httk.atomistic.cell

The Cell class for httk-atomistic.

Classes

Cell	A crystallographic cell: its basis, the 3x3 matrix of cell vectors, held exactly.

Module Contents

class httk.atomistic.cell.Cell(basis: httk.core.VectorLike, scale: Any = 1)

A crystallographic cell: its basis, the 3x3 matrix of cell vectors, held exactly.

The lattice vectors are the rows of basis. Internally a Cell factors that basis into a positive SurdScalar scale times an unscaled_basis (a SurdVector of shape (3, 3)), with basis == scale * unscaled_basis. The split lets an overall length factor be carried symbolically: a hexagonal cell of lattice parameter a and ratio c/a is the exact unscaled rows (1, 0, 0), (-1/2, sqrt(3)/2, 0), (0, 0, c/a) scaled by a — so the sqrt(3) stays exact regardless of a. A cell built from an absolute basis simply has scale == 1.

Numbers embed exactly: rationals (and rational-valued floats) stay rational, and a SurdVector basis keeps its radicals. Derived quantities are exact whenever the geometry is metric-rational (the crystallographic case): lengths come from sqrt_of() of the rational squared row lengths, angles (degrees) from the exact reverse-Niven acos_degrees() where possible, volume from the exact determinant, and metric is the exact rational Gram matrix. When a squared length happens to be irrational, lengths/angles fall back to a deterministic rational approximation (documented per accessor). Exact accessors return vector objects — render them with .to_floats() (nested plain-float lists, numpy-free), float(...) on scalars, numeric() (true numpy arrays), or a view of your choice.

property scale: httk.core.SurdScalar

The overall (strictly positive) length factor, as an exact SurdScalar.

property unscaled_basis: httk.core.SurdVector

The 3x3 cell vectors before applying scale, as an exact SurdVector.

property basis: httk.core.SurdVector

The 3x3 lattice vectors scale * unscaled_basis (one vector per row), exact.

numeric() → httk.atomistic.numeric_cell.NumericCell

A plain-numpy presentation of this cell (requires the httk-atomistic[numpy] extra).

metric() → httk.core.SurdVector

The exact Gram matrix matrix * matrix^T (rational for a metric-rational cell).

property lengths: tuple[httk.core.SurdScalar, Ellipsis]

The lengths of the three cell vectors (the scaled row norms).

Exact via sqrt_of() whenever the row’s squared length is rational (the crystallographic case); otherwise a deterministic rational-approximation SurdScalar at _FALLBACK_PREC (the length would be a nested radical, outside the surd field).

property angles: tuple[fractions.Fraction, Ellipsis]

The cell angles (alpha, beta, gamma) in degrees, as exact Fraction values.

Following the crystallographic convention, alpha is the angle between rows b and c, beta between a and c, and gamma between a and b. Angles are scale-independent, so they are computed from the unscaled basis. The cosine is formed exactly in the surd field and reversed through the Niven table (acos_degrees()) for an exact answer; a non-Niven angle falls back to a deterministic acos() at _FALLBACK_PREC.

property volume: httk.core.SurdScalar

The cell volume, the exact absolute determinant of basis.