Regular Expressions with multiple dots in Linux bash shell give strange results - regex

Question

I tried to match a substring including a lot of dots, and it failed in Debian Linux shell. I made a simple script to look how dots are processed and found it completely out of rules. I retried it Bash, perl, Ubunta shell it all the same. The script and output are below.
#!/bin/sh
my_regex=u2734523abcABCB.C123.ABC.abc.1..2.34.2
Numbering=123456789_123456789_123456789_123456789
echo "$my_regex"
echo "$Numbering"
echo `expr index "$my_regex" '(ABC)'`
echo `expr index "$my_regex" '(ABC\.)'`
echo `expr index "$my_regex" '(\.\.)'`
echo `expr index "$my_regex" '(.)'`
echo `expr index "$my_regex" '(\.1)'`
Output:
u2734523abcABCB.C123.ABC.abc.1..2.34.2
123456789_123456789_123456789_123456789
12
12
16
16
16
The first regex should match ABC and return number-position of first character. It works.
The second one should find ABC followed by dot, it looks like it ignores dot.
The third one should find two dots but it finds first occurrence of one dot. Ignores again?
The fourth should find first any character, but it still finds the dot on position 16.
The fifth should find a dot followed by 1, it still finds the first occurrence of dot.
It seems like neither \ nor [ ] (I tried it too), nor the dot itself works as in common regular expression.
Why?

Answer 1

expr index has nothing to do with regular expressions.
expr index STRING CHARS outputs the index of the first occurrance of any of the CHARS in STRING. So your first search for '(ABC)' finds the first left parenthesis, A, B, C, or right parenthesis in your string. The first one is the A at position 12.
'(ABC\.)' does the same thing, except it's now also looking for a backslash or period. But the A is still the first match at position 12.
'(\.\.)' looks only for a parenthesis, backslash, or period. The first match is the period at position 16.
Likewise, all your other searches find the period at position 16, because none of the other characters you're listing come before that.
(On a side note, it's silly to capture the output with backticks only to immediately echo it. You'd get the same result by omitting the echo and backticks.)

Answer 2

You are incorrectly using index function of expr. As per man expr:
index STRING CHARS - index in STRING where any CHARS is found, or 0
So 2 things to note here:
index doesn't do any regex matching
index will find position of any of the char is found in string
If you want regex matching then use:
STRING : REGEXP
like this:
my_regex='u2734523abcABCB.C123.ABC.abc.1..2.34.2'
expr u2734523abcABCB.C123.ABC.abc.1..2.34.2 : '.*ABC'
24
expr u2734523abcABCB.C123.ABC.abc.1..2.34.2 : '.*ABC\.'
25
expr u2734523abcABCB.C123.ABC.abc.1..2.34.2 : '.*\.\.'
32
expr u2734523abcABCB.C123.ABC.abc.1..2.34.2 : '.*.'
38
expr u2734523abcABCB.C123.ABC.abc.1..2.34.2 : '.*\.1'
30
The numbers after each expr command is actually the length of the match.
There is no need to use echo here as expr anyway writes output on stdout.
You might want to take a look at BASH built-in =~ operator for regex matching.