please write a code for problem 1 using sage math

Problem 1: For a matrix M with integer values a, b, c, d, Ta 67 M the determinant is det(M) = ad-bc. A matrix, whose determinant is equal to +1, is called a uni- modular matrix. Consider a polynomial function f in two variables u and y, ie. f(,y) and an associated vector t = (a, b). The vector t can be used to change the coordinates of the polynomial function f, based on a matrix M, whose first row consists of the vector t and whose determinant is equal to +1, ie. det(M) = +1 (either is equally valid). The values c, d must be determined to ensure that that det(M)= +1. The unimodular change of coordinates is performed in the following way. Once c, d have been determined such that det(M) = +1, the old coordinates x,y are changed to new coordinates X, Y in the following way. =xy (2) (3) Finally, with the new coordinates, the polynomial function f(x,y) becomes a rational expression f(X,Y). y=X'yd Write a function F, which on input takes a polynomial f as a symbolic expression in variables x and y, and a list of values t = [a,b] (ie. F(f(x,y), [a,b]))and returns a rational expression f(X,Y) as illustrated above. As part of your solution to this problem, include the answers for F(xy + xy5 + xy + % y +x+y+1, [2,3]) F(x+4y17 + xy + xy + x2y3 + x2 + y2, [-4, 3]) it is in general difficult to find a recurrence relation or a closed Problem 1: For a matrix M with integer values a, b, c, d, Ta 67 M the determinant is det(M) = ad-bc. A matrix, whose determinant is equal to +1, is called a uni- modular matrix. Consider a polynomial function f in two variables u and y, ie. f(,y) and an associated vector t = (a, b). The vector t can be used to change the coordinates of the polynomial function f, based on a matrix M, whose first row consists of the vector t and whose determinant is equal to +1, ie. det(M) = +1 (either is equally valid). The values c, d must be determined to ensure that that det(M)= +1. The unimodular change of coordinates is performed in the following way. Once c, d have been determined such that det(M) = +1, the old coordinates x,y are changed to new coordinates X, Y in the following way. =xy (2) (3) Finally, with the new coordinates, the polynomial function f(x,y) becomes a rational expression f(X,Y). y=X'yd Write a function F, which on input takes a polynomial f as a symbolic expression in variables x and y, and a list of values t = [a,b] (ie. F(f(x,y), [a,b]))and returns a rational expression f(X,Y) as illustrated above. As part of your solution to this problem, include the answers for F(xy + xy5 + xy + % y +x+y+1, [2,3]) F(x+4y17 + xy + xy + x2y3 + x2 + y2, [-4, 3]) it is in general difficult to find a recurrence relation or a closed