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converts this to char, because the final result will be a char matrix. Character 0 is displayed as space, and the non-zero entries will be written with the appropriate letters.

reads the input letter, adds 7 to its ASCII code, and negates the result. For input 'a' whis gives −104, which is a multiple of 26, so circularly shifting by this amount will do nothing. If the input is b this gives −105, which shifts the string 1 step to the left to produce 'bcd···yza'; etc.

The next step is to define the order in which the shifted string will be written into the nozero positions of the matrix. To this end,

subtracts 7 from the latter, brings the former to top, substracts 4 from it, and negates it. The 7 and 4 specify an origin of coordinates, so that the angles of the position vectors of the non-zero entries with respect to that origin define the desired order.

computes the two-argument arctangent modulo 2*pi to produce those angles. Now the smallest angle, which is zero, corresponds to the entry where the first letter should go, and the rest advance counter-clockwise.

rearranges the letters in the string according to those angles, so that when the letters are written into the non-zero entries of the matrix in column-major order (down, then across) the result will be correct. This is done by

so that 'u' will correctly go to the first (in column-major order) non-zero entry, which is entry (3,1) in matrix notation; 't' will go to (4,1), 's' to (5,1); 'v' to (2,2) etc.

converts this to char, because the final result will be a char matrix. Character 0 is displayed as space, and the nonzero entries will be written with the appropriate letters.

reads the input letter, adds 7 to its ASCII code, and negates the result. For input 'a' this gives −104, which is a multiple of 26, so circularly shifting by this amount will do nothing. If the input is b this gives −105, which shifts the string 1 step to the left to produce 'bcd···yza'; etc.

The next step is to define the order in which the shifted string will be written into the nonzero entries of the matrix. To this end,

subtracts 7 from the latter, brings the former to top, substracts 4 from it, and negates it. The 7 and 4 specify an origin of coordinates, so that the angles of the position vectors of the nonzero entries with respect to that origin define the desired order.

computes the two-argument arctangent modulo 2*pi to produce those angles. Now the smallest angle, which is 0, corresponds to the entry where the first letter should go, and the rest advance counter-clockwise.

rearranges the letters in the string according to those angles, so that when the letters are written into the nonzero entries of the matrix in column-major order (down, then across) the result will be correct. This is done by

so that 'u' will correctly go to the first (in column-major order) nonzero entry, which is (3,1) in matrix notation; 't' will go to (4,1), 's' to (5,1); 'v' to (2,2) etc:

 ······ v· ·· u · t · s · ·· ·· ······ 

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converts this to char, because the final result will be a char matrix.

alters the order of the letters in the string according to those angles, so that when the letters are written into the non-zero entries of the matrix in column-major order (down, then across), which is done by

yg( 

the result will be correct.

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converts this to char, because the final result will be a char matrix. Character 0 is displayed as space, and the non-zero entries will be written with the appropriate letters.

rearranges the letters in the string according to those angles, so that when the letters are written into the non-zero entries of the matrix in column-major order (down, then across) the result will be correct. This is done by

yg( 

For example, if the input is 'a' the string was not circularly shifted:

abcdefghijklmnopqrstuvwxyz 

The rearranging as per the angles transforms this into

utsvrwqxpyoznamblckdjeifgh 

so that 'u' will correctly go to the first (in column-major order) non-zero entry, which is entry (3,1) in matrix notation; 't' will go to (4,1), 's' to (5,1); 'v' to (2,2) etc.

which is the top left quadrant of a matrix specfying the positions of the letters. Then

reflects the matrix vertically without repeating the last row, and horizontally repeating the last column:

converts them to char. Then

reads the input letter, adds 7 to its ASCII code, and negates the result. For input 'a' whis gives -104, which is a multiple of 26, so circularly shifting by this amount will do nothing. If the input is b this gives -105, which shifts the string 1 step the left to give 'bcd···yza'; etc.

subtracts 7 from the latter, brings the second to top, substracts 4 from it, and negates it. The 7 and 4 specify an origin of coordinates, so that the angles of the position vectors with respect to that origin define the desired order.

computes the two-argument arctangent modjulo 2*pi to produce those angles. Now the smallest angle, which is zero, corresponds to the entry where the first letter should go, and the rest advance counter-clockwise.

which is the top left quadrant of a matrix specfying the positions of the letters.

reflects that quadrant vertically without repeating the last row, and horizontally repeating the last column to produce the full matrix:

converts this to char, because the final result will be a char matrix.

reads the input letter, adds 7 to its ASCII code, and negates the result. For input 'a' whis gives −104, which is a multiple of 26, so circularly shifting by this amount will do nothing. If the input is b this gives −105, which shifts the string 1 step to the left to produce 'bcd···yza'; etc.

subtracts 7 from the latter, brings the former to top, substracts 4 from it, and negates it. The 7 and 4 specify an origin of coordinates, so that the angles of the position vectors of the non-zero entries with respect to that origin define the desired order.

computes the two-argument arctangent modulo 2*pi to produce those angles. Now the smallest angle, which is zero, corresponds to the entry where the first letter should go, and the rest advance counter-clockwise.