"Strict" software for playing and learning with private and public key my question is just for teaching/learning practice and I think it's not meaningful for the real world.

I've played with openssl a lot but from my understanding it's somehow not strict in the format of the input because it's capable of understanding different format or doing some operations not transparently to the user.

Getting to the question: is there way by using openssl to get just the private key from the key pair and from that private one to compute the public key? An example:

When I do openssl rsa -in private.key -pubout I know that openssl does not compute the public key from the private but it just extracts the information that is alredy stored in the keypair (private.key is indeed a store for the pair).

Also openssl pkey -in private.key -text claims to extract the private key but how I can be sure that it's not another keypair storage? Ideally I would use another software than openssl that IS stricter with the input it receives and feed it with the private key and that would complain if as input it's given the keypair.

It might be that the confusion I'm trying to clear comes from the fact that maybe I'm missing some details of the cryptography but I'd like to check that by playing with different softwares (i.e. encrypting data with one software and decrypting it with another), again a software that is strict about what it gets as input, in another terms not-user-friendly but learner-friendly :-)

For software I prefer to have something at hand and not to compile anything.

Thanks for reading till here :-)

Alex
I'd suggest to get OpenSSL source, build it, and run it under debugger,
watching exactly what "-text" is doing to private key.
One could verify exponentiation operations with a calculator having big numbers capability.
ASN.1/DER parser could be handy to see private key file.