{
 "app": "MathPad",
 "version": 3,
 "nextId": 151,
 "name": "性能测试.mpad",
 "regions": [
  {
   "id": 1,
   "x": 56,
   "y": 40,
   "kind": "text",
   "latex": "",
   "text": "性能测试（重活合集）· 5 个两层 for 循环自定义函数 · 10 个图像算子 + imshow · 2 张 3D 曲面 · 3 张多曲线图 · 11 个符号求解。"
  },
  {
   "id": 2,
   "x": 56,
   "y": 80,
   "kind": "text",
   "latex": "",
   "text": "看右下角状态条：⚡ 计算总耗时 · 重算块数 · 线程数 · GPU。按 F9 或工具栏「重新计算」= 整篇从头算一遍。"
  },
  {
   "id": 3,
   "x": 56,
   "y": 120,
   "kind": "text",
   "latex": "",
   "text": "① 两层 for 循环自定义函数：f1 40×40、f2 40×40、f3 50×50、f4 60×40、f5 64×64（每次调用 1600~4096 次内层迭代）。"
  },
  {
   "id": 4,
   "x": 56,
   "y": 160,
   "kind": "math",
   "latex": "f1\\left(k,n\\right):=\\begin{gathered}s\\leftarrow 0\\\\\\text{for }i\\in 1..40\\\\\\begin{gathered}\\text{for }j\\in 1..40\\\\s\\leftarrow s+\\sin(i\\cdot j+k)/50+i\\cdot0.01\\\\\\end{gathered}\\\\\\text{return }s\\\\\\end{gathered}",
   "text": ""
  },
  {
   "id": 5,
   "x": 56,
   "y": 304,
   "kind": "math",
   "latex": "f2\\left(k,n\\right):=\\begin{gathered}s\\leftarrow 0\\\\\\text{for }i\\in 1..40\\\\\\begin{gathered}\\text{for }j\\in 1..40\\\\s\\leftarrow s+\\cos(i\\cdot j)\\cdot\\exp(-k/5)\\\\\\end{gathered}\\\\\\text{return }s\\\\\\end{gathered}",
   "text": ""
  },
  {
   "id": 6,
   "x": 56,
   "y": 448,
   "kind": "math",
   "latex": "f3\\left(k,n\\right):=\\begin{gathered}s\\leftarrow 0\\\\\\text{for }i\\in 1..50\\\\\\begin{gathered}\\text{for }j\\in 1..50\\\\s\\leftarrow s+\\frac{i\\cdot j}{1+k\\cdot k}+0.001\\\\\\end{gathered}\\\\\\text{return }s\\\\\\end{gathered}",
   "text": ""
  },
  {
   "id": 7,
   "x": 56,
   "y": 594,
   "kind": "math",
   "latex": "f4\\left(k,n\\right):=\\begin{gathered}s\\leftarrow 0\\\\\\text{for }i\\in 1..60\\\\\\begin{gathered}\\text{for }j\\in 1..40\\\\s\\leftarrow s+\\sqrt{i\\cdot j+k}-0.5\\\\\\end{gathered}\\\\\\text{return }s\\\\\\end{gathered}",
   "text": ""
  },
  {
   "id": 8,
   "x": 56,
   "y": 738,
   "kind": "math",
   "latex": "f5\\left(k,n\\right):=\\begin{gathered}s\\leftarrow 0\\\\\\text{for }i\\in 1..64\\\\\\begin{gathered}\\text{for }j\\in 1..64\\\\s\\leftarrow s+\\sin(i+j\\cdot k)\\cdot\\cos(i\\cdot0.1)\\\\\\end{gathered}\\\\\\text{return }s\\\\\\end{gathered}",
   "text": ""
  },
  {
   "id": 9,
   "x": 56,
   "y": 882,
   "kind": "math",
   "latex": "f1(1,1)=",
   "text": ""
  },
  {
   "id": 10,
   "x": 56,
   "y": 936,
   "kind": "math",
   "latex": "f2(2,2)=",
   "text": ""
  },
  {
   "id": 11,
   "x": 56,
   "y": 990,
   "kind": "math",
   "latex": "f3(3,3)=",
   "text": ""
  },
  {
   "id": 12,
   "x": 56,
   "y": 1044,
   "kind": "math",
   "latex": "f4(4,4)=",
