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"Not a CAS operation" is not a reason: the Math OS rule in AGENTS.md #1216

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Rafael-SOWNet merged 1 commit into from
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"Not a CAS operation" is not a reason: the Math OS rule in AGENTS.md #1216

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21 changes: 19 additions & 2 deletions AGENTS.md
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For AI agents working on AngouriMath. Humans: [CONTRIBUTING.md](CONTRIBUTING.md) is yours, and
everything below applies to you too.

AngouriMath is a computer algebra system. The thing being built is *mathematics*, and the code is
how it is expressed. Read this as instructions for doing mathematics well, using C# and F#.
AngouriMath is a Math OS in the making — [#746](https://github.com/asc-community/AngouriMath/issues/746)
says what that means — of which the computer algebra system is the part that exists. The thing being
built is *mathematics*, and the code is how it is expressed. Read this as instructions for doing
mathematics well, using C# and F#.

## The one rule everything else follows from

Expand Down Expand Up @@ -83,6 +85,21 @@ needed three branches on the sign of `a`; the answer is the single interval `[-|
for either sign and for `a = 0`, and it collapses to exactly the old output when the roots are
concrete. Enumerating cases is usually a sign that an identity has been missed.

### "Not a CAS operation" is not a reason either

This is a Math OS ([#746](https://github.com/asc-community/AngouriMath/issues/746)), not a computer
algebra system that happens to do calculus. A question is not out of scope because its notation is
statistical, combinatorial, number-theoretic or about a sequence: an expectation over a distribution,
a probability of an event, a recurrence and the limit of the sequence it defines, a divisibility, a
count of the members of a set, an extremum over an interval, the inverse of a named function. Each
of those is mathematical notation with a definition, and the definition is what to fit as a node —
the closest symbol the mathematics already uses, not an English word and not a note saying the
library does not do that kind of thing. `sum` and `integral` are binders that reduce to arithmetic;
`E[f(X)]` for `X ~ U(0, 1)` reduces to an integral the same way, and a node that reduces is a node
worth having. Where the reduction is a theorem rather than a computation, say which theorem and
what the node would need to state it, and leave the answer unevaluated rather than absent.
[#1212](https://github.com/asc-community/AngouriMath/issues/1212) is where this was said.

## Output has a contract too

**Parsing what `Stringize` prints must give back the expression it printed.** Anything else makes
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