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

     Copyright 1998 - 2010 W3C.

     Use and distribution of this code are permitted under the terms of the
     W3C Software Notice and License.
     http://www.w3.org/Consortium/Legal/2002/copyright-software-20021231.html

     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 5.x.

     References to the VARIANT SELECTOR 1 character (&#x0FE00;)
     should match the uses listed in Unicode Technical Report 25.

     Entity names in this file are derived from files carrying the
     following notice:

     (C) International Organization for Standardization 1991
     Permission to copy in any form is granted for use with
     conforming SGML systems and applications as defined in
     ISO 8879, provided this notice is included in all copies.

-->


<!-- 

       Public identifier: -//W3C//ENTITIES Added Math Symbols: Relations//EN//XML
       System identifier: http://www.w3.org/2003/entities/2007/isoamsr.ent

     The public identifier should always be used verbatim.
     The system identifier may be changed to suit local requirements.

     Typical invocation:

       <!ENTITY % isoamsr PUBLIC
         "-//W3C//ENTITIES Added Math Symbols: Relations//EN//XML"
         "http://www.w3.org/2003/entities/2007/isoamsr.ent"
       >
       %isoamsr;

-->

<!ENTITY ape              "&#x0224A;" ><!--ALMOST EQUAL OR EQUAL TO -->
<!ENTITY apE              "&#x02A70;" ><!--APPROXIMATELY EQUAL OR EQUAL TO -->
<!ENTITY apid             "&#x0224B;" ><!--TRIPLE TILDE -->
<!ENTITY asymp            "&#x02248;" ><!--ALMOST EQUAL TO -->
<!ENTITY Barv             "&#x02AE7;" ><!--SHORT DOWN TACK WITH OVERBAR -->
<!ENTITY bcong            "&#x0224C;" ><!--ALL EQUAL TO -->
<!ENTITY bepsi            "&#x003F6;" ><!--GREEK REVERSED LUNATE EPSILON SYMBOL -->
<!ENTITY bowtie           "&#x022C8;" ><!--BOWTIE -->
<!ENTITY bsim             "&#x0223D;" ><!--REVERSED TILDE -->
<!ENTITY bsime            "&#x022CD;" ><!--REVERSED TILDE EQUALS -->
<!ENTITY bsolhsub         "&#x027C8;" ><!--REVERSE SOLIDUS PRECEDING SUBSET -->
<!ENTITY bump             "&#x0224E;" ><!--GEOMETRICALLY EQUIVALENT TO -->
<!ENTITY bumpe            "&#x0224F;" ><!--DIFFERENCE BETWEEN -->
<!ENTITY bumpE            "&#x02AAE;" ><!--EQUALS SIGN WITH BUMPY ABOVE -->
<!ENTITY cire             "&#x02257;" ><!--RING EQUAL TO -->
<!ENTITY Colon            "&#x02237;" ><!--PROPORTION -->
<!ENTITY colone           "&#x02254;" ><!--COLON EQUALS -->
<!ENTITY Colone           "&#x02A74;" ><!--DOUBLE COLON EQUAL -->
<!ENTITY congdot          "&#x02A6D;" ><!--CONGRUENT WITH DOT ABOVE -->
<!ENTITY csub             "&#x02ACF;" ><!--CLOSED SUBSET -->
<!ENTITY csube            "&#x02AD1;" ><!--CLOSED SUBSET OR EQUAL TO -->
<!ENTITY csup             "&#x02AD0;" ><!--CLOSED SUPERSET -->
<!ENTITY csupe            "&#x02AD2;" ><!--CLOSED SUPERSET OR EQUAL TO -->
<!ENTITY cuepr            "&#x022DE;" ><!--EQUAL TO OR PRECEDES -->
