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130 lines
389 KiB
130 lines
389 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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|
\\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
|
|
\\Delta = 0\\text{\u65B9\u7A0B\u6709\u4E24\u4E2A\u76F8\u7B49\u7684\u5B9E\u6839} \\ \r
|
|
\\Delta \\lt 0\\text{\u65B9\u7A0B\u65E0\u5B9E\u6839} \r
|
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\\end{matrix}\\right. \r
|
|
\\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
|
|
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
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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 \\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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nt(){go.CommandHandler.call(this),this._arrowKeyBehavior="move",this._pasteOffset=new go.Point(10,10),this._lastPasteOffset=new go.Point(0,0)}go.Diagram.inherit(nt,go.CommandHandler),nt.prototype.canAlignSelection=function(){var le=this.diagram;return!(le===null||le.isReadOnly||le.isModelReadOnly||le.selection.count<2)},nt.prototype.alignLeft=function(){var le=this.diagram;le.startTransaction("aligning left");var Pe=1/0;le.selection.each(function(ce){ce instanceof go.Link||(Pe=Math.min(ce.position.x,Pe))}),le.selection.each(function(ce){ce instanceof go.Link||ce.move(new go.Point(Pe,ce.position.y))}),le.commitTransaction("aligning left")},nt.prototype.alignRight=function(){var le=this.diagram;le.startTransaction("aligning right");var Pe=-1/0;le.selection.each(function(ce){if(!(ce instanceof go.Link)){var _e=ce.actualBounds.x+ce.actualBounds.width;Pe=Math.max(_e,Pe)}}),le.selection.each(function(ce){ce instanceof go.Link||ce.move(new 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${Le}-submenu-rtl ${Le}-vertical`]:{[`${Le}-submenu-arrow`]:{"&::before":{transform:`rotate(-45deg) translateY(-${fe})`},"&::after":{transform:`rotate(45deg) translateY(${fe})`}}}}};const Tt=Me=>Object.assign({},(0,xe.oN)(Me));var At=(Me,Le)=>{const{componentCls:fe,itemColor:Ge,itemSelectedColor:ke,groupTitleColor:gt,itemBg:pt,subMenuItemBg:Et,itemSelectedBg:bt,activeBarHeight:zt,activeBarWidth:yt,activeBarBorderWidth:It,motionDurationSlow:en,motionEaseInOut:un,motionEaseOut:ln,itemPaddingInline:Wt,motionDurationMid:tn,itemHoverColor:nn,lineType:vn,colorSplit:on,itemDisabledColor:cn,dangerItemColor:Fn,dangerItemHoverColor:Sn,dangerItemSelectedColor:In,dangerItemActiveBg:gn,dangerItemSelectedBg:Cn,itemHoverBg:Zn,itemActiveBg:qn,menuSubMenuBg:la,horizontalItemSelectedColor:ga,horizontalItemSelectedBg:An,horizontalItemBorderRadius:fa,horizontalItemHoverBg:oa,popupBg:ua}=Me;return{[`${fe}-${Le}, ${fe}-${Le} > ${fe}`]:{color:Ge,background:pt,[`&${fe}-root:focus-visible`]:Object.assign({},Tt(Me)),[`${fe}-item-group-title`]:{color:gt},[`${fe}-submenu-selected`]:{[`> ${fe}-submenu-title`]:{color:ke}},[`${fe}-item-disabled, ${fe}-submenu-disabled`]:{color:`${cn} !important`},[`${fe}-item:not(${fe}-item-selected):not(${fe}-submenu-selected)`]:{[`&:hover, > ${fe}-submenu-title:hover`]:{color:nn}},[`&:not(${fe}-horizontal)`]:{[`${fe}-item:not(${fe}-item-selected)`]:{"&:hover":{backgroundColor:Zn},"&:active":{backgroundColor:qn}},[`${fe}-submenu-title`]:{"&:hover":{backgroundColor:Zn},"&:active":{backgroundColor:qn}}},[`${fe}-item-danger`]:{color:Fn,[`&${fe}-item:hover`]:{[`&:not(${fe}-item-selected):not(${fe}-submenu-selected)`]:{color:Sn}},[`&${fe}-item:active`]:{background:gn}},[`${fe}-item