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167 lines
429 KiB
167 lines
429 KiB
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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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\\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:E.formatMessage({id:"markdownEditor.geometry",defaultMessage:"\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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\\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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a \\gt b,c \\lt 0 \\Rightarrow ac \\lt bc \r
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a \\gt b \\gt 0,n \\in N^{\\ast},n \\gt 1 \\ \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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a,b \\in R \\ \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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\\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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\\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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de.KX("strokeDashArray","dash")),mt(de.bn,{width:100,height:20,strokeWidth:0,fill:"transparent"}),mt(de.al,{margin:1,textAlign:"center",overflow:de.al.OverflowEllipsis,editable:!0},new de.KX("text").makeTwoWay(),new de.KX("stroke","color"))),Le.current.nodeTemplate.toolTip=mt("ToolTip",mt(de.s_,"Vertical",{maxSize:new de.$u(200,NaN)},mt(de.al,{font:"bold 10pt sans-serif",textAlign:"center"},new de.KX("text")),mt(de.al,{font:"10pt sans-serif",textAlign:"center"},new de.KX("text","details"))));function Se(nt,$t){var xt=(Pt,mn)=>{Pt.handled=!0,Pt.diagram.model.commit(gn=>{var xn=mn.part.adornedPart,Fn=new de.E9().setRectSpot(xn.actualBounds,nt);Fn.subtract(xn.location),Fn.scale(2,2),Fn.x+=Math.sign(Fn.x)*130,Fn.y+=Math.sign(Fn.y)*130,Fn.add(xn.location),Fn.snapToGridPoint(Pt.diagram.grid.gridOrigin,Pt.diagram.grid.gridCellSize);var Gn=gn.copyNodeData(xn.data);gn.setGroupKeyForNodeData(Gn,gn.getGroupKeyForNodeData(xn.data)),gn.addNodeData(Gn);var 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${fe}-submenu-rtl ${fe}-vertical`]:{[`${fe}-submenu-arrow`]:{"&::before":{transform:`rotate(-45deg) translateY(-${Pe})`},"&::after":{transform:`rotate(45deg) translateY(${Pe})`}}}}};const yt=Te=>Object.assign({},(0,Be.oN)(Te));var st=(Te,fe)=>{const{componentCls:Pe,itemColor:he,itemSelectedColor:Ce,groupTitleColor:Ye,itemBg:tt,subMenuItemBg:vt,itemSelectedBg:bt,activeBarHeight:At,activeBarWidth:jt,activeBarBorderWidth:Ht,motionDurationSlow:an,motionEaseInOut:ut,motionEaseOut:It,itemPaddingInline:Ut,motionDurationMid:dn,itemHoverColor:pe,lineType:xe,colorSplit:Ve,itemDisabledColor:ft,dangerItemColor:ht,dangerItemHoverColor:Rt,dangerItemSelectedColor:kt,dangerItemActiveBg:Ot,dangerItemSelectedBg:Tt,itemHoverBg:Kt,itemActiveBg:Vt,menuSubMenuBg:ln,horizontalItemSelectedColor:on,horizontalItemSelectedBg:Pn,horizontalItemBorderRadius:vn,horizontalItemHoverBg:nn,popupBg:qt}=Te;return{[`${Pe}-${fe}, ${Pe}-${fe} > ${Pe}`]:{color:he,background:tt,[`&${Pe}-root:focus-visible`]:Object.assign({},yt(Te)),[`${Pe}-item-group-title`]:{color:Ye},[`