   "text": ""
  },
  {
   "id": 13,
   "x": 56,
   "y": 1098,
   "kind": "math",
   "latex": "f5(5,5)=",
   "text": ""
  },
  {
   "id": 14,
   "x": 56,
   "y": 1152,
   "kind": "math",
   "latex": "f1(1,1)+f2(2,2)+f3(3,3)+f4(4,4)+f5(5,5)=",
   "text": ""
  },
  {
   "id": 15,
   "x": 56,
   "y": 1206,
   "kind": "text",
   "latex": "",
   "text": "② 图像处理：10 个算子（FFT 频谱 / 卷积 / 边缘 / 阈值 / 高斯 / 中值 / 自适应直方图 / 形态学 / 缩放 / 通道），全部 512×512，每个都 imshow。"
  },
  {
   "id": 16,
   "x": 56,
   "y": 1263,
   "kind": "math",
   "latex": "imgp:=imread(\\text{“sample-cameraman.png”})",
   "text": ""
  },
  {
   "id": 17,
   "x": 56,
   "y": 1317,
   "kind": "text",
   "latex": "",
   "text": "频谱图（低频在中心）—— 512×512 复数 FFT："
  },
  {
   "id": 18,
   "x": 56,
   "y": 1357,
   "kind": "math",
   "latex": "sp:=fftspec(imgp)",
   "text": ""
  },
  {
   "id": 19,
   "x": 56,
   "y": 1411,
   "kind": "math",
   "latex": "imshow(sp)",
   "text": ""
  },
  {
   "id": 20,
   "x": 56,
   "y": 2001,
   "kind": "text",
   "latex": "",
   "text": "3×3 均值核卷积（numpy 直接卷积）："
  },
  {
   "id": 21,
   "x": 56,
   "y": 2041,
   "kind": "math",
   "latex": "k9:=\\begin{pmatrix}\\frac{1}{9}&\\frac{1}{9}&\\frac{1}{9}\\\\\\frac{1}{9}&\\frac{1}{9}&\\frac{1}{9}\\\\\\frac{1}{9}&\\frac{1}{9}&\\frac{1}{9}\\end{pmatrix}",
   "text": ""
  },
  {
   "id": 22,
   "x": 56,
   "y": 2140,
   "kind": "math",
   "latex": "bl:=conv2(imgp,k9)",
   "text": ""
  },
  {
   "id": 23,
   "x": 56,
   "y": 2194,
   "kind": "math",
   "latex": "imshow(bl)",
   "text": ""
  },
  {
   "id": 24,
   "x": 56,
   "y": 2784,
   "kind": "text",
   "latex": "",
   "text": "Sobel 边缘："
  },
  {
   "id": 25,
   "x": 56,
   "y": 2824,
   "kind": "math",
   "latex": "ed:=imedge(imgp,\\text{“sobel”})",
   "text": ""
  },
  {
   "id": 26,
   "x": 56,
   "y": 2878,
   "kind": "math",
   "latex": "imshow(ed)",
   "text": ""
  },
  {
   "id": 27,
   "x": 56,
   "y": 3468,
   "kind": "text",
   "latex": "",
   "text": "Otsu 阈值 + 形态学闭运算（两级流水线）："
  },
  {
   "id": 28,
   "x": 56,
   "y": 3508,
   "kind": "math",
   "latex": "th:=imthresh(imgp,\\text{“otsu”})",
   "text": ""
  },
  {
   "id": 29,
   "x": 56,
   "y": 3562,
   "kind": "math",
   "latex": "imshow(th)",
   "text": ""
  },
  {
   "id": 30,
   "x": 56,
   "y": 4152,
   "kind": "math",
   "latex": "cl:=imclose(th,3)",
   "text": ""
  },
  {
   "id": 31,
   "x": 56,
   "y": 4206,
   "kind": "math",
   "latex": "imshow(cl)",
   "text": ""
  },
  {
   "id": 32,
   "x": 56,
   "y": 4796,
   "kind": "text",
   "latex": "",
   "text": "空域滤波：高斯 1.5 / 中值 3×3："
  },
  {
   "id": 33,
   "x": 56,
   "y": 4836,
   "kind": "math",
