Programming Language: Python

Namespace/Package Name: sage.structure.parent

Class/Type: Parent

Examples at hotexamples.com: 60

The `sage.structure.parent.Parent` class is a base class for all parent instances in SageMath. It defines the basic interface for creating elements, testing membership of elements, and creating new subrings, subfields, or subgroups.

Here are some code examples using `Parent`:

**Example 1:**

This code creates a polynomial ring `R` over the rational numbers `QQ`, then creates a quotient ring `S` by factoring out the ideal generated by `x^2 + 1`. Finally, it creates a parent instance `P` that represents the ring `S`.

Package/Library: SageMath

**Example 2:**

Here are some code examples using `Parent`:

R.= PolynomialRing(QQ) S = R.quotient(x^2 + 1) P = S.parent()

This code creates a polynomial ring `R` over the rational numbers `QQ`, then creates a quotient ring `S` by factoring out the ideal generated by `x^2 + 1`. Finally, it creates a parent instance `P` that represents the ring `S`.

Package/Library: SageMath

V = VectorSpace(GF(2), 3) W = V.subspace([ (1,0,1), (0,1,1) ]) P = W.parent()This code creates a vector space `V` over the finite field `GF(2)` with dimension 3. Then it creates a subspace `W` of `V` generated by the two vectors `(1,0,1)` and `(0,1,1)`. Finally, it creates a parent instance `P` that represents the subspace `W`. Package/Library: SageMath Overall, `Parent` is a fundamental class in SageMath that provides a way to represent mathematical objects such as rings, groups, fields, vector spaces, etc., and their substructures.

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