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This question already has an answer here:

How can I take a bitcoin private key encoded in hex:

d1d9a2e9fd3da7e7710310ea17a9edff9e08845c7a6f2ea3d650ba4ae7ee0d3b

and convert it to the corresponding public key:

0478a2a9be183f26e2745c9254957e3b714e8bf161f8bf992f9c628fbddc634e149f52aab6a45cd93187593e2413baf14378e7b2c14c0429f98cbe90c723e1e179

I am NOT looking for a program/tool that does this, but how to do this mathematically. If you can't find that out, you can also give a solution in python 3, which I can understand and convert to something mathematical

marked as duplicate by Jestin, Jimmy Song, Murch Jul 4 '16 at 14:01

This question has been asked before and already has an answer. If those answers do not fully address your question, please ask a new question.

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I'm voting to close since this is very similar to the other question, but what you want to be doing is scalar multiplication of the private key to the generator point using Elliptical Curve Cryptography. The curve parameters, including the generator point is defined in SECP256K1. The resulting x and y coordinates are encoded via SEC uncompressed format to get the public key.

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