sage: R.= PolynomialRing(QQ) sage: R Polynomial Ring in x over Rational Field
sage: R.= PolynomialRing(GF(2)) sage: R Multivariate Polynomial Ring in x, y, z over Finite Field of degree 1
sage: R.In this example, we create a polynomial ring in one variable called `t` with coefficients that are polynomials in `a`, `b`, and `c`. We use the `ZZ['a','b','c']` syntax to create a polynomial ring over the integer ring with variables `a`, `b`, and `c`. The output confirms that we have created a polynomial ring in `t` over a univariate polynomial ring in `a`, `b`, and `c` over the integer ring. In summary, the `PolynomialRing` constructor in SageMath is a powerful tool for creating polynomial rings with custom variables, coefficients, and other properties. This constructor is part of the `sage.rings.polynomial.polynomial_ring_constructor` package library in SageMath.= PolynomialRing(ZZ['a','b','c']) sage: R Polynomial Ring in t over Univariate Polynomial Ring in a, b, c over Integer Ring