${Pe}-submenu-selected`]:{[`> ${Pe}-submenu-title`]:{color:Ce}},[`${Pe}-item-disabled, ${Pe}-submenu-disabled`]:{color:`${ft} !important`},[`${Pe}-item:not(${Pe}-item-selected):not(${Pe}-submenu-selected)`]:{[`&:hover, > ${Pe}-submenu-title:hover`]:{color:pe}},[`&:not(${Pe}-horizontal)`]:{[`${Pe}-item:not(${Pe}-item-selected)`]:{"&:hover":{backgroundColor:Kt},"&:active":{backgroundColor:Vt}},[`${Pe}-submenu-title`]:{"&:hover":{backgroundColor:Kt},"&:active":{backgroundColor:Vt}}},[`${Pe}-item-danger`]:{color:ht,[`&${Pe}-item:hover`]:{[`&:not(${Pe}-item-selected):not(${Pe}-submenu-selected)`]:{color:Rt}},[`&${Pe}-item:active`]:{background:Ot}},[`${Pe}-item a`]:{"&, &:hover":{color:"inherit"}},[`${Pe}-item-selected`]:{color:Ce,[`&${Pe}-item-danger`]:{color:kt},"a, a:hover":{color:"inherit"}},[`& ${Pe}-item-selected`]:{backgroundColor:bt,[`&${Pe}-item-danger`]:{backgroundColor:Tt}},[`${Pe}-item, ${Pe}-submenu-title`]:{[`&:not(${Pe}-item-disabled):focus-visible`]:Object.assign({},yt(Te))},[`&${Pe}-submenu > ${Pe}`]:{backgroundColor:ln},[`&${Pe}-popup > ${Pe}`]:{backgroundColor:qt},[`&${Pe}-horizontal`]:Object.assign(Object.assign({},fe==="dark"?{borderBottom:0}:{}),{[`> ${Pe}-item, > ${Pe}-submenu`]:{top:Ht,marginTop:-Ht,marginBottom:0,borderRadius:vn,"&::after":{position:"absolute",insetInline:Ut,bottom:0,borderBottom:`${At}px solid transparent`,transition:`border-color ${an} ${ut}`,content:'""'},"&:hover, &-active, &-open":{background:nn,"&::after":{borderBottomWidth:At,borderBottomColor:on}},"&-selected":{color:on,backgroundColor:Pn,"&:hover":{backgroundColor:Pn},"&::after":{borderBottomWidth:At,borderBottomColor:on}}}}),[`&${Pe}-root`]:{[`&${Pe}-inline, &${Pe}-vertical`]:{borderInlineEnd:`${Ht}px ${xe} ${Ve}`}},[`&${Pe}-inline`]:{[`${Pe}-sub${Pe}-inline`]:{background:vt},[`${Pe}-item, ${Pe}-submenu-title`]:Ht&&jt?{width:`calc(100% + ${Ht}px)`}:{},[`${Pe}-item`]:{position:"relative","&::after":{position:"absolute",insetBlock:0,insetInlineEnd:0,borderInlineEnd:`${jt}px solid ${Ce}`,transform:"scaleY(0.0001)",opacity:0,transition:[`transform ${dn} ${It}`,`opacity ${dn} ${It}`].join(","),content:'""'},[`&${Pe}-item-danger`]:{"&::after":{borderInlineEndColor:kt}}},[`${Pe}-selected, ${Pe}-item-selected`]:{"&::after":{transform:"scaleY(1)",opacity:1,transition:[`transform ${dn} ${ut}`,`opacity ${dn} ${ut}`].join(",")}}}}}};const Qe=Te=>{const{componentCls:fe,itemHeight:Pe,itemMarginInline:he,padding:Ce,menuArrowSize:Ye,marginXS:tt,itemMarginBlock:vt}=Te,bt=Ce+Ye+tt;return{[`${fe}-item`]:{position:"relative",overflow:"hidden"},[`${fe}-item, ${fe}-submenu-title`]:{height:Pe,lineHeight:`${Pe}px`,paddingInline:Ce,overflow:"hidden",textOverflow:"ellipsis",marginInline:he,marginBlock:vt,width:`calc(100% - ${he*2}px)`},[`> ${fe}-item,
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> ${fe}-submenu > ${fe}-submenu-title`]:{height:Pe,lineHeight:`${Pe}px`},[`${fe}-item-group-list ${fe}-submenu-title,