   "latex": "sm:=imgaussfilt(imgp,1.5)",
   "text": ""
  },
  {
   "id": 34,
   "x": 56,
   "y": 4890,
   "kind": "math",
   "latex": "imshow(sm)",
   "text": ""
  },
  {
   "id": 35,
   "x": 56,
   "y": 5480,
   "kind": "math",
   "latex": "me:=immedfilt(imgp,3)",
   "text": ""
  },
  {
   "id": 36,
   "x": 56,
   "y": 5534,
   "kind": "math",
   "latex": "imshow(me)",
   "text": ""
  },
  {
   "id": 37,
   "x": 56,
   "y": 6124,
   "kind": "text",
   "latex": "",
   "text": "自适应直方图均衡（8 块）+ 降采样到 256×256："
  },
  {
   "id": 38,
   "x": 56,
   "y": 6164,
   "kind": "math",
   "latex": "ad:=adapthisteq(imgp,8)",
   "text": ""
  },
  {
   "id": 39,
   "x": 56,
   "y": 6218,
   "kind": "math",
   "latex": "imshow(ad)",
   "text": ""
  },
  {
   "id": 40,
   "x": 56,
   "y": 6808,
   "kind": "math",
   "latex": "rs:=imresize(imgp,0.5)",
   "text": ""
  },
  {
   "id": 41,
   "x": 56,
   "y": 6862,
   "kind": "math",
   "latex": "imshow(rs)",
   "text": ""
  },
  {
   "id": 42,
   "x": 56,
   "y": 7196,
   "kind": "text",
   "latex": "",
   "text": "彩色图取通道（640×480 三维矩阵 → 单通道）："
  },
  {
   "id": 43,
   "x": 56,
   "y": 7236,
   "kind": "math",
   "latex": "cl0:=imread(\\text{“sample-color.png”})",
   "text": ""
  },
  {
   "id": 44,
   "x": 56,
   "y": 7290,
   "kind": "math",
   "latex": "rd:=imch(cl0,\\text{“r”})",
   "text": ""
  },
  {
   "id": 45,
   "x": 56,
   "y": 7344,
   "kind": "math",
   "latex": "imshow(rd)",
   "text": ""
  },
  {
   "id": 46,
   "x": 56,
   "y": 7843,
   "kind": "text",
   "latex": "",
   "text": "③ 三维曲面（WebGL / GPU 加速）：第一张网格 220×220，第二张 240×240（都 ≥200×200，共 10 万个点以上）。"
  },
  {
   "id": 47,
   "x": 56,
   "y": 7883,
   "kind": "math",
   "latex": "surf(\\sin(\\sqrt{x\\text{\\textasciicircum}^{2}+y\\text{\\textasciicircum}^{2}})\\cdot\\exp(-0.08\\cdot(x\\text{\\textasciicircum}^{2}+y\\text{\\textasciicircum}^{2})),-8,8,220)",
   "text": "",
   "style": {
    "dash": "solid",
    "width": 2,
    "color": "#185FA5",
    "marker": "none",
    "msize": 6,
    "grid": true,
    "box": true,
    "title": "",
    "xlabel": "",
    "ylabel": "",
    "titleSize": 14,
    "titleColor": "#1a1a1a",
    "xlabelSize": 11,
    "xlabelColor": "#1a1a1a",
    "ylabelSize": 11,
    "ylabelColor": "#1a1a1a",
    "tickSize": 11,
    "tickColor": "#3a4550",
    "legendPos": "",
    "legendSize": 11,
    "gridColor": "#e8ebee",
    "axisColor": "#b9c0c7",
    "xmin": "",
    "xmax": "",
    "ymin": "",
    "ymax": "",
    "xlog": false,
    "ylog": false,
    "axes": true,
    "xaxisPos": "edge",
    "yaxisPos": "edge",
    "colorscale": "Blues",
    "levels": 10,
    "labels": true,
    "barw": 0.6,
