OpenMath Content Dictionary: list3

Canonical URL:

http://www.openmath.org/cd/list3.ocd

CD File:

list3.ocd

CD as XML Encoded OpenMath:

list3.omcd

Defines:

difference, entry, length, list_of_lengthn, select

Date:

2004-03-02

Version:

1 (Revision 1)

Review Date:

2004-11-01

Status:

experimental

Uses CD:

quant1, relation1, list1

Several basic list functions related to length are given in this CD.

Initiated by Arjeh M. Cohen 2004-03-02

length

Description:

This symbol represents a function whose argument should be a list. It returns the length of its argument.

Example:

The length of the list [1,2,3] is 3.

OpenMath XML (source)

<OMOBJ xmlns="http://www.openmath.org/OpenMath" version="2.0">
  <OMA><OMS cd="relation1" name="eq"/>
       <OMA><OMS cd="list3" name="length"/>
            <OMA><OMS cd="list1" name="list"/>
                 <OMI> 1 </OMI>
                 <OMI> 2 </OMI>
                 <OMI> 3 </OMI>
            </OMA>
       </OMA>
       <OMI> 3 </OMI>
  </OMA>
</OMOBJ>

Strict Content MathML

<math xmlns="http://www.w3.org/1998/Math/MathML">
 <apply><csymbol cd="relation1">eq</csymbol>
  <apply><csymbol cd="list3">length</csymbol>
   <apply><csymbol cd="list1">list</csymbol><cn>1</cn><cn>2</cn><cn>3</cn></apply>
  </apply>
  <cn>3</cn>
 </apply>
</math>

Prefix

eq (length (list ( 1 , 2 , 3 ) ) , 3 )

Popcorn

list3.length([1 , 2 , 3]) = 3

Rendered Presentation MathML

$$\mathrm{length}\left((1,2,3)\right)=3$$

Signatures:

sts

list_of_lengthn

Description:

This symbol represents a function with two arguments, the first of which is a natural number and the second of which is a list. The first argument is the length of the list.

Example:

A list L of length 3:

OpenMath XML (source)

<OMOBJ xmlns="http://www.openmath.org/OpenMath" version="2.0">
  <OMA><OMS cd="list3" name="list_of_lengthn"/>
       <OMI> 3 </OMI>
       <OMA><OMS cd="list1" name="list"/>
            <OMV name="L"/>
       </OMA>
  </OMA>
</OMOBJ>

Strict Content MathML

<math xmlns="http://www.w3.org/1998/Math/MathML">
 <apply><csymbol cd="list3">list_of_lengthn</csymbol>
  <cn>3</cn>
  <apply><csymbol cd="list1">list</csymbol><ci>L</ci></apply>
 </apply>
</math>

Prefix

list_of_lengthn ( 3 , list ( L) )

Popcorn

list3.list_of_lengthn(3, [$L])

Rendered Presentation MathML

$$\mathrm{list\_of\_lengthn}(3,\left(L\right))$$

Signatures:

sts

entry

Description:

This symbol represents a binary function whose first argument should be a list L and whose second argument should be a positive integer i such that the absolute value of i is in the interval [1..n], where n is the length of L. If i is positive, it returns the i-th entry L[i] of L, if i is negative it returns the (n+1-i)-th entry of L.

Example:

The second entry of the list [1,2,3] is 2.

OpenMath XML (source)

<OMOBJ xmlns="http://www.openmath.org/OpenMath" version="2.0">
  <OMA><OMS cd="relation1" name="eq"/>
       <OMA><OMS cd="list3" name="entry"/>
            <OMA><OMS cd="list1" name="list"/>
                 <OMI> 1 </OMI>
                 <OMI> 2 </OMI>
                 <OMI> 3 </OMI>
            </OMA>
            <OMI> 2 </OMI>
       </OMA>
       <OMI> 2 </OMI>
  </OMA>
</OMOBJ>

Strict Content MathML

<math xmlns="http://www.w3.org/1998/Math/MathML">
 <apply><csymbol cd="relation1">eq</csymbol>
  <apply><csymbol cd="list3">entry</csymbol>
   <apply><csymbol cd="list1">list</csymbol><cn>1</cn><cn>2</cn><cn>3</cn></apply>
   <cn>2</cn>
  </apply>
  <cn>2</cn>
 </apply>
</math>

Prefix

eq (entry (list ( 1 , 2 , 3 ) , 2 ) , 2 )

Popcorn

list3.entry([1 , 2 , 3], 2) = 2

Rendered Presentation MathML

$$\mathrm{entry}((1,2,3),2)=2$$

Example:

Specification of the second element of the list [1,..,6] counted from the end.

OpenMath XML (source)

<OMOBJ xmlns="http://www.openmath.org/OpenMath" version="2.0">
  <OMA><OMS cd="relation1" name="eq"/>
       <OMA><OMS cd="list3" name="entry"/>
            <OMA><OMS cd="list1" name="list"/>
                 <OMI> 1 </OMI>      <OMI> 2 </OMI>      <OMI> 3 </OMI>
                 <OMI> 4 </OMI>      <OMI> 5 </OMI>      <OMI> 6 </OMI>
            </OMA>
            <OMI>-2</OMI> 
       </OMA>
       <OMI>5</OMI> 
  </OMA>
</OMOBJ>

Strict Content MathML

<math xmlns="http://www.w3.org/1998/Math/MathML">
 <apply><csymbol cd="relation1">eq</csymbol>
  <apply><csymbol cd="list3">entry</csymbol>
   <apply><csymbol cd="list1">list</csymbol>
    <cn>1</cn>
    <cn>2</cn>
    <cn>3</cn>
    <cn>4</cn>
    <cn>5</cn>
    <cn>6</cn>
   </apply>
   <cn>-2</cn>
  </apply>
  <cn>5</cn>
 </apply>
</math>

Prefix

eq (entry (list ( 1 , 2 , 3 , 4 , 5 , 6 ) , -2) , 5)

Popcorn

list3.entry([1 , 2 , 3 , 4 , 5 , 6], -2) = 5

Rendered Presentation MathML

$$\mathrm{entry}((1,2,3,4,5,6),-2)=5$$

Signatures:

sts

difference

Description:

This symbol takes two arguments both a list. It represents a function which returns a list made up of all the elements of the first list which are not in the second.