<!ENTITY cuesc            "&#x022DF;" ><!--EQUAL TO OR SUCCEEDS -->
<!ENTITY dashv            "&#x022A3;" ><!--LEFT TACK -->
<!ENTITY Dashv            "&#x02AE4;" ><!--VERTICAL BAR DOUBLE LEFT TURNSTILE -->
<!ENTITY easter           "&#x02A6E;" ><!--EQUALS WITH ASTERISK -->
<!ENTITY ecir             "&#x02256;" ><!--RING IN EQUAL TO -->
<!ENTITY ecolon           "&#x02255;" ><!--EQUALS COLON -->
<!ENTITY eDDot            "&#x02A77;" ><!--EQUALS SIGN WITH TWO DOTS ABOVE AND TWO DOTS BELOW -->
<!ENTITY eDot             "&#x02251;" ><!--GEOMETRICALLY EQUAL TO -->
<!ENTITY efDot            "&#x02252;" ><!--APPROXIMATELY EQUAL TO OR THE IMAGE OF -->
<!ENTITY eg               "&#x02A9A;" ><!--DOUBLE-LINE EQUAL TO OR GREATER-THAN -->
<!ENTITY egs              "&#x02A96;" ><!--SLANTED EQUAL TO OR GREATER-THAN -->
<!ENTITY egsdot           "&#x02A98;" ><!--SLANTED EQUAL TO OR GREATER-THAN WITH DOT INSIDE -->
<!ENTITY el               "&#x02A99;" ><!--DOUBLE-LINE EQUAL TO OR LESS-THAN -->
<!ENTITY els              "&#x02A95;" ><!--SLANTED EQUAL TO OR LESS-THAN -->
<!ENTITY elsdot           "&#x02A97;" ><!--SLANTED EQUAL TO OR LESS-THAN WITH DOT INSIDE -->
<!ENTITY equest           "&#x0225F;" ><!--QUESTIONED EQUAL TO -->
<!ENTITY equivDD          "&#x02A78;" ><!--EQUIVALENT WITH FOUR DOTS ABOVE -->
<!ENTITY erDot            "&#x02253;" ><!--IMAGE OF OR APPROXIMATELY EQUAL TO -->
<!ENTITY esdot            "&#x02250;" ><!--APPROACHES THE LIMIT -->
<!ENTITY esim             "&#x02242;" ><!--MINUS TILDE -->
<!ENTITY Esim             "&#x02A73;" ><!--EQUALS SIGN ABOVE TILDE OPERATOR -->
<!ENTITY fork             "&#x022D4;" ><!--PITCHFORK -->
<!ENTITY forkv            "&#x02AD9;" ><!--ELEMENT OF OPENING DOWNWARDS -->
<!ENTITY frown            "&#x02322;" ><!--FROWN -->
<!ENTITY gap              "&#x02A86;" ><!--GREATER-THAN OR APPROXIMATE -->
<!ENTITY gE               "&#x02267;" ><!--GREATER-THAN OVER EQUAL TO -->
<!ENTITY gel              "&#x022DB;" ><!--GREATER-THAN EQUAL TO OR LESS-THAN -->
<!ENTITY gEl              "&#x02A8C;" ><!--GREATER-THAN ABOVE DOUBLE-LINE EQUAL ABOVE LESS-THAN -->
<!ENTITY ges              "&#x02A7E;" ><!--GREATER-THAN OR SLANTED EQUAL TO -->
<!ENTITY gescc            "&#x02AA9;" ><!--GREATER-THAN CLOSED BY CURVE ABOVE SLANTED EQUAL -->
<!ENTITY gesdot           "&#x02A80;" ><!--GREATER-THAN OR SLANTED EQUAL TO WITH DOT INSIDE -->
<!ENTITY gesdoto          "&#x02A82;" ><!--GREATER-THAN OR SLANTED EQUAL TO WITH DOT ABOVE -->
<!ENTITY gesdotol         "&#x02A84;" ><!--GREATER-THAN OR SLANTED EQUAL TO WITH DOT ABOVE LEFT -->
<!ENTITY gesl             "&#x022DB;&#x0FE00;" ><!--GREATER-THAN slanted EQUAL TO OR LESS-THAN -->
<!ENTITY gesles           "&#x02A94;" ><!--GREATER-THAN ABOVE SLANTED EQUAL ABOVE LESS-THAN ABOVE SLANTED EQUAL -->
<!ENTITY Gg               "&#x022D9;" ><!--VERY MUCH GREATER-THAN -->
<!ENTITY gl               "&#x02277;" ><!--GREATER-THAN OR LESS-THAN -->