    "chartType": "",
    "barmode": "group",
    "bargap": -0.2,
    "barline": "",
    "points": "",
    "bins": "",
    "w": 560,
    "h": 300,
    "page": "",
    "mrow": 6,
    "mcol": 6,
    "paperbg": "#ffffff",
    "plotbg": "#ffffff",
    "exportScale": 2,
    "channel": "auto",
    "imgfit": "contain",
    "interp": "smooth",
    "azimuth": 1.3,
    "elevation": 0.6,
    "fill": false,
    "fillalpha": "",
    "series": []
   }
  },
  {
   "id": 48,
   "x": 56,
   "y": 8363,
   "kind": "math",
   "latex": "surf(\\sin(x)\\cdot\\cos(y)+0.3\\cdot\\sin(3\\cdot x),-6,6,240)",
   "text": ""
  },
  {
   "id": 49,
   "x": 56,
   "y": 8821,
   "kind": "text",
   "latex": "",
   "text": "④ 多曲线图：左上每条曲线 400 个采样点、3 条曲线；下面这张每条 300 点、3 条曲线（都在图里用分号分组）。"
  },
  {
   "id": 50,
   "x": 56,
   "y": 8861,
   "kind": "math",
   "latex": "plot(\\sin(x);\\cos(x);\\sin(2\\cdot x),-12,12,400)",
   "text": ""
  },
  {
   "id": 51,
   "x": 56,
   "y": 9219,
   "kind": "math",
   "latex": "plot(\\frac{\\sin(x)}{x};\\cos(x)\\cdot\\exp(-x\\text{\\textasciicircum}^{2}/8);\\frac{1}{1+x\\text{\\textasciicircum}^{2}},-10,10,300)",
   "text": ""
  },
  {
   "id": 52,
   "x": 56,
   "y": 9594,
   "kind": "text",
   "latex": "",
   "text": "再放一张数据图（4000 点排序结果，序号横轴从 0 起）："
  },
  {
   "id": 53,
   "x": 56,
   "y": 9634,
   "kind": "math",
   "latex": "zz:=sort(randn(4000,1))",
   "text": ""
  },
  {
   "id": 54,
   "x": 56,
   "y": 9723,
   "kind": "math",
   "latex": "plot(zz)",
   "text": ""
  },
  {
   "id": 55,
   "x": 56,
   "y": 10077,
   "kind": "text",
   "latex": "",
   "text": "⑤ 符号求解 / 化简 / 微积分（11 个，全部走 SymPy 符号路径）：多项式方程数值根、三角方程、带 assume 的符号解、方程组、因式分解、化简、展开、一阶/二阶导数、不定积分、求和化简。"
  },
  {
   "id": 56,
   "x": 56,
   "y": 10129,
   "kind": "math",
   "latex": "x\\text{\\textasciicircum}^{2}-5\\cdot x+6=0=",
   "text": ""
  },
  {
   "id": 57,
   "x": 56,
   "y": 10200,
   "kind": "math",
   "latex": "x\\text{\\textasciicircum}^{3}-2\\cdot x+1=0=",
   "text": ""
  },
  {
   "id": 58,
   "x": 56,
   "y": 10301,
   "kind": "math",
   "latex": "\\sin(x)=\\frac{1}{2}=",
   "text": ""
  },
  {
   "id": 59,
   "x": 56,
   "y": 10372,
   "kind": "math",
   "latex": "x\\text{\\textasciicircum}^{2}-4=0\\to solve,\\text{assume }x>0",
   "text": ""
  },
  {
   "id": 60,
   "x": 56,
   "y": 10432,
   "kind": "math",
   "latex": "x+y=3, x-y=1=",
   "text": ""
  },
  {
   "id": 61,
   "x": 56,
   "y": 10483,
   "kind": "math",
   "latex": "x\\text{\\textasciicircum}^{4}-1\\to factor",
   "text": ""
  },
  {
   "id": 62,
   "x": 56,
   "y": 10537,
   "kind": "math",
   "latex": "\\frac{x\\text{\\textasciicircum}^{2}-1}{x-1}\\to simplify",
