CA-S8-T2

1331 days ago by ks332606

# A solution to Task 2 of Series 8 of homework in Commutative Algebra, # 2014-11-25
# a ring of polynomials with 3 variables P1.<x,y,z> = PolynomialRing(QQ, 3, order='lex') # a list of polynomials F = [x - y^2, y - z^3, z^2 - 1] # given polynomial f f = x*y^2*z^2 + x*y - y*z # division algorithm f.reduce(F) 
       
z
# a ring of polynomials with 3 variables P1.<x,y,z> = PolynomialRing(QQ, 3, order='deglex') # a list of polynomials F = [x - y^2, y - z^3, z^2 - 1] # given polynomial f f = x*y^2*z^2 + x*y - y*z # division algorithm f.reduce(F) 
       
x^2 + x*y - y*z
# a ring of polynomials with 3 variables P1.<x,y,z> = PolynomialRing(QQ, 3, order='lex') # a list of polynomials F = [z^2 - 1, y - z^3, x - y^2] # given polynomial f f = x*y^2*z^2 + x*y - y*z # division algorithm f.reduce(F) 
       
z
# a ring of polynomials with 3 variables P1.<x,y,z> = PolynomialRing(QQ, 3, order='deglex') # a list of polynomials F = [z^2 - 1, y - z^3, x - y^2] # given polynomial f f = x*y^2*z^2 + x*y - y*z # division algorithm f.reduce(F) 
       
x^2 + x*y - y*z