Maths DTD, from: http://mish161.cern.ch/sc4wg6/math/MATH.TXT

<!-- Outline of SGML Maths DTD for ISO 12083. Comments to
erp@ipg.ph.kcl.ac.uk please. 
 
8th May 1996 E R Pike, King's College, London and Stilo
Technology Ltd.
 
This DTD tags structure only. All formatting information must
be machine added by any application designed to present a 
conventional visual display on screen or paper. The
mathematical expressions generated will be syntactically
complete and may, therefore, be machine converted into input
for mathematical manipulation systems such as Reduce, Maple,
MathCad, Matlab and Mathematica, or into any programming code
such as C, PASCAL or FORTRAN for evaluation, They may also be
converted for any typesetting system or to TEX. The DTD is
targetted at the originator; conversion of legacy hard copy or
even of TEX mathematics at publishing houses will not always
be feasible except by specialists in the particular branch of
mathematics concerned. 
 
Mathematics of any sort are basic document elements and will be
contained in a required and repeatable "or" model group ie
<!ELEMENT   (Para(or whatever)|(%Math;))+   >
 
The eight-character limit for names is not convenient for
mathematics and, since it will most probably be changed to 16
or 32 in the reference concrete syntax of the next upgrade of 
SGML, it has not been observed in this DTD. We have also 
assumed that typing full math tags will not be necessary with 
any application sophisticated enough to tackle mathematics 
so brevity has given way to clarity for the most part.-->
 
<!--The following are marked-section INCLUDE switches. Fields
of mathematics not required should be switched out.
 
Arithmetic is always included -->
  
<!ENTITY % Alg         "INCLUDE"   -- Algebra-- >
<!ENTITY % Arrays      "INCLUDE"   -- Algebra with arrays-- >
<!ENTITY % Trig        "INCLUDE"   -- Trigonometry-- >
<!ENTITY % Calc        "INCLUDE"   -- Calculus-- >
<!ENTITY % Stats       "INCLUDE"   -- Statistics-- >
<!ENTITY % FnAn        "INCLUDE"   -- Functional Analysis-- >
<!ENTITY % Sturm       "INCLUDE"   -- Sturm Liouville Theory-- >
<!ENTITY % QM          "INCLUDE"   -- Quantum Mechanics-- >
<!ENTITY % HEP         "INCLUDE"   -- High Energy Physics-- >
<!ENTITY % Lists       "INCLUDE"   -- Lists-- >
<!ENTITY % Other       "IGNORE"    -- Additional function sets   
                        need to be added to complete this maths DTD -->

<!-- Mathematical expressions are structured as a recursive
nested sequence of functions. Each function may have another
function as its argument but finally, at the lowest level, the
arguments are <MathElements>. Each MathExpression is a single
expression which in principle is calculable (non-Boolean).
Adornments to functions, eg. integral, sum and product signs,
would be added by a formatting application but are irrelevent
to the SGML document. The numbers of parameters and arguments
of each function, together with layout information which will
specify their relative order and meaning are implied
attributes, which may be consulted by the originator for
correct entry or used by any formatting or mathematical
manipulation application.
 
For example, logbasen will have a single mandatory parameter
(the base) and a single argument (which could be another
function) and it can be agreed (in 12083, say,) that the
parameter is specified as the first element in the function
and the argument second. On the other hand, a quantum
mechanical commutator will have no parameters but two ordered
arguments (either or both of which may again be functions). 
Another example is a one-dimensional definite integral which
has a single argument as the integrand and lower and upper
limits and the integration variable as three parameters to be
agreed, say, in the above order. In this case the limit
parameters may again be functions (the use of an equation for
a limit is a formatting choice). A final example is a
fraction, which has two arguments, the numerator first, say,
and the denominator second, each of which, of course, can
again be functions; in this case the layout attribute will
specify the style of the fraction.
 
The left- and right-hand sides of an equation are each
<MathExpressions> and are separated by a verb. Verbs have been
separated into an arithmetic set and a set used in functional
analysis which may be switched in if required. 
 
The functions declared below are illustrative only, each field
should be carefully considered and completed by appropriate
specialist committees. As a start they should be extended to
include all the functions supported by existing mathematical
packages such as those mentioned above. An element "FnUser",
is provided for new or unknown operations but this should not
normally need to be used. New elements should arise less 
frequently than in other SGML applications and would have to
be incorporated at updating revisions by the community. -- >
 
 
<!ENTITY % FnArit
"Plus|Minus|Times|Divide|Fraction|Sqrt|Sqr|Exp|Ln|Log10|Abs|
Round|Gcd|Lcd|Max|Min|Sum|Prod|CoProd|Logbasen|nRoot|nPower|
Modulo|Div|Factorial|Pr" >
 
<!ENTITY % VbArit
"Equals|NotEquals|IdEquals|NIdEquals|ApprEquals|LessThan|
NLessThan|GtThan|NGtThan|LArrow|RArrow" >
 
<![%Alg[<!ENTITY % FnAlg
"|Vector|VectorName|VectComp|Tensor|TensorName|TensorComp|
Trace|Dim|Hom|Ker|Infimum|Supremum|LimInf|LimSup|Lim">]]> 
 
<!ENTITY % FnAlg "" >
 
<![%Arrays[<!ENTITY % FnArr "
|Det|DetName|DetComp|Matrix|MatrixName|MatrixComp|Trace|Rank|
Transpose|Inverse|Adjoint|HermConj">]]>
 
