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These are the CSymbol extensions to MathML currently recognized by the Connexions project:


- Adjoint (often called Hermitian):

   'definitionURL="http://cnx.rice.edu/cd/cnxmath.ocd#adjoint"'

   Example code::

     <m:apply>
       <m:csymbol definitionURL="http://cnx.rice.edu/cd/cnxmath.ocd#adjoint"/>
       <m:ci type='matrix'>U</m:ci>
     </m:apply>

   This prints an 'H' as a superscript on the matrix 'U'.

- Arg max:

   'definitionURL="http://cnx.rice.edu/cd/cnxmath.ocd#argmax"'

   Condition and domainofapplication tags can be used with argmax.  Example code::

     <m:apply>
       <m:csymbol definitionURL="http://cnx.rice.edu/cd/cnxmath.ocd#argmax"/>
       <m:domainofapplication>
         <m:ci type='vector'>&theta;</m:ci>
       </m:domainofapplication>
       <m:apply>
         <m:ci type='fn'>p</m:ci>
         <m:ci type='vector'>x</m:ci>
       </m:apply>
     </m:apply>

- Arg min:

   'definitionURL="http://cnx.rice.edu/cd/cnxmath.ocd#argmin"'

   Condition and domainofapplication tags can be used with argmin.

- Combination:

   'definitionURL="http://www.openmath.org/cd/combinat1.ocd"'

   Example code::

     <m:apply>
       <m:csymbol definitionURL="http://www.openmath.org/cd/combinat1.ocd"/>
       <m:ci>N</m:ci>
       <m:ci>n</m:ci>
     </m:apply>

   (the 'N' prints on top and the 'n' on bottom).

- Complement

   'definitionURL="http://cnx.rice.edu/cd/cnxmath.ocd#complement"'

   Example code::

     <m:apply>
       <m:csymbol definitionURL="http://cnx.rice.edu/cd/cnxmath.ocd#complement"/>
       <m:ci>A</m:ci>
     </m:apply>

   This prints 'A' with a prime (&#8242;) symbol to denote complement.

- Convolution:

   'definitionURL="http://cnx.rice.edu/cd/cnxmath.ocd#convolve"'

   Any number of functions can be convoluted with each other.  Here is an example using three functions that yields: x(t) = R(t) '*' h(-t) '*' h(t)::

     <m:apply>
       <m:eq/>
       <m:apply>
         <m:ci type='fn'>x</m:ci>
         <m:ci>t</m:ci>
       </m:apply>
       <m:apply>
   <m:csymbol definitionURL="http://cnx.rice.edu/cd/cnxmath.ocd#convolve"/>
     <m:apply>
             <m:ci type='fn'>R</m:ci>
             <m:ci>t</m:ci>
           </m:apply>
     <m:apply>
             <m:ci type='fn'>h</m:ci>
             <m:apply>
               <m:minus/>
     <m:ci>t</m:ci>
             </m:apply>
     </m:apply>
     <m:apply>
             <m:ci type='fn'>h</m:ci>
             <m:ci>t</m:ci>
     </m:apply>
  </m:apply>
     </m:apply>


- Cumulative Distribution Function

   'definitionURL="http://cnx.rice.edu/cd/cnxmath.ocd#cdf'

   bvar and condition tags are used with cdf.  Example code::

     <m:apply>
       <m:csymbol definitionURL='http://cnx.rice.edu/cd/cnxmath.ocd#cdf'>f</m:csymbol>
       <m:bvar>
         <m:ci>&theta;</m:ci>
       </m:bvar>
       <m:ci>x</m:ci>
     </m:apply>

- Directional Derivative

   'definitionURL="http://cnx.rice.edu/cd/cnxmath.ocd#vectorderivative'

   This should be used with the 'diff' tag, as shown in this example::

     <m:apply>
       <m:diff definitionURL='http://cnx.rice.edu/cd/cnxmath.ocd#vectorderivative'/>
       <m:bvar>
         <m:ci>&theta;</m:ci>
       </m:bvar>
       <m:apply>
         <m:ci type='vector'>s</m:ci>
         <m:ci>&theta;</m:ci>
       </m:apply>
     </m:apply>


- Distance

   'definitionURL="http://cnx.rice.edu/cd/cnxmath.ocd#distance"' 

   Used in the context of the Kulback-Leibler Distance. Takes two children.
   Example code::