   "text": ""
  },
  {
   "id": 63,
   "x": 56,
   "y": 10607,
   "kind": "math",
   "latex": "(x+1)\\text{\\textasciicircum}^{6}\\to expand",
   "text": ""
  },
  {
   "id": 64,
   "x": 56,
   "y": 10668,
   "kind": "math",
   "latex": "\\frac{d}{dx}(x\\text{\\textasciicircum}^{3}\\cdot\\sin(x))=",
   "text": ""
  },
  {
   "id": 65,
   "x": 56,
   "y": 10734,
   "kind": "math",
   "latex": "\\int x\\text{\\textasciicircum}^{2}\\cdot\\sin(x)\\,\\mathrm{d}x=",
   "text": ""
  },
  {
   "id": 66,
   "x": 56,
   "y": 10806,
   "kind": "math",
   "latex": "\\sum_{k=1}^{n}k\\text{\\textasciicircum}^{2}\\to simplify",
   "text": ""
  },
  {
   "id": 67,
   "x": 56,
   "y": 10892,
   "kind": "text",
   "latex": "",
   "text": "试试把 f5 里的 64 改成 96，或把 surf 的 220 改成 320 —— 整篇级联重算，状态条上的数字就是这次刷新的真实开销。"
  },
  {
   "id": 68,
   "x": 56,
   "y": 10992,
   "kind": "text",
   "latex": "",
   "text": "积分家族与级数（新增）—— 不定积分 / 定积分 / 二重三重积分 / 曲线曲面积分 / 阶乘 / 求和求积，每类 5 条，共 30 条。"
  },
  {
   "id": 69,
   "x": 56,
   "y": 11030,
   "kind": "text",
   "latex": "",
   "text": "不定积分 5 条 —— 写法：∫ f dx（末尾 d 变量就是要积的变量）"
  },
  {
   "id": 70,
   "x": 56,
   "y": 11068,
   "kind": "math",
   "latex": "\\int x\\text{\\textasciicircum}^{2}\\cdot\\sin\\left(x\\right)\\,\\mathrm{d}x=",
   "text": ""
  },
  {
   "id": 71,
   "x": 56,
   "y": 11138,
   "kind": "math",
   "latex": "\\int\\frac{1}{1+x\\text{\\textasciicircum}^{2}}\\,\\mathrm{d}x=",
   "text": ""
  },
  {
   "id": 72,
   "x": 56,
   "y": 11208,
   "kind": "math",
   "latex": "\\int x\\cdot e\\text{\\textasciicircum}^{x}\\,\\mathrm{d}x=",
   "text": ""
  },
  {
   "id": 73,
   "x": 56,
   "y": 11278,
   "kind": "math",
   "latex": "\\int\\ln\\left(x\\right)\\,\\mathrm{d}x=",
   "text": ""
  },
  {
   "id": 74,
   "x": 56,
   "y": 11348,
   "kind": "math",
   "latex": "\\int\\cos\\left(2x\\right)\\,\\mathrm{d}x=",
   "text": ""
  },
  {
   "id": 75,
   "x": 56,
   "y": 11419,
   "kind": "text",
   "latex": "",
   "text": "定积分 5 条 —— 写法：∫ 带上下限"
  },
  {
   "id": 76,
   "x": 56,
   "y": 11457,
   "kind": "math",
   "latex": "\\int_{0}^{\\pi}\\sin\\left(x\\right)\\,\\mathrm{d}x=",
   "text": ""
  },
  {
   "id": 77,
   "x": 56,
   "y": 11532,
   "kind": "math",
   "latex": "\\int_{0}^{1}x\\text{\\textasciicircum}^{2}\\,\\mathrm{d}x=",
   "text": ""
  },
  {
   "id": 78,
   "x": 56,
   "y": 11607,
   "kind": "math",
   "latex": "\\int_{1}^{e}\\frac{1}{x}\\,\\mathrm{d}x=",
   "text": ""
  },
  {
   "id": 79,
   "x": 56,
   "y": 11679,
   "kind": "math",
   "latex": "\\int_{0}^{1}\\frac{1}{1+x\\text{\\textasciicircum}^{2}}\\,\\mathrm{d}x=",
   "text": ""
  },
  {
