[Om] Can OpenMath-Objects be compared to another in terms of equality?

[David Carlisle]

On 22/02/2019 01:57, Phu Nguyen wrote:
> im actually interested in comparing two OpenMath-Objects with each other 
> in terms of equality (despite being build a bit differently in XML) by 
> using Java.
> 
> For example I want "x^2+2x-35=0" to be equal to "-35+2x+x^2=0".
> 
> So im wondering if there is a way to achieve this. I at least understand 
> OpenMath as some sort of tree structure and thought there might be a way 
> to compare them.
> 
> I already tried writing the expressions for those two equations, but 
> ended up with no luck or good idea.
> 
> *|Equation 1: x^2+2x-35=0|*/|<OMOBJ xmlns='http://www.openmath.org/OpenMath' version='2.0' 
> cdbase='http://www.openmath.org/cd'> <OMA> <OMS cd='relation1' 
> name='eq'/> <OMA> <OMS cd='arith1' name='minus'/> <OMA> <OMS cd='arith1' 
> name='plus'/> <OMA> <OMS cd='arith1' name='power'/> <OMV name='x'/> 
> <OMI> 2 </OMI> </OMA> <OMA style='invisible'> <OMS cd='arith1' 
> name='times'/> <OMI> 2 </OMI> <OMV name='x'/> </OMA> </OMA> <OMI> 35 
> </OMI> </OMA> <OMI> 0 </OMI> </OMA> </OMOBJ> |/*|Equation 2: -35+2x+x^2|*/|<OMOBJ xmlns='http://www.openmath.org/OpenMath' version='2.0' 
> cdbase='http://www.openmath.org/cd'> <OMA> <OMS cd='relation1' 
> name='eq'/> <OMA> <OMS cd='arith1' name='plus'/> <OMA> <OMS cd='arith1' 
> name='unary_minus'/> <OMI> 35 </OMI> </OMA> <OMA style='invisible'> <OMS 
> cd='arith1' name='times'/> <OMI> 2 </OMI> <OMV name='x'/> </OMA> <OMA> 
> <OMS cd='arith1' name='power'/> <OMV name='x'/> <OMI> 2 </OMI> </OMA> 
> </OMA> <OMI> 0 </OMI> </OMA> </OMOBJ>|/
> 
> Thank you for your time
> 
> Sincerely
> 
> Phu
> 

The usual OpenMath model is that it encodes the data in a system-neutral 
way, but reasoning about that data happens in the application, so 
typically you'd import the two OpenMath polynomials into a computer 
algebra system test for equality and write out an OpenMath boolean.

If writing custom code it would be easier to check for equality if using 
a specific more constrained polynomial constructor rather than generic 
symbolic arith1 expressions.
unfortunately there are several possible formulations so all are classed 
as experimental but in for example

https://www.openmath.org/cd/polyr.html

such a polynomial is just modelled as a sequence of the coefficients in 
order of exponent on the variable, and so the two forms you show would
be normalized to the same thing while creating the OpenMath (which may 
or may not be a good thing, depending on the use case)

David

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