Modular[FractionFreeRightEuclidean](Poly1, Poly2, p, A, 'c1', 'c2') calling sequence returns a list [m, S] where m is a positive integer and S is an array with m elements storing the subresultant sequence of the first kind of Poly1 and Poly2.

The Modular[FractionFreeRightEuclidean] command requires that Poly1 and Poly2 be fraction-free, and that the commutation rule of the Ore algebra A also be fraction-free.

If the optional fourth argument to the FractionFreeRightEuclidean command c1 is specified, it is assigned the first co-sequence of Poly1 and Poly2 so that:

and c1[m+1] Poly2 is a least common left multiple (LCLM) of Poly1 and Poly2.

If the optional fifth argument to the FractionFreeRightEuclidean command c2 is specified, it is assigned the second co-sequence of Poly1 and Poly2 so that:

and c1[m+1] Poly2 = - c2[m+1] Poly1 mod p is an LCLM of Poly1 and Poly2.

Modular[RightEuclidean](Poly1, Poly2, p, A, 'c1', 'c2') calling sequence returns a list [m, S] where m is a positive integer and S is an array with m elements storing the right Euclidean polynomial remainder sequence of Poly1 and Poly2.

If the optional fourth argument to the FractionFreeRightEuclidean command c1 is specified, it is assigned the first co-sequence of Poly1 and Poly2 so that:

and c1[m+1] Poly2 is a least common left multiple (LCLM) of Poly1 and Poly2.

If the optional fifth argument to the Modular[RightEuclidean] command c2 is specified, it is assigned the second co-sequence of Poly1 and Poly2 so that:

and c1[m+1] Poly2 = - c2[m+1] Poly1 mod p is an LCLM of Poly1 and Poly2.

Li, Z. "A subresultant theory for Ore polynomials with applications." Proc. of ISSAC'98, pp.132-139. Edited by O. Gloor. ACM Press, 1998.