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70 lines
16 KiB
70 lines
16 KiB
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"},{value:"\\ddot{a}"},{value:"{f}^{\\prime}"},{value:"{f}^{\\prime\\prime}"},{value:"{f}^{(n)}"}]},{name:"\u6A21\u7B97\u672F Modular arithmetic",data:[{value:"a \\bmod b"},{value:"a \\equiv b \\pmod{m} "},{value:"\\gcd(m, n) "},{value:"\\operatorname{lcm}(m, n) "}]}]},{name:"\u6839\u5F0F\u89D2\u6807",value:"\\sqrt{x}",children:[{name:"\u6839\u5F0F Radicals",data:[{value:"\\sqrt{x}"},{value:"\\sqrt[y]{x}"}]},{name:"\u4E0A\u4E0B\u6807 Sub&Super",data:[{value:"x^{a}"},{value:"x_{a}"},{value:"x_{a}^{b} "},{value:"_{a}^{b} x"},{value:"x_{a}^{b} "}]},{name:"\u91CD\u97F3\u7B26\u53CA\u5176\u4ED6 Accents and Others",data:[{value:"\\hat{a} "},{value:"\\sqrt[y]{x}"},{value:"\\check{} "},{value:"\\grave{a} "},{value:"\\acute{a}"},{value:"\\tilde{a}"},{value:"\\breve{a}"},{value:"\\bar{a}"},{value:"\\vec{a}"},{value:"\\not{a}"},{value:"\\widetilde{abc}"},{value:"\\widehat{abc}"},{value:"\\overleftarrow{abc} 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"}]}]},{name:"\u4E09\u89D2\u51FD\u6570",value:"\\sin a",children:[{name:"\u4E09\u89D2\u51FD\u6570 Trigonometric functions",data:[{value:"\\sin a"},{value:"\\cos a"},{value:"\\tan a"},{value:"\\cot a "},{value:"\\sec a "},{value:"\\csc a "}]},{name:"\u53CD\u4E09\u89D2\u51FD\u6570 Inverse trigonometric functions",data:[{value:"\\sin^{-1}"},{value:"\\cos^{-1}"},{value:"\\tan^{-1}"},{value:"\\cot^{-1}"},{value:"\\sec^{-1}"},{value:"\\csc^{-1}"},{value:"\\arcsin a"},{value:"\\arccos a"},{value:"\\arctan a"},{value:"\\operatorname{arccot} a"},{value:"\\operatorname{arcsec} a"},{value:"\\operatorname{arccsc} a"}]},{name:"\u53CC\u66F2\u51FD\u6570 Hyperblic functions",data:[{value:"\\sinh a"},{value:"\\cosh a"},{value:"\\tanh a"},{value:"\\coth a"},{value:"\\operatorname{sech} a"},{value:"\\operatorname{csch} a"}]},{name:"\u53CD\u53CC\u66F2\u51FD\u6570 Inverse hyperbolic functions",data:[{value:"\\sinh^{-1}"},{value:"a\\cosh^{-1} a"},{value:"\\tanh^{-1} a"},{value:"\\coth^{-1} a"},{value:"\\operatorname{sech}^{-1} a"},{value:"\\operatorname{csch}^{-1} a"}]}]},{name:"\u79EF\u5206\u8FD0\u7B97",value:"\\int_{a}^{b}",children:[{name:"\u79EF\u5206 Integral",data:[{value:"\\int"},{value:"\\int_{a}^{b}"},{value:"\\int\\limits_{a}^{b}"}]},{name:"\u53CC\u91CD\u79EF\u5206 Double integral",data:[{value:"\\iint"},{value:"\\iint_{a}^{b} "},{value:"\\iint\\limits_{a}^{b} "}]},{name:"\u4E09\u91CD\u79EF\u5206 Triple integral",data:[{value:"\\iiint"},{value:"\\iiint_{a}^{b}"},{value:"\\iiint\\limits_{a}^{b} "}]},{name:"\u66F2\u7EBF\u79EF\u5206 Closed line or path integral",data:[{value:"\\oint"},{value:"\\oint_{a}^{b} "}]}]},{name:"\u5927\u578B\u8FD0\u7B97",value:"\\sum_{a}^{b}",children:[{name:"\u6C42\u548C Summation",data:[{value:"\\sum"},{value:"\\sum_{a}^{b}"},{value:"{\\textstyle \\sum_{a}^{b}} "}]},{name:"\u4E58\u79EF\u4F59\u79EF Product and coproduct",data:[{value:"\\prod"},{value:"\\prod_{a}^{b}"},{value:"{\\textstyle \\prod_{a}^{b}}"},{value:"\\coprod"},{value:"\\coprod_{a}^{b}"},{value:"{\\textstyle \\coprod_{a}^{b}} "}]},{name:"\u5E76\u96C6\u4EA4\u96C6 Union and intersection",data:[{value:"\\bigcup"},{value:"\\bigcup_{a}^{b}"},{value:"{\\textstyle \\bigcup_{a}^{b}}"},{value:"\\bigcap"},{value:"\\bigcap_{a}^{b}"}]},{name:"\u6790\u53D6\u5408\u53D6 Disjunction and conjunction",data:[{value:"\\bigvee"},{value:"\\bigvee_{a}^{b}"},{value:"\\bigwedge"},{value:"\\bigwedge_{a}^{b}"}]}]},{name:"\u62EC\u53F7\u53D6\u6574",value:"\\left [ \\left ( \\right ) \\right ] ",children:[{name:"\u62EC\u53F7 Brackets",data:[{value:"\\left ( \\right )"},{value:"\\left [ \\right ]"},{value:"\\left \\langle \\right \\rangle "},{value:"\\left | \\right | "},{value:"\\left \\lfloor \\right \\rfloor "},{value:"\\left \\lceil \\right \\rceil "}]}]}],B=[{name:"\u4EE3\u6570",value:"\\sqrt{a^2+b^2}",children:[{data:[{value:"\\left(x-1\\right)\\left(x+3\\right) "},{value:"\\sqrt{a^2+b^2}"},{value:"\\left ( \\frac{a}{b}\\right )^{n}= \\frac{a^{n}}{b^{n}}"},{value:"\\frac{a}{b}\\pm \\frac{c}{d}= \\frac{ad \\pm bc}{bd} "},{value:"\\frac{x^{2}}{a^{2}}-\\frac{y^{2}}{b^{2}}=1 "},{value:"\\frac{1}{\\sqrt{a}}=\\frac{\\sqrt{a}}{a},a\\ge 0\\frac{1}{\\sqrt{a}}=\\frac{\\sqrt{a}}{a},a\\ge 0 "},{value:"\\sqrt[n]{a^{n}}=\\left ( \\sqrt[n]{a}\\right )^{n} "},{value:"x ={-b \\pm \\sqrt{b^2-4ac}\\over 2a} "},{value:"y-y_{1}=k \\left( x-x_{1}\\right) "},{value:`\\left\\{\\begin{matrix} \r
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x=a + r\\text{cos}\\theta \\ \r
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y=b + r\\text{sin}\\theta \r
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\\end{matrix}\\right. `},{value:`\\begin{array}{l} \r
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\\text{\u5BF9\u4E8E\u65B9\u7A0B\u5F62\u5982\uFF1A}x^{3}-1=0 \\ \r
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\\text{\u8BBE}\\text{:}\\omega =\\frac{-1+\\sqrt{3}i}{2} \\ \r
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x_{1}=1,x_{2}= \\omega =\\frac{-1+\\sqrt{3}i}{2} \\ \r
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x_{3}= \\omega ^{2}=\\frac{-1-\\sqrt{3}i}{2} \r
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\\end{array} `},{value:`\\begin{array}{l} \r
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a\\mathop{{x}}\\nolimits^{{2}}+bx+c=0 \\ \r
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\\Delta =\\mathop{{b}}\\nolimits^{{2}}-4ac \\ \r
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\\left\\{\\begin{matrix} \r
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\\Delta \\gt 0\\text{\u65B9\u7A0B\u6709\u4E24\u4E2A\u4E0D\u76F8\u7B49\u7684\u5B9E\u6839} \\ \r
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\\Delta = 0\\text{\u65B9\u7A0B\u6709\u4E24\u4E2A\u76F8\u7B49\u7684\u5B9E\u6839} \\ \r
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\\Delta \\lt 0\\text{\u65B9\u7A0B\u65E0\u5B9E\u6839} \r
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\\end{matrix}\\right. \r
