I was working on a project as a researcher. The whole project was financed by an external grant from a private foundation (nonprofit organization) and my salary was paid through this grant during my work as a researcher. During the project, I faced a problem that I had to solve it numerically. I had my own license and I paid for the software, the software that I used to solve the problem, I have not asked the principal investigator (PI) of the project to refund my license payment.
I solved all the numerical problems, I sent the results and outputs to the PI and we wrote the manuscript out of our findings. Now at the end of my contract, the PI of the project asked me to send him all the data that I have produced during my work and I said I will send all the data except that I cannot send him the input file of the numerical solutions using my software; I mean the method that I used to solve the problems. He said I have to send them as I was paid to work on project. I said I sent you the results, but the method of solving the problems is my intellectual property and I have paid for the software by myself, but he insisted that does not give me any right to keep them.
Who is right? Are these my intellectual properties?
I have to mention that in the contract that I had signed there was nothing about the copyrights and intellectual property. The solutions are not a big deal, but the point is, there is a possibility that they use them in their future research without mentioning my name.