That's not generally true: typically you can compute the public key from the private key, but not vice versa (i.e. crypto_scalarmult_base() in libsodium). In R

That's not generally true: typically you can compute the public key from the private key, but not vice versa (i.e. crypto_scalarmult_base() in libsodium). In RSA, that isn't possible (without assumptions), so a private key file also contains the public key data.