     <m:apply>
       <m:csymbol definitionURL="http://cnx.rice.edu/cd/cnxmath.ocd#distance"/>
       <m:ci><m:msub>
           <m:mi>p</m:mi>
           <m:mn>1</m:mn>
         </m:msub></m:ci>
       <m:ci><m:msub>
           <m:mi>p</m:mi>
           <m:mn>0</m:mn>
         </m:msub></m:ci>
     </m:apply>


- Distributed In

   'definitionURL="http://cnx.rice.edu/cd/cnxmath.ocd#distributedin"'

   Used to specify the identifier for any statistical distribution.
   Example: see Normal Distribution

- Estimate

   'definitionURL="http://cnx.rice.edu/cd/cnxmath.ocd#estimate"'

   Example::

     <m:apply>
       <m:csymbol definitionURL="http://cnx.rice.edu/cd/cnxmath.ocd#estimate"/>
       <m:ci><m:msub>
           <m:mi>&theta;</m:mi>
           <m:mi>ML</m:mi>
         </m:msub></m:ci>
     </m:apply>

- Evaluated At

   'definitionURL='http://cnx.rice.edu/cd/cnxmath.ocd#evaluateat'

   This will be used for displaying a vertical bar with a subcript or subscript/superscript.
   Apply a csymbol with the definitionURL above, a bvar, and either a condition, an interval, or a lowlimit and an uplimit.
   For Example, you may want to display the integral of x squared evaluated at x=0;x=3.
   This can be done with the following code::


     <m:apply>
       <m:csymbol definitionURL='http://cnx.rice.edu/cd/cnxmath.ocd#evaluateat'/>
       <m:bvar>
   <m:ci>x</m:ci>
       </m:bvar>
       <m:interval>
         <m:cn>0</m:cn>
   <m:cn>3</m:cn>
       </m:interval>
       <m:apply>
         <m:int/>
         <m:bvar>
     <m:ci>x</m:ci>
   </m:bvar>
         <m:apply>
           <m:power/>
     <m:ci>x</m:ci>
           <m:cn>2</m:cn>
         </m:apply>
       </m:apply>
     </m:apply>

- Expected Value

   'definitionURL="http://cnx.rice.edu/cd/cnxmath.ocd#expectedvalue"'

   The bvar is optional and prints as a subscript on the cursive E.  Also accepts condition.
   Example::
 
     <m:apply>
       <m:csymbol definitionURL="http://cnx.rice.edu/cd/cnxmath.ocd#expectedvalue"/>
       <m:bvar>
         <m:cn>0</m:cn>
       </m:bvar>
       <m:apply>
         <m:ci type='fn'>&Lambda;</m:ci>
         <m:ci type='vector'>r</m:ci>
       </m:apply>
     </m:apply>

- Infimum

   'definitionURL="http://cnx.rice.edu/cd/cnxmath.ocd#infimum"'

   Accepts bvar and condition.


- Mutual Information

   'definitionURL="http://cnx.rice.edu/cd/cnxmath.ocd#mutualinformation"'

   Example::

     <m:apply>
       <m:csymbol definitionURL="http://cnx.rice.edu/cd/cnxmath.ocd#mutualinformation"/>
       <m:ci><m:msub>
         <m:mi>r</m:mi>
         <m:mn>1</m:mn>
       </m:msub></m:ci>
       <m:ci><m:msub>
         <m:mi>r</m:mi>
         <m:mn>2</m:mn>
       </m:msub></m:ci>
     </m:apply>

- Norm:

   'definitionURL="http://cnx.rice.edu/cd/cnxmath.ocd#norm"'
  
   Csymbol for the Norm.  To specify which norm (2-norm, 3-norm, p-norm, etc.), use "domainofapplication" tags as in the example.  The 
   semantic default domainofapplication is 2, which will not display unless the domainofapplication tag is present as below.  Example::

     <m:apply>
       <m:csymbol definitionURL="http://cnx.rice.edu/cd/cnxmath.ocd#norm"/>
       <m:domainofapplication>
         <m:cn>2</m:cn>
       </m:domainofapplication>
       <m:ci type='vector'>x</m:ci>
     </m:apply>

- Normal Distribution

   'definitionURL="http://cnx.rice.edu/cd/cnxmath.ocd#normaldistribution"'

   Csymbol for the Normal Distribution. Does not specify an identifier. To specify the name of the 
   random variable use 'Distributedin' csymbol. Takes two children, the mean and the variance of the distribution.
   Example: X ~ N(mu,sigma)::