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${fe}-submenu-title`]:{paddingInlineEnd:bt}}};var Oe=Te=>{const{componentCls:fe,iconCls:Pe,itemHeight:he,colorTextLightSolid:Ce,dropdownWidth:Ye,controlHeightLG:tt,motionDurationMid:vt,motionEaseOut:bt,paddingXL:At,itemMarginInline:jt,fontSizeLG:Ht,motionDurationSlow:an,paddingXS:ut,boxShadowSecondary:It,collapsedWidth:Ut,collapsedIconSize:dn}=Te,pe={height:he,lineHeight:`${he}px`,listStylePosition:"inside",listStyleType:"disc"};return[{[fe]:{"&-inline, &-vertical":Object.assign({[`&${fe}-root`]:{boxShadow:"none"}},Qe(Te))},[`${fe}-submenu-popup`]:{[`${fe}-vertical`]:Object.assign(Object.assign({},Qe(Te)),{boxShadow:It})}},{[`${fe}-submenu-popup ${fe}-vertical${fe}-sub`]:{minWidth:Ye,maxHeight:`calc(100vh - ${tt*2.5}px)`,padding:"0",overflow:"hidden",borderInlineEnd:0,"&:not([class*='-active'])":{overflowX:"hidden",overflowY:"auto"}}},{[`${fe}-inline`]:{width:"100%",[`&${fe}-root`]:{[`${fe}-item, ${fe}-submenu-title`]:{display:"flex",alignItems:"center",transition:[`border-color ${an}`,`background ${an}`,`padding ${vt} ${bt}`].join(","),[`> ${fe}-title-content`]:{flex:"auto",minWidth:0,overflow:"hidden",textOverflow:"ellipsis"},"> *":{flex:"none"}}},[`${fe}-sub${fe}-inline`]:{padding:0,border:0,borderRadius:0,boxShadow:"none",[`& > ${fe}-submenu > ${fe}-submenu-title`]:pe,[`& ${fe}-item-group-title`]:{paddingInlineStart:At}},[`${fe}-item`]:pe}},{[`${fe}-inline-collapsed`]:{width:Ut,[`&${fe}-root`]:{[`${fe}-item, ${fe}-submenu ${fe}-submenu-title`]:{[`> ${fe}-inline-collapsed-noicon`]:{fontSize:Ht,textAlign:"center"}}},[`> ${fe}-item,
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> ${fe}-item-group > ${fe}-item-group-list > ${fe}-item,
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> ${fe}-item-group > ${fe}-item-group-list > ${fe}-submenu > ${fe}-submenu-title,
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> ${fe}-submenu > ${fe}-submenu-title`]:{insetInlineStart:0,paddingInline:`calc(50% - ${Ht/2}px - ${jt}px)`,textOverflow:"clip",[`
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${fe}-submenu-arrow,
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${fe}-submenu-expand-icon
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`]:{opacity:0},[`${fe}-item-icon, ${Pe}`]:{margin:0,fontSize:dn,lineHeight:`${he}px`,"+ span":{display:"inline-block",opacity:0}}},[`${fe}-item-icon, ${Pe}`]:{display:"inline-block"},"&-tooltip":{pointerEvents:"none",[`${fe}-item-icon, ${Pe}`]:{display:"none"},"a, a:hover":{color:Ce}},[`${fe}-item-group-title`]:Object.assign(Object.assign({},Be.vS),{paddingInline:ut})}}]};const Ue=Te=>{const{componentCls:fe,motionDurationSlow:Pe,motionDurationMid:he,motionEaseInOut:Ce,motionEaseOut:Ye,iconCls:tt,iconSize:vt,iconMarginInlineEnd:bt}=Te;return{[`${fe}-item, ${fe}-submenu-title`]:{position:"relative",display:"block",margin:0,whiteSpace:"nowrap",cursor:"pointer",transition:[`border-color ${Pe}`,`background ${Pe}`,`padding ${Pe} ${Ce}`].join(","),[`${fe}-item-icon, ${tt}`]:{minWidth:vt,fontSize:vt,transition:[`font-size ${he} ${Ye}`,`margin ${Pe} ${Ce}`,`color ${Pe}`].join(","),"+ span":{marginInlineStart:bt,opacity:1,transition:[`opacity ${Pe} ${Ce}`,`margin ${Pe}`,`color 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&-inline ${Pe}-submenu-arrow`]:{"&::before":{transform:`rotate(-45deg) translateX(${Ut})`},"&::after":{transform:`rotate(45deg) translateX(-${Ut})`}},[`${Pe}-submenu-open${Pe}-submenu-inline > ${Pe}-submenu-title > ${Pe}-submenu-arrow`]:{transform:`translateY(-${It*.2}px)`,"&::after":{transform:`rotate(-45deg) translateX(-${Ut})`},"&::before":{transform:`rotate(45deg) translateX(${Ut})`}}})},{[`${fe}-layout-header`]:{[Pe]:{lineHeight:"inherit"}}}]};var 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p${Ie}-text,
