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150 lines
418 KiB
150 lines
418 KiB
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x=a + r\\text{cos}\\theta \\ \r
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\\text{\u5BF9\u4E8E\u65B9\u7A0B\u5F62\u5982\uFF1A}x^{3}-1=0 \\ \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 \\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,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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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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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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P_{n}=n! \\\\ \r
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A_{n}^{k}=\\frac{n!}{\\left( n-k \\left) !\\right. \\right.} \r
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> ${ue}-item-active,
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> ${ue}-submenu > ${ue}-submenu-title`]:{height:Pe,lineHeight:`${Pe}px`},[`${ue}-item-group-list ${ue}-submenu-title,
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${ue}-submenu-title`]:{paddingInlineEnd:Nt}}};var Fe=Ge=>{const{componentCls:ue,iconCls:Pe,itemHeight:_e,colorTextLightSolid:qe,dropdownWidth:ut,controlHeightLG:ht,motionDurationMid:Bt,motionEaseOut:Nt,paddingXL:Wt,itemMarginInline:wt,fontSizeLG:_t,motionDurationSlow:ln,paddingXS:ft,boxShadowSecondary:Ut,collapsedWidth:Kt,collapsedIconSize:Jt}=Ge,pe={height:_e,lineHeight:`${_e}px`,listStylePosition:"inside",listStyleType:"disc"};return[{[ue]:{"&-inline, &-vertical":Object.assign({[`&${ue}-root`]:{boxShadow:"none"}},We(Ge))},[`${ue}-submenu-popup`]:{[`${ue}-vertical`]:Object.assign(Object.assign({},We(Ge)),{boxShadow:Ut})}},{[`${ue}-submenu-popup ${ue}-vertical${ue}-sub`]:{minWidth:ut,maxHeight:`calc(100vh - ${ht*2.5}px)`,padding:"0",overflow:"hidden",borderInlineEnd:0,"&:not([class*='-active'])":{overflowX:"hidden",overflowY:"auto"}}},{[`${ue}-inline`]:{width:"100%",[`&${ue}-root`]:{[`${ue}-item, ${ue}-submenu-title`]:{display:"flex",alignItems:"center",transition:[`border-color ${ln}`,`background ${ln}`,`padding ${Bt} ${Nt}`].join(","),[`> ${ue}-title-content`]:{flex:"auto",minWidth:0,overflow:"hidden",textOverflow:"ellipsis"},"> *":{flex:"none"}}},[`${ue}-sub${ue}-inline`]:{padding:0,border:0,borderRadius:0,boxShadow:"none",[`& > ${ue}-submenu > ${ue}-submenu-title`]:pe,[`& ${ue}-item-group-title`]:{paddingInlineStart:Wt}},[`${ue}-item`]:pe}},{[`${ue}-inline-collapsed`]:{width:Kt,[`&${ue}-root`]:{[`${ue}-item, ${ue}-submenu ${ue}-submenu-title`]:{[`> ${ue}-inline-collapsed-noicon`]:{fontSize:_t,textAlign:"center"}}},[`> ${ue}-item,
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> ${ue}-item-group > ${ue}-item-group-list > ${ue}-item,
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> ${ue}-item-group > ${ue}-item-group-list > ${ue}-submenu > ${ue}-submenu-title,
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> ${ue}-submenu > ${ue}-submenu-title`]:{insetInlineStart:0,paddingInline:`calc(50% - ${_t/2}px - ${wt}px)`,textOverflow:"clip",[`
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${ue}-submenu-arrow,
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${ue}-submenu-expand-icon
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|
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p${Ne}-text,
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p${Ne}-hint
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`]:{color:ce.colorTextDisabled}}}}}},xn=ce=>{const{componentCls:Ne,antCls:ze,iconCls:je,fontSize:at,lineHeight:gt}=ce,Qe=`${Ne}-list-item`,He=`${Qe}-actions`,Tt=`${Qe}-action`,xe=Math.round(at*gt);return{[`${Ne}-wrapper`]:{[`${Ne}-list`]:Object.assign(Object.assign({},(0,on.dF)()),{lineHeight:ce.lineHeight,[Qe]:{position:"relative",height:ce.lineHeight*at,marginTop:ce.marginXS,fontSize:at,display:"flex",alignItems:"center",transition:`background-color ${ce.motionDurationSlow}`,"&:hover":{backgroundColor:ce.controlItemBgHover},[`${Qe}-name`]:Object.assign(Object.assign({},on.vS),{padding:`0 ${ce.paddingXS}px`,lineHeight:gt,flex:"auto",transition:`all ${ce.motionDurationSlow}`}),[He]:{[Tt]:{opacity:0},[`${Tt}${ze}-btn-sm`]:{height:xe,border:0,lineHeight:1,"> span":{transform:"scale(1)"}},[`
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${Tt}:focus-visible,
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&.picture ${Tt}
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${gt}${gt}-picture,
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${gt}${gt}-picture-card,
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${gt}${gt}-picture-circle
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`]:{[Qe]:{position:"relative",height:je+ce.lineWidth*2+ce.paddingXS*2,padding:ce.paddingXS,border:`${ce.lineWidth}px ${ce.lineType} ${ce.colorBorder}`,borderRadius:ce.borderRadiusLG,"&:hover":{background:"transparent"},[`${Qe}-thumbnail`]:Object.assign(Object.assign({},on.vS),{width:je,height:je,lineHeight:`${je+ce.paddingSM}px`,textAlign:"center",flex:"none",[ze]:{fontSize:ce.fontSizeHeading2,color:ce.colorPrimary},img:{display:"block",width:"100%",height:"100%",overflow:"hidden"}}),[`${Qe}-progress`]:{bottom:at,width:`calc(100% - ${ce.paddingSM*2}px)`,marginTop:0,paddingInlineStart:je+ce.paddingXS}},[`${Qe}-error`]:{borderColor:ce.colorError,[`${Qe}-thumbnail ${ze}`]:{[`svg path[fill='${na.blue[0]}']`]:{fill:ce.colorErrorBg},[`svg path[fill='${na.blue.primary}']`]:{fill:ce.colorError}}},[`${Qe}-uploading`]:{borderStyle:"dashed",[`${Qe}-name`]:{marginBottom:at}}},[`${gt}${gt}-picture-circle ${Qe}`]:{[`&, &::before, ${Qe}-thumbnail`]:{borderRadius:"50%"}}}}},ye=ce=>{const{componentCls:Ne,iconCls:ze,fontSizeLG:je,colorTextLightSolid:at}=ce,gt=`${Ne}-list`,Qe=`${gt}-item`,He=ce.uploadPicCardSize;return{[`
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${Ne}-wrapper${Ne}-picture-card-wrapper,
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${Ne}-wrapper${Ne}-picture-circle-wrapper
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`]:Object.assign(Object.assign({},(0,on.dF)()),{display:"inline-block",width:"100%",[`${Ne}${Ne}-select`]:{width:He,height:He,marginInlineEnd:ce.marginXS,marginBottom:ce.marginXS,textAlign:"center",verticalAlign:"top",backgroundColor:ce.colorFillAlter,border:`${ce.lineWidth}px dashed ${ce.colorBorder}`,borderRadius:ce.borderRadiusLG,cursor:"pointer",transition:`border-color ${ce.motionDurationSlow}`,[`> ${Ne}`]:{display:"flex",alignItems:"center",justifyContent:"center",height:"100%",textAlign:"center"},[`&:not(${Ne}-disabled):hover`]:{borderColor:ce.colorPrimary}},[`${gt}${gt}-picture-card, ${gt}${gt}-picture-circle`]:{[`${gt}-item-container`]:{display:"inline-block",width:He,height:He,marginBlock:`0 ${ce.marginXS}px`,marginInline:`0 ${ce.marginXS}px`,verticalAlign:"top"},"&::after":{display:"none"},[Qe]:{height:"100%",margin:0,"&::before":{position:"absolute",zIndex:1,width:`calc(100% - ${ce.paddingXS*2}px)`,height:`calc(100% - 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en=(0,yn.Z)("Upload",ce=>{const{fontSizeHeading3:Ne,fontSize:ze,lineHeight:je,lineWidth:at,controlHeightLG:gt}=ce,Qe=Math.round(ze*je),He=(0,Fn.TS)(ce,{uploadThumbnailSize:Ne*2,uploadProgressOffset:Qe/2+at,uploadPicCardSize:gt*2.55});return[Gt(He),dn(He),Ee(He),ye(He),xn(He),Zn(He),bt(He),(0,hn.Z)(He)]},ce=>({actionsColor:ce.colorTextDescription})),Yt=function(ce,Ne,ze,je){function at(gt){return gt instanceof ze?gt:new ze(function(Qe){Qe(gt)})}return