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I've checked the other parts properly take absolute values of determinants.

Here are a few ones that should be investigated:

I am not confident with the mat_get_determinant_d3 in spacegroup.c.
@atztogo Are these if-statements fine without taking absolute values?

mat_get_determinant_d3(orig_lattice) > symprec in spacegroup.c is used to find (a, b, c) vectors similar to the user input basis vectors.

Depending on symmetry, spglib might result in permutations like (b, c, a), etc., but it tries to align to (a, b, c). If the input basis vectors are in a left-handed coordinate system, spglib does not attempt to align them.

mat_get_determinant_d3(orig_lattice) > symprec in spacegroup.c is used to find (a, b, c) vectors similar to the user input basis vectors.

I see. I understand abs are not required for these parts.

I am still lost on this, probably because the naming orig_lattice is not descriptive. What happens if there are 2 permutations of the vector such that it is positive again? What does the determinant and its absolute mean in this case?

I am still lost on this, probably because the naming orig_lattice is not descriptive. What happens if there are 2 permutations of the vector such that it is positive again? What does the determinant and its absolute mean in this case?

I may not understand your question fully, but it happens. The determinant is mostly used for calculating the volume of the unit cell (primitive cell, conventional unit cell, some cell that arises intermediately, etc), for which we take absolute. The volume can be used for various check for consistency check. For example, volume is not around zero, ratio of volumes of two cells is about integer, etc. When we want to check right handed or left handed, we don't take absolute. Positive or negative is checked. If negative, in some routine, the basis vectors are changed to right handed.

I may not understand your question fully, but it happens. The determinant is mostly used for calculating the volume of the unit cell (primitive cell, conventional unit cell, some cell that arises intermediately, etc), for which we take absolute. The volume can be used for various check for consistency check. For example, volume is not around zero, ratio of volumes of two cells is about integer, etc. When we want to check right handed or left handed, we don't take absolute. Positive or negative is checked. If negative, in some routine, the basis vectors are changed to right handed.

Ok, but what about in the context of the 4 snippets above? According to the explanation it is only checking if the basis set is right-handed, but then why does it completely throw away the left-handed ones? Is it always supposed to be right-handed in that case, and if so an assert should be added to clarify it. Why are some checks against mat_get_determinant_d3() < 0, while the inverse is against mat_get_determinant_d3() > symprec if they are only checking for left/right handiness.

It is not theoretical. It is just for letting users feel better. This is not a mandatory procedure. So we don't need to be strict.

Spglib returns transformation matrix, which suggest basis vectors of a conventinal unit cell (a_s, b_s, c_s) as written athttps://spglib.readthedocs.io/en/latest/definition.html#transformation-matrix-boldsymbol-p-and-origin-shift-boldsymbol-p.

If the user input cell (a, b, c) is right handed and conventional unit cell, I wanted to return similar basis vectors in Cartesian coordinates, (a, b, c) ~ (a_s, b_s, c_s). But since the returned basis vectors must be right handed per definition, if the user input cell is left handed, these never become similar. So searching similar basis vectors is not performed.