Of course you can apply at the same time.
The key issue is to clarify the difference between software copyright and patent rights: after the software work is completed, regardless of whether the computer software copyright is registered or not, the copyright is generated in accordance with the law. In order to obtain clear evidence and prevent future disputes, you can apply for software copyright registration. Patent rights require an application to be granted.
A computer program has the nature of a work, and its code expression is protected by copyright law. Copyright does not protect the "idea" itself, only the "form".
Invention patent applications:
1. Invention patent applications involving automation technology processing processes;
2. Invention patent applications involving improvements in computer internal operating performance;
3. Invention patent applications involving measurement or testing of computer program testing processes, etc. These programs are combined with related product equipment, computers or measuring devices to form a complete technical solution, which can be patented. The computer program must be independently completed and original. As long as it is an original work, regardless of whether it is similar to a published work, it can obtain independent copyright. Patent rights are only granted to the first applicant, requiring novelty, inventiveness, etc.
If a software system applies for software copyright first, it can apply for a patent. Although the software copyright is applied for first, the technical core, concept, model, etc. of the software system are not disclosed. If you apply for a patent, there will be no loss of novelty when applying for software copyright, because there is no novelty, only originality.