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147 lines
410 KiB
147 lines
410 KiB
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te=re(67294),Le=re(71230),Je=re(15746),je=re(66368),ce=re(71577),Oe=re(85725),se=re(71736),Ue=re(84279),be=re(67294);const Te=(0,te.forwardRef)(({callback:_e,showSaveButton:Me,value:Ie=""},ae)=>{const a=(0,te.useRef)(),y=[{name:"\u5206\u6570\u5F97\u5206",value:"\\frac{x}{y}",children:[{name:"\u5206\u6570 Fractions",data:[{value:"\\frac{a}{b}"},{value:"x\\tfrac{x}{a} "},{value:"\\mathrm{d}t"},{value:"\\partial t"},{value:"\\frac{\\partial y}{\\partial x}"},{value:"\\nabla\\psi"},{value:"\\frac{\\partial^2}{\\partial x_1\\partial x_2}y"},{value:"\\cfrac{1}{a + \\cfrac{7}{b + \\cfrac{2}{9}}} = c"}]},{name:"\u5BFC\u6570 Derivative",data:[{value:"\\dot{a} "},{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) 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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
|
|
\\Rightarrow a^{2}+b^{2}\\gt 2ab \\ \r
|
|
\\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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\\forall A \\in S \\\\ \r
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P \\left( A \\right) \\ge 0 \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}`}]}]}],b=ee=>{a.current.setValue(a.current.getValue()+" "+ee.value+" 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ve=1/0;ue.selection.each(function(he){he instanceof go.Link||(ve=Math.min(he.position.y,ve))}),ue.selection.each(function(he){he instanceof go.Link||he.move(new go.Point(he.position.x,ve))}),ue.commitTransaction("alignTop")},it.prototype.alignBottom=function(){var ue=this.diagram;ue.startTransaction("aligning bottom");var ve=-1/0;ue.selection.each(function(he){if(!(he instanceof go.Link)){var Ge=he.actualBounds.y+he.actualBounds.height;ve=Math.max(Ge,ve)}}),ue.selection.each(function(he){he instanceof go.Link||he.move(new go.Point(he.actualBounds.x,ve-he.actualBounds.height))}),ue.commitTransaction("aligning bottom")},it.prototype.alignCenterX=function(){var ue=this.diagram,ve=ue.selection.first();if(ve){ue.startTransaction("aligning Center X");var he=ve.actualBounds.x+ve.actualBounds.width/2;ue.selection.each(function(Ge){Ge instanceof go.Link||Ge.move(new go.Point(he-Ge.actualBounds.width/2,Ge.actualBounds.y))}),ue.commitTransaction("aligning Center 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> ${Ee}-item-active,
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> ${Ee}-submenu ${Ee}-submenu-title:hover`]:{backgroundColor:"transparent"},[`${Ee}-item, ${Ee}-submenu-title`]:{transition:[`border-color ${ye}`,`background ${ye}`].join(",")},[`${Ee}-submenu-arrow`]:{display:"none"}}}},lt=Ze=>{let{componentCls:Ee,menuArrowOffset:ye}=Ze;return{[`${Ee}-rtl`]:{direction:"rtl"},[`${Ee}-submenu-rtl`]:{transformOrigin:"100% 0"},[`${Ee}-rtl${Ee}-vertical,
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> ${Ee}-submenu > ${Ee}-submenu-title`]:{height:ye,lineHeight:`${ye}px`},[`${Ee}-item-group-list ${Ee}-submenu-title,
