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Previously asked at MSE: Briefly speaking, I'm looking for a description of the equational theory of the orthocenter function, $\mathsf{orth}$. By $\mathsf{orth}$ I mean the (partial) function sending ...

Let $T$ be the "almost everywhere" equational theory of the orthocenter function, "tweaked appropriately" to avoid partiality issues (see this earlier question of mine for details)....