
<!--
     File mmlextra.ent produced by the XSL script characters.xsl
     from input data in unicode.xml.

     Please report any errors to David Carlisle
     via the public W3C list www-math@w3.org.

     The numeric character values assigned to each entity
     (should) match the Unicode assignments in Unicode 3.2.

-->

<!ENTITY % plane1D  "&#38;#38;#x1D">

<!ENTITY af               "&#x02061;" ><!--character showing function application in presentation tagging -->
<!ENTITY aopf             "%plane1D;552;" ><!-- -->
<!ENTITY asympeq          "&#x0224D;" ><!--Old ISOAMSR asymp (for HTML compatibility) -->
<!ENTITY bopf             "%plane1D;553;" ><!-- -->
<!ENTITY copf             "%plane1D;554;" ><!-- -->
<!ENTITY Cross            "&#x02A2F;" ><!--cross or vector product -->
<!ENTITY DD               "&#x02145;" ><!--D for use in differentials, e.g., within integrals -->
<!ENTITY dd               "&#x02146;" ><!--d for use in differentials, e.g., within integrals -->
<!ENTITY dopf             "%plane1D;555;" ><!-- -->
<!ENTITY DownArrowBar     "&#x02913;" ><!--down arrow to bar -->
<!ENTITY DownBreve        "&#x00311;" ><!--breve, inverted (non-spacing) -->
<!ENTITY DownLeftRightVector "&#x02950;" ><!--left-down-right-down harpoon -->
<!ENTITY DownLeftTeeVector "&#x0295E;" ><!--left-down harpoon from bar -->
<!ENTITY DownLeftVectorBar "&#x02956;" ><!--left-down harpoon to bar -->
<!ENTITY DownRightTeeVector "&#x0295F;" ><!--right-down harpoon from bar -->
<!ENTITY DownRightVectorBar "&#x02957;" ><!--right-down harpoon to bar -->
<!ENTITY ee               "&#x02147;" ><!--e use for the exponential base of the natural logarithms -->
<!ENTITY EmptySmallSquare "&#x025FB;" ><!--empty small square -->
<!ENTITY EmptyVerySmallSquare "&#x025AB;" ><!--empty small square -->
<!ENTITY eopf             "%plane1D;556;" ><!-- -->
<!ENTITY Equal            "&#x02A75;" ><!--two consecutive equal signs -->
<!ENTITY FilledSmallSquare "&#x025FC;" ><!--filled small square -->
<!ENTITY FilledVerySmallSquare "&#x025AA;" ><!--filled very small square -->
<!ENTITY fopf             "%plane1D;557;" ><!-- -->
<!ENTITY gopf             "%plane1D;558;" ><!-- -->
<!ENTITY GreaterGreater   "&#x02AA2;" ><!--alias for GT -->
<!ENTITY Hat              "&#x0005E;" ><!--circumflex accent -->
<!ENTITY hopf             "%plane1D;559;" ><!-- -->
<!ENTITY HorizontalLine   "&#x02500;" ><!--short horizontal line  -->
<!ENTITY ic               "&#x02063;" ><!--short form of  &InvisibleComma; -->
<!ENTITY ii               "&#x02148;" ><!--i for use as a square root of -1 -->
<!ENTITY iopf             "%plane1D;55A;" ><!-- -->
<!ENTITY it               "&#x02062;" ><!--marks multiplication when it is understood without a mark -->
<!ENTITY jopf             "%plane1D;55B;" ><!-- -->
<!ENTITY kopf             "%plane1D;55C;" ><!-- -->
<!ENTITY larrb            "&#x021E4;" ><!--leftwards arrow to bar -->
<!ENTITY LeftDownTeeVector "&#x02961;" ><!--down-left harpoon from bar -->
<!ENTITY LeftDownVectorBar "&#x02959;" ><!--down-left harpoon to bar -->
<!ENTITY LeftRightVector  "&#x0294E;" ><!--left-up-right-up harpoon -->
<!ENTITY LeftTeeVector    "&#x0295A;" ><!--left-up harpoon from bar -->
<!ENTITY LeftTriangleBar  "&#x029CF;" ><!--not left triangle, vertical bar -->
<!ENTITY LeftUpDownVector "&#x02951;" ><!--up-left-down-left harpoon -->
<!ENTITY LeftUpTeeVector  "&#x02960;" ><!--up-left harpoon from bar -->
<!ENTITY LeftUpVectorBar  "&#x02958;" ><!--up-left harpoon to bar -->
<!ENTITY LeftVectorBar    "&#x02952;" ><!--left-up harpoon to bar -->
<!ENTITY LessLess         "&#x02AA1;" ><!--alias for Lt -->
<!ENTITY lopf             "%plane1D;55D;" ><!-- -->
<!ENTITY mapstodown       "&#x021A7;" ><!--downwards arrow from bar -->
<!ENTITY mapstoleft       "&#x021A4;" ><!--leftwards arrow from bar -->
<!ENTITY mapstoup         "&#x021A5;" ><!--upwards arrow from bar -->
