Hotfix: remove star-insertion; rely on implicit_multiplication_application

app.py

@@ -1,4 +1,4 @@
-\
+
 import re
 import gradio as gr
 import sympy as sp
@@ -9,34 +9,27 @@ from sympy.parsing.sympy_parser import (
 
 TITLE = "LanguageBridge — Math Fast Agent (SymPy)"
 
-# ---- 正規化：全形→半形、√→sqrt、^→**、自動補乘號（隱式→顯式） ----
+# ---- 僅做安全正規化：全形→半形、^→**、√→sqrt ----
 def normalize_ascii(s: str) -> str:
     table = str.maketrans({
-        '（':'(', '）':')', '，':',', '；':';', '：':':',
-        '＝':'=', '－':'-', '＋':'+', '＊':'*', '／':'/', '。':'.',
-        '×':'*', '√':'sqrt'
+        "（":"(", "）":")", "，":",", "；":";", "：":":",
+        "＝":"=", "－":"-", "＋":"+", "＊":"*", "／":"/", "。":".",
+        "×":"*", "√":"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 *
+    s = s.replace("^", "**")  # 2^3 -> 2**3
+    # ⛔ 不再自動補 *，避免把 sin(x) 變成 sin*(x)
     return s
 
+# SymPy 解析：啟用隱式乘法與 ^ 號處理
 TRANS = standard_transformations + (implicit_multiplication_application, convert_xor)
 
 def to_sympy_expr(s: str):
-    s = preprocess(s)
-    return parse_expr(s, transformations=TRANS)
+    return parse_expr(preprocess(s), transformations=TRANS)
 
 def to_sympy_eq(s: str):
     s = preprocess(s)
@@ -49,32 +42,32 @@ def to_sympy_eq(s: str):
 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)"
+        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
+        # 多行 / 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）
+        # 任何一行有 '=' → 解（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
+                    syms |= e.free_symbols | getattr(e, "rhs", sp.Integer(0)).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(
+            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
+        # 否則：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)}")
@@ -88,7 +81,7 @@ def solve_math(q: str):
             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}"
+        return "\n".join(out) if out else f"結果：{expr}"
 
     except Exception as e:
         return f"解析失敗：{e}"
@@ -96,8 +89,7 @@ def solve_math(q: str):
 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)`。"
+        "貼上算式（可多行 / 分號 `;` 分隔）。支援隱式乘法（例：`3x`, `2(x+1)`, `(x+1)(x-1)`, `2sqrt(x)`）與 `^`。"
     )
     q = gr.Textbox(lines=6, label="題目 / 算式（可含聯立方程）")
     out = gr.Textbox(lines=12, label="輸出")