use strict;
my $str = '\\end{theorem}
A $k$-periodic sequence has the property that $s_i = s_{i + k}$ for all $i = 0,1,\\dots$.
Thus a $k$-periodic sequence $(s_i)_{i = 0}^\\infty$ may be represented by any finite sequence $(s_i)_{i=a}^{a+k - 1}$, where $a$ is usually chosen to be $0$.
Sadly our Fibonacci sequence examples are not defined over a finite field but over the naturals and thus are not necessarily periodic.
Examples such as these may be interpreted to have a period of $\\infty$.
The period and related stability of linear recurrence sequences in regard to linear complexity has a very rich and broadly studied background~\\cite{DingZiaoShan1991}.
\\begin{theorem}
\\label{th: max period is m-sequence}
\\cite[Theorem~6.33]{LidlNiederreiter1994}
A linear recurrence sequence $s$ over a finite field $\\gf_2$ with linear complexity $n$ has a maximum possible period of $2^n-1$.
\\end{theorem}
\\begin{definition}
\\label{de: m-sequence}
A sequence which has maximum period for giv';
my $regex = qr/(\$[^\n$]*[^\s$])(-|=|\+)([^\s$][^\n$]*\$)/p;
if ( $str =~ /$regex/g ) {
print "Whole match is ${^MATCH} and its start/end positions can be obtained via \$-[0] and \$+[0]\n";
# print "Capture Group 1 is $1 and its start/end positions can be obtained via \$-[1] and \$+[1]\n";
# print "Capture Group 2 is $2 ... and so on\n";
}
# ${^POSTMATCH} and ${^PREMATCH} are also available with the use of '/p'
# Named capture groups can be called via $+{name}
Please keep in mind that these code samples are automatically generated and are not guaranteed to work. If you find any syntax errors, feel free to submit a bug report. For a full regex reference for Perl, please visit: http://perldoc.perl.org/perlre.html