a`]:{"&, &:hover":{color:"inherit"}},[`${fe}-item-selected`]:{color:ke,[`&${fe}-item-danger`]:{color:In},"a, a:hover":{color:"inherit"}},[`& ${fe}-item-selected`]:{backgroundColor:bt,[`&${fe}-item-danger`]:{backgroundColor:Cn}},[`${fe}-item, ${fe}-submenu-title`]:{[`&:not(${fe}-item-disabled):focus-visible`]:Object.assign({},Tt(Me))},[`&${fe}-submenu > ${fe}`]:{backgroundColor:la},[`&${fe}-popup > ${fe}`]:{backgroundColor:ua},[`&${fe}-horizontal`]:Object.assign(Object.assign({},Le==="dark"?{borderBottom:0}:{}),{[`> ${fe}-item, > ${fe}-submenu`]:{top:It,marginTop:-It,marginBottom:0,borderRadius:fa,"&::after":{position:"absolute",insetInline:Wt,bottom:0,borderBottom:`${zt}px solid transparent`,transition:`border-color ${en} ${un}`,content:'""'},"&:hover, &-active, &-open":{background:oa,"&::after":{borderBottomWidth:zt,borderBottomColor:ga}},"&-selected":{color:ga,backgroundColor:An,"&:hover":{backgroundColor:An},"&::after":{borderBottomWidth:zt,borderBottomColor:ga}}}}),[`&${fe}-root`]:{[`&${fe}-inline, &${fe}-vertical`]:{borderInlineEnd:`${It}px ${vn} ${on}`}},[`&${fe}-inline`]:{[`${fe}-sub${fe}-inline`]:{background:Et},[`${fe}-item, ${fe}-submenu-title`]:It&&yt?{width:`calc(100% + ${It}px)`}:{},[`${fe}-item`]:{position:"relative","&::after":{position:"absolute",insetBlock:0,insetInlineEnd:0,borderInlineEnd:`${yt}px solid ${ke}`,transform:"scaleY(0.0001)",opacity:0,transition:[`transform ${tn} ${ln}`,`opacity ${tn} ${ln}`].join(","),content:'""'},[`&${fe}-item-danger`]:{"&::after":{borderInlineEndColor:In}}},[`${fe}-selected, ${fe}-item-selected`]:{"&::after":{transform:"scaleY(1)",opacity:1,transition:[`transform ${tn} ${un}`,`opacity ${tn} ${un}`].join(",")}}}}}};const Ut=Me=>{const{componentCls:Le,itemHeight:fe,itemMarginInline:Ge,padding:ke,menuArrowSize:gt,marginXS:pt,itemMarginBlock:Et}=Me,bt=ke+gt+pt;return{[`${Le}-item`]:{position:"relative",overflow:"hidden"},[`${Le}-item, ${Le}-submenu-title`]:{height:fe,lineHeight:`${fe}px`,paddingInline:ke,overflow:"hidden",textOverflow:"ellipsis",marginInline:Ge,marginBlock:Et,width:`calc(100% - ${Ge*2}px)`},[`> ${Le}-item,
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> ${Le}-submenu > ${Le}-submenu-title`]:{height:fe,lineHeight:`${fe}px`},[`${Le}-item-group-list ${Le}-submenu-title,