Example:

Specification of the list [1,..,6], apart from the first 3 elements.

OpenMath XML (source)

<OMOBJ xmlns="http://www.openmath.org/OpenMath" version="2.0">
  <OMA><OMS cd="relation1" name="eq"/>
       <OMA><OMS cd="list3" name="difference"/>
            <OMA><OMS cd="list1" name="list"/>
                 <OMI> 1 </OMI>      <OMI> 2 </OMI>      <OMI> 3 </OMI>
                 <OMI> 4 </OMI>      <OMI> 5 </OMI>      <OMI> 6 </OMI>
            </OMA>
            <OMA><OMS cd="list1" name="list"/>
                 <OMI> 1 </OMI>      <OMI> 2 </OMI>      <OMI> 3 </OMI>
            </OMA>
       </OMA>
       <OMA><OMS cd="list1" name="list"/>
            <OMI> 4 </OMI>      <OMI> 5 </OMI>      <OMI> 6 </OMI>
       </OMA>
  </OMA>
</OMOBJ>

Strict Content MathML

<math xmlns="http://www.w3.org/1998/Math/MathML">
 <apply><csymbol cd="relation1">eq</csymbol>
  <apply><csymbol cd="list3">difference</csymbol>
   <apply><csymbol cd="list1">list</csymbol>
    <cn>1</cn>
    <cn>2</cn>
    <cn>3</cn>
    <cn>4</cn>
    <cn>5</cn>
    <cn>6</cn>
   </apply>
   <apply><csymbol cd="list1">list</csymbol><cn>1</cn><cn>2</cn><cn>3</cn></apply>
  </apply>
  <apply><csymbol cd="list1">list</csymbol><cn>4</cn><cn>5</cn><cn>6</cn></apply>
 </apply>
</math>

Prefix

eq (difference (list ( 1 , 2 , 3 , 4 , 5 , 6 ) , list ( 1 , 2 , 3 ) ) , list ( 4 , 5 , 6 ) )

Popcorn

list3.difference([1 , 2 , 3 , 4 , 5 , 6], [1 , 2 , 3]) = [4 , 5 , 6]

Rendered Presentation MathML

$$\mathrm{difference}((1,2,3,4,5,6),(1,2,3))=(4,5,6)$$

Signatures:

sts

select

Description:

This symbol takes two lists as arguments, L and M say. The second argument is a list containing only entries from [1..n], where n is the length of L. The symbol represents the function which returns a list whose length is equal to the length of M, and having at position k the value of L at position M_k.

Example:

OpenMath XML (source)

<OMOBJ xmlns="http://www.openmath.org/OpenMath" version="2.0">
  <OMA><OMS name="eq" cd="relation1"/>
       <OMA><OMS cd="list3" name="select"/>
            <OMA><OMS cd="list1" name="list"/>
                 <OMI> 4 </OMI>      <OMI> 5 </OMI>      <OMI> 6 </OMI>
                 <OMI> 7 </OMI>      <OMI> 8 </OMI>      <OMI> 9 </OMI>
            </OMA>
            <OMA><OMS cd="list1" name="list"/>
                 <OMI> 3 </OMI>      <OMI> 5 </OMI>
                 <OMI> 2 </OMI>      <OMI> 2 </OMI>
            </OMA>
       </OMA>
       <OMA><OMS cd="list1" name="list"/>
            <OMI> 6 </OMI>   <OMI> 8 </OMI>
            <OMI> 5 </OMI>   <OMI> 5 </OMI>
       </OMA>
  </OMA>
</OMOBJ>

Strict Content MathML

<math xmlns="http://www.w3.org/1998/Math/MathML">
 <apply><csymbol cd="relation1">eq</csymbol>
  <apply><csymbol cd="list3">select</csymbol>
   <apply><csymbol cd="list1">list</csymbol>
    <cn>4</cn>
    <cn>5</cn>
    <cn>6</cn>
    <cn>7</cn>
    <cn>8</cn>
    <cn>9</cn>
   </apply>
   <apply><csymbol cd="list1">list</csymbol>
    <cn>3</cn>
    <cn>5</cn>
    <cn>2</cn>
    <cn>2</cn>
   </apply>
  </apply>
  <apply><csymbol cd="list1">list</csymbol>
   <cn>6</cn>
   <cn>8</cn>
   <cn>5</cn>
   <cn>5</cn>
  </apply>
 </apply>
</math>

Prefix

eq (select (list ( 4 , 5 , 6 , 7 , 8 , 9 ) , list ( 3 , 5 , 2 , 2 ) ) , list ( 6 , 8 , 5 , 5 ) )

Popcorn

list3.select([4 , 5 , 6 , 7 , 8 , 9], [3 , 5 , 2 , 2]) = [6 , 8 , 5 , 5]

Rendered Presentation MathML

$$\mathrm{select}((4,5,6,7,8,9),(3,5,2,2))=(6,8,5,5)$$

Signatures:

sts