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\\end{array} `},{value:`\\begin{array}{l} \r
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a\\mathop{{x}}\\nolimits^{{2}}+bx+c=0 \\ \r
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\\Delta =\\mathop{{b}}\\nolimits^{{2}}-4ac \\ \r
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\\mathop{{x}}\\nolimits_{{1,2}}=\\frac{{-b \\pm \r
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\\sqrt{{\\mathop{{b}}\\nolimits^{{2}}-4ac}}}}{{2a}} \\ \r
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\\mathop{{x}}\\nolimits_{{1}}+\\mathop{{x}}\\nolimits_{{2}}=-\\frac{{b}}{{a}} \\ \r
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\\mathop{{x}}\\nolimits_{{1}}\\mathop{{x}}\\nolimits_{{2}}=\\frac{{c}}{{a}} \r
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\\end{array} `}]}]},{name:"\u51E0\u4F55",value:"\\Delta A B C ",children:[{data:[{value:"\\Delta A B C "},{value:"a \\parallel c,b \\parallel c \\Rightarrow a \\parallel b "},{value:"l \\perp \\beta ,l \\subset \\alpha \\Rightarrow \\alpha \\perp \\beta"},{value:`\\left.\\begin{matrix} \r
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a \\perp \\alpha \\ \r
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b \\perp \\alpha \r
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\\end{matrix}\\right\\}\\Rightarrow a \\parallel b`},{value:"P \\in \\alpha ,P \\in \\beta , \\alpha \\cap \\beta =l \\Rightarrow P \\in l "},{value:`\\alpha \\perp \\beta , \\alpha \\cap \\beta =l,a \\subset \\alpha ,a \\perp l \r
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\\Rightarrow a \\perp \\beta `},{value:`\\left.\\begin{matrix} \r
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a \\subset \\beta ,b \\subset \\beta ,a \\cap b=P \\ \r
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a \\parallel \\partial ,b \\parallel \\partial \r
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\\end{matrix}\\right\\}\\Rightarrow \\beta \\parallel \\alpha `},{value:"\\alpha \\parallel \\beta , \\gamma \\cap \\alpha =a, \\gamma \\cap \\beta =b \\Rightarrow a \\parallel b "},{value:"A \\in l,B \\in l,A \\in \\alpha ,B \\in \\alpha \\Rightarrow l \\subset \\alpha "},{value:`\\left.\\begin{matrix} \r
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m \\subset \\alpha ,n \\subset \\alpha ,m \\cap n=P \\ \r
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a \\perp m,a \\perp n \r
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\\end{matrix}\\right\\}\\Rightarrow a \\perp \\alpha `},{value:`\\begin{array}{c} \r
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\\text{\u76F4\u89D2\u4E09\u89D2\u5F62\u4E2D,\u76F4\u89D2\u8FB9\u957Fa,b,\u659C\u8FB9\u8FB9\u957Fc} \\ \r
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a^{2}+b^{2}=c^{2} \r
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\\end{array}`}]}]},{name:"\u4E0D\u7B49\u5F0F",value:"a > b",children:[{data:[{value:"a > b,b > c \\Rightarrow a > c "},{value:"a > b,c > d \\Rightarrow a+c > b+d "},{value:"a > b > 0,c > d > 0 \\Rightarrow ac bd "},{value:`\\begin{array}{c} \r
