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167 lines
431 KiB
167 lines
431 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
|
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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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\\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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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( \\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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|
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|
|
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
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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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${fe}-submenu-rtl ${fe}-vertical`]:{[`${fe}-submenu-arrow`]:{"&::before":{transform:`rotate(-45deg) translateY(-${Se})`},"&::after":{transform:`rotate(45deg) translateY(${Se})`}}}}};const vt=ke=>Object.assign({},(0,Fe.oN)(ke));var ct=(ke,fe)=>{const{componentCls:Se,itemColor:Pe,itemSelectedColor:xe,groupTitleColor:Ye,itemBg:nt,subMenuItemBg:pt,itemSelectedBg:Lt,activeBarHeight:At,activeBarWidth:jt,activeBarBorderWidth:Ht,motionDurationSlow:an,motionEaseInOut:mt,motionEaseOut:zt,itemPaddingInline:Ut,motionDurationMid:dn,itemHoverColor:ve,lineType:Be,colorSplit:Ke,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}=ke;return{[`${Se}-${fe}, ${Se}-${fe} > ${Se}`]:{color:Pe,background:nt,[`&${Se}-root:focus-visible`]:Object.assign({},vt(ke)),[`${Se}-item-group-title`]:{color:Ye},[`${Se}-submenu-selected`]:{[`> ${Se}-submenu-title`]:{color:xe}},[`${Se}-item-disabled, ${Se}-submenu-disabled`]:{color:`${ft} !important`},[`${Se}-item:not(${Se}-item-selected):not(${Se}-submenu-selected)`]:{[`&:hover, > ${Se}-submenu-title:hover`]:{color:ve}},[`&:not(${Se}-horizontal)`]:{[`${Se}-item:not(${Se}-item-selected)`]:{"&:hover":{backgroundColor:Kt},"&:active":{backgroundColor:Vt}},[`${Se}-submenu-title`]:{"&:hover":{backgroundColor:Kt},"&:active":{backgroundColor:Vt}}},[`${Se}-item-danger`]:{color:ht,[`&${Se}-item:hover`]:{[`&:not(${Se}-item-selected):not(${Se}-submenu-selected)`]:{color:Rt}},[`&${Se}-item:active`]:{background:Ot}},[`${Se}-item a`]:{"&, &:hover":{color:"inherit"}},[`${Se}-item-selected`]:{color:xe,[`&${Se}-item-danger`]:{color:kt},"a, a:hover":{color:"inherit"}},[`& ${Se}-item-selected`]:{backgroundColor:Lt,[`&${Se}-item-danger`]:{backgroundColor:Tt}},[`${Se}-item, ${Se}-submenu-title`]:{[`&:not(${Se}-item-disabled):focus-visible`]:Object.assign({},vt(ke))},[`&${Se}-submenu > ${Se}`]:{backgroundColor:ln},[`&${Se}-popup > ${Se}`]:{backgroundColor:qt},[`&${Se}-horizontal`]:Object.assign(Object.assign({},fe==="dark"?{borderBottom:0}:{}),{[`> ${Se}-item, > ${Se}-submenu`]:{top:Ht,marginTop:-Ht,marginBottom:0,borderRadius:vn,"&::after":{position:"absolute",insetInline:Ut,bottom:0,borderBottom:`${At}px solid transparent`,transition:`border-color ${an} ${mt}`,content:'""'},"&:hover, &-active, &-open":{background:nn,"&::after":{borderBottomWidth:At,borderBottomColor:on}},"&-selected":{color:on,backgroundColor:Pn,"&:hover":{backgroundColor:Pn},"&::after":{borderBottomWidth:At,borderBottomColor:on}}}}),[`&${Se}-root`]:{[`&${Se}-inline, &${Se}-vertical`]:{borderInlineEnd:`${Ht}px ${Be} ${Ke}`}},[`&${Se}-inline`]:{[`${Se}-sub${Se}-inline`]:{background:pt},[`${Se}-item, ${Se}-submenu-title`]:Ht&&jt?{width:`calc(100% + ${Ht}px)`}:{},[`${Se}-item`]:{position:"relative","&::after":{position:"absolute",insetBlock:0,insetInlineEnd:0,borderInlineEnd:`${jt}px solid ${xe}`,transform:"scaleY(0.0001)",opacity:0,transition:[`transform ${dn} ${zt}`,`opacity ${dn} ${zt}`].join(","),content:'""'},[`&${Se}-item-danger`]:{"&::after":{borderInlineEndColor:kt}}},[`${Se}-selected, ${Se}-item-selected`]:{"&::after":{transform:"scaleY(1)",opacity:1,transition:[`transform ${dn} ${mt}`,`opacity ${dn} ${mt}`].join(",")}}}}}};const Ve=ke=>{const{componentCls:fe,itemHeight:Se,itemMarginInline:Pe,padding:xe,menuArrowSize:Ye,marginXS:nt,itemMarginBlock:pt}=ke,Lt=xe+Ye+nt;return{[`${fe}-item`]:{position:"relative",overflow:"hidden"},[`${fe}-item, ${fe}-submenu-title`]:{height:Se,lineHeight:`${Se}px`,paddingInline:xe,overflow:"hidden",textOverflow:"ellipsis",marginInline:Pe,marginBlock:pt,width:`calc(100% - ${Pe*2}px)`},[`> ${fe}-item,
