const data = {
  name: "代数",
  code: "algebra",
  source: "algebra",
  children: [
    {
      output: "\\left(x-1\\right)\\left(x+3\\right) ",
      source: "algebra_1",
    },
    {
      output: "\\sqrt{a^2+b^2}  ",
      source: "algebra_2",
    },
    {
      output: "\\left ( \\frac{a}{b}\\right )^{n}= \\frac{a^{n}}{b^{n}} ",
      source: "algebra_3",
    },
    {
      output: "\\frac{a}{b}\\pm \\frac{c}{d}= \\frac{ad \\pm bc}{bd} ",
      source: "algebra_4",
    },
    {
      output: "\\frac{x^{2}}{a^{2}}-\\frac{y^{2}}{b^{2}}=1 ",
      source: "algebra_5",
    },
    {
      output:
        "\\frac{1}{\\sqrt{a}}=\\frac{\\sqrt{a}}{a},a\\ge 0\\frac{1}{\\sqrt{a}}=\\frac{\\sqrt{a}}{a},a\\ge 0 ",
      source: "algebra_6",
    },
    {
      output: "\\sqrt[n]{a^{n}}=\\left ( \\sqrt[n]{a}\\right )^{n} ",
      source: "algebra_7",
    },
    {
      output: "x ={-b \\pm \\sqrt{b^2-4ac}\\over 2a} ",
      source: "algebra_8",
    },
    {
      output: "y-y_{1}=k \\left( x-x_{1}\\right) ",
      source: "algebra_9",
    },
    {
      output: `
\\left\\{\\begin{matrix} 
  x=a + r\\text{cos}\\theta \\\\  
  y=b + r\\text{sin}\\theta 
\\end{matrix}\\right.
`,
      source: "algebra_10",
    },
    {
      output: `
\\begin{array}{l} 
  \\text{对于方程形如：}x^{3}-1=0 \\\\ 
  \\text{设}\\text{:}\\omega =\\frac{-1+\\sqrt{3}i}{2} \\\\ 
  x_{1}=1,x_{2}= \\omega =\\frac{-1+\\sqrt{3}i}{2} \\\\ 
  x_{3}= \\omega ^{2}=\\frac{-1-\\sqrt{3}i}{2} 
\\end{array} 
      `,
      source: "algebra_11",
    },
    {
      output: `
\\begin{array}{l} 
  a\\mathop{{x}}\\nolimits^{{2}}+bx+c=0 \\\\ 
  \\Delta =\\mathop{{b}}\\nolimits^{{2}}-4ac \\\\ 
  \\left\\{\\begin{matrix} 
  \\Delta \\gt 0\\text{方程有两个不相等的实根} \\\\ 
  \\Delta = 0\\text{方程有两个相等的实根} \\\\ 
  \\Delta \\lt 0\\text{方程无实根} 
\\end{matrix}\\right.    
\\end{array} 
      `,
      source: "algebra_12",
    },
    {
      output: `
\\begin{array}{l} 
  a\\mathop{{x}}\\nolimits^{{2}}+bx+c=0 \\\\ 
  \\Delta =\\mathop{{b}}\\nolimits^{{2}}-4ac \\\\ 
  \\mathop{{x}}\\nolimits_{{1,2}}=\\frac{{-b \\pm  
  \\sqrt{{\\mathop{{b}}\\nolimits^{{2}}-4ac}}}}{{2a}} \\\\ 
  \\mathop{{x}}\\nolimits_{{1}}+\\mathop{{x}}\\nolimits_{{2}}=-\\frac{{b}}{{a}} \\\\ 
  \\mathop{{x}}\\nolimits_{{1}}\\mathop{{x}}\\nolimits_{{2}}=\\frac{{c}}{{a}} 
\\end{array} 
      `,
      source: "algebra_13",
    },
  ],
};

export default data;
