### How can I formally multiply two polynomials from different rings.

Suppose I take a polynomial from ~~$R[x]$ ~~$K[x]$, say ~~$x^2+5x$ ~~$x^2 + 5x$,
and another polynomial from ~~$R[y]$ ~~$K[y]$, say ~~$y^3$. ~~$y^3$.
I want to formally multiply them and ~~print ~~get $x^2y^3 ~~+5xy^3$ ~~+ 5xy^3$ as the ~~output. ~~output.

How can I do that?

Note: ~~K ~~`K`

is the finite field of size 4 in ~~'a'~~`a`

.

My efforts:

~~R_1=PolynomialRing(K,['z%s'%p ~~sage: K.<a> = FiniteField(4)
sage: R_1 = PolynomialRing(K, ['z%s' % p for p in ~~range(1,3)])
R_2=PolynomialRing(K,['x%s'%p ~~range(1, 3)])
sage: R_2 = PolynomialRing(K, ['x%s' % p for p in ~~range(1,3)])
pp=R_1.random_element()
~~range(1, 3)])
sage: pp = R_1.random_element()
sage: pp
(a + 1)*z1^2 + (a)*z1*z2 + (a + 1)*z2 + (a)
~~qq=R_2.random_element()
~~sage: qq = R_2.random_element()
sage: qq
x1*x2 + (a + 1)*x2^2 + x1 + 1

When I do `pp*qq`

I get the following output

`unsupported operand parent(s) for *: 'Multivariate Polynomial `~~Ring ~~Ring
in z1, z2 over Finite Field in a of size 2^2' and 'Multivariate ~~Polynomial ~~Polynomial
Ring in x1, x2 over Finite Field in a of size 2^2'