<think>
Okay, I need to implement the slug_word and slug_make functions as per the given interface. Let me start by understanding what each function is supposed to do.

First, slug_word takes a word and processes it. The goal is to lower the word and remove any characters that aren't letters or digits. So, for example, if the input is "Hello!", the output should be "hello". Also, accented letters like "ç" might be a problem. The task says to drop any character that's not a letter or digit. But the note mentions that handling accented letters isn't specified. Since the problem says to drop non-alphanumeric characters, I think accented letters are considered letters here. But maybe the problem expects to lower them and then check if they are alphanumeric. Wait, the problem says to drop every character that is not a letter or a digit. So, perhaps the idea is to keep only letters (a-z, A-Z) and digits (0-9), and then lower them. But how to handle accented letters? The problem doesn't specify, so maybe we should consider that accented letters are not considered letters here. Wait, but in Python, the default string handling might include them. Hmm, but the problem says to drop any character that is not a letter or a digit. So perhaps we need to check if a character is alphanumeric. But in Python, the isalnum() method returns True for letters and digits, but accented letters might not be considered as letters. Wait, for example, 'ç' is not considered a letter in the default isalnum() check. So, perhaps the problem expects that any character that is not a letter (a-z, A-Z) or digit is dropped. So, the slug_word function should process the input word by converting to lowercase, then filtering out any characters that are not alphanumeric. Wait, but the problem says "drops every character that is not a letter or a digit". So, the steps are: lower the word, then remove any characters that are not letters or digits. So, for example, if the input is "c3", it becomes "c3". If the input is "C3!", it becomes "c3". If the input is "C3", it becomes "c3". So, the function should process each character in the word, lower it, and keep only those that are alphanumeric.

So, for slug_word, the steps are:

1. Convert the input word to lowercase.
2. Iterate over each character in the word.
3. For each character, check if it is a letter (a-z, A-Z) or a digit (0-9). But since the word is already lowercased, we can check if the character is alphanumeric. Wait, but in Python, the isalnum() method for a single character would return True if it's a letter or a digit. However, for example, 'ç' is not considered alphanumeric in the default settings. So, perhaps the problem expects that we check if the character is a letter (a-z) or a digit (0-9). So, maybe the correct approach is to check if the character is in the set of lowercase letters (a-z) or digits (0-9). So, for each character in the lowercased word, we check if it is a letter (a-z) or a digit (0-9). If yes, keep it; else, drop it.

So, the slug_word function can be implemented by first converting the input to lowercase, then filtering each character to keep only those that are alphanumeric. Wait, but how to check if a character is a letter or digit. For example, in Python, the isalpha() method returns True if the character