Naive: how to generate EC public key from EC private key?

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I?ve an extremely na?ve question. I am generating ephemeral EC keys for
ECDH, following the example in
https://wiki.openssl.org/index.php/EVP_Key_and_Parameter_Generation

But it looks like the example ends on generation of the private key:
/* Generate the key */
if (!EVP_PKEY_keygen(kctx, &key)) goto err;

The next step must be obvious, but somehow I can?t figure it out. So my
question is: from having EVP_PKEY *privateECKey how do I get EVP_PKEY
*publicECKey?

Thanks!

P.S. The same question applies to RSA as well.
-- 
Regards,
Uri Blumenthal


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