<!ENTITY gla              "&#x02AA5;" ><!--GREATER-THAN BESIDE LESS-THAN -->
<!ENTITY glE              "&#x02A92;" ><!--GREATER-THAN ABOVE LESS-THAN ABOVE DOUBLE-LINE EQUAL -->
<!ENTITY glj              "&#x02AA4;" ><!--GREATER-THAN OVERLAPPING LESS-THAN -->
<!ENTITY gsim             "&#x02273;" ><!--GREATER-THAN OR EQUIVALENT TO -->
<!ENTITY gsime            "&#x02A8E;" ><!--GREATER-THAN ABOVE SIMILAR OR EQUAL -->
<!ENTITY gsiml            "&#x02A90;" ><!--GREATER-THAN ABOVE SIMILAR ABOVE LESS-THAN -->
<!ENTITY Gt               "&#x0226B;" ><!--MUCH GREATER-THAN -->
<!ENTITY gtcc             "&#x02AA7;" ><!--GREATER-THAN CLOSED BY CURVE -->
<!ENTITY gtcir            "&#x02A7A;" ><!--GREATER-THAN WITH CIRCLE INSIDE -->
<!ENTITY gtdot            "&#x022D7;" ><!--GREATER-THAN WITH DOT -->
<!ENTITY gtquest          "&#x02A7C;" ><!--GREATER-THAN WITH QUESTION MARK ABOVE -->
<!ENTITY gtrarr           "&#x02978;" ><!--GREATER-THAN ABOVE RIGHTWARDS ARROW -->
<!ENTITY homtht           "&#x0223B;" ><!--HOMOTHETIC -->
<!ENTITY lap              "&#x02A85;" ><!--LESS-THAN OR APPROXIMATE -->
<!ENTITY lat              "&#x02AAB;" ><!--LARGER THAN -->
<!ENTITY late             "&#x02AAD;" ><!--LARGER THAN OR EQUAL TO -->
<!ENTITY lates            "&#x02AAD;&#x0FE00;" ><!--LARGER THAN OR slanted EQUAL -->
<!ENTITY lE               "&#x02266;" ><!--LESS-THAN OVER EQUAL TO -->
<!ENTITY leg              "&#x022DA;" ><!--LESS-THAN EQUAL TO OR GREATER-THAN -->
<!ENTITY lEg              "&#x02A8B;" ><!--LESS-THAN ABOVE DOUBLE-LINE EQUAL ABOVE GREATER-THAN -->
<!ENTITY les              "&#x02A7D;" ><!--LESS-THAN OR SLANTED EQUAL TO -->
<!ENTITY lescc            "&#x02AA8;" ><!--LESS-THAN CLOSED BY CURVE ABOVE SLANTED EQUAL -->
<!ENTITY lesdot           "&#x02A7F;" ><!--LESS-THAN OR SLANTED EQUAL TO WITH DOT INSIDE -->
<!ENTITY lesdoto          "&#x02A81;" ><!--LESS-THAN OR SLANTED EQUAL TO WITH DOT ABOVE -->
<!ENTITY lesdotor         "&#x02A83;" ><!--LESS-THAN OR SLANTED EQUAL TO WITH DOT ABOVE RIGHT -->
<!ENTITY lesg             "&#x022DA;&#x0FE00;" ><!--LESS-THAN slanted EQUAL TO OR GREATER-THAN -->
<!ENTITY lesges           "&#x02A93;" ><!--LESS-THAN ABOVE SLANTED EQUAL ABOVE GREATER-THAN ABOVE SLANTED EQUAL -->
<!ENTITY lg               "&#x02276;" ><!--LESS-THAN OR GREATER-THAN -->
<!ENTITY lgE              "&#x02A91;" ><!--LESS-THAN ABOVE GREATER-THAN ABOVE DOUBLE-LINE EQUAL -->
<!ENTITY Ll               "&#x022D8;" ><!--VERY MUCH LESS-THAN -->
<!ENTITY lsim             "&#x02272;" ><!--LESS-THAN OR EQUIVALENT TO -->
<!ENTITY lsime            "&#x02A8D;" ><!--LESS-THAN ABOVE SIMILAR OR EQUAL -->
<!ENTITY lsimg            "&#x02A8F;" ><!--LESS-THAN ABOVE SIMILAR ABOVE GREATER-THAN -->
<!ENTITY Lt               "&#x0226A;" ><!--MUCH LESS-THAN -->
<!ENTITY ltcc             "&#x02AA6;" ><!--LESS-THAN CLOSED BY CURVE -->
<!ENTITY ltcir            "&#x02A79;" ><!--LESS-THAN WITH CIRCLE INSIDE -->
