<SYSTEM_TASK:>
Solve the following problem using Python, implementing the functions described below, one line at a time
<END_TASK>
<USER_TASK:>
Description:
 def compute_arxiv_re(report_pattern, report_number):
 """Compute arXiv report-number."""

    if report_number is None:
        report_number = r"\g<name>"
    report_re = re.compile(r"(?<!<cds\.REPORTNUMBER>)(?<!\w)" +
                           "(?P<name>" + report_pattern + ")" +
                           old_arxiv_numbers, re.U | re.I)
    return report_re, report_number