Dimensional analysis of a formula: MathS.Dimensions.Of and DimensionlessGroups #2292

What it is. Given the dimension of each variable (a map Variable → Dimension over the seven SI base dimensions, with rational exponents), say whether a formula is physically meaningful, what dimension it has, and where it stops making sense; and give the Buckingham π groups of a set of variables.

var (L, T) = (Dimension.Length, Dimension.Time);
var dims = new Dictionary<Entity.Variable, Dimension> { ["g"] = L / T.Pow(2), ["h"] = L, ["t"] = T };
MathS.Dimensions.Of("sqrt(2 g h)", dims);   // Consistent: L T^-1
MathS.Dimensions.Of("h + g t", dims);       // Inconsistent at h + g * t: h has dimension L and g * t has dimension L T^-1, ...
// pipe: rho M L^-3, v L T^-1, d L, mu M L^-1 T^-1
MathS.Dimensions.DimensionlessGroups(new Entity.Variable[] { "rho", "v", "d", "mu" }, pipe);   // [ mu / (rho * v * d) ]

Why here. Units libraries (UnitsNet) check values; nothing in .NET checks a formula. The walk needs every node type, which the kernel has.

Design points to agree on.

• The dimension map is passed, not attached to variables, so nothing about printing, parsing or simplification changes, and the type layer of Typed variables #1237 / Pending breakages: changes agreed or arguable that cannot ship before a major version #1019 is not pre-empted.
• Three-valued: Consistent, Inconsistent (with the subexpression and a reason), Undetermined (undeclared variable, unread node, dimensional base to a symbolic power). Never a guess.
• Nothing is simplified first: sin(x) - sin(x) with x a length is inconsistent.
• A literal 0 or oo fits any dimension where added or compared (v = 0).
• Exponents of a dimensional base must be rational; L^pi is inconsistent.

Packaging (Packaging.md §4). No clause fires: no dependency, no floor raise, no data, composes the kernel; not on any default path, so (B) does not apply. → kernel. A UnitsNet bridge would be (D) and separate; not part of this.

Implementation, for judging the design against working code. Branch feat/dimensional-analysis, one commit on master 87a0eff: Functions/Dimensions/*, Convenience/MathS.Dimensions.cs, Tests/UnitTests/Convenience/DimensionsTest.cs (38 cases), +54 lines of PublicApi.txt. UnitTests 18335 passed / 13 skipped, FSharpWrapperUnitTests 134 passed. No existing answer moves, so no BREAKING-CHANGES entry. The pull request will follow Accepted.

Worked use, together with the shader-source feature (#2293). A water wave from ω² = g k tanh(k h): the check gives ω the dimension T⁻¹ and rejects the shallow-water typo ω = √(g k h) inside the phase; the π groups are k A, k h and g k t².

Milestone: 2.7.0 (additive).