  Index

# _space_group.transform_Pp_abc

Name:
'_space_group.transform_Pp_abc'

Definition:

```   This item specifies the transformation (P,p) of the basis
vectors from the setting used in the CIF (a,b,c) to the
reference setting given in _space_group.reference_setting
(a',b',c'). The value is given in Jones-Faithful notation
corresponding to the rotational matrix P combined with the
origin shift vector p in the expression:

(a',b',c') = (a,b,c)P + p.

P is a post-multiplication matrix of a row (a,b,c) of column
vectors. It is related to the inverse transformation (Q,q) by:

P = Q^-1^
p = Pq = -(Q^-1^)q.

These transformations are applied as follows:

atomic coordinates  (x',y',z') = Q(x,y,z) + q
Miller indices      (h',k',l') = (h,k,l)P
symmetry operations         W' = (Q,q)W(P,p)
basis vectors       (a',b',c') = (a,b,c)P + p

This item is given as a character string involving the
characters a, b and c with commas separating the expressions
for the a', b' and c' vectors. The numeric values may be
given as integers, fractions or real numbers. Multiplication
is implicit, division must be explicit. White space within
the string is optional.

```

Examples:

 '-b+c, a+c, -a+b+c' R3:r to R3:h
 'a-1/4, b-1/4, c-1/4' Pnnn:1 to Pnnn:2
 'b-1/2, c-1/2, a-1/2' Bbab:1 to Ccca:2

Mandatory item: no

Category: space_group