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a \\gt b,c \\gt 0 \\Rightarrow ac \\gt bc \\ \r
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a \\gt b,c \\lt 0 \\Rightarrow ac \\lt bc \r
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\\end{array}`},{value:"\\left | a-b \\right | \\geqslant \\left | a \\right | -\\left | b \\right | "},{value:"-\\left | a \\right |\\leq a\\leqslant \\left | a \\right | "},{value:"\\left | a \\right |\\leqslant b \\Rightarrow -b \\leqslant a \\leqslant \\left | b \\right | "},{value:"\\left | a+b \\right | \\leqslant \\left | a \\right | + \\left | b \\right | "},{value:`\\begin{array}{c} \r
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a \\gt b \\gt 0,n \\in N^{\\ast},n \\gt 1 \\ \r
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\\Rightarrow a^{n}\\gt b^{n}, \\sqrt[n]{a}\\gt \\sqrt[n]{b} \r
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\\end{array}`},{value:`\\left( \\sum_{k=1}^n a_k b_k \\right)^{\\!\\!2}\\leq \r
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\\left( \\sum_{k=1}^n a_k^2 \\right) \\left( \\sum_{k=1}^n b_k^2 \\right) `},{value:`\\begin{array}{c} \r
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a,b \\in R^{+} \\ \r
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\\Rightarrow \\frac{a+b}{{2}}\\ge \\sqrt{ab} \\ \r
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\\left( \\text{\u5F53\u4E14\u4EC5\u5F53}a=b\\text{\u65F6\u53D6\u201C}=\\text{\u201D\u53F7}\\right) \r
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\\end{array}`},{value:`\\begin{array}{c} \r
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a,b \\in R \\ \r
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\\Rightarrow a^{2}+b^{2}\\gt 2ab \\ \r
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\\left( \\text{\u5F53\u4E14\u4EC5\u5F53}a=b\\text{\u65F6\u53D6\u201C}=\\text{\u201D\u53F7}\\right) \r
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\\end{array}`},{value:`\\begin{array}{c} \r
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H_{n}=\\frac{n}{\\sum \\limits_{i=1}^{n}\\frac{1}{x_{i}}}= \\frac{n}{\\frac{1}{x_{1}}+ \\frac{1}{x_{2}}+ \\cdots + \\frac{1}{x_{n}}} \\ G_{n}=\\sqrt[n]{\\prod \\limits_{i=1}^{n}x_{i}}= \\sqrt[n]{x_{1}x_{2}\\cdots x_{n}} \\ A_{n}=\\frac{1}{n}\\sum \\limits_{i=1}^{n}x_{i}=\\frac{x_{1}+ x_{2}+ \\cdots + x_{n}}{n} \\ Q_{n}=\\sqrt{\\sum \\limits_{i=1}^{n}x_{i}^{2}}= \\sqrt{\\frac{x_{1}^{2}+ x_{2}^{2}+ \\cdots + x_{n}^{2}}{n}} \\ H_{n}\\leq G_{n}\\leq A_{n}\\leq Q_{n} \r
