Module dimension 

Buckingham-π dimensional reduction (a discovery prior for phop).

In the pure EML grammar every internal node is exp(x) − ln(y), so every argument to a node must be dimensionless. An in-loss dimensional penalty on single-variable leaves would therefore be degenerate (it could only forbid using a dimensioned variable at all). The productive, EML-appropriate way to bring dimensional analysis into the search — the same way AI-Feynman uses it — is as a preprocessing reduction: combine the dimensioned inputs into the maximal set of independent dimensionless groups (the Buckingham-π theorem) and let phop discover a law over those. The number of groups is n_features − rank(D), where D is the dimension matrix.

Each feature carries a Dimension — integer exponents over the seven SI base units [s, m, kg, A, K, mol, cd]. pi_groups returns an integer basis of the nullspace of D (each basis vector e gives a dimensionless monomial ∏ xᵢ^{eᵢ}); DataSet::to_dimensionless materializes those monomials as the new feature columns.

Constants

DIMENSIONLESS

The dimensionless dimension (all exponents zero).

LENGTH

Length [m].

MASS

Mass [kg].

TIME

Time [s].

Functions

pi_groups

Integer basis of the nullspace of the dimension matrix of dims.

Type Aliases

Dimension

Integer exponents over the seven SI base units [s, m, kg, A, K, mol, cd].