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165 lines
451 KiB
165 lines
451 KiB
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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 "}]}]}],E=[{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
|
|
x=a + r\\text{cos}\\theta \\ \r
|
|
y=b + r\\text{sin}\\theta \r
|
|
\\end{matrix}\\right. `},{value:`\\begin{array}{l} \r
|
|
\\text{\u5BF9\u4E8E\u65B9\u7A0B\u5F62\u5982\uFF1A}x^{3}-1=0 \\ \r
|
|
\\text{\u8BBE}\\text{:}\\omega =\\frac{-1+\\sqrt{3}i}{2} \\ \r
|
|
x_{1}=1,x_{2}= \\omega =\\frac{-1+\\sqrt{3}i}{2} \\ \r
|
|
x_{3}= \\omega ^{2}=\\frac{-1-\\sqrt{3}i}{2} \r
|
|
\\end{array} `},{value:`\\begin{array}{l} \r
|
|
a\\mathop{{x}}\\nolimits^{{2}}+bx+c=0 \\ \r
|
|
\\Delta =\\mathop{{b}}\\nolimits^{{2}}-4ac \\ \r
|
|
\\left\\{\\begin{matrix} \r
|
|
\\Delta \\gt 0\\text{\u65B9\u7A0B\u6709\u4E24\u4E2A\u4E0D\u76F8\u7B49\u7684\u5B9E\u6839} \\ \r
|
|
\\Delta = 0\\text{\u65B9\u7A0B\u6709\u4E24\u4E2A\u76F8\u7B49\u7684\u5B9E\u6839} \\ \r
|
|
\\Delta \\lt 0\\text{\u65B9\u7A0B\u65E0\u5B9E\u6839} \r
|
|
\\end{matrix}\\right. \r
|
|
\\end{array} `},{value:`\\begin{array}{l} \r
|
|
a\\mathop{{x}}\\nolimits^{{2}}+bx+c=0 \\ \r
|
|
\\Delta =\\mathop{{b}}\\nolimits^{{2}}-4ac \\ \r
|
|
\\mathop{{x}}\\nolimits_{{1,2}}=\\frac{{-b \\pm \r
|
|
\\sqrt{{\\mathop{{b}}\\nolimits^{{2}}-4ac}}}}{{2a}} \\ \r
|
|
\\mathop{{x}}\\nolimits_{{1}}+\\mathop{{x}}\\nolimits_{{2}}=-\\frac{{b}}{{a}} \\ \r
|
|
\\mathop{{x}}\\nolimits_{{1}}\\mathop{{x}}\\nolimits_{{2}}=\\frac{{c}}{{a}} \r
|
|
\\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
|
|
a \\perp \\alpha \\ \r
|
|
b \\perp \\alpha \r
|
|
\\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
|
|
\\Rightarrow a \\perp \\beta `},{value:`\\left.\\begin{matrix} \r
|
|
a \\subset \\beta ,b \\subset \\beta ,a \\cap b=P \\ \r
|
|
a \\parallel \\partial ,b \\parallel \\partial \r
|
|
\\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
|
|
m \\subset \\alpha ,n \\subset \\alpha ,m \\cap n=P \\ \r
|
|
a \\perp m,a \\perp n \r
|
|
\\end{matrix}\\right\\}\\Rightarrow a \\perp \\alpha `},{value:`\\begin{array}{c} \r
|
|
\\text{\u76F4\u89D2\u4E09\u89D2\u5F62\u4E2D,\u76F4\u89D2\u8FB9\u957Fa,b,\u659C\u8FB9\u8FB9\u957Fc} \\ \r
|
|
a^{2}+b^{2}=c^{2} \r
|
|
\\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
|
|
a \\gt b,c \\gt 0 \\Rightarrow ac \\gt bc \\ \r
|
|
a \\gt b,c \\lt 0 \\Rightarrow ac \\lt bc \r
|
|
\\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
|
|
a \\gt b \\gt 0,n \\in N^{\\ast},n \\gt 1 \\ \r
|
|
\\Rightarrow a^{n}\\gt b^{n}, \\sqrt[n]{a}\\gt \\sqrt[n]{b} \r
|
|
\\end{array}`},{value:`\\left( \\sum_{k=1}^n a_k b_k \\right)^{\\!\\!2}\\leq \r
|
|
\\left( \\sum_{k=1}^n a_k^2 \\right) \\left( \\sum_{k=1}^n b_k^2 \\right) `},{value:`\\begin{array}{c} \r
|
|
a,b \\in R^{+} \\ \r
|
|
\\Rightarrow \\frac{a+b}{{2}}\\ge \\sqrt{ab} \\ \r
|
|
\\left( \\text{\u5F53\u4E14\u4EC5\u5F53}a=b\\text{\u65F6\u53D6\u201C}=\\text{\u201D\u53F7}\\right) \r
|
|
\\end{array}`},{value:`\\begin{array}{c} \r
|
|
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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\\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
|
|
S= \\binom{N}{n},A_{k}=\\binom{M}{k}\\cdot \\binom{N-M}{n-k} \\\\ \r
|
|
P\\left ( A_{k}\\right ) = \\frac{\\binom{M}{k}\\cdot \\binom{N-M}{n-k}}{\\binom{N}{n}} \r
|
|
\\end{array}`},{value:`\\begin{array}{c} \r
|
|
P_{n}=n! \\\\ \r
|
|
A_{n}^{k}=\\frac{n!}{\\left( n-k \\left) !\\right. \\right.} \r
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\\end{array}`}]}]}],b=ee=>{a.current.setValue(a.current.getValue()+" "+ee.value+" 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> ${xe}-item-group > ${xe}-item-group-list > ${xe}-item,
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${xe}-submenu-arrow,
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|
|
p${ze}-text,
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p${ze}-hint
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`]:{color:he.colorTextDisabled}}}}}},In=he=>{const{componentCls:ze,antCls:Be,iconCls:Te,fontSize:gt,lineHeight:Ye}=he,nt=`${ze}-list-item`,_e=`${nt}-actions`,Vt=`${nt}-action`,Ot=Math.round(gt*Ye);return{[`${ze}-wrapper`]:{[`${ze}-list`]:Object.assign(Object.assign({},(0,Wt.dF)()),{lineHeight:he.lineHeight,[nt]:{position:"relative",height:he.lineHeight*gt,marginTop:he.marginXS,fontSize:gt,display:"flex",alignItems:"center",transition:`background-color ${he.motionDurationSlow}`,"&:hover":{backgroundColor:he.controlItemBgHover},[`${nt}-name`]:Object.assign(Object.assign({},Wt.vS),{padding:`0 ${he.paddingXS}px`,lineHeight:Ye,flex:"auto",transition:`all ${he.motionDurationSlow}`}),[_e]:{[Vt]:{opacity:0},[`${Vt}${Be}-btn-sm`]:{height:Ot,border:0,lineHeight:1,"> span":{transform:"scale(1)"}},[`
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${Vt}:focus-visible,
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&.picture ${Vt}
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|
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${Ye}${Ye}-picture,
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${Ye}${Ye}-picture-card,
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${Ye}${Ye}-picture-circle
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alt async autoComplete autoFocus autoPlay capture cellPadding cellSpacing challenge
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onMouseEnter onMouseLeave onMouseMove onMouseOut onMouseOver onMouseUp onSelect onTouchCancel
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onDurationChange onEmptied onEncrypted onEnded onError onLoadedData onLoadedMetadata
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