Subresultant polynomial remainder sequence of two polynomials
SubresultantPolynomialRemainders[poly1, poly2, var]
SubresultantPolynomialRemainders[poly1, poly2, var, Modulus -> p]
SubresultantPolynomialRemainders[(x - 1) ^ 2(x - 2)(x - 3), (x - 1)(x - 4) ^ 2, x]
→ {6 - 17*x + 17*x^2 - 7*x^3 + x^4, -16 + 24*x - 9*x^2 + x^3, 38 - 49*x + 11*x^2, -36 + 36*x}SubresultantPolynomialRemainders[a x ^ 4 + b x + c, d x ^ 3 + e x + f, x]
→ {c + b*x + a*x^4, f + e*x + d*x^3, c*d^2 + b*d^2*x - a*d*f*x - a*d*e*x^2, b*c*d^3 - a*c*d^2*f + a^2*e^2*f + b^2*d^3*x + a*c*d^2*e*x + a^2*e^3*x - 2*a*b*d^2*f*x + a^2*d*f^2*x, c^3*d^4 + b^2*c*d^3*e + 2*a*c^2*d^2*e^2 + a^2*c*e^4 - b^3*d^3*f - 5*a*b*c*d^2*e*f - a^2*b*e^3*f + 3*a*b^2*d^2*f^2 + 4*a^2*c*d*e*f^2 - 3*a^2*b*d*f^3 + a^3*f^4}SubresultantPolynomialRemainders[-10 + 4x + 3x ^ 2 + 2x ^ 3 + x ^ 8, -19 + 7x + 6x ^ 2 + 5x ^ 3 + x ^ 7, x]
→ {-10 + 4*x + 3*x^2 + 2*x^3 + x^8, -19 + 7*x + 6*x^2 + 5*x^3 + x^7, -10 + 23*x - 4*x^2 - 4*x^3 - 5*x^4, -18585 + 20008*x + 1606*x^2 - 3029*x^3, 452264 + 143056*x - 595320*x^2, -692132416 + 692132416*x}