     <m:apply>
       <m:csymbol definitionURL="http://cnx.rice.edu/cd/cnxmath.ocd#distributedin"/>
       <m:ci>X</m:ci>
       <m:apply>
         <m:csymbol definitionURL="http://cnx.rice.edu/cd/cnxmath.ocd#normaldistribution"/>
         <m:ci>mu</m:ci>
         <m:ci>sigma</m:ci>
       </m:apply>
     </m:apply>

- Piecewise Stochastic Process

   'definitionURL="http://cnx.rice.edu/cd/cnxmath.ocd#stochastic"'

   Example::

     <m:apply>
       <m:csymbol definitionURL="http://cnx.rice.edu/cd/cnxmath.ocd#stochastic">
       <m:apply>
         <m:csymbol definitionURL="http://cnx.rice.edu/cd/cnxmath.ocd#stochasticpiece"/>
         <m:cn>1</m:cn>
         <m:ci>p</m:ci>
       </m:apply>
       <m:apply>
         <m:csymbol definitionURL="http://cnx.rice.edu/cd/cnxmath.ocd#stochasticpiece"/>
         <m:cn>0</m:cn>
         <m:apply>
           <m:minus/>
           <m:cn>1</m:cn>
           <m:ci>p</m:ci>
         </m:apply>
       </m:apply>
     </m:apply>

- Probability

   'definitionURL="http://cnx.rice.edu/cd/cnxmath.ocd#probability"'

   condition can be used  to make the display Pr [ x | y ].  Example ::

     <m:apply>
       <m:csymbol definitionURL='http://cnx.rice.edu/cd/cnxmath.ocd#probability'/>
       <m:condition>
         <m:ci>Y</m:ci>
       </m:condition>
       <m:ci>X</m:ci>
     </m:apply>


- Probability Density Function

   'definitionURL="http://cnx.rice.edu/cd/cnxmath.ocd#pdf"'

   Csymbol for the probability density function.  For probability mass function, use this csymbol with class='discrete', as in the second 
   example.  Example code: The following is a sample of how to code p(x|theta) with r|theta as a subscript to the p::

     <m:apply>
       <m:csymbol definitionURL="http://cnx.rice.edu/cd/cnxmath.ocd#pdf">p</m:csymbol>
       <m:bvar>
         <m:ci>r</m:ci>
       </m:bvar>
       <m:condition>
         <m:ci>theta</m:ci>
       </m:condition>
       <m:ci>x</m:ci>
     </m:apply> 


- Probability Mass Function

   'definitionURL="http://cnx.rice.edu/cd/cnxmath.ocd#pdf"'

   Csymbol for the probability density function.  For probability mass function, use this csymbol with class='discrete', as in the second 
   example.  Example::

     <m:apply>
       <m:csymbol class='discrete' definitionURL="http://cnx.rice.edu/cd/cnxmath.ocd#pdf">p</m:csymbol>
       <m:bvar>
         <m:ci>r</m:ci>
       </m:bvar>
       <m:condition>
         <m:ci>theta</m:ci>
       </m:condition>
       <m:ci>x</m:ci>
     </m:apply> 


- Surface Integral:

   'definitionURL="http://cnx.rice.edu/cd/cnxmath.ocd#surfaceintegral"'

   Example::

     <m:apply>
       <m:csymbol definitionURL="http://cnx.rice.edu/cd/cnxmath.ocd#surfaceintegral"/>
       <m:bvar>
         <m:ci>S</m:ci>
       </m:bvar>
       <m:domainofapplication>
         <m:ci>s</m:ci>
       </m:domainofapplication>
       <m:ci>D</m:ci>
     </m:apply>



From lizzardg Thu Jun 3 15:41:31 -0500 2004
From: lizzardg
Date: Thu, 03 Jun 2004 15:41:31 -0500
Subject: Proposal: Q-function
Message-ID: <20040603154131-0500@mountainbunker.org>

- Q Function:
  
  definitionURL="http://cnx.rice.edu/cd/cnxmath.ocd#qfunction"

  Csymbol for the Q-function, also know as the Error Function in statistics.  Generally denoted as Q(x).  
  Example::

      <m:apply>
         <m:csymbol definitionURL="http://cnx.rice.edu/cd/cnxmath.ocd#qfunction"/>
         <m:apply>
            <m:root/>
            <m:ci>E</m:ci>
         </m:apply>
       <m:apply>


From lizzardg Thu Jun 3 15:50:08 -0500 2004
From: lizzardg
Date: Thu, 03 Jun 2004 15:50:08 -0500
Subject: Proposal: Covariance Function
Message-ID: <20040603155008-0500@mountainbunker.org>

