How can I list the available Cipher algorithms?

Once I have a list of providers, as described in JB Nizet’s post, I still don’t have a list of algorithms. I found that each Provider functions as a Properties object, and the Properties encode the algorithm names. I’m not entirely clear on if this is the correct way to look for them or not, and what exactly all the other properties mean, but I just wrote a routine that spewed all properties to System.out and grepped for various strings describing what I was looking for until I found it.

import java.security.*;

for (Provider provider: Security.getProviders()) {
  System.out.println(provider.getName());
  for (String key: provider.stringPropertyNames())
    System.out.println("\t" + key + "\t" + provider.getProperty(key));
}