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Sifting algorithm for group generated by a set

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Problem Detail: 

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

I have some confusions.

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


Asked By : Mike SQ
Answered By : D.W.

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.

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