List of elements in array needs to check each one in a string

For the shown data

use warnings;
use strict;

use List::Util qw(none);

my @terms = qw(int frac prod sum oint bigvee bigcup bigcap bigoplus bigotimes);

my ($paren_L, $paren_R) = map { quotemeta $_ } '\left(', '\right)';

while (my $line = <DATA>)
{
    if (none { $line =~ /$_/ } @terms) 
    {   
        $line =~ s|$paren_L|(|; 
        $line =~ s|$paren_R|)|;
    }
    print $line;
}

__DATA__
"\left({H^1}, \int {H^2}\right)"
"\left({H^1},\bigoplus{H^2}\right)"
"\left({H^1},{H^2}\right)"
"\left({H^1}, \bigvee {H^2}\right)"

with output

"\left({H^1}, \int {H^2}\right)"
"\left({H^1},\bigoplus{H^2}\right)"
"({H^1},{H^2})"
"\left({H^1}, \bigvee {H^2}\right)"

Notes.

• This doesn't account for multiple bracketed expressions on a single line

• There are (many) other ways to specify parens in Latex (\big(, \Bigg( etc).

On the other hand, the shown data is reasonable in a Latex document.

This goes over the line multiple times but is far more flexible than a single regex.

With such simple patterns we need not start the regex engine for each term, but can instead build one pattern with alternations. Substitutions can also be done in one pass, using named capture groups

my $re_terms = '(?:' . join('|', @terms) . ')';

while (my $line = <DATA>) 
{
    if ($line !~ /$re_terms/)
    {   
        $line =~ s/(?<L>$paren_L)|(?<R>$paren_R)/$+{L} ? '(' : ')'/eg;
    }   
    print $line;
}

which produces the same output.

This does expect data in the shown format: parens always paired, one set on a line.