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\\end{array}`}]}]},{name:"\u79EF\u5206",value:"\\frac{\\mathrm{d}\\partial}{\\partial x}",children:[{data:[{value:"\\frac{\\mathrm{d}}{\\mathrm{d}x}x^n=nx^{n-1} "},{value:"\\frac{\\mathrm{d}}{\\mathrm{d}x}e^{ax}=a\\,e^{ax} "},{value:"\\frac{\\mathrm{d}}{\\mathrm{d}x}\\ln(x)=\\frac{1}{x} "},{value:"\\frac{\\mathrm{d}}{\\mathrm{d}x}\\sin x=\\cos x "},{value:"\\frac{\\mathrm{d}}{\\mathrm{d}x}\\cos x=-\\sin x "},{value:"\\int k\\mathrm{d}x = kx+C "},{value:"\\frac{\\mathrm{d}}{\\mathrm{d}x}\\tan x=\\sec^2 x "},{value:"\\frac{\\mathrm{d}}{\\mathrm{d}x}\\cot x=-\\csc^2 x "},{value:"\\int \\frac{1}{x}\\mathrm{d}x= \\ln \\left| x \\right| +C "},{value:"\\int \\frac{1}{\\sqrt{1-x^{2}}}\\mathrm{d}x= \\arcsin x +C "},{value:"\\int \\frac{1}{1+x^{2}}\\mathrm{d}x= \\arctan x +C "},{value:"\\int u \\frac{\\mathrm{d}v}{\\mathrm{d}x}\\,\\mathrm{d}x=uv-\\int \\frac{\\mathrm{d}u}{\\mathrm{d}x}v\\,\\mathrm{d}x "},{value:"f(x) = \\int_{-\\infty}^\\infty \\hat f(x)\\xi\\,e^{2 \\pi i \\xi x} \\,\\mathrm{d}\\xi "},{value:"\\int x^{\\mu}\\mathrm{d}x=\\frac{x^{\\mu +1}}{\\mu +1}+C, \\left({\\mu \\neq -1}\\right) "}]}]},{name:"\u4E09\u89D2",value:"e^{i \\theta}",children:[{name:"\u6C42\u548C Summation",data:[{value:"e^{i \\theta} "},{value:"\\left(\\frac{\\pi}{2}-\\theta \\right ) "},{value:"\\text{sin}^{2}\\frac{\\alpha}{2}=\\frac{1- \\text{cos}\\alpha}{2} "},{value:"\\text{cos}^{2}\\frac{\\alpha}{2}=\\frac{1+ \\text{cos}\\alpha}{2} "},{value:"\\text{tan}\\frac{\\alpha}{2}=\\frac{\\text{sin}\\alpha}{1+ \\text{cos}\\alpha} "},{value:"\\sin \\alpha + \\sin \\beta =2 \\sin \\frac{\\alpha + \\beta}{2}\\cos \\frac{\\alpha - \\beta}{2} "},{value:"\\sin \\alpha - \\sin \\beta =2 \\cos \\frac{\\alpha + \\beta}{2}\\sin \\frac{\\alpha - \\beta}{2} "},{value:"\\cos \\alpha + \\cos \\beta =2 \\cos \\frac{\\alpha + \\beta}{2}\\cos \\frac{\\alpha - \\beta}{2} "},{value:"\\cos \\alpha - \\cos \\beta =-2\\sin \\frac{\\alpha + \\beta}{2}\\sin \\frac{\\alpha - \\beta}{2} "},{value:"a^{2}=b^{2}+c^{2}-2bc\\cos A "},{value:"\\frac{\\sin A}{a}=\\frac{\\sin B}{b}=\\frac{\\sin C}{c}=\\frac{1}{2R} "},{value:"\\sin \\left ( \\frac{\\pi}{2}-\\alpha \\right ) = \\cos \\alpha "},{value:"\\sin \\left ( \\frac{\\pi}{2}+\\alpha \\right ) = \\cos \\alpha "}]}]},{name:"\u7EDF\u8BA1",value:"C_{r}^{n}",children:[{data:[{value:"C_{r}^{n} "},{value:"\\frac{n!}{r!(n-r)!} "},{value:"\\sum_{i=1}^{n}{X_i} "},{value:"\\sum_{i=1}^{n}{X_i^2} "},{value:"X_1, \\cdots,X_n "},{value:"\\frac{x-\\mu}{\\sigma} "},{value:"\\sum_{i=1}^{n}{(X_i - \\overline{X})^2} "},{value:`\\begin{array}{c} \r
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\\text{\u82E5}P \\left( AB \\right) =P \\left( A \\right) P \\left( B \\right) \\\\ \r
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\\text{\u5219}P \\left( A \\left| B\\right. \\right) =P \\left({B}\\right) \r
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\\end{array}`},{value:"P(E) ={n \\choose k}p^k (1-p)^{n-k} "},{value:"P \\left( A \\right) = \\lim \\limits_{n \\to \\infty}f_{n}\\left ( A \\right ) "},{value:"P \\left( \\bigcup \\limits_{i=1}^{+ \\infty}A_{i}\\right) = \\prod \\limits_{i=1}^{+ \\infty}P{\\left( A_{i}\\right)} "},{value:`\\begin{array}{c} \r
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P \\left( \\emptyset \\right) =0 \\\\ \r
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P \\left( S \\right) =1 \r
