# Sifting algorithm for group generated by a set

On page 38 of "Lecture Notes in Computer Science" by Christoph M. Hoffmann, there is an algorithm (ALGORITHM 2).

I have some confusions.

Why it is written that an entry $M_{i,j}, j < i$, cannot be referenced? what is the meaning of "reference" here?

Thanks.

• Lecture Notes in Computer Science is the name of the series, not of the specific monograph. It's like saying 'On page 38 of "Book"'. – Yuval Filmus Jul 16 '16 at 8:53
• It feels like we are missing a lot of background here. Try to re-read the first 37 pages, and surely you'll find an answer to your question. – Yuval Filmus Jul 16 '16 at 8:54
• @YuvalFilmus I read it. What is the meaning of "reference" as a word (in this context) here? – Michael Jul 16 '16 at 9:23
• It's an entry that "doesn't exist" or "hasn't been assigned". Only you can tell, since only you read the first 37 pages. Perhaps you should concentrate on the definition of partially completed representation matrix. – Yuval Filmus Jul 16 '16 at 9:25
• @YuvalFilmus Yes I have read it but the word reference seems out of context to me.Both 'partially completed representation matrix' and 'reference' used for the first time on page 38.Partially completed representation matrix is understandable, it means there are some entries in $M$ but it is not completed i.e. There are some empty entries in $M$ .If one wants to represent $\pi$ as products of entries of $M$, $M$ needs to be completed. We use $\pi$ to complete $M$, through 'sifting' process (line 7 to 11).But I don't get the word "reference" here. What does it mean? – Michael Jul 16 '16 at 9:41

One possible explanation is that it is indicating that you should never try to read or use any matrix element $M_{i,j}$ where $i<j$. "Referenced" might be talking about "de-referencing" a pointer, i.e., reading a memory cell, i.e., reading an entry of the matrix. Perhaps the text is indicating that the matrix entries $M_{i,j}$ are only defined for $i \ge j$.

I suggest you read the text with this possible perspective in mind and see if it seems consistent with the surrounding context.