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${Le}-submenu-title`]:{paddingInlineEnd:bt}}};var Be=Me=>{const{componentCls:Le,iconCls:fe,itemHeight:Ge,colorTextLightSolid:ke,dropdownWidth:gt,controlHeightLG:pt,motionDurationMid:Et,motionEaseOut:bt,paddingXL:zt,itemMarginInline:yt,fontSizeLG:It,motionDurationSlow:en,paddingXS:un,boxShadowSecondary:ln,collapsedWidth:Wt,collapsedIconSize:tn}=Me,nn={height:Ge,lineHeight:`${Ge}px`,listStylePosition:"inside",listStyleType:"disc"};return[{[Le]:{"&-inline, &-vertical":Object.assign({[`&${Le}-root`]:{boxShadow:"none"}},Ut(Me))},[`${Le}-submenu-popup`]:{[`${Le}-vertical`]:Object.assign(Object.assign({},Ut(Me)),{boxShadow:ln})}},{[`${Le}-submenu-popup ${Le}-vertical${Le}-sub`]:{minWidth:gt,maxHeight:`calc(100vh - ${pt*2.5}px)`,padding:"0",overflow:"hidden",borderInlineEnd:0,"&:not([class*='-active'])":{overflowX:"hidden",overflowY:"auto"}}},{[`${Le}-inline`]:{width:"100%",[`&${Le}-root`]:{[`${Le}-item, ${Le}-submenu-title`]:{display:"flex",alignItems:"center",transition:[`border-color ${en}`,`background ${en}`,`padding ${Et} ${bt}`].join(","),[`> ${Le}-title-content`]:{flex:"auto",minWidth:0,overflow:"hidden",textOverflow:"ellipsis"},"> *":{flex:"none"}}},[`${Le}-sub${Le}-inline`]:{padding:0,border:0,borderRadius:0,boxShadow:"none",[`& > ${Le}-submenu > ${Le}-submenu-title`]:nn,[`& ${Le}-item-group-title`]:{paddingInlineStart:zt}},[`${Le}-item`]:nn}},{[`${Le}-inline-collapsed`]:{width:Wt,[`&${Le}-root`]:{[`${Le}-item, ${Le}-submenu ${Le}-submenu-title`]:{[`> ${Le}-inline-collapsed-noicon`]:{fontSize:It,textAlign:"center"}}},[`> ${Le}-item,
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> ${Le}-item-group > ${Le}-item-group-list > ${Le}-item,
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> ${Le}-item-group > ${Le}-item-group-list > ${Le}-submenu > ${Le}-submenu-title,
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> ${Le}-submenu > ${Le}-submenu-title`]:{insetInlineStart:0,paddingInline:`calc(50% - ${It/2}px - ${yt}px)`,textOverflow:"clip",[`
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${Le}-submenu-arrow,
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${Le}-submenu-expand-icon
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`]:{opacity:0},[`${Le}-item-icon, ${fe}`]:{margin:0,fontSize:tn,lineHeight:`${Ge}px`,"+ span":{display:"inline-block",opacity:0}}},[`${Le}-item-icon, ${fe}`]:{display:"inline-block"},"&-tooltip":{pointerEvents:"none",[`${Le}-item-icon, ${fe}`]:{display:"none"},"a, a:hover":{color:ke}},[`${Le}-item-group-title`]:Object.assign(Object.assign({},xe.vS),{paddingInline:un})}}]};const Ye=Me=>{const{componentCls:Le,motionDurationSlow:fe,motionDurationMid:Ge,motionEaseInOut:ke,motionEaseOut:gt,iconCls:pt,iconSize:Et,iconMarginInlineEnd:bt}=Me;return{[`${Le}-item, ${Le}-submenu-title`]:{position:"relative",display:"block",margin:0,whiteSpace:"nowrap",cursor:"pointer",transition:[`border-color ${fe}`,`background ${fe}`,`padding ${fe} ${ke}`].join(","),[`${Le}-item-icon, ${pt}`]:{minWidth:Et,fontSize:Et,transition:[`font-size ${Ge} ${gt}`,`margin ${fe} ${ke}`,`color ${fe}`].join(","),"+ span":{marginInlineStart:bt,opacity:1,transition:[`opacity ${fe} ${ke}`,`margin ${fe}`,`color 