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  {
   "id": "2",
   "x": 63,
   "y": 224,
   "kind": "text",
   "latex": "",
   "text": "① \"名字 := 表达式\" 是**定义**（右边不显示任何东西）；\n② 式子末尾敲一个 **=** 才是**求值**，结果直接接在等号后面。",
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   }
  },
  {
   "id": "3",
   "x": 63,
   "y": 291,
   "kind": "text",
   "latex": "",
   "text": "一、算数与变量",
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  },
  {
   "id": 4,
   "x": 79,
   "y": 331,
   "kind": "math",
   "latex": "2+3=",
   "text": ""
  },
  {
   "id": "5",
   "x": 63,
   "y": 381,
   "kind": "text",
   "latex": "",
   "text": "给变量存值，后面随便用：",
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  },
  {
   "id": 6,
   "x": 79,
   "y": 421,
   "kind": "math",
   "latex": "a:=1",
   "text": ""
  },
  {
   "id": 7,
   "x": 79,
   "y": 471,
   "kind": "math",
   "latex": "b:=2",
   "text": ""
  },
  {
   "id": 8,
   "x": 79,
   "y": 521,
   "kind": "math",
   "latex": "a\\cdot b+10=",
   "text": ""
  },
  {
   "id": "9",
   "x": 63,
   "y": 601,
   "kind": "text",
   "latex": "",
   "text": "改一下 a 的值（点进去改数字），全篇引用它的地方会自动重算——这就是\"活文档\"。",
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   }
  },
  {
   "id": "10",
   "x": 63,
   "y": 641,
   "kind": "text",
   "latex": "",
   "text": "二、函数",
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  },
  {
   "id": 11,
   "x": 79,
   "y": 681,
   "kind": "math",
   "latex": "f(x):=x\\text{\\textasciicircum}^2+5\\cdot x",
   "text": "",
   "w": 220
  },
  {
   "id": "12",
   "x": 63,
   "y": 730,
   "kind": "text",
   "latex": "",
   "text": "调用就像写数学：",
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  },
  {
   "id": 13,
   "x": 79,
   "y": 770,
   "kind": "math",
   "latex": "f(6)=",
   "text": ""
  },
  {
   "id": 14,
   "x": 79,
   "y": 819,
   "kind": "math",
   "latex": "f(2)+f(3)=",
   "text": ""
  },
  {
   "id": "15",
   "x": 62,
   "y": 893,
   "kind": "text",
   "latex": "",
   "text": "三、单位：直接跟在数字后面，自动换算、自动查量纲，单位切换在求解式生效，不在定义式生效",
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  {
   "id": "21",
   "x": 86,
   "y": 1144,
   "kind": "text",
   "latex": "",
   "text": "点一下结果可以切换单位，数值自动换算。\n角度也直接写：sin(30°) = 0.5。",
   "html": "<b>点一下结果</b>可以切换单位，数值自动换算。<br>角度也直接写：sin(30°) = 0.5。",
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   },
   "w": 352
  },
  {
   "id": 22,
   "x": 82,
   "y": 1211,
   "kind": "math",
   "latex": "\\sin(30^{\\circ})=",
   "text": ""
  },
  {
   "id": "23",
   "x": 71,
   "y": 1409,
   "kind": "text",
   "latex": "",
   "text": "四、矩阵与索引（索引从 1 起数，用方括号下标）",
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   }
  },
  {
   "id": 24,
   "x": 87,
   "y": 1497,
   "kind": "math",
   "latex": "M:=\\begin{pmatrix}2&0&1\\\\1&3&0\\\\0&1&4\\end{pmatrix}",
   "text": ""
  },
  {
   "id": 25,
   "x": 81,
   "y": 1639,
   "kind": "math",
   "latex": "M_{[1,2]}=",
   "text": ""
  },
  {
   "id": 26,
   "x": 81,
   "y": 1739,
   "kind": "math",
   "latex": "M_{[:,1]}=",
   "text": ""
  },
  {
   "id": 27,
   "x": 81,
   "y": 1845,
   "kind": "math",
   "latex": "\\det(M)=",
   "text": ""
  },
  {
   "id": 28,
   "x": 81,
   "y": 1895,
