A proposal for vector math in ADQL

With tables containing massive amounts of vectors (e.g., the collections of low-resolution spectra within Gaia DR3 or the Digitised Byurakan Surveys), giving TAP users a toolset to do server-side work with arrays becomes highly desirable and will significantly enhance the power of ADQL to do server-side analyses. This is an attempt to provide a baseline feature set for that.

TAP servers supporting this should declare that by defining a language feature. While no IVOA specification exists for array operations, use the VECTORMATH key from GAVO's ADQL extensions standards record, like this:

<languageFeatures type="ivo://org.gavo.dc/std/exts#extra-adql-keywords">
  <feature>
    <form>VECTORMATH</form>
      <description>You can compute with vectors here. See
        https://wiki.ivoa.net/twiki/bin/view/IVOA/ADQLVectorMath
        for an overview of the functions and operators available.
      </description>
   </feature>
</languageFeatures>

Basic Math

• vec1+vec2 is the component-wise sum of two vectors. Where vec1 and vec2 have unequal length, the result is padded with NaNs to the length of the longer vector.
• vec1-vec2 is the component-wise difference of two vectors. Where vec1 and vec2 have unequal length, the result is padded with NaNs to the length of the longer vector.
• vec1*vec2 is the scalar product of two vectors. Where vec1 and vec2 have unequal length, the shorter vector is padded with NaNs to the length of the longer vector. That is, the scalar product of vectors of unequal length is NaN.
• scal*vec and vec*scal is the scalar multiplication of a vector.