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So the idea is I was first working over

R.<w,x,y,z>=QQ[]

I have a function f and J is the Jacobian of f belonging to the ring above. I do some stuff and I end with a polynomial g in a symbolic ring in variables w,x,z. I want to lift g. So I want to do

q1, q2, q3, q4 = g.lift(J)
q1=1/3 * q1(w,x,y,z).derivative(w)
q2=1/3 *q2(w,x,y,z).derivative(x)
q3=1/3 *q3(w,x,y,z).derivative(y)
q4=1/3*q4(w,x,y,z).derivative(z)
h1=q1+q2+q3+q4

Now, the Symbolic ring has no attribute lift. This can be fixed by moving to Multivariate Polynomiial Ring by doing

g=g.polynomial(QQ)

The issue is, because g is only a function in w,x,z, this moves g to the Multivariate Polynomial Ring of w,x,z. This gives error as the Jacobian and function f is in Multivariate Polynomial Ring of w,x,y,z. I want g to be in the Multivariate Polynomial Ring of w,x,y,z even though there is no y in g. How can I do this? See attachment. C:\fakepath\Screenshot (126).png

So the idea is I was first working over

R.<w,x,y,z>=QQ[]

I have a function f and J is the Jacobian of f belonging to the ring above. I do some stuff and I end with a polynomial g in a symbolic ring in variables w,x,z. I want to lift g. So I want to do

q1, q2, q3, q4 = g.lift(J)
q1=1/3 * q1(w,x,y,z).derivative(w)
q2=1/3 *q2(w,x,y,z).derivative(x)
q3=1/3 *q3(w,x,y,z).derivative(y)
q4=1/3*q4(w,x,y,z).derivative(z)
h1=q1+q2+q3+q4

Now, the Symbolic ring has no attribute lift. This can be fixed by moving to Multivariate Polynomiial Ring by doing

g=g.polynomial(QQ)

The issue is, because g is only a function in w,x,z, this moves g to the Multivariate Polynomial Ring of w,x,z. This gives error as the Jacobian and function f is in Multivariate Polynomial Ring of w,x,y,z. I want g to be in the Multivariate Polynomial Ring of w,x,y,z even though there is no y in g. How can I do this? See attachment. C:\fakepath\Screenshot (126).pngC:\fakepath\Screenshot (123).png

So the idea is I was first working over

R.<w,x,y,z>=QQ[]

I have a function f and J is the Jacobian of f belonging to the ring above. I do some stuff and I end with a polynomial g in a symbolic ring in variables w,x,z. I want to lift g. So I want to do

q1, q2, q3, q4 = g.lift(J)
q1=1/3 * q1(w,x,y,z).derivative(w)
q2=1/3 *q2(w,x,y,z).derivative(x)
q3=1/3 *q3(w,x,y,z).derivative(y)
q4=1/3*q4(w,x,y,z).derivative(z)
h1=q1+q2+q3+q4

Now, the Symbolic ring has no attribute lift. This can be fixed by moving to Multivariate Polynomiial Ring by doing

g=g.polynomial(QQ)

The issue is, because g is only a function in w,x,z, this moves g to the Multivariate Polynomial Ring of w,x,z. This gives error as the Jacobian and function f is in Multivariate Polynomial Ring of w,x,y,z. I want g to be in the Multivariate Polynomial Ring of w,x,y,z even though there is no y in g. How can I do this? See attachment. attachment. In the attachment, h2 plays the role of g in my explanation above. C:\fakepath\Screenshot (126).pngC:\fakepath\Screenshot (123).png

So the idea is I was first working over

R.<w,x,y,z>=QQ[]

I have a function f and J is the Jacobian of f belonging to the ring above. I do some stuff and I end with a polynomial g in a symbolic ring in variables w,x,z. I want to lift g. So I want to do

q1, q2, q3, q4 = g.lift(J)
q1=1/3 * q1(w,x,y,z).derivative(w)
q2=1/3 *q2(w,x,y,z).derivative(x)
q3=1/3 *q3(w,x,y,z).derivative(y)
q4=1/3*q4(w,x,y,z).derivative(z)
h1=q1+q2+q3+q4

Now, the Symbolic ring has no attribute lift. This can be fixed by moving to Multivariate Polynomiial Ring by doing

g=g.polynomial(QQ)

The issue is, because g is only a function in w,x,z, this moves g to the Multivariate Polynomial Ring of w,x,z. This gives error as the Jacobian and function f is in Multivariate Polynomial Ring of w,x,y,z. I want g to be in the Multivariate Polynomial Ring of w,x,y,z even though there is no y in g. How can I do this? See my 2 attachment. In the attachment, h2 plays the role of g in my explanation above. C:\fakepath\Screenshot (126).pngC:\fakepath\Screenshot (123).png