Add the non-kernel functions: Sigmoid, Average, VectorLength (#321)

[Rafael-SOWNet]

Addresses #321.

Three functions worth being able to write, which need no node of their own because the kernel can already say what they mean:

Sigmoid(x)	1 / (1 + e ^ (-x))
Average(m)	the sum of a matrix's cells over their count
VectorLength(v)	Abs of the vector

VectorLength is a name, not a capability

abs([3, 4]) has always answered 5 — which is exactly @WhiteBlackGoose's observation on the issue:

VectorLength is Abs. Avg will take Matrix as an argument. Sigmoid will take Entity.

So it is here so the operation can be found under the name a caller reaches for, and a test requires the two to agree, so they cannot drift into two definitions of one thing.

Being an ordinary expression is the point

Nothing in this PR teaches the library to differentiate a sigmoid or take its limit. Both work anyway, and the tests are written to show that rather than to check one-line formulas:

d/dx Sigmoid(x)   ->  e ^ (-x) / (e ^ (-x) + 1) ^ 2
Sigmoid at +oo    ->  1
Sigmoid at -oo    ->  0

Adding a node instead would mean the eleven steps of Docs/Contributing/AddingNode.cs and a new shape for every rule to ignore, for no reach these do not already have. That is what "non-kernel" buys.

Average is symbolic: of [a, b] it is (a + b) / 2 rather than a refusal.

Scope, against the issue's checklist

• Taylor series was already implemented and ticked — I verified rather than assumed.
• Max / Min / Mean are struck through on the issue.
• Mode and median are not expressible this way, which is why @Happypig375 and @WhiteBlackGoose disagreed about them in the thread. This PR does not settle that, and I would rather it were decided on the issue than smuggled in here.

Evidence

• suite 7274 passed, 0 failed, 14 skipped
• 11 new tests, including that VectorLength and Abs agree, that Average reads every cell of a 2×2 matrix, and that null is refused rather than dereferenced
• PublicApi.txt regenerated: three members added, nothing else moved
• purely additive — no answer changes, so no BREAKING-CHANGES.md entry

🤖 Generated with Claude Code