   "id": 80,
   "x": 56,
   "y": 11754,
   "kind": "math",
   "latex": "\\int_{-1}^{1}\\left(x\\text{\\textasciicircum}^{3}+x\\right)\\,\\mathrm{d}x=",
   "text": ""
  },
  {
   "id": 81,
   "x": 56,
   "y": 11830,
   "kind": "text",
   "latex": "",
   "text": "二重 / 三重积分 5 条 —— 写法：∫ 连着写，最右边那个 d 属于最外层（先算里层）"
  },
  {
   "id": 82,
   "x": 56,
   "y": 11868,
   "kind": "math",
   "latex": "\\int_{0}^{1}\\int_{0}^{1}x\\cdot y\\,\\mathrm{d}y\\,\\mathrm{d}x=",
   "text": ""
  },
  {
   "id": 83,
   "x": 56,
   "y": 11943,
   "kind": "math",
   "latex": "\\int_{0}^{2}\\int_{0}^{1}\\left(x+y\\right)\\,\\mathrm{d}y\\,\\mathrm{d}x=",
   "text": ""
  },
  {
   "id": 84,
   "x": 56,
   "y": 12018,
   "kind": "math",
   "latex": "\\int_{0}^{1}\\int_{0}^{1-x}\\left(x+y\\right)\\,\\mathrm{d}y\\,\\mathrm{d}x=",
   "text": ""
  },
  {
   "id": 85,
   "x": 56,
   "y": 12093,
   "kind": "math",
   "latex": "\\int_{0}^{1}\\int_{0}^{1}\\int_{0}^{1}x\\cdot y\\cdot z\\,\\mathrm{d}z\\,\\mathrm{d}y\\,\\mathrm{d}x=",
   "text": ""
  },
  {
   "id": 86,
   "x": 56,
   "y": 12168,
   "kind": "math",
   "latex": "\\int_{0}^{1}\\int_{0}^{1}\\int_{0}^{1}\\left(x+y+z\\right)\\,\\mathrm{d}z\\,\\mathrm{d}y\\,\\mathrm{d}x=",
   "text": ""
  },
  {
   "id": 87,
   "x": 56,
   "y": 12243,
   "kind": "text",
   "latex": "",
   "text": "曲线积分 5 条 —— 位置变量固定用 x、y、z，曲线参数 t："
  },
  {
   "id": 88,
   "x": 56,
   "y": 12281,
   "kind": "text",
   "latex": "",
   "text": "lineint(f, X(t), Y(t), t, a, b)：第一类（弧长 ds）；lineint(f, X, Y, Z, t, a, b)：空间曲线；lineint2(P, Q, X, Y, t, a, b)：第二类 P dx + Q dy"
  },
  {
   "id": 89,
   "x": 56,
   "y": 12319,
   "kind": "math",
   "latex": "lineint\\left(1,\\cos\\left(t\\right),\\sin\\left(t\\right),t,0,2\\pi\\right)=",
   "text": ""
  },
  {
   "id": 90,
   "x": 56,
   "y": 12372,
   "kind": "math",
   "latex": "lineint\\left(x\\text{\\textasciicircum}^{2}+y\\text{\\textasciicircum}^{2},\\cos\\left(t\\right),\\sin\\left(t\\right),t,0,2\\pi\\right)=",
   "text": ""
  },
  {
   "id": 91,
   "x": 56,
   "y": 12425,
   "kind": "math",
   "latex": "lineint\\left(1,\\cos\\left(t\\right),\\sin\\left(t\\right),t,t,0,2\\pi\\right)=",
   "text": ""
  },
  {
   "id": 92,
   "x": 56,
   "y": 12479,
   "kind": "math",
   "latex": "lineint2\\left(-y,x,\\cos\\left(t\\right),\\sin\\left(t\\right),t,0,2\\pi\\right)=",
   "text": ""
  },
  {
   "id": 93,
   "x": 56,
   "y": 12532,
   "kind": "math",
   "latex": "lineint2\\left(y,x,t,t\\text{\\textasciicircum}^{2},t,0,1\\right)=",
   "text": ""
  },
  {
   "id": 94,
   "x": 56,
   "y": 12585,
   "kind": "text",
   "latex": "",
   "text": "曲面积分 5 条 —— 曲面参数用 u、v（球面取 r = sin u·cos v, sin u·sin v, cos u）："