   "kind": "math",
   "latex": "trace(M)=",
   "text": ""
  },
  {
   "id": "30",
   "x": 61,
   "y": 1945,
   "kind": "text",
   "latex": "",
   "text": "五、解方程与符号运算",
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  },
  {
   "id": 31,
   "x": 77,
   "y": 1985,
   "kind": "math",
   "latex": "x\\text{\\textasciicircum}^2-4=0\\to solve,\\text{assume }x<0",
   "text": ""
  },
  {
   "id": "32",
   "x": 61,
   "y": 2088,
   "kind": "text",
   "latex": "",
   "text": "也可以点名要哪种化简——在式子后面写箭头和关键词（工具栏有菜单）：",
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  },
  {
   "id": 33,
   "x": 77,
   "y": 2128,
   "kind": "math",
   "latex": "x\\text{\\textasciicircum}^4-1\\to factor",
   "text": "",
   "w": 430
  },
  {
   "id": 34,
   "x": 77,
   "y": 2183,
   "kind": "math",
   "latex": "\\frac{x\\text{\\textasciicircum}^{2}-1}{x-1}\\to simplify",
   "text": "",
   "w": 425
  },
  {
   "id": 35,
   "x": 77,
   "y": 2288,
   "kind": "math",
   "latex": "\\frac{d}{dx}\\left(\\sin\\left(x\\text{\\textasciicircum}^2\\right)\\right)=",
   "text": "",
   "w": 398
  },
  {
   "id": 36,
   "x": 77,
   "y": 2411,
   "kind": "math",
   "latex": "\\int_0^1x\\text{\\textasciicircum}^2\\,dx=",
   "text": "",
   "w": 412
  },
  {
   "id": "37",
   "x": 77,
   "y": 2749,
   "kind": "text",
   "latex": "",
   "text": "逻辑判断（逻辑区的 =）：两边都能算出确定值时，= 回答 true / false：",
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  },
  {
   "id": 38,
   "x": 93,
   "y": 2789,
   "kind": "math",
   "latex": "2<3=",
   "text": ""
  },
  {
   "id": 39,
   "x": 93,
   "y": 2838,
   "kind": "math",
   "latex": "2+3=5=",
   "text": ""
  },
  {
   "id": "40",
   "x": 76,
   "y": 2622,
   "kind": "text",
   "latex": "",
   "text": "带假设的求解：solve(方程, 变量) 前提 x>0 时只留正根；假设会显示在箭头下方。在 符号-假设 里面进行设置，这些算式还可以复制到word，鼠标挪动到上方可以看到复制按钮。",
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   },
   "w": 859
  },
  {
   "id": 41,
   "x": 84,
   "y": 2689,
   "kind": "math",
   "latex": "x\\text{\\textasciicircum}^{2}-4=0\\to solve,\\text{assume }x<0",
   "text": ""
  },
  {
   "id": "42",
   "x": 62,
   "y": 2887,
   "kind": "text",
   "latex": "",
   "text": "六、绘图（图形选项里能换图型 / 调采样点数）",
   "fmt": {
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   }
  },
  {
   "id": 43,
   "x": 78,
   "y": 2927,
   "kind": "math",
   "latex": "plot(\\sin(x),-6,6)",
   "text": ""
  },
  {
   "id": "44",
   "x": 62,
   "y": 3280,
   "kind": "text",
   "latex": "",
   "text": "多条曲线用分号隔开：",
   "fmt": {
    "size": "18"
   }
  },
  {
   "id": 45,
   "x": 78,
   "y": 3320,
   "kind": "math",
   "latex": "plot(\\sin(x);\\cos(x),-6,6)",
   "text": ""
  },
  {
   "id": "46",
   "x": 71,
   "y": 4249,
   "kind": "text",
   "latex": "",
   "text": "继续学习：菜单「文件」里有 绘图示例（画法大全）、图像处理示例、信号变换示例（傅里叶 / 卷积/小波）。\n帮助按 F1，每个函数都有说明，可以直接把模板插进公式。",
   "fmt": {
    "size": "18"
   },
   "w": 903
  },
  {
   "id": 480,
   "x": 97,
   "y": 933,
   "kind": "math",
   "latex": "t\\coloneqq\\,10s",
   "text": ""
  },
  {
   "id": 482,
   "x": 90,
   "y": 983,
   "kind": "math",
   "latex": "v_1\\coloneqq\\,\\frac{d}{t}=",
   "text": "",
   "unit": "m/s"
  },
  {
   "id": 483,
   "x": 244,
   "y": 934,
   "kind": "math",