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|
> ${fe}-submenu > ${fe}-submenu-title`]:{height:Se,lineHeight:`${Se}px`},[`${fe}-item-group-list ${fe}-submenu-title,
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|
${fe}-submenu-title`]:{paddingInlineEnd:Lt}}};var Ge=ke=>{const{componentCls:fe,iconCls:Se,itemHeight:Pe,colorTextLightSolid:xe,dropdownWidth:Ye,controlHeightLG:nt,motionDurationMid:pt,motionEaseOut:Lt,paddingXL:At,itemMarginInline:jt,fontSizeLG:Ht,motionDurationSlow:an,paddingXS:mt,boxShadowSecondary:zt,collapsedWidth:Ut,collapsedIconSize:dn}=ke,ve={height:Pe,lineHeight:`${Pe}px`,listStylePosition:"inside",listStyleType:"disc"};return[{[fe]:{"&-inline, &-vertical":Object.assign({[`&${fe}-root`]:{boxShadow:"none"}},Ve(ke))},[`${fe}-submenu-popup`]:{[`${fe}-vertical`]:Object.assign(Object.assign({},Ve(ke)),{boxShadow:zt})}},{[`${fe}-submenu-popup ${fe}-vertical${fe}-sub`]:{minWidth:Ye,maxHeight:`calc(100vh - ${nt*2.5}px)`,padding:"0",overflow:"hidden",borderInlineEnd:0,"&:not([class*='-active'])":{overflowX:"hidden",overflowY:"auto"}}},{[`${fe}-inline`]:{width:"100%",[`&${fe}-root`]:{[`${fe}-item, ${fe}-submenu-title`]:{display:"flex",alignItems:"center",transition:[`border-color ${an}`,`background ${an}`,`padding ${pt} ${Lt}`].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`]:ve,[`& ${fe}-item-group-title`]:{paddingInlineStart:At}},[`${fe}-item`]:ve}},{[`${fe}-inline-collapsed`]:{width:Ut,[`&${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, ${Se}`]:{margin:0,fontSize:dn,lineHeight:`${Pe}px`,"+ span":{display:"inline-block",opacity:0}}},[`${fe}-item-icon, ${Se}`]:{display:"inline-block"},"&-tooltip":{pointerEvents:"none",[`${fe}-item-icon, ${Se}`]:{display:"none"},"a, a:hover":{color:xe}},[`${fe}-item-group-title`]:Object.assign(Object.assign({},Fe.vS),{paddingInline:mt})}}]};const _e=ke=>{const{componentCls:fe,motionDurationSlow:Se,motionDurationMid:Pe,motionEaseInOut:xe,motionEaseOut:Ye,iconCls:nt,iconSize:pt,iconMarginInlineEnd:Lt}=ke;return{[`${fe}-item, ${fe}-submenu-title`]:{position:"relative",display:"block",margin:0,whiteSpace:"nowrap",cursor:"pointer",transition:[`border-color ${Se}`,`background ${Se}`,`padding ${Se} ${xe}`].join(","),[`${fe}-item-icon, ${nt}`]:{minWidth:pt,fontSize:pt,transition:[`font-size ${Pe} ${Ye}`,`margin ${Se} ${xe}`,`color ${Se}`].join(","),"+ span":{marginInlineStart:Lt,opacity:1,transition:[`opacity ${Se} ${xe}`,`margin ${Se}`,`color 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&-inline ${Se}-submenu-arrow`]:{"&::before":{transform:`rotate(-45deg) translateX(${Ut})`},"&::after":{transform:`rotate(45deg) translateX(-${Ut})`}},[`${Se}-submenu-open${Se}-submenu-inline > ${Se}-submenu-title > ${Se}-submenu-arrow`]:{transform:`translateY(-${zt*.2}px)`,"&::after":{transform:`rotate(-45deg) translateX(-${Ut})`},"&::before":{transform:`rotate(45deg) translateX(${Ut})`}}})},{[`${fe}-layout-header`]:{[Se]:{lineHeight:"inherit"}}}]};var 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p${ze}-text,
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p${ze}-hint
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${_t}:focus-visible,
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${qe}${qe}-picture,
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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
|
|
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|
|
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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|
|
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|
|
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|
|
onDrag onDragEnd onDragEnter onDragExit onDragLeave onDragOver onDragStart onDrop onMouseDown
|
|
onMouseEnter onMouseLeave onMouseMove onMouseOut onMouseOver onMouseUp onSelect onTouchCancel
|
|
onTouchEnd onTouchMove onTouchStart onScroll onWheel onAbort onCanPlay onCanPlayThrough
|
|
onDurationChange onEmptied onEncrypted onEnded onError onLoadedData onLoadedMetadata
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