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${Ee}-submenu-title`]:{paddingInlineEnd:ct}}};var Ae=Ze=>{const{componentCls:Ee,iconCls:ye,itemHeight:pe,colorTextLightSolid:we,dropdownWidth:$e,controlHeightLG:et,motionDurationMid:St,motionEaseOut:ct,paddingXL:wt,itemMarginInline:Mt,fontSizeLG:It,motionDurationSlow:rn,paddingXS:gn,boxShadowSecondary:_t,collapsedWidth:Rt,collapsedIconSize:dn}=Ze,qt={height:pe,lineHeight:`${pe}px`,listStylePosition:"inside",listStyleType:"disc"};return[{[Ee]:{"&-inline, &-vertical":Object.assign({[`&${Ee}-root`]:{boxShadow:"none"}},cn(Ze))},[`${Ee}-submenu-popup`]:{[`${Ee}-vertical`]:Object.assign(Object.assign({},cn(Ze)),{boxShadow:_t})}},{[`${Ee}-submenu-popup ${Ee}-vertical${Ee}-sub`]:{minWidth:$e,maxHeight:`calc(100vh - ${et*2.5}px)`,padding:"0",overflow:"hidden",borderInlineEnd:0,"&:not([class*='-active'])":{overflowX:"hidden",overflowY:"auto"}}},{[`${Ee}-inline`]:{width:"100%",[`&${Ee}-root`]:{[`${Ee}-item, ${Ee}-submenu-title`]:{display:"flex",alignItems:"center",transition:[`border-color ${rn}`,`background ${rn}`,`padding ${St} ${ct}`].join(","),[`> ${Ee}-title-content`]:{flex:"auto",minWidth:0,overflow:"hidden",textOverflow:"ellipsis"},"> *":{flex:"none"}}},[`${Ee}-sub${Ee}-inline`]:{padding:0,border:0,borderRadius:0,boxShadow:"none",[`& > ${Ee}-submenu > ${Ee}-submenu-title`]:qt,[`& ${Ee}-item-group-title`]:{paddingInlineStart:wt}},[`${Ee}-item`]:qt}},{[`${Ee}-inline-collapsed`]:{width:Rt,[`&${Ee}-root`]:{[`${Ee}-item, ${Ee}-submenu ${Ee}-submenu-title`]:{[`> ${Ee}-inline-collapsed-noicon`]:{fontSize:It,textAlign:"center"}}},[`> ${Ee}-item,
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> ${Ee}-item-group > ${Ee}-item-group-list > ${Ee}-item,
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> ${Ee}-item-group > ${Ee}-item-group-list > ${Ee}-submenu > ${Ee}-submenu-title,
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> ${Ee}-submenu > ${Ee}-submenu-title`]:{insetInlineStart:0,paddingInline:`calc(50% - ${It/2}px - ${Mt}px)`,textOverflow:"clip",[`
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${Ee}-submenu-arrow,
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${Ee}-submenu-expand-icon
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`]:{opacity:0},[`${Ee}-item-icon, ${ye}`]:{margin:0,fontSize:dn,lineHeight:`${pe}px`,"+ span":{display:"inline-block",opacity:0}}},[`${Ee}-item-icon, ${ye}`]:{display:"inline-block"},"&-tooltip":{pointerEvents:"none",[`${Ee}-item-icon, ${ye}`]:{display:"none"},"a, a:hover":{color:we}},[`${Ee}-item-group-title`]:Object.assign(Object.assign({},Re.vS),{paddingInline:gn})}}]};const Qe=Ze=>{const{componentCls:Ee,motionDurationSlow:ye,motionDurationMid:pe,motionEaseInOut:we,motionEaseOut:$e,iconCls:et,iconSize:St,iconMarginInlineEnd:ct}=Ze;return{[`${Ee}-item, ${Ee}-submenu-title`]:{position:"relative",display:"block",margin:0,whiteSpace:"nowrap",cursor:"pointer",transition:[`border-color ${ye}`,`background ${ye}`,`padding ${ye} ${we}`].join(","),[`${Ee}-item-icon, ${et}`]:{minWidth:St,fontSize:St,transition:[`font-size ${pe} ${$e}`,`margin ${ye} ${we}`,`color ${ye}`].join(","),"+ span":{marginInlineStart:ct,opacity:1,transition:[`opacity ${ye} ${we}`,`margin ${ye}`,`color 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