slatex / sTeX

A semantic Extension of TeX/LaTeX
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pointwise and scalar operations on function sequences. #301

Open kohlhase opened 2 years ago

kohlhase commented 2 years ago

I want to preload

Screenshot 2022-05-08 at 12 16 19

And I already have in MiKoMH/AI/source/game-play/mod/linear-evaluation.en.tex:

    \begin{sdefinition}
      \vardef{varn}[name=n,type=\NaturalNumbers]{\comp{n}}
      \varseq{seqw}[name=w,type=\RealNumbers]1\varn{\comp{w}_{#1}}
      \varseq{seqf}[name=f,type=\funspace\RealNumbers\RealNumbers]1\varn{\comp{f}_{#1}}

      A common approach is to use a \definame{weighted-linear-function} for $f$,
      i.e. given a set of \symname[post=s]{feature}
      $\fun{\seqf{i}}\RealNumbers\RealNumbers$ and a corresponding sequence of
      \symname[post=s]{weight}, $\inset{\seqw{i}}\RealNumbers$ $f$ is of the form:
       \[\fundefeq{x}{\apply{f}x}{\seqw{1}\seqf{1}+\seqw{2}\seqf{2}+\cdots+\seqw{n}\seqf{n}}\]
  \end{sdefinition}

To preload the last line of the definition I would like to write something like \pointwiseop\realadd{\scalarop\realtimes\seqw\seqf} probably a couple of times eta-expanded or so.

Here I think of a flexary operator \pointwiseop that takes an operator G->G->G and functions ?->G and gives a function ?-G, i.e. something like

\symdef{pointwiseop}[args=ia]{#1}{##1 #1 ##2}

hmmm, that also makes little sense so far, since that mixes levels, ...

I hope that @Jazzpirate can make sense of this.