- Correlation Function

  definitionURL="http://cnx.rice.edu/cd/cnxmath.ocd#covariance"
  
  Csymbol for the covariance function.  Generally denoted as K_X(t_1,t_2) or cov(X_t_1,X_t_2), where "_" denotes subscripts.  To denote the random variable concerned, use bvar tags.  Example::

     <m:apply>
         <m:csymbol definitionURL="http://cnx.rice.edu/cd/cnxmath.ocd#covariance"/>
         <m:bvar>
            <m:ci>X</m:ci>
         </m:bvar>
         <m:ci><m:msub>
              <m:mi>t</m:mi>
              <m:mn>1</m:mn>
             </m:msub></m:ci>
         <m:ci><m:msub>
              <m:mi>t</m:mi>
              <m:mn>1</m:mn>
             </m:msub></m:ci>
      </m:apply>

From lizzardg Thu Jun 3 15:51:57 -0500 2004
From: lizzardg
Date: Thu, 03 Jun 2004 15:51:57 -0500
Subject: Proposal: Covariance Function
Message-ID: <20040603155157-0500@mountainbunker.org>
In-reply-to: <20040603155008-0500@mountainbunker.org>

top line should say "Covariance Function"

From lizzardg Thu Jun 3 15:56:05 -0500 2004
From: lizzardg
Date: Thu, 03 Jun 2004 15:56:05 -0500
Subject: Proposal: Autocorrelation Function
Message-ID: <20040603155605-0500@mountainbunker.org>

- Autocorrelation Function

   definitionURL="http://cnx.rice.edu/cd/cnxmath.ocd#autocorr"

   Csymbol for the autocorrelation function.  Generally denoted as R_X(t_1,t_2), defined as 
   E[X_t_1*X_t_2], where "_" denoted subscripts and E[] denotes the expected value.  The random variable 
   involved should be denoted using bvar tags.  Example::

     <m:apply>
         <m:csymbol definitionURL="http://cnx.rice.edu/cd/cnxmath.ocd#autocorr"/>
         <m:bvar>
            <m:ci>X</m:ci>
         </m:bvar>
         <m:ci><m:msub>
              <m:mi>t</m:mi>
              <m:mn>1</m:mn>
             </m:msub></m:ci>
         <m:ci><m:msub>
              <m:mi>t</m:mi>
              <m:mn>1</m:mn>
             </m:msub></m:ci>
     </m:apply>         

From lizzardg Thu Jun 3 15:58:35 -0500 2004
From: lizzardg
Date: Thu, 03 Jun 2004 15:58:35 -0500
Subject: Proposal: Cross-Correlation Function
Message-ID: <20040603155835-0500@mountainbunker.org>

- Cross-Correlation Function

 definitionURL="http://cnx.rice.edu/cd/cnxmath.ocd#xcorr"

 Csymbol for the cross-correlation function. Generally denoted as R_XY(t_1,t_2), defined as E[X_t_1*Y_t_2]?, where "_" denoted subscripts and E[] denotes the expected value. The random variables involved should be denoted using separate bvar tags. Example::

     <m:apply>
         <m:csymbol definitionURL="http://cnx.rice.edu/cd/cnxmath.ocd#autocorr"/>
         <m:bvar>
            <m:ci>X</m:ci>
         </m:bvar>
         <m:bvar>
            <m:ci>Y</m:ci>
         </m:bvar>
         <m:ci><m:msub>
              <m:mi>t</m:mi>
              <m:mn>1</m:mn>
             </m:msub></m:ci>
         <m:ci><m:msub>
              <m:mi>t</m:mi>
              <m:mn>1</m:mn>
             </m:msub></m:ci>
     </m:apply>       

From lizzardg Thu Jun 3 15:59:48 -0500 2004
From: lizzardg
Date: Thu, 03 Jun 2004 15:59:48 -0500
Subject: Addendum: Cross-correlation Function
Message-ID: <20040603155948-0500@mountainbunker.org>

Example should say::

     <m:csymbol definitionURL="http://cnx.rice.edu/cd/cnxmath.ocd#xcorr"/>

From reedstrm Tue Dec 5 09:01:37 -0600 2006
From: reedstrm
Date: Tue, 05 Dec 2006 09:01:37 -0600
Subject: 
Message-ID: <20061205090137-0600@mountainbunker.org>

Disjoint union for Prof. Pfeiffer: he has his own symbol!