From 57056f658bbba0ea1b3dd9fece8dc00c17e2dade Mon Sep 17 00:00:00 2001 From: Sebastiano Tronto Date: Fri, 29 Mar 2024 12:37:10 +0100 Subject: Some fixes to the coordinate page --- src/speedcubing/coordinates/coordinates.md | 26 +++++++++++++------------- 1 file changed, 13 insertions(+), 13 deletions(-) (limited to 'src/speedcubing/coordinates') diff --git a/src/speedcubing/coordinates/coordinates.md b/src/speedcubing/coordinates/coordinates.md index 5640bca..afae46f 100644 --- a/src/speedcubing/coordinates/coordinates.md +++ b/src/speedcubing/coordinates/coordinates.md @@ -36,7 +36,7 @@ To work with cube coordinates, we need to implement the following: valid cube object. * A function `move()` that takes as input a coordinate, a move m and an integer x in [0..n-1] and returns an integer y in [0..n-1] such - that `y == index(m(to_cube(x)))` (here m(c) is the cube c moved by m). + that `y == index(m(to_cube(x)))` (here `m(c)` is the cube c moved by m). * If applicable, a `transform()` function that applies a transformation in a similar way as `move()` applies a move. For coordinates this is not possible, because they do not capture enough of the cube state. @@ -65,15 +65,15 @@ by the integer `n` and the functions `index()` and `to_cube()` defined above. This is the type of coordinate that "does not exist" in the code, because they are just a special case of *composite coordinates*. -### Composite coordinates (COMP_COORD) +### Composite coordinates (COMP\_COORD) Composite coordinates are, like the name says, a composition of many basic -coordinates. They are given by a list of basic coordinates (n_1, index_1(), -to_cube_1()), ..., (n_k, index_k(), to_cube_k()). The value of such a +coordinates. They are given by a list of basic coordinates (n\_1, index\_1(), +to\_cube\_1()), ..., (n\_k, index\_k(), to\_cube\_k()). The value of such a composite coordinate on cube c is computed as -index_1(c) + n_1 * (index_2(c) + n_2 * (...)). +`index_1(c) + n_1 * (index_2(c) + n_2 * (...))`. -### Symmetric coordinates (SYM_COORD) +### Symmetric coordinates (SYM\_COORD) A symmetric coordinate consists of a basic coordinate reduced by symmetry. Symmetric coordinates must be initialized from a given set of *cube @@ -93,7 +93,7 @@ the following data: a list of *self-symmetries*. This will be useful when computing the pruning table associated to this coordinate. -### Symmetric-composite coordinates (SYMCOMP_COORD) +### Symmetric-composite coordinates (SYMCOMP\_COORD) A symmetric-composite coordinate is based on two other coordinates, a symmetric coordinate and a composite coordinate. To compute the value @@ -106,13 +106,13 @@ composite coordinate, and finally combine the two. More precisely and with less tong-twisting, for a given cube c one must take the following steps: -* Compute the value x_s of the symmetric coordinate at c, the value - x_b of the *basic* coordinate associated with the symmetric coordinate - and the value x_c of the composite coordinate. -* Read from the table the transformation t that brings x_b to its +* Compute the value x\_s of the symmetric coordinate at c, the value + x\_b of the *basic* coordinate associated with the symmetric coordinate + and the value x\_c of the composite coordinate. +* Read from the table the transformation t that brings x\_b to its representative. -* Apply t to the composite coordinate value x_c to obtain x_t. -* Compute the value x_s * n_c + x_t, where n_c is the maximum value +1 +* Apply t to the composite coordinate value x\_c to obtain x\_t. +* Compute the value x\_s * n\_c + x\_t, where n\_c is the maximum value +1 of the composite coordinate. ## Moving coordinates -- cgit v1.3