  },
  {
   "id": 95,
   "x": 56,
   "y": 12623,
   "kind": "text",
   "latex": "",
   "text": "surfint(f, X, Y, Z, u, a, b, v, c, d)：第一类 dS；surfint2(P, Q, R, X, Y, Z, u, a, b, v, c, d)：第二类（通量）"
  },
  {
   "id": 96,
   "x": 56,
   "y": 12661,
   "kind": "math",
   "latex": "surfint\\left(1,\\sin\\left(u\\right)\\cos\\left(v\\right),\\sin\\left(u\\right)\\sin\\left(v\\right),\\cos\\left(u\\right),u,0,\\pi,v,0,2\\pi\\right)=",
   "text": ""
  },
  {
   "id": 97,
   "x": 56,
   "y": 12714,
   "kind": "math",
   "latex": "surfint\\left(x\\text{\\textasciicircum}^{2},\\sin\\left(u\\right)\\cos\\left(v\\right),\\sin\\left(u\\right)\\sin\\left(v\\right),\\cos\\left(u\\right),u,0,\\pi,v,0,2\\pi\\right)=",
   "text": ""
  },
  {
   "id": 98,
   "x": 56,
   "y": 12777,
   "kind": "math",
   "latex": "surfint\\left(1,u\\cdot\\cos\\left(v\\right),u\\cdot\\sin\\left(v\\right),0,u,0,1,v,0,2\\pi\\right)=",
   "text": ""
  },
  {
   "id": 99,
   "x": 56,
   "y": 12830,
   "kind": "math",
   "latex": "surfint2\\left(x,y,z,\\sin\\left(u\\right)\\cos\\left(v\\right),\\sin\\left(u\\right)\\sin\\left(v\\right),\\cos\\left(u\\right),u,0,\\pi,v,0,2\\pi\\right)=",
   "text": ""
  },
  {
   "id": 100,
   "x": 56,
   "y": 12883,
   "kind": "math",
   "latex": "surfint2\\left(0,0,1,u,v,0,u,0,1,v,0,1\\right)=",
   "text": ""
  },
  {
   "id": 101,
   "x": 56,
   "y": 12935,
   "kind": "text",
   "latex": "",
   "text": "阶乘 5 条 —— 直接写 ! 就行（也支持组合数写法）"
  },
  {
   "id": 102,
   "x": 56,
   "y": 12973,
   "kind": "math",
   "latex": "5!=",
   "text": ""
  },
  {
   "id": 103,
   "x": 56,
   "y": 13025,
   "kind": "math",
   "latex": "10!=",
   "text": ""
  },
  {
   "id": 104,
   "x": 56,
   "y": 13077,
   "kind": "math",
   "latex": "12!=",
   "text": ""
  },
  {
   "id": 105,
   "x": 56,
   "y": 13129,
   "kind": "math",
   "latex": "\\frac{10!}{7!}=",
   "text": ""
  },
  {
   "id": 106,
   "x": 56,
   "y": 13193,
   "kind": "math",
   "latex": "\\frac{20!}{18!\\cdot 2!}=",
   "text": ""
  },
  {
   "id": 107,
   "x": 56,
   "y": 13257,
   "kind": "text",
   "latex": "",
   "text": "求和 / 求积 5 条 —— Σ 求和、Π 连乘，上下限写 _{i=下}^{上}"
  },
  {
   "id": 108,
   "x": 56,
   "y": 13295,
   "kind": "math",
   "latex": "\\sum_{i=1}^{10}i\\text{\\textasciicircum}^{2}=",
   "text": ""
  },
  {
   "id": 109,
   "x": 56,
   "y": 13382,
   "kind": "math",
   "latex": "\\sum_{k=1}^{n}k=",
   "text": ""
  },
  {
   "id": 110,
   "x": 56,
   "y": 13466,
   "kind": "math",
   "latex": "\\sum_{i=1}^{5}i!=",
   "text": ""
  },
  {
   "id": 111,
   "x": 56,
   "y": 13553,
   "kind": "math",
   "latex": "\\prod_{i=1}^{5}i=",
