OpenMath

OpenMath is an extensible standard for representing the semantics of mathematical objects.

https://openmath.github.io

OpenMath Signatures

Type System: sts
Content Dictionary: polyd
CD Signature File: polyd.sts

official 
               
Date:  2001-10-12
Author: Bill Naylor

DMP 

<OMOBJ xmlns="http://www.openmath.org/OpenMath"> 
  <OMA>
    <OMS name="mapsto" cd="sts"/>
    <OMA>
      <OMS name="structure" cd="sts"/>
      <OMS name="polynomial_ring" cd="polysts"/>
    </OMA>
    <OMV name="SDMPObject"/>
    <OMS name="polynomial_ring" cd="polysts"/>
  </OMA>
</OMOBJ>
( polynomial_ring SDMPObject >> polynomial_ring )

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DMPL 

<OMOBJ xmlns="http://www.openmath.org/OpenMath"> 
  <OMA>
    <OMS name="mapsto" cd="sts"/>
    <OMA>
      <OMS name="structure" cd="sts"/>
      <OMS name="polynomial_ring" cd="polysts"/>
    </OMA>
    <OMA>
      <OMS name="nary" cd="sts"/>
      <OMS name="SDMP" cd="polyd"/>
    </OMA>
    <OMV name="PolynomialRingList"/>
  </OMA>
</OMOBJ>
( polynomial_ring ( SDMP * ) >> PolynomialRingList )

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SDMP 

<OMOBJ xmlns="http://www.openmath.org/OpenMath"> 
  <OMA>
    <OMS name="mapsto" cd="sts"/>
    <OMA>
      <OMS name="nary" cd="sts"/>
      <OMV name="MonomialD"/>
    </OMA>
    <OMV name="SDMPObject"/>
  </OMA>
</OMOBJ>
( ( MonomialD * ) >> SDMPObject )

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term 

<OMOBJ xmlns="http://www.openmath.org/OpenMath"> 
  <OMA>
    <OMS name="mapsto" cd="sts"/>
    <OMV name="Ring"/>
    <OMA>
      <OMS name="nary" cd="sts"/>
      <OMS name="N" cd="setname1"/>
    </OMA>
    <OMV name="MonomialD"/>
  </OMA>
</OMOBJ>
( Ring ( N * ) >> MonomialD )

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poly_ring_d 

<OMOBJ xmlns="http://www.openmath.org/OpenMath"> 
  <OMA>
    <OMS name="mapsto" cd="sts"/>
    <OMA>
      <OMS name="structure" cd="sts"/>
      <OMV name="Ring"/>
    </OMA>
    <OMV name="PositiveInteger"/>
    <OMA>
      <OMS name="structure" cd="sts"/>
      <OMS name="polynomial_ring" cd="polysts"/>
    </OMA>
  </OMA>
</OMOBJ>
( Ring PositiveInteger >> polynomial_ring )

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poly_ring_d_named 

<OMOBJ xmlns="http://www.openmath.org/OpenMath"> 
  <OMA>
    <OMS name="mapsto" cd="sts"/>
    <OMA>
      <OMS name="structure" cd="sts"/>
      <OMV name="Ring"/>
    </OMA>
    <OMA>
      <OMS name="nary" cd="sts"/>
      <OMV name="PolynomialVariable"/>
    </OMA>
    <OMA>
      <OMS name="structure" cd="sts"/>
      <OMS name="polynomial_ring" cd="polysts"/>
    </OMA>
  </OMA>
</OMOBJ>
( Ring ( PolynomialVariable * ) >> polynomial_ring )

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anonymous 

<OMOBJ xmlns="http://www.openmath.org/OpenMath"> 
  <OMV name="PolynomialVariable"/>
</OMOBJ>
PolynomialVariable

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ordering 

<OMOBJ xmlns="http://www.openmath.org/OpenMath"> 
  <OMS name="Object" cd="sts"/>
</OMOBJ>
Object

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lexicographic 

<OMOBJ xmlns="http://www.openmath.org/OpenMath"> 
  <OMS name="ordering" cd="polyd"/>
</OMOBJ>
ordering

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reverse_lexicographic 

<OMOBJ xmlns="http://www.openmath.org/OpenMath"> 
  <OMS name="ordering" cd="polyd"/>
</OMOBJ>
ordering

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graded_lexicographic 

<OMOBJ xmlns="http://www.openmath.org/OpenMath"> 
  <OMS name="ordering" cd="polyd"/>
</OMOBJ>
ordering

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graded_reverse_lexicographic 

<OMOBJ xmlns="http://www.openmath.org/OpenMath"> 
  <OMS name="ordering" cd="polyd"/>
</OMOBJ>
ordering

