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CSymbol

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last edited 2 years ago by jenn

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 (′) 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>


comments:

Proposal: Q-function --lizzardg, Thu, 03 Jun 2004 15:41:31 -0500 reply
- 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>

Proposal: Covariance Function --lizzardg, Thu, 03 Jun 2004 15:50:08 -0500 reply
- 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>

Proposal: Covariance Function --lizzardg, Thu, 03 Jun 2004 15:51:57 -0500 reply
top line should say "Covariance Function"

Proposal: Autocorrelation Function --lizzardg, Thu, 03 Jun 2004 15:56:05 -0500 reply
- 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>

Proposal: Cross-Correlation Function --lizzardg, Thu, 03 Jun 2004 15:58:35 -0500 reply
- 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>

Addendum: Cross-correlation Function --lizzardg, Thu, 03 Jun 2004 15:59:48 -0500 reply
Example should say: 

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

... --reedstrm, Tue, 05 Dec 2006 09:01:37 -0600 reply
Disjoint union for Prof. Pfeiffer: he has his own symbol!
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