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The Euclidean['right'](Poly1, Poly2, A) or Euclidean(Poly1, Poly2, A) calling sequence returns a list [m, S] where m is a positive integer and S is an array with m nonzero Ore polynomials such that:
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In addition, Remainder['right'](S[m-1], S[m], A) = 0. S is called the right Euclidean polynomial remainder sequence of Poly1 and Poly2.
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If the fourth argument c1 of Euclidean['right'] or Euclidean is specified, it is assigned the first co-sequence of Poly1 and Poly2 so that:
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and c1[m+1] Poly1 is a least common left multiple (LCLM) of Poly1 and Poly2.
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If the fifth argument c2 of Euclidean['right'] or Euclidean is specified, it is assigned the second co-sequence of Poly1 and Poly2 so that:
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and is an LCLM of Poly1 and Poly2.
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The Euclidean['left'](Poly1, Poly2, A) calling sequence returns a list [m, S] where m is a positive integer and S is an array with m nonzero Ore polynomials such that:
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In addition, . S is called the left Euclidean polynomial remainder sequence of Poly1 and Poly2.
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If the fourth argument c1 of Euclidean['left'] is specified, it is assigned the first co-sequence of Poly1 and Poly2 so that:
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and Poly1 c1[m+1] is a least common right multiple (LCRM) of Poly1 and Poly2.
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If the fifth argument c2 of Euclidean['left'] is is specified, it is assigned the second co-sequence of Poly1 and Poly2 so that:
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and Poly1 c1[m+1]= - Poly2 c2[m+1] is an LCRM of Poly1 and Poly2.
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