OpenMath Content Dictionary: set1p

Canonical URL:

CD File:

set1p.ocd

CD as XML Encoded OpenMath:

set1p.omcd

Defines:

cartesian_product_n

Date:

2002-10-04

Version:

0 (Revision 1)

Review Date:

2017-12-31

Status:

experimental

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  Author: Nobuki Takayama

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cartesian_product_n

Description:

the cartesian product of n copies of the first argument. Binary function.

Commented Mathematical property (CMP):

$ Z^m \times Z^n = Z^{m+n} $

Formal Mathematical property (FMP):

OpenMath XML (source)

<OMOBJ xmlns="http://www.openmath.org/OpenMath">
  <OMA><OMS cd="relation1" name="eq"/>
    <OMA><OMS cd="set1" name="cartesian_product"/>
      <OMA><OMS cd="set1p" name="cartesian_product_n"/>
        <OMS cd="setname1" name="Z"/>
        <OMV name="m"/>
      </OMA>
      <OMA><OMS cd="set1p" name="cartesian_product_n"/>
        <OMS cd="setname1" name="Z"/>
        <OMV name="n"/>
      </OMA>
    </OMA>
    <OMA><OMS cd="set1p" name="cartesian_product_n"/>
      <OMS cd="setname1" name="Z"/>
      <OMA><OMS cd="arith1" name="plus"/>
        <OMV name="m"/>
        <OMV name="n"/>
      </OMA>
    </OMA>
  </OMA>
</OMOBJ>

Strict Content MathML

<math xmlns="http://www.w3.org/1998/Math/MathML">
 <apply><csymbol cd="relation1">eq</csymbol>
  <apply><csymbol cd="set1">cartesian_product</csymbol>
   <apply><csymbol cd="set1p">cartesian_product_n</csymbol><csymbol cd="setname1">Z</csymbol><ci>m</ci></apply>
   <apply><csymbol cd="set1p">cartesian_product_n</csymbol><csymbol cd="setname1">Z</csymbol><ci>n</ci></apply>
  </apply>
  <apply><csymbol cd="set1p">cartesian_product_n</csymbol>
   <csymbol cd="setname1">Z</csymbol>
   <apply><csymbol cd="arith1">plus</csymbol><ci>m</ci><ci>n</ci></apply>
  </apply>
 </apply>
</math>

Prefix

eq (cartesian_product (cartesian_product_n (Z, m) , cartesian_product_n (Z, n) ) , cartesian_product_n (Z, plus ( m, n) ) )

Popcorn

set1.cartesian_product(set1p.cartesian_product_n(setname1.Z, $m), set1p.cartesian_product_n(setname1.Z, $n)) = set1p.cartesian_product_n(setname1.Z, $m + $n)

Rendered Presentation MathML

$$\mathrm{cartesian\_product\_n}(\mathbb{Z},m)\times \mathrm{cartesian\_product\_n}(\mathbb{Z},n)=\mathrm{cartesian\_product\_n}(\mathbb{Z},m+n)$$

Signatures:

sts

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