Final Comments to Author: The authors had successfully addressed our major review comments: 1. paper structure-wise: cleaned up the tables to appendix in order to expand the deduction and principles 2. implementation-wise: examples are added for illustration of the package utility Besides, the novelty of the package is clear as this may be frontier to address the dilema of the lack of a tool in this research field.

Do you ENDORSE THE PUBLICATION of this manuscript in its current form? Yes

Does this manuscript conform to the definition below of Methods articles? If not, please contact the Frontiers Editorial Office (editorial.office@frontiersin.org).

Methods articles present a new method, or emerging technique that opens new avenues for the investigation of important issues in a field. Method articles should include (1) objectives and validation of the method with a detailed protocol; (2) example(s) of its application and effectiveness; (3) advantages and limitations. No Examples of its application are lacked.

Is the language, specifically the grammar, of sufficient quality? If no, please specify if the authors should send this manuscript to an expert in English editing and academic writing. Yes.

What is the new method or technique presented in this manuscript? The development of a Mathematica package applying group theory to fields such as solid-state physics and photonics.

Does the title clearly and precisely reflect the findings of the manuscript, as described in the author guidelines? Yes.

Please comment on the Abstract section. Key elements to consider: - appropriateness of context - purpose of method The context was illustrated appropriately to address the goal and methodology.

Please comment on the method. Key elements to consider: - objective errors or fundamental flaws in the methodology - purpose of new method or technique - appropriateness of context - comprehensive description of procedures - quality of figures and tables Many functions lack basic mathematical definitions and reasoning, 13 tables are redundant and some may be better in supplemental tables.

Is the method sufficiently described to allow others to reproduce or apply the experiment/study? If not, please list the missing elements. The package lacks basic application examples, e.g. using the package to derive validated theories in solid physics.

Do the examples or applications provided validate the method? No

Have any ethical issues been identified in the proposed methodology? No

For research involving human subjects or animals, do the author(s) identify the committee approving the study and have all patients provided their written informed consent? Not Applicable

For research involving biohazards, biological select agents, toxins, restricted materials or reagents, have the standard biosecurity or institutional safety procedures been carried out? Not Applicable

For any complementary data (e.g. nucleotide/amino acid sequences, crystallographic or NMR data, RNAseq) submitted to an online repository or database, do the author(s) provide the accession number? Not Applicable

Is prior work properly and fully cited? No

Please provide your further comments and overall recommendation to the authors, including the level of revisions (minor, moderate, substantial). Beyond lacking an example to apply this package in a specific field as proof of methodological validity and usefulness, the choice of of using Mathematica favored scientists in the pure and theoretical mathematics, while Matlab, R, Python may be more popularized among physics scientists and engineers. Using Mathematica also makes it difficult to transition project analysis between multiple programming languages.