   "latex": "d\\coloneqq\\,10m",
   "text": ""
  },
  {
   "id": 498,
   "x": 90,
   "y": 1044,
   "kind": "math",
   "latex": "d_2\\coloneqq\\,v_1\\times2\\times t=",
   "text": "",
   "unit": "mm"
  },
  {
   "id": 503,
   "x": 86,
   "y": 1094,
   "kind": "math",
   "latex": "d_3\\coloneqq\\,2\\times d_2=",
   "text": "",
   "unit": "m"
  },
  {
   "id": 539,
   "x": 81,
   "y": 1279,
   "kind": "math",
   "latex": "30.123456\\degree=",
   "text": "",
   "unit": "°′″"
  },
  {
   "id": 567,
   "x": 59,
   "y": 3673,
   "kind": "math",
   "latex": "还支持未定义参数的函数图像绘制,将自动添加滑块,您可以自定义其范围和步长",
   "text": ""
  },
  {
   "id": 573,
   "x": 60,
   "y": 3722,
   "kind": "math",
   "latex": "f\\left(x\\right)\\coloneqq\\,a\\times x\\text{\\textasciicircum}^2+b\\times x+c",
   "text": ""
  },
  {
   "id": 574,
   "x": 62,
   "y": 3798,
   "kind": "math",
   "latex": "g\\left(x\\right)\\coloneqq\\,a\\times x",
   "text": ""
  },
  {
   "id": 584,
   "x": 56,
   "y": 3896,
   "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,
    "title": "",
    "xlabel": "",
    "ylabel": "",
    "titleSize": 14,
    "xlabelSize": 11,
    "ylabelSize": 11,
    "tickSize": 11,
    "legendPos": "",
    "legendSize": 11,
    "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": "",
    "bins": "",
    "w": 560,
    "h": 300,
    "page": "",
    "mrow": 6,
    "mcol": 6,
    "exportScale": 2,
    "channel": "auto",
    "imgfit": "contain",
    "interp": "smooth",
    "azimuth": 1.3,
    "elevation": 0.6,
    "fill": false,
    "fillalpha": "",
    "series": [
     {},
     {
      "dash": "dashed",
      "color": "#d719bd"
     },
     {
      "color": "#07cf4a"
     }
    ]
   },
   "pv": {
    "g0:b": -3.54,
    "g0:a": 1.31,
    "g0:c": -1.16,
    "g1:a": 2.96,
    "g2:A": -4.97,
    "g2:k": 0.58,
    "g2:omega": -4.5,
    "g2:varphi": 3.76
   },
   "pr": {
    "g0:a": {
     "min": -4,
     "max": 4,
     "step": 0.01
    },
    "g0:b": {
     "min": -10,
     "max": 10,
     "step": 0.01
    },
    "g0:c": {
     "min": -10,
     "max": 10,
     "step": 0.01
    }
   }
  },
  {
   "id": 588,
   "x": 63,
   "y": 3847,
   "kind": "math",
   "latex": "wavetest\\left(x\\right)\\coloneqq\\,A\\times sin\\left(\\omega\\times x+\\varphi\\right)+k",
   "text": ""
  },
  {
   "id": 630,
   "x": 246,
   "y": 1211,
   "kind": "math",
   "latex": "sin\\left(\\pi\\right)=",
   "text": ""
  },
  {
   "id": 639,
   "x": 467,
   "y": 1206,
   "kind": "math",
   "latex": "\\colorbox{yellow}{$ 输入p并按ctrl+g,可以把字母转换为希腊字母,p对应\\pi,P对应\\Pi,b对应\\beta,w对应\\omega,很好用吧,更多符号请查看符号-希腊字母 $}",
   "text": "",
   "w": 1121
  },
  {
   "id": 652,
   "x": 395,
   "y": 1519,
   "kind": "text",
   "latex": "",
   "text": "矩阵可以通过鼠标右键插入也可以在上方矩阵按钮功能区插入，可以在视图设置里选择方括号/圆括号",
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    "bg": "#eaea62"
   }
  },
  {
   "id": 661,
   "x": 366,
   "y": 1655,
   "kind": "text",
   "latex": "",
   "text": "矩阵索引：按[ 自动下标，按] 自动恢复，索引从1开始",
   "fmt": {
    "size": "18",
    "bg": "#eaea62"
   }
  },
  {
   "id": 666,
   "x": 547,
   "y": 1960,
   "kind": "text",
   "latex": "",
   "text": "快捷键ctrl+.（数字小键盘的小数点.）键入箭头，可以用很多符号求解功能",
