demo.launch(share=True)