$.$ Implement the following functions:

a$.$ To determine the number of authors a book has.

b$.$ To determine the number of authors of a book who belong to a publishing house.

c$.$ To determine the books of an author for a publishing house.

d$.$ AuthorName. To present the author's name in full format $($First and Last Name$),$ reduced format $1($First name, First letter of the second name with a dot if it has one, and Last Name$),$ reduced format $2($First name, First letter of the second name with a dot if it has one, First last name, Second letter of the second last name with a dot, if it has one$).$ It is assumed that the last two words of 'name' are surnames, the rest are first names.

e$.$ BookAuthors. To return a string with the names in reduced format $2,$ of the authors of a book separated by commas

Use the database squema in the image Dado el siguiente diagrama de datos: