Fix: How to get X and Y coordiantes with GMP library on secp256k1 curve?

 To get X and Y coordinates on the secp256k1 elliptic curve using the GMP (GNU Multiple Precision) library, you'll typically work with Big Integers to perform the necessary calculations. Here's an example of how to compute the X and Y coordinates for a point on the secp256k1 curve in C/C++ using the GMP library:

```c

#include <stdio.h>

#include <gmp.h>

#include <secp256k1.h>

int main() {

    // Initialize GMP variables for the coordinates

    mpz_t x, y;

    mpz_inits(x, y, NULL);

    // Initialize secp256k1 context

    secp256k1_context_t* ctx = secp256k1_context_create(SECP256K1_CONTEXT_SIGN);

    // Example private key (you'd typically generate a random one)

    const char* private_key_hex = "0123456789abcdef0123456789abcdef0123456789abcdef0123456789abcdef";

    // Convert the private key to a GMP integer

    mpz_set_str(x, private_key_hex, 16);

    // Compute the corresponding public key

    secp256k1_pubkey pubkey;

    if (secp256k1_ec_pubkey_create(ctx, &pubkey, mpz_get_mpz_t(x)) == 1) {

        // Extract X and Y coordinates from the public key

        mpz_import(x, 33, 1, 1, 0, 0, secp256k1_ec_pubkey_tweak_mul(&pubkey, mpz_get_mpz_t(x)));

        mpz_import(y, 33, 1, 1, 0, 0, secp256k1_ec_pubkey_tweak_add(&pubkey, x));

    }

    // Print X and Y coordinates

    gmp_printf("X: %Zx\nY: %Zx\n", x, y);

    // Clean up

    secp256k1_context_destroy(ctx);

    mpz_clears(x, y, NULL);

    return 0;

}

```

In this example:

1. We initialize GMP variables `x` and `y` to store the X and Y coordinates.

2. We initialize the secp256k1 context.

3. We set a sample private key (you'd typically generate a random private key).

4. We compute the corresponding public key using `secp256k1_ec_pubkey_create`.

5. We extract the X and Y coordinates from the public key using `secp256k1_ec_pubkey_tweak_mul` and `secp256k1_ec_pubkey_tweak_add`.

6. Finally, we print the X and Y coordinates using `gmp_printf`.

Make sure to include the GMP and secp256k1 libraries in your project, and adjust the private key and error handling as needed for your specific application.