**Decision problems in Integer Linear Programming** have Lenstra type algorithms (https://www.math.leidenuniv.nl/~lenstrahw/PUBLICATIONS/1983i/art.pdf) have been generalized to convex integer program techniques (See [Complexity of integer quasiconvex polynomial optimization by Sebastian Heinz](https://pdf.sciencedirectassets.com/272569/1-s2.0-S0885064X05X00851/1-s2.0-S0885064X05000348/main.pdf?X-Amz-Security-Token=IQoJb3JpZ2luX2VjEKz%2F%2F%2F%2F%2F%2F%2F%2F%2F%2FwEaCXVzLWVhc3QtMSJGMEQCIBS4E%2BhnTZepR%2F5MUAaFMUUXOrjYKtirYruHKwWfkXQeAiA76hnz9KRqHRrWUbsKKxtE2KP1pMD9H%2BmBZhkGfvCQCCq8BQjF%2F%2F%2F%2F%2F%2F%2F%2F%2F%2F8BEAUaDDA1OTAwMzU0Njg2NSIM%2FhuZ2BzWR5gzd8ohKpAFLUvUIZo6PhJKxhdRxk3nx1DbETn%2B9%2B2I%2BTTGSysCHwr4nJZ2xZxduddYJbCzvLN%2FHKXFRTRzMbaRfp6pTzvq00fLkNDzEzIubiMNCHugmqbdZXCY9n0dZ1YOwtPX98BhdS90%2FlsX2kiBgXUXZwCApvOLUz8L0psSqam5dBf0494Dxo5WkXa1V%2FVAB7j4HrtK5QzgmqR3C%2FELC0S3NnZEtlS76kYc1gaQ3D7ZXIY2jHKCdlii9v0OdGDK0D7Grd9KRWJbkc8fHoxvv19OdZBpn4CP1RPq4pEKF96wiL3o1%2BIWTHrxaZ7qumLLH0STT6XfaV%2FWSlFy43xGNg7POCNKdTLQ2sSt0%2FFcqMMc96TrOqkRFNXZKc6SaONSNfnMM%2FRQdcS2AqQchHi8n%2BMtwa8505tn0QTzvHXKKkyz%2B8PH8%2F8S%2BvuMgT9uLENOfvd7b7W9%2BmpZKqzxNDAnI%2F0YxF8FM5%2BxfupsS5ErcXoxj58KuQ6P0gniDuXuLAB%2Fh%2FiMWWlXnQOCD5GQXcvz1%2F6%2FI5oWlRlxFG2DxzpE9z47aBBEtgrWsKp0jzGOjhH7BmxNTR%2BxmyQ3nsaZHuCf6xACUY6gKwIJ4ENEHQJK7teRDuFEAd9ElEMLdog%2F1RPORDIE474CRbrEIzqdCEr9qlwc1NNiOmHdTVMUgFkCU5bS2Wmix5qPdxmgatOURthoXCE%2BRLsFZJohuX76sJRS7bCks3KdR7UANRJ1IEEW2pGlDxgpsdN9R2t0miH5MhMCsrQthTfwWHBmL7k6dwGWMMDtJq8wY0NKoy3pCI%2FDy6BH7jUvPqjreDlcGOU3Wd18cYTgLyGuMjpZsi3AhXQSpD0Z6mSIVCm8FbxCAxTPjk4AB2jKZIAwqcvdtgY6sgH%2FGybaQTSmEHvZzj1qk7cLietHFN9CVORmDP2K4oNf%2FtKKzR0rNaK%2B%2BXZP6w4GDOP38pELSKPPk6sZoWtRI7XKd4VrZIFHJJ8Eywg3XAxm%2Fd0OqCNOQJGXJSS7LQKW0Yl4G2y9PMM6WBNQNkkyJCr4ECKanzTr8ltExbdmlEObA14HD%2BXLOm0fR%2FU68MR98eSe57rMMgzFNIHapdxUV5bRN7cP%2F5Zx%2BP1cdU%2F0VVsFRa%2FG&X-Amz-Algorithm=AWS4-HMAC-SHA256&X-Amz-Date=20240903T201232Z&X-Amz-SignedHeaders=host&X-Amz-Expires=300&X-Amz-Credential=ASIAQ3PHCVTY2ETUZYXD%2F20240903%2Fus-east-1%2Fs3%2Faws4_request&X-Amz-Signature=feaf9fdb40d96cd31a0a6f0f27e3d6c0470084d8f9a90530e2426fcd5bd523b0&hash=3bdd1181aa8d047de90990be1fb3114e56e1d2cb86579eac51f184da2ecfe640&host=68042c943591013ac2b2430a89b270f6af2c76d8dfd086a07176afe7c76c2c61&pii=S0885064X05000348&tid=spdf-1b5b64f9-f0ba-453c-a8f6-d5905c954d0a&sid=aa38ea2f1407a746b91a3456e2a391115793gxrqa&type=client&tsoh=d3d3LnNjaWVuY2VkaXJlY3QuY29t&ua=1b175a02035c57505d&rr=8bd8652f4912cf23&cc=us)). What is the difficulty in generalizing Barvinok type **counting integer points in Linear Integer Programming** techniques (https://barvinok.sourceforge.io/) to **counting integer points in convex integer programming**?