<!ENTITY ltdot            "&#x022D6;" ><!--LESS-THAN WITH DOT -->
<!ENTITY ltlarr           "&#x02976;" ><!--LESS-THAN ABOVE LEFTWARDS ARROW -->
<!ENTITY ltquest          "&#x02A7B;" ><!--LESS-THAN WITH QUESTION MARK ABOVE -->
<!ENTITY ltrie            "&#x022B4;" ><!--NORMAL SUBGROUP OF OR EQUAL TO -->
<!ENTITY mcomma           "&#x02A29;" ><!--MINUS SIGN WITH COMMA ABOVE -->
<!ENTITY mDDot            "&#x0223A;" ><!--GEOMETRIC PROPORTION -->
<!ENTITY mid              "&#x02223;" ><!--DIVIDES -->
<!ENTITY mlcp             "&#x02ADB;" ><!--TRANSVERSAL INTERSECTION -->
<!ENTITY models           "&#x022A7;" ><!--MODELS -->
<!ENTITY mstpos           "&#x0223E;" ><!--INVERTED LAZY S -->
<!ENTITY pr               "&#x0227A;" ><!--PRECEDES -->
<!ENTITY Pr               "&#x02ABB;" ><!--DOUBLE PRECEDES -->
<!ENTITY prap             "&#x02AB7;" ><!--PRECEDES ABOVE ALMOST EQUAL TO -->
<!ENTITY prcue            "&#x0227C;" ><!--PRECEDES OR EQUAL TO -->
<!ENTITY pre              "&#x02AAF;" ><!--PRECEDES ABOVE SINGLE-LINE EQUALS SIGN -->
<!ENTITY prE              "&#x02AB3;" ><!--PRECEDES ABOVE EQUALS SIGN -->
<!ENTITY prsim            "&#x0227E;" ><!--PRECEDES OR EQUIVALENT TO -->
<!ENTITY prurel           "&#x022B0;" ><!--PRECEDES UNDER RELATION -->
<!ENTITY ratio            "&#x02236;" ><!--RATIO -->
<!ENTITY rtrie            "&#x022B5;" ><!--CONTAINS AS NORMAL SUBGROUP OR EQUAL TO -->
<!ENTITY rtriltri         "&#x029CE;" ><!--RIGHT TRIANGLE ABOVE LEFT TRIANGLE -->
<!ENTITY sc               "&#x0227B;" ><!--SUCCEEDS -->
<!ENTITY Sc               "&#x02ABC;" ><!--DOUBLE SUCCEEDS -->
<!ENTITY scap             "&#x02AB8;" ><!--SUCCEEDS ABOVE ALMOST EQUAL TO -->
<!ENTITY sccue            "&#x0227D;" ><!--SUCCEEDS OR EQUAL TO -->
<!ENTITY sce              "&#x02AB0;" ><!--SUCCEEDS ABOVE SINGLE-LINE EQUALS SIGN -->
<!ENTITY scE              "&#x02AB4;" ><!--SUCCEEDS ABOVE EQUALS SIGN -->
<!ENTITY scsim            "&#x0227F;" ><!--SUCCEEDS OR EQUIVALENT TO -->
<!ENTITY sdote            "&#x02A66;" ><!--EQUALS SIGN WITH DOT BELOW -->
<!ENTITY sfrown           "&#x02322;" ><!--FROWN -->
<!ENTITY simg             "&#x02A9E;" ><!--SIMILAR OR GREATER-THAN -->
<!ENTITY simgE            "&#x02AA0;" ><!--SIMILAR ABOVE GREATER-THAN ABOVE EQUALS SIGN -->
<!ENTITY siml             "&#x02A9D;" ><!--SIMILAR OR LESS-THAN -->
<!ENTITY simlE            "&#x02A9F;" ><!--SIMILAR ABOVE LESS-THAN ABOVE EQUALS SIGN -->
<!ENTITY smid             "&#x02223;" ><!--DIVIDES -->
<!ENTITY smile            "&#x02323;" ><!--SMILE -->
<!ENTITY smt              "&#x02AAA;" ><!--SMALLER THAN -->
<!ENTITY smte             "&#x02AAC;" ><!--SMALLER THAN OR EQUAL TO -->
<!ENTITY smtes            "&#x02AAC;&#x0FE00;" ><!--SMALLER THAN OR slanted EQUAL -->
<!ENTITY spar             "&#x02225;" ><!--PARALLEL TO -->
<!ENTITY sqsub            "&#x0228F;" ><!--SQUARE IMAGE OF -->
<!ENTITY sqsube           "&#x02291;" ><!--SQUARE IMAGE OF OR EQUAL TO -->