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a`]:{"&::before":{position:"absolute",inset:0,backgroundColor:"transparent",content:'""'}},[`${fe}-item-divider`]:{overflow:"hidden",lineHeight:0,borderColor:zt,borderStyle:tn,borderWidth:0,borderTopWidth:yt,marginBlock:yt,padding:0,"&-dashed":{borderStyle:"dashed"}}}),Ye(Me)),{[`${fe}-item-group`]:{[`${fe}-item-group-list`]:{margin:0,padding:0,[`${fe}-item, ${fe}-submenu-title`]:{paddingInline:`${Ge*2}px ${bt}px`}}},"&-submenu":{"&-popup":{position:"absolute",zIndex:It,borderRadius:en,boxShadow:"none",transformOrigin:"0 0",[`&${fe}-submenu`]:{background:"transparent"},"&::before":{position:"absolute",inset:`${nn}px 0 0`,zIndex:-1,width:"100%",height:"100%",opacity:0,content:'""'}},"&-placement-rightTop::before":{top:0,insetInlineStart:nn},"\n &-placement-leftTop,\n &-placement-bottomRight,\n ":{transformOrigin:"100% 0"},"\n &-placement-leftBottom,\n &-placement-topRight,\n ":{transformOrigin:"100% 100%"},"\n &-placement-rightBottom,\n &-placement-topLeft,\n ":{transformOrigin:"0 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&-inline ${fe}-submenu-arrow`]:{"&::before":{transform:`rotate(-45deg) translateX(${Wt})`},"&::after":{transform:`rotate(45deg) translateX(-${Wt})`}},[`${fe}-submenu-open${fe}-submenu-inline > ${fe}-submenu-title > ${fe}-submenu-arrow`]:{transform:`translateY(-${ln*.2}px)`,"&::after":{transform:`rotate(-45deg) translateX(-${Wt})`},"&::before":{transform:`rotate(45deg) translateX(${Wt})`}}})},{[`${Le}-layout-header`]:{[fe]:{lineHeight:"inherit"}}}]};var Lt=(Me,Le)=>(0,Nt.Z)("Menu",Ge=>{if(Le===!1)return[];const{colorBgElevated:ke,colorPrimary:gt,colorTextLightSolid:pt,controlHeightLG:Et,fontSize:bt,darkItemColor:zt,darkDangerItemColor:yt,darkItemBg:It,darkSubMenuItemBg:en,darkItemSelectedColor:un,darkItemSelectedBg:ln,darkDangerItemSelectedBg:Wt,darkItemHoverBg:tn,darkGroupTitleColor:nn,darkItemHoverColor:vn,darkItemDisabledColor:on,darkDangerItemHoverColor:cn,darkDangerItemSelectedColor:Fn,darkDangerItemActiveBg:Sn}=Ge,In=bt/7*5,gn=(0,ye.TS)(Ge,{menuArrowSize:In,menuHorizontalHeight:Et*1.15,menuArrowOffset:`${In*.25}px`,menuPanelMaskInset:-7,menuSubMenuBg:ke}),Cn=(0,ye.TS)(gn,{itemColor:zt,itemHoverColor:vn,groupTitleColor:nn,itemSelectedColor:un,itemBg:It,popupBg:It,subMenuItemBg:en,itemActiveBg:"transparent",itemSelectedBg:ln,activeBarHeight:0,activeBarBorderWidth:0,itemHoverBg:tn,itemDisabledColor:on,dangerItemColor:yt,dangerItemHoverColor:cn,dangerItemSelectedColor:Fn,dangerItemActiveBg:Sn,dangerItemSelectedBg:Wt,menuSubMenuBg:en,horizontalItemSelectedColor:pt,horizontalItemSelectedBg:gt});return[tt(gn),dt(gn),Be(gn),At(gn,"light"),At(Cn,"dark"),ot(gn),(0,De.Z)(gn),(0,qe.oN)(gn,"slide-up"),(0,qe.oN)(gn,"slide-down"),(0,Ct._y)(gn,"zoom-big")]},Ge=>{const{colorPrimary:ke,colorError:gt,colorTextDisabled:pt,colorErrorBg:Et,colorText:bt,colorTextDescription:zt,colorBgContainer:yt,colorFillAlter:It,colorFillContent:en,lineWidth:un,lineWidthBold:ln,controlItemBgActive:Wt,colorBgTextHover:tn,controlHeightLG:nn,lineHeight:vn,colorBgElevated:on,marginXXS:cn,padding:Fn,fontSize:Sn,controlHeightSM:In,fontSizeLG:gn,colorTextLightSolid:Cn,colorErrorHover:Zn}=Ge,qn=new 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