new(ze||(ze=Promise))(function(gt,Qe){function He(Rt){try{xe(je.next(Rt))}catch(tn){Qe(tn)}}function Tt(Rt){try{xe(je.throw(Rt))}catch(tn){Qe(tn)}}function xe(Rt){Rt.done?gt(Rt.value):at(Rt.value).then(He,Tt)}xe((je=je.apply(ce,Ne||[])).next())})};const 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Dn={file:Ht,fileList:nn};wn&&(Dn.event=wn),(!En||nn.some(sa=>sa.uid===Ht.uid))&&(0,$e.flushSync)(()=>{xe==null||xe(Dn)})},ha=(Ht,mn)=>Yt(void 0,void 0,void 0,function*(){const{beforeUpload:wn,transformFile:nn}=ce;let En=Ht;if(wn){const Dn=yield wn(Ht,mn);if(Dn===!1)return!1;if(delete Ht[At],Dn===At)return Object.defineProperty(Ht,At,{value:!0,configurable:!0}),!1;typeof Dn=="object"&&Dn&&(En=Dn)}return nn&&(En=yield nn(En)),En}),Xt=Ht=>{const mn=Ht.filter(En=>!En.file[At]);if(!mn.length)return;const wn=mn.map(En=>Wt(En.file));let nn=(0,fe.Z)(vn);wn.forEach(En=>{nn=wt(En,nn)}),wn.forEach((En,Dn)=>{let sa=En;if(mn[Dn].parsedFile)En.status="uploading";else{const{originFileObj:Bn}=En;let Sa;try{Sa=new File([Bn],Bn.name,{type:Bn.type})}catch(Ea){Sa=new Blob([Bn],{type:Bn.type}),Sa.name=Bn.name,Sa.lastModifiedDate=new Date,Sa.lastModified=new Date().getTime()}Sa.uid=En.uid,sa=Sa}Xn(sa,nn)})},Pn=(Ht,mn,wn)=>{try{typeof Ht=="string"&&(Ht=JSON.parse(Ht))}catch(Dn){}if(!_t(mn,vn))return;const nn=Wt(mn);nn.status="done",nn.percent=100,nn.response=Ht,nn.xhr=wn;const En=wt(nn,vn);Xn(nn,En)},Jn=(Ht,mn)=>{if(!_t(mn,vn))return;const wn=Wt(mn);wn.status="uploading",wn.percent=Ht.percent;const nn=wt(wn,vn);Xn(wn,nn,Ht)},Mn=(Ht,mn,wn)=>{if(!_t(wn,vn))return;const nn=Wt(wn);nn.error=Ht,nn.response=mn,nn.status="error";const En=wt(nn,vn);Xn(nn,En)},da=Ht=>{let mn;Promise.resolve(typeof at=="function"?at(Ht):at).then(wn=>{var nn;if(wn===!1)return;const En=ln(Ht,vn);En&&(mn=Object.assign(Object.assign({},Ht),{status:"removed"}),vn==null||vn.forEach(Dn=>{const sa=mn.uid!==void 0?"uid":"name";Dn[sa]===mn[sa]&&!Object.isFrozen(Dn)&&(Dn.status="removed")}),(nn=ga.current)===null||nn===void 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gt=="boolean"?{}:gt,Cn=(Ht,mn)=>gt?ae.createElement(Vt,{prefixCls:Nn,listType:Qe,items:vn,previewFile:tn,onPreview:He,onDownload:Tt,onRemove:da,showRemoveIcon:!Un&&ba,showPreviewIcon:zt,showDownloadIcon:Pt,removeIcon:Lt,previewIcon:Ot,downloadIcon:un,iconRender:kn,locale:Object.assign(Object.assign({},La),Sn),isImageUrl:tt,progress:Ft,appendAction:Ht,appendActionVisible:mn,itemRender:fn,disabled:Un}):Ht,_n=Ie()(`${Nn}-wrapper`,Et,Pa,va,Gn==null?void 0:Gn.className,{[`${Nn}-rtl`]:pa==="rtl",[`${Nn}-picture-card-wrapper`]:Qe==="picture-card",[`${Nn}-picture-circle-wrapper`]:Qe==="picture-circle"}),Tn=Object.assign(Object.assign({},Gn==null?void 0:Gn.style),Zt);if(gn==="drag"){const Ht=Ie()(va,Nn,`${Nn}-drag`,{[`${Nn}-drag-uploading`]:vn.some(mn=>mn.status==="uploading"),[`${Nn}-drag-hover`]:oa==="dragover",[`${Nn}-disabled`]:Un,[`${Nn}-rtl`]:pa==="rtl"});return ca(ae.createElement("span",{className:_n},ae.createElement("div",{className:Ht,style:Tn,onDrop:ea,onDragOver:ea,onDragLeave:ea},ae.createElement(be,Object.assign({},la,{ref:ga,className:`${Nn}-btn`}),ae.createElement("div",{className:`${Nn}-drag-container`},an))),Cn()))}const jn=Ie()(Nn,`${Nn}-select`,{[`${Nn}-disabled`]:Un}),ta=(Ht=>ae.createElement("div",{className:jn,style:Ht},ae.createElement(be,Object.assign({},la,{ref:ga}))))(an?void 0:{display:"none"});return ca(Qe==="picture-card"||Qe==="picture-circle"?ae.createElement("span",{className:_n},Cn(ta,!!an)):ae.createElement("span",{className:_n},ta,Cn()))};var An=ae.forwardRef(bn),lt=function(ce,Ne){var ze={};for(var je in ce)Object.prototype.hasOwnProperty.call(ce,je)&&Ne.indexOf(je)<0&&(ze[je]=ce[je]);if(ce!=null&&typeof Object.getOwnPropertySymbols=="function")for(var 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