<!ENTITY MediumSpace      "&#x0205F;" ><!--space of width 4/18 em -->
<!ENTITY mopf             "%plane1D;55E;" ><!-- -->
<!ENTITY nbump            "&#x0224E;&#x00338;" ><!--not bumpy equals -->
<!ENTITY nbumpe           "&#x0224F;&#x00338;" ><!--not bumpy single equals -->
<!ENTITY nesim            "&#x02242;&#x00338;" ><!--not equal or similar -->
<!ENTITY NewLine          "&#x0000A;" ><!--force a line break; line feed -->
<!ENTITY NoBreak          "&#x02060;" ><!--never break line here -->
<!ENTITY nopf             "%plane1D;55F;" ><!-- -->
<!ENTITY NotCupCap        "&#x0226D;" ><!--alias for &nasymp; -->
<!ENTITY NotHumpEqual     "&#x0224F;&#x00338;" ><!--alias for &nbumpe; -->
<!ENTITY NotLeftTriangleBar "&#x029CF;&#x00338;" ><!--not left triangle, vertical bar -->
<!ENTITY NotNestedGreaterGreater "&#x02AA2;&#x00338;" ><!--not double greater-than sign -->
<!ENTITY NotNestedLessLess "&#x02AA1;&#x00338;" ><!--not double less-than sign -->
<!ENTITY NotRightTriangleBar "&#x029D0;&#x00338;" ><!--not vertical bar, right triangle -->
<!ENTITY NotSquareSubset  "&#x0228F;&#x00338;" ><!--square not subset -->
<!ENTITY NotSquareSuperset "&#x02290;&#x00338;" ><!--negated set-like partial order operator -->
<!ENTITY NotSucceedsTilde "&#x0227F;&#x00338;" ><!--not succeeds or similar -->
<!ENTITY oopf             "%plane1D;560;" ><!-- -->
<!ENTITY OverBar          "&#x000AF;" ><!--over bar -->
<!ENTITY OverBrace        "&#x0FE37;" ><!--over brace  -->
<!ENTITY OverBracket      "&#x023B4;" ><!--over bracket -->
<!ENTITY OverParenthesis  "&#x0FE35;" ><!--over parenthesis -->
<!ENTITY planckh          "&#x0210E;" ><!--the ring (skew field) of quaternions -->
<!ENTITY popf             "%plane1D;561;" ><!-- -->
<!ENTITY Product          "&#x0220F;" ><!--alias for &prod -->
<!ENTITY qopf             "%plane1D;562;" ><!-- -->
<!ENTITY rarrb            "&#x021E5;" ><!--leftwards arrow to bar -->
<!ENTITY RightDownTeeVector "&#x0295D;" ><!--down-right harpoon from bar -->
<!ENTITY RightDownVectorBar "&#x02955;" ><!--down-right harpoon to bar -->
<!ENTITY RightTeeVector   "&#x0295B;" ><!--right-up harpoon from bar -->
<!ENTITY RightTriangleBar "&#x029D0;" ><!--vertical bar, right triangle -->
<!ENTITY RightUpDownVector "&#x0294F;" ><!--up-right-down-right harpoon -->
<!ENTITY RightUpTeeVector "&#x0295C;" ><!--up-right harpoon from bar -->
<!ENTITY RightUpVectorBar "&#x02954;" ><!--up-right harpoon to bar -->
<!ENTITY RightVectorBar   "&#x02953;" ><!--up-right harpoon to bar -->
<!ENTITY ropf             "%plane1D;563;" ><!-- -->
<!ENTITY RoundImplies     "&#x02970;" ><!--round implies -->
<!ENTITY RuleDelayed      "&#x029F4;" ><!--rule-delayed (colon right arrow) -->
<!ENTITY sopf             "%plane1D;564;" ><!-- -->
<!ENTITY Tab              "&#x00009;" ><!--tabulator stop; horizontal tabulation -->
<!ENTITY ThickSpace       "&#x02009;&#x0200A;&#x0200A;" ><!--space of width 5/18 em -->
<!ENTITY topf             "%plane1D;565;" ><!-- -->
<!ENTITY UnderBar         "&#x00332;" ><!--combining low line -->
<!ENTITY UnderBrace       "&#x0FE38;" ><!--under brace  -->
<!ENTITY UnderBracket     "&#x023B5;" ><!--under bracket -->
<!ENTITY UnderParenthesis "&#x0FE36;" ><!--under parenthesis -->
<!ENTITY uopf             "%plane1D;566;" ><!-- -->
<!ENTITY UpArrowBar       "&#x02912;" ><!--up arrow to bar -->
<!ENTITY Upsilon          "&#x003A5;" ><!--ISOGRK1 Ugr, HTML4 Upsilon -->
<!ENTITY VerticalLine     "&#x0007C;" ><!--alias ISONUM verbar -->
<!ENTITY VerticalSeparator "&#x02758;" ><!--vertical separating operator -->
<!ENTITY vopf             "%plane1D;567;" ><!-- -->
<!ENTITY wopf             "%plane1D;568;" ><!-- -->
<!ENTITY xopf             "%plane1D;569;" ><!-- -->
<!ENTITY yopf             "%plane1D;56A;" ><!-- -->
<!ENTITY ZeroWidthSpace   "&#x0200B;" ><!--zero width space -->
<!ENTITY zopf             "%plane1D;56B;" ><!-- -->