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\\end{array}`},{value:`\\begin{array}{c} \r
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\\forall A \\in S \\\\ \r
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P \\left( A \\right) \\ge 0 \r
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\\end{array}`},{value:"P \\left( \\bigcup \\limits_{i=1}^{n}A_{i}\\right) = \\prod \\limits_{i=1}^{n}P \\left( A_{i}\\right) "},{value:`\\begin{array}{c} \r
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S= \\binom{N}{n},A_{k}=\\binom{M}{k}\\cdot \\binom{N-M}{n-k} \\\\ \r
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P\\left ( A_{k}\\right ) = \\frac{\\binom{M}{k}\\cdot \\binom{N-M}{n-k}}{\\binom{N}{n}} \r
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\\end{array}`},{value:`\\begin{array}{c} \r
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P_{n}=n! \\\\ \r
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A_{n}^{k}=\\frac{n!}{\\left( n-k \\left) !\\right. \\right.} \r
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\\end{array}`}]}]}],f=e=>{m.current.setValue(m.current.getValue()+" "+e.value+" ")},A=[{key:"1",label:"\u5FEB\u6377\u6A21\u677F",children:a.createElement(n.Z,{className:t.Z.lists,gutter:[10,10]},C.map((e,v)=>a.createElement(i.Z,{flex:"110px",className:t.Z.item},a.createElement("div",null,a.createElement(c.Z,{value:`$$${e.value}$$`}),e.name),a.createElement("div",{className:t.Z.children},e.children.map((l,o)=>a.createElement("div",{key:o},a.createElement("h1",null,l.name),a.createElement(n.Z,{gutter:[10,10]},l.data.map((u,b)=>a.createElement(i.Z,{key:b,onClick:()=>f(u),className:t.Z.diamond},a.createElement(c.Z,{value:"`$$"+u.value+"$$`"}))))))))))},{key:"2",label:"\u516C\u5F0F\u6A21\u677F",children:a.createElement(n.Z,{className:t.Z.lists,gutter:[10,10]},B.map((e,v)=>a.createElement(i.Z,{flex:"110px",className:t.Z.item},a.createElement("div",null,a.createElement(c.Z,{value:"`$$"+e.value+"$$`"}),e.name),a.createElement("div",{className:t.Z.children},e.children.map((l,o)=>a.createElement("div",{key:o},l.name&&a.createElement("h1",null,l.name),a.createElement(n.Z,{gutter:[10,10]},l.data.map((u,b)=>a.createElement(i.Z,{key:b,onClick:()=>f(u),className:t.Z.diamond},a.createElement(c.Z,{value:"`$$"+u.value+"$$`"}))))))))))}],p=()=>{var e=document.createElement("div");e.innerHTML=m.current.getValue();var v=e.innerText;return d&&d(v),v};return(0,h.useImperativeHandle)(D,()=>({getData:p})),a.createElement("div",{className:t.Z.mathWrap},a.createElement(x.default,{defaultActiveKey:"1",items:A}),a.createElement("math-field",{locale:"zh_cn",className:t.Z.mathField,placeholder:"\u8BF7\u6253\u5F00\u952E\u76D8\uFF0C\u8F93\u5165\u516C\u5F0F",ref:m,style:{width:800,marginTop:30,fontSize:18}},y||""),F&&a.createElement("div",{className:t.Z.button},a.createElement(_.ZP,{size:"large",onClick:p,style:{zIndex:8,marginTop:10},type:"primary"},"\u4FDD\u5B58\u5230\u7F16\u8F91\u5668")))});s.Z=E}}]);
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