Tietze transformations with weighted substring search

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Abstract

We describe how, by generalizing the notion of the length of words in a group presentation, we have developed a computer program which can be directed by the user towards finding relators of a certain type. We present evidence to show that the user can direct the program, by choosing a suitable length function, towards finding the order of a specified generator. Evidence also suggests that simpler final presentations are obtained if the length function is chosen so that the program is positively directed towards increasing occurrences of certain generators that the elimination routine is directed to retain.

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