Programming Language: Python

Namespace/Package Name: sage.all

Class/Type: PolynomialRing

Examples at hotexamples.com: 60

PolynomialRing is a part of the Python package SageMath and it allows you to create polynomial rings from a given field. PolynomialRing is used for polynomial algebra and it makes performing algebraic computations much easier.

**Example 1:** Creation of a polynomial ring

The following code is an example of how to create a polynomial ring with a variable 'x' over the field of rational numbers:

**Example 2:** Polynomial evaluation

In this example, we create a polynomial in the variable 'x' and then evaluate it at a specific value:

The result of this code would be 0, since the polynomial evaluates to 0 when x=1.

**Example 3:** Polynomial arithmetic

PolynomialRing allows for polynomial arithmetic. Here is an example of polynomial addition:

The following code is an example of how to create a polynomial ring with a variable 'x' over the field of rational numbers:

R.= PolynomialRing(QQ)

In this example, we create a polynomial in the variable 'x' and then evaluate it at a specific value:

R.= PolynomialRing(QQ) f = x^2 - 3*x + 2 print(f(1))

The result of this code would be 0, since the polynomial evaluates to 0 when x=1.

PolynomialRing allows for polynomial arithmetic. Here is an example of polynomial addition:

R.The result of this code would be x^3 + 3x^2 - 6x + 3. In summary, PolynomialRing is a package library that is used for performing algebraic computations with polynomials. It is a part of the SageMath package for Python. The examples shown above illustrate some of the basic functionalities of this package library.= PolynomialRing(QQ) f = x^2 - 3*x + 2 g = x^3 + 2*x^2 - 3*x + 1 h = f + g print(h)

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