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   }
  },
  {
   "id": 672,
   "x": 448,
   "y": 2248,
   "kind": "text",
   "latex": "",
   "text": "定积分不定积分都可以",
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   }
  },
  {
   "id": 679,
   "x": 418,
   "y": 2689,
   "kind": "text",
   "latex": "",
   "text": "点击内部后，选择上方符号-假设，即可设置条件",
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    "bg": "#eaea62"
   }
  },
  {
   "id": 687,
   "x": 850,
   "y": 3217,
   "kind": "text",
   "latex": "",
   "text": "支持直接画确定函数的曲线",
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    "bg": "#eaea62"
   }
  },
  {
   "id": 693,
   "x": 1012,
   "y": 3843,
   "kind": "text",
   "latex": "",
   "text": "有未定义参数的函数，将自动出现滑块，可以设置范围、步长、联动等\n尝试拉动滑块观察曲线的变化吧！",
   "fmt": {
    "size": "18",
    "bg": "#eaea62"
   }
  },
  {
   "id": 711,
   "x": 917,
   "y": 3653,
   "kind": "text",
   "latex": "",
   "text": "如果你不知道有什么函数，就按ctrl+E查看函数窗口吧，一定会用到的！",
   "fmt": {
    "size": "18",
    "bg": "#eaea62"
   }
  },
  {
   "id": 716,
   "x": 116,
   "y": 4620,
   "kind": "math",
   "latex": "plot\\left(fd\\left(x\\right);4sin\\left(x\\right)\\right)",
   "text": "",
   "style": {
    "dash": "solid",
    "width": 2,
    "color": "#185FA5",
    "marker": "none",
    "msize": 6,
    "grid": true,
    "box": true,
    "title": "",
    "xlabel": "",
    "ylabel": "",
    "titleSize": 14,
    "xlabelSize": 11,
    "ylabelSize": 11,
    "tickSize": 11,
    "legendPos": "",
    "legendSize": 11,
    "xmin": "-5",
    "xmax": "5",
    "ymin": "-10",
    "ymax": "10",
    "xlog": false,
    "ylog": false,
    "zmin": "",
    "zmax": "",
    "axes": true,
    "xaxisPos": "zero",
    "yaxisPos": "zero",
    "colorscale": "",
    "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,
    "exportScale": 2,
    "channel": "auto",
    "imgfit": "contain",
    "interp": "smooth",
    "azimuth": 1.3,
    "elevation": 0.6,
    "fill": false,
    "fillalpha": "",
    "series": []
   },
   "pv": {
    "g2:fe": -0.28,
    "g1:lambda": -1.16
   }
  },
  {
   "id": 723,
   "x": 266,
   "y": 4450,
   "kind": "math",
   "latex": "fd\\left(x\\right)\\coloneqq\\,\\left\\{\\begin{array}{l}x\\text{\\textasciicircum}^2,x>0\\\\ -x,x\\le0\\end{array}\\right.",
   "text": ""
  },
  {
   "id": 727,
   "x": 66,
   "y": 4342,
   "kind": "text",
   "latex": "",
   "text": "七、自定义函数",
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  },
  {
   "id": 731,
   "x": 105,
   "y": 4406,
   "kind": "text",
   "latex": "",
   "text": "① 普通分段函数，shift+Enter加行，逗号区分条件，比较符号可以在上方点击添加"
  },
  {
   "id": 736,
   "x": 108,
   "y": 5020,
   "kind": "text",
   "latex": "",
   "text": "① if、for等编程自定义函数，ctrl+Enter加行，逗号区分条件，比较符号可以在上方点击添加"
  },
  {
   "id": 740,
   "x": 153,
   "y": 5084,
   "kind": "math",
   "latex": "f5\\left(k,n\\right):=\\left\\{\\begin{array}{l}s\\leftarrow0\\\\ \\text{for }i\\in1..64\\\\ \\quad\\left|\\begin{array}{l}\\text{for }j\\in1..64\\\\ s\\leftarrow s+\\sin(i+j\\cdot k)\\cdot\\cos(n\\times i\\cdot0.1)\\end{array}\\right.\\\\ \\text{return }s\\end{array}\\right.",
   "text": ""
  },
  {
   "id": 741,
   "x": 138,
   "y": 5266,
   "kind": "math",
   "latex": "plot(f5(k,1))",
