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Abstract Algebra

Below you can find a complete list of the existing commands related to Abstract Algebra. You can access the dedicated documentation for each command by clicking on its name.

adjoint_element

Adjoint element of a finite field quotient a polynomial

annihilating_polynomial

Annihilating polynomial of an irrational

base

Base ring of an extension

cardinal

Cardinality of a set

characteristic

Characteristic of a ring

components

Element components in a ring

conjugates

Conjugate of an element over the base field of an extension

content_and_primitive_part

Content and primitive part of a polynomial

content

Content of a polynomial

element_of_order

Element of a desired order in a ring

elements

Elements of a set

element

Element of a set

extension

Algebraic extension constructor

field?

Checks if a set is a field

field

Field where an element belongs

finite_field

Finite field constructor

finite?

Checks if a ring is finite

frobenius

Frobenius endomorphism

index

Position of an element in a set

irreducible_polynomials

Irreducible polynomials of the desired degree

irreducible_polynomial

Irreducible polynomial of the desired degree

irreducible?

Checks if a polynomial is irreducible

number_of_irreducible_polynomials

Amount of irreducible polynomials

order

Order of an element over a field

power_modulo

Power of a polynomial modulo another polynomial

precedent

Precedent algebraic structure of an extension

primitive_element

Primitive element of a field

primitive_part

Primitive part of a polynomial

pseudoremainder

Pseudoremainder of two polynomials

relative_degree

Relative degree of an extension

resultant

Resultant of two polynomials

resultant_matrix

Resultant matrix of two polynomials

ring?

Checks if a set is a ring

subextension?

Checks if an extension is a subextension

total_degree

Total degree of a field extension

tower

Tower of an extension

Zn

Zp constructor