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Ideals of non-commutative polynomials

asked 12 years ago

Martin Brandenburg gravatar image

updated 12 years ago

Basically I have the same question as here, but in the non-commutative case: Given non-commutative polynomials f1,,fsQx1,,xn, how can I test (with sage, or any other program which can do this) that some gQx1,,xn satisfies gf1,,fs (two-sided ideal), and find an explicit linear combination g=iaifibi which demonstrates this?

In trac ticket #11068 non-commutative quotient rings were implemented. However, according to the reference manual on quotient rings, this assumes that one defines a reduce method by hand. But in my example , it is not clear how to do this.

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answered 11 years ago

Starx gravatar image

What you're asking for doesn't exist in complete generality because this would imply a solution to the word problem. The GAP package GBNP implements Grobner bases for non-commutative polynomial rings. The algorithm need not terminate, but when it does it solves the problem you're asking about.

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Asked: 12 years ago

Seen: 441 times

Last updated: Oct 18 '13