   "text": "",
   "style": {
    "dash": "solid",
    "width": 2,
    "color": "#185FA5",
    "marker": "none",
    "msize": 6,
    "grid": true,
    "box": true,
    "title": "",
    "xlabel": "",
    "ylabel": "",
    "titleSize": 14,
    "xlabelSize": 11,
    "ylabelSize": 11,
    "tickSize": 11,
    "legendPos": "",
    "legendSize": 11,
    "xmin": "",
    "xmax": "",
    "ymin": "",
    "ymax": "",
    "xlog": false,
    "ylog": false,
    "axes": true,
    "xaxisPos": "edge",
    "yaxisPos": "edge",
    "colorscale": "",
    "levels": 10,
    "labels": true,
    "barw": 0.6,
    "chartType": "",
    "barmode": "group",
    "bargap": -0.2,
    "barline": "",
    "points": "100",
    "bins": "",
    "w": 560,
    "h": 300,
    "page": "",
    "mrow": 6,
    "mcol": 6,
    "exportScale": 2,
    "channel": "auto",
    "imgfit": "contain",
    "interp": "smooth",
    "azimuth": 1.3,
    "elevation": 0.6,
    "fill": false,
    "fillalpha": "",
    "series": []
   },
   "pv": {
    "g0:n": -0.4
   },
   "pr": {
    "g0:n": {
     "min": -7,
     "max": 7,
     "step": 0.01
    }
   }
  },
  {
   "id": 746,
   "x": 63,
   "y": 181,
   "kind": "text",
   "latex": "",
   "text": "这是一份 10 分钟能过完的入门。先记两条规矩：",
   "fmt": {
    "size": "20",
    "bg": "#9aff75"
   }
  },
  {
   "id": 761,
   "x": 65,
   "y": 54,
   "kind": "text",
   "latex": "",
   "text": "欢迎使用 MathPad！让计算更直观自然。从课堂教学到专业科研，涵盖数值与矩阵计算、函数绘图、符号求解及 NumPy 原生图像处理。",
   "fmt": {
    "size": "20",
    "bg": "#9aff75"
   },
   "w": 1315
  },
  {
   "id": 777,
   "x": 434,
   "y": 3722,
   "kind": "text",
   "latex": "",
   "text": "←打印的时候不想显示错误提示信息吗？视图中可以设置隐藏哦",
   "fmt": {
    "bg": "#fbfb18",
    "size": "14",
    "underline": "1"
   }
  },
  {
   "id": 849,
   "x": 642,
   "y": 4495,
   "kind": "math",
   "latex": "\\lambda\\coloneqq\\,1",
   "text": ""
  },
  {
   "id": 900,
   "x": 79,
   "y": 5706,
   "kind": "math",
   "latex": "\\left\\{\\begin{array}{l}x+y=10\\\\ 2x+3y=24\\end{array}\\right.\\to solve",
   "text": "",
   "w": 473
  },
  {
   "id": 901,
   "x": 92,
   "y": 5789,
   "kind": "math",
   "latex": "x=",
   "text": ""
  },
  {
   "id": 902,
   "x": 86,
   "y": 5865,
   "kind": "math",
   "latex": "\\left\\{\\begin{array}{l}x+y=10\\\\ 2x+3y=24\\end{array}\\right.\\to solve",
   "text": "",
   "style": {
    "solDef": true
   },
   "w": 473
  },
  {
   "id": 903,
   "x": 86,
   "y": 5948,
   "kind": "math",
   "latex": "x=",
   "text": "",
   "w": 52
  },
  {
   "id": 906,
   "x": 462,
   "y": 5789,
   "kind": "text",
   "latex": "",
   "text": "可以设置是否将求解结果定义给变量",
   "fmt": {
    "size": "16",
    "bg": "#ffff00"
   }
  },
  {
   "id": 916,
   "x": 1147,
   "y": 6115,
   "kind": "math",
   "latex": "tststs_{[3,2]}\\coloneqq\\,1",
   "text": ""
  },
  {
   "id": 919,
   "x": 1197,
   "y": 6249,
   "kind": "math",
   "latex": "tststs=",
   "text": ""
  },
  {
   "id": 963,
   "x": 336,
   "y": 427,
   "kind": "math",
   "latex": "test\\_r_{down}^{up}\\coloneqq\\,22",
   "text": ""
  },
  {
   "id": 964,
   "x": 332,
   "y": 501,
   "kind": "math",
   "latex": "\\left(test\\_r_{down}^{up}\\right)\\text{\\textasciicircum}^2=",
   "text": ""
  }
 ]
}