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elimination 

<OMOBJ xmlns="http://www.openmath.org/OpenMath"> 
  <OMA>
    <OMS name="mapsto" cd="sts"/>
    <OMS name="N" cd="setname1"/>
    <OMS name="ordering" cd="polyd"/>
    <OMS name="ordering" cd="polyd"/>
    <OMS name="ordering" cd="polyd"/>
  </OMA>
</OMOBJ>
( N ordering ordering >> ordering )

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matrix_ordering 

<OMOBJ xmlns="http://www.openmath.org/OpenMath"> 
  <OMA>
    <OMS name="mapsto" cd="sts"/>
    <OMV name="OrderingMatrix"/>
    <OMS name="ordering" cd="polyd"/>
  </OMA>
</OMOBJ>
( OrderingMatrix >> ordering )

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weighted 

<OMOBJ xmlns="http://www.openmath.org/OpenMath"> 
  <OMA>
    <OMS name="mapsto" cd="sts"/>
    <OMV name="IntWeightList"/>
    <OMS name="ordering" cd="polyd"/>
    <OMS name="ordering" cd="polyd"/>
  </OMA>
</OMOBJ>
( IntWeightList ordering >> ordering )

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   Note that N is not right, since weights can be negative

weighted_degree 

<OMOBJ xmlns="http://www.openmath.org/OpenMath"> 
 <OMA>
   <OMS name="mapsto" cd="sts"/>
    <OMS name="polynomial_ring" cd="polysts"/>
    <OMS name="Z" cd="setname1"/>
 </OMA>
</OMOBJ>
( polynomial_ring >> Z )

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groebnered 

<OMOBJ xmlns="http://www.openmath.org/OpenMath"> 
  <OMA>
    <OMS name="mapsto" cd="sts"/>
    <OMS name="ordering" cd="polyd"/>
    <OMV name="PolynomialRingList"/>
    <OMV name="GroebnerBasis"/>
  </OMA>
</OMOBJ>
( ordering PolynomialRingList >> GroebnerBasis )

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completely_reduced 

<OMOBJ xmlns="http://www.openmath.org/OpenMath"> 
  <OMS name="Object" cd="sts"/>
</OMOBJ>
Object

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plus 

<OMOBJ xmlns="http://www.openmath.org/OpenMath"> 
  <OMA>
    <OMS name="mapsto" cd="sts"/>
    <OMV name="PolynomialRingList"/>
    <OMA>
      <OMS name="poly_ring_d" cd="polyd"/>
      <OMV name="Ring"/>
      <OMS name="Z" cd="setname1"/>
    </OMA>
  </OMA>
</OMOBJ>
( PolynomialRingList >> poly_ring_d Ring Z )

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times 

<OMOBJ xmlns="http://www.openmath.org/OpenMath"> 
  <OMA>
    <OMS name="mapsto" cd="sts"/>
    <OMV name="PolynomialRingList"/>
    <OMA>
      <OMS name="poly_ring_d" cd="polyd"/>
      <OMV name="Ring"/>
      <OMS name="Z" cd="setname1"/>
    </OMA>
  </OMA>
</OMOBJ>
( PolynomialRingList >> poly_ring_d Ring Z )

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power 

<OMOBJ xmlns="http://www.openmath.org/OpenMath"> 
  <OMA>
    <OMS name="mapsto" cd="sts"/>
    <OMV name="PolynomialR"/>
    <OMS name="Z" cd="setname1"/>
    <OMA>
      <OMS name="poly_ring_d" cd="polyd"/>
      <OMV name="Ring"/>
      <OMS name="Z" cd="setname1"/>
    </OMA>
  </OMA>
</OMOBJ>
( PolynomialR Z >> poly_ring_d Ring Z )

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groebner 

<OMOBJ xmlns="http://www.openmath.org/OpenMath"> 
  <OMA>
    <OMS name="mapsto" cd="sts"/>
    <OMS name="ordering" cd="polyd"/>
    <OMV name="PolynomialRingList"/>
    <OMV name="GroebnerBasis"/>
  </OMA>
</OMOBJ>
( ordering PolynomialRingList >> GroebnerBasis )

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reduce 

<OMOBJ xmlns="http://www.openmath.org/OpenMath"> 
  <OMA>
    <OMS name="mapsto" cd="sts"/>
    <OMV name="PolynomialRing"/>
    <OMV name="GroebnerBasis"/>
    <OMS name="polynomial_ring" cd="polysts"/>
  </OMA>
</OMOBJ>
( PolynomialRing GroebnerBasis >> polynomial_ring )

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