<!ENTITY % FnArr "" >
 
<![%Trig[<!ENTITY % FnTrig
"|Deg|Rad|Sin|Cos|Tan|Sec|Cosec|Cot|Sinh|Cosh|Tanh|Sech|
Cosech|Cotanh|ArcCos|ArcSin|ArcTan|Length|Area|Perimeter" >]]>
 
<!ENTITY % FnTrig "" >
 
<![%Calc[<!ENTITY % FnCalc
"|Deriv|ParDeriv|CapDelta|LCDelta|Int|nInt|ContInt|PrvalInt|
nDeriv|nPrderiv|TotDeriv|TotDiff|Jacobian|Div|Grad|Curl|
Laplace|Box" >]]>
 
<!ENTITY % FnCalc "" >
 
<![%Stats[<!ENTITY % FnStats 
"|Mean|Median|Mode|Var|StandDev|nMoment" >]]>
 
<!ENTITY % FnStats "" >
 
<![%FnAn[<!ENTITY % FnFnAn
"|CompNo|RealPtof|ImPtof|Mod|Arg|CompConj|Mapping|DirSum|
DirProd|SemiDirProd|Set|SetName|SetElement|Group|GroupName|
GroupElement" >]]>
 
<!ENTITY % VbFnAn
"|Cup|Cap|Vee|Wedge|ElemIncl|SetIncl|NotElInc|NtSetInc|
ForAll|MapsInto|TendsTo" >]]>
 
<!ENTITY % FnFnAn "" >
 
<!ENTITY % VbFnAn "" >
 
<![%SturmL[<!ENTITY % FnStrmL
"|OBessel|Hankel|Ai|Bi|Ci|nBessel|nHankel|Jacobi|OneF1|
OneF2|Hypergeo" >]]>
 
<!ENTITY % FnStrmL "" >
 
<![%QM[<!ENTITY % FnQM
"|Bra|Ket|Bracket|MatrixEl|Commutator|Anticommutator|
NormOrdr|AntNOrdr|CreationOp|AnnihilOp|Operator|HermAdj" >]]>
 
<!ENTITY % FnQM "" >
 
<![%Lists[<!ENTITY % FnLists
"|First|Second|Third|Reverse|List|Append|Cons|Join|Part|
Rest" >]]>
 
<!ENTITY % FnLists "" >
 
<![%Other[<!ENTITY % FnOther "" -- Additional function sets
                need to be added to complete this maths DTD -- >]]>
 
<!ENTITY % FnOther "" >
 
<!ENTITY % Fn
"%FnArit;%FnAlg;%FnArr;%FnTrig;%FnCalc;%FnStats;%FnFnAn;
%FnStrmL;%FnQM;%FnLists;%FnOther;%FnUser;" >
 
<!ENTITY    % Verb        "%VbArit;%VbFnAn;" >
 
<!ENTITY    % Label       "pre|post|sub|sup|subsup|circon" >
 
<!ENTITY    % Math        "%Label;|M|%Fn;|%Verb;|E|EA"
                         --M=MathElement,E=Equation,EA=EqnArray-- >

<!ENTITY    % MathExpression   "((M|%Fn;),M*,(%Fn;)*)"   >

<!ELEMENT   FnUser        - O    (M+,(%Fn;)*)       
               -- for user-defined functions, emergency use only-- >

<!ATTLIST   FnUser        Syntax        CDATA      #REQUIRED
                          Layout        CDATA      #REQUIRED

      --Syntax is order-of-entry information for parameters and
        arguments. First MathElement is Function Name. Layout
        is format information --  >
 
<!ELEMENT   MATHSDTD      - - (Paragraph*,Ref*) >
 
<!ELEMENT   Paragraph     - - (#PCDATA|%Math;)+    >
 
<!ELEMENT   M             O O ((%Label;)*,#PCDATA)     >

<!ATTLIST   M             Type  (Integer|Real|Complex)   #IMPLIED>
    
<!ELEMENT   (%Fn;)        - O (%MathExpression;)  >
 
<!ATTLIST   (%Fn;)       Syntax         CDATA      #IMPLIED
                         Layout   (1|2|3|4|5|6)    #IMPLIED

      -- Syntax is order-of-entry information for parameters and
         arguments. (Syntax could also be specified as comment for
         each function or "off-line" in instruction book or in help
         file (or all three)). Layout is function-dependan format 
         information e.g. bar or solidus for fractions etc. normally
         defaulted by the application.     -->

<!ELEMENT   (%Verb;)      - O EMPTY >
     
<!ELEMENT   (%Label;)     - O (#PCDATA|(%Math;))+      
                              -- Note that %Label is opened before
                              the MathElement requiring the label--  >

<!ATTLIST   (subsup|circon)    Syntax   CDATA      #IMPLIED >
 
<!ELEMENT   E             - - ((%MathExpression;)?,
                               ((%Verb;),(%MathExpression;))+)  >   
                                           
<!ATTLIST   E       EqNoType (Number|NoNumber)         Number
                    Type     (InLine|SetOut)           SetOut
                    id       ID                     #IMPLIED  >
     
<!ELEMENT   EA            - - (E*|EA*)+ >
 
<!ATTLIST   EA        EqNoType (NoNumber|One|All)   "All"
                      id       ID                     #IMPLIED >
 
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