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p${Ie}-hint
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${_t}:focus-visible,
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${Je}${Je}-picture,
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${Je}${Je}-picture-card,
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${Je}${Je}-picture-circle
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Je=="boolean"?{}:Je,Ft=(Zt,Qt)=>Je?ne.createElement(Ot,{prefixCls:On,listType:it,items:Bn,previewFile:rn,onPreview:Ze,onDownload:_t,onRemove:Un,showRemoveIcon:!Xn&&fa,showPreviewIcon:Pa,showDownloadIcon:pa,removeIcon:va,previewIcon:Dt,downloadIcon:wt,iconRender:zn,locale:Object.assign(Object.assign({},ba),fn),isImageUrl:Rn,progress:In,appendAction:Zt,appendActionVisible:Qt,itemRender:mn,disabled:Xn}):Zt,Gt=Ne()(`${On}-wrapper`,nt,ua,ha,Mn==null?void 0:Mn.className,{[`${On}-rtl`]:ca==="rtl",[`${On}-picture-card-wrapper`]:it==="picture-card",[`${On}-picture-circle-wrapper`]:it==="picture-circle"}),Sn=Object.assign(Object.assign({},Mn==null?void 0:Mn.style),Pt);if($t==="drag"){const Zt=Ne()(ha,On,`${On}-drag`,{[`${On}-drag-uploading`]:Bn.some(Qt=>Qt.status==="uploading"),[`${On}-drag-hover`]:sa==="dragover",[`${On}-disabled`]:Xn,[`${On}-rtl`]:ca==="rtl"});return 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|
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alt async autoComplete autoFocus autoPlay capture cellPadding cellSpacing challenge
|
|
charSet checked classID className colSpan cols content contentEditable contextMenu
|
|
controls coords crossOrigin data dateTime default defer dir disabled download draggable
|
|
encType form formAction formEncType formMethod formNoValidate formTarget frameBorder
|
|
headers height hidden high href hrefLang htmlFor httpEquiv icon id inputMode integrity
|
|
is keyParams keyType kind label lang list loop low manifest marginHeight marginWidth max maxLength media
|
|
mediaGroup method min minLength multiple muted name noValidate nonce open
|
|
optimum pattern placeholder poster preload radioGroup readOnly rel required
|
|
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|
|
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|
|
summary tabIndex target title type useMap value width wmode wrap`,Xe=`onCopy onCut onPaste onCompositionEnd onCompositionStart onCompositionUpdate onKeyDown
|
|
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|
|
onDrag onDragEnd onDragEnter onDragExit onDragLeave onDragOver onDragStart onDrop onMouseDown
|
|
onMouseEnter onMouseLeave onMouseMove onMouseOut onMouseOver onMouseUp onSelect onTouchCancel
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|
onTouchEnd onTouchMove onTouchStart onScroll onWheel onAbort onCanPlay onCanPlayThrough
|
|
onDurationChange onEmptied onEncrypted onEnded onError onLoadedData onLoadedMetadata
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