<!ENTITY sqsup            "&#x02290;" ><!--SQUARE ORIGINAL OF -->
<!ENTITY sqsupe           "&#x02292;" ><!--SQUARE ORIGINAL OF OR EQUAL TO -->
<!ENTITY ssmile           "&#x02323;" ><!--SMILE -->
<!ENTITY Sub              "&#x022D0;" ><!--DOUBLE SUBSET -->
<!ENTITY subE             "&#x02AC5;" ><!--SUBSET OF ABOVE EQUALS SIGN -->
<!ENTITY subedot          "&#x02AC3;" ><!--SUBSET OF OR EQUAL TO WITH DOT ABOVE -->
<!ENTITY submult          "&#x02AC1;" ><!--SUBSET WITH MULTIPLICATION SIGN BELOW -->
<!ENTITY subplus          "&#x02ABF;" ><!--SUBSET WITH PLUS SIGN BELOW -->
<!ENTITY subrarr          "&#x02979;" ><!--SUBSET ABOVE RIGHTWARDS ARROW -->
<!ENTITY subsim           "&#x02AC7;" ><!--SUBSET OF ABOVE TILDE OPERATOR -->
<!ENTITY subsub           "&#x02AD5;" ><!--SUBSET ABOVE SUBSET -->
<!ENTITY subsup           "&#x02AD3;" ><!--SUBSET ABOVE SUPERSET -->
<!ENTITY Sup              "&#x022D1;" ><!--DOUBLE SUPERSET -->
<!ENTITY supdsub          "&#x02AD8;" ><!--SUPERSET BESIDE AND JOINED BY DASH WITH SUBSET -->
<!ENTITY supE             "&#x02AC6;" ><!--SUPERSET OF ABOVE EQUALS SIGN -->
<!ENTITY supedot          "&#x02AC4;" ><!--SUPERSET OF OR EQUAL TO WITH DOT ABOVE -->
<!ENTITY suphsol          "&#x027C9;" ><!--SUPERSET PRECEDING SOLIDUS -->
<!ENTITY suphsub          "&#x02AD7;" ><!--SUPERSET BESIDE SUBSET -->
<!ENTITY suplarr          "&#x0297B;" ><!--SUPERSET ABOVE LEFTWARDS ARROW -->
<!ENTITY supmult          "&#x02AC2;" ><!--SUPERSET WITH MULTIPLICATION SIGN BELOW -->
<!ENTITY supplus          "&#x02AC0;" ><!--SUPERSET WITH PLUS SIGN BELOW -->
<!ENTITY supsim           "&#x02AC8;" ><!--SUPERSET OF ABOVE TILDE OPERATOR -->
<!ENTITY supsub           "&#x02AD4;" ><!--SUPERSET ABOVE SUBSET -->
<!ENTITY supsup           "&#x02AD6;" ><!--SUPERSET ABOVE SUPERSET -->
<!ENTITY thkap            "&#x02248;" ><!--ALMOST EQUAL TO -->
<!ENTITY thksim           "&#x0223C;" ><!--TILDE OPERATOR -->
<!ENTITY topfork          "&#x02ADA;" ><!--PITCHFORK WITH TEE TOP -->
<!ENTITY trie             "&#x0225C;" ><!--DELTA EQUAL TO -->
<!ENTITY twixt            "&#x0226C;" ><!--BETWEEN -->
<!ENTITY vBar             "&#x02AE8;" ><!--SHORT UP TACK WITH UNDERBAR -->
<!ENTITY Vbar             "&#x02AEB;" ><!--DOUBLE UP TACK -->
<!ENTITY vBarv            "&#x02AE9;" ><!--SHORT UP TACK ABOVE SHORT DOWN TACK -->
<!ENTITY vdash            "&#x022A2;" ><!--RIGHT TACK -->
<!ENTITY vDash            "&#x022A8;" ><!--TRUE -->
<!ENTITY Vdash            "&#x022A9;" ><!--FORCES -->
<!ENTITY VDash            "&#x022AB;" ><!--DOUBLE VERTICAL BAR DOUBLE RIGHT TURNSTILE -->
<!ENTITY Vdashl           "&#x02AE6;" ><!--LONG DASH FROM LEFT MEMBER OF DOUBLE VERTICAL -->
<!ENTITY vltri            "&#x022B2;" ><!--NORMAL SUBGROUP OF -->
<!ENTITY vprop            "&#x0221D;" ><!--PROPORTIONAL TO -->
<!ENTITY vrtri            "&#x022B3;" ><!--CONTAINS AS NORMAL SUBGROUP -->
<!ENTITY Vvdash           "&#x022AA;" ><!--TRIPLE VERTICAL BAR RIGHT TURNSTILE -->