   "text": ""
  },
  {
   "id": 112,
   "x": 56,
   "y": 13640,
   "kind": "math",
   "latex": "\\prod_{k=1}^{n}k=",
   "text": ""
  },
  {
   "id": 121,
   "x": 52,
   "y": 13772,
   "kind": "math",
   "latex": "f\\left(x\\right)\\coloneqq\\,a\\times x\\text{\\textasciicircum}^2+b\\times x+c",
   "text": ""
  },
  {
   "id": 122,
   "x": 54,
   "y": 13848,
   "kind": "math",
   "latex": "g\\left(x\\right)\\coloneqq\\,a\\times x",
   "text": ""
  },
  {
   "id": 129,
   "x": 48,
   "y": 13948,
   "kind": "math",
   "latex": "plot\\left(f\\left(x\\right);g\\left(x\\right);wavetest\\left(x\\right)\\right)",
   "text": "",
   "style": {
    "dash": "solid",
    "width": 2,
    "color": "#185FA5",
    "marker": "none",
    "msize": 6,
    "grid": true,
    "box": true,
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    "xlabel": "",
    "ylabel": "",
    "titleSize": 14,
    "titleColor": "#1a1a1a",
    "xlabelSize": 11,
    "xlabelColor": "#1a1a1a",
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    "ylabelColor": "#1a1a1a",
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    "tickColor": "#3a4550",
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    "legendSize": 11,
    "gridColor": "#e8ebee",
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    "xmin": "-10",
    "xmax": "10",
    "ymin": "-10",
    "ymax": "10",
    "xlog": false,
    "ylog": false,
    "axes": true,
    "xaxisPos": "zero",
    "yaxisPos": "zero",
    "colorscale": "",
    "levels": 10,
    "labels": true,
    "barw": 0.6,
    "chartType": "",
    "barmode": "group",
    "bargap": -0.2,
    "barline": "",
    "points": "",
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    "w": 560,
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    "page": "",
    "mrow": 6,
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    "paperbg": "#ffffff",
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    "exportScale": 2,
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   "pv": {
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    "g0:c": 0.95,
    "g1:a": 3.55,
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    "g0:c": {
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  },
  {
   "id": 131,
   "x": 55,
   "y": 13898,
   "kind": "math",
   "latex": "wavetest\\left(x\\right)\\coloneqq\\,A\\times sin\\left(\\omega\\times x+\\varphi\\right)+k",
   "text": ""
  },
  {
   "id": 146,
   "x": 66,
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   "kind": "math",
   "latex": "polar(A\\sin(\\omega\\times t+\\varphi)+k,0,6.28)",
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