Category:Polynomial Theory
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This category contains results about Polynomial Theory.
Definitions specific to this category can be found in Definitions/Polynomial Theory.
Polynomial theory is a branch of abstract algebra which studies polynomials.
Subcategories
This category has the following 73 subcategories, out of 73 total.
B
- Boubaker Polynomials (7 P)
C
- Companion Matrices (1 P)
- Constant Polynomials (1 P)
D
- Descartes's Rule of Signs (7 P)
- Difference of Two Squares (8 P)
E
F
- Formal Laurent Series (empty)
- Formal Power Series (empty)
- Fundamental Theorem of Algebra (10 P)
G
- Galois Groups of Polynomials (1 P)
H
I
K
L
- Linear Functions (1 P)
- Little Bézout Theorem (4 P)
M
- Monic Polynomials (1 P)
- Monomials (8 P)
O
P
- Polynomial Addition (1 P)
- Polynomial Division (empty)
- Polynomial Factor Theorem (4 P)
- Polynomial Rings (15 P)
Q
- Quadratic Polynomials (empty)
R
- Roots of Polynomials (empty)
S
- Separable Polynomials (empty)
- Splitting Polynomials (empty)
- Symmetric Polynomials (1 P)
T
- Tschirnhaus Transformations (1 P)
V
Pages in category "Polynomial Theory"
The following 117 pages are in this category, out of 117 total.
A
C
- Canonical Homomorphism to Polynomial Ring is Ring Monomorphism
- Coefficients of Polynomial Product
- Coefficients of Product of Two Polynomials
- Complex Roots of Polynomial with Real Coefficients occur in Conjugate Pairs
- Condition for Linear Divisor of Polynomial
- Conjugate of Polynomial is Polynomial of Conjugate
- Content of Scalar Multiple
D
- Definition of Polynomial from Polynomial Ring over Sequences
- Degree of Product of Polynomials over Integral Domain not Less than Degree of Factors
- Degree of Product of Polynomials over Ring
- Degree of Sum of Polynomials
- Descartes's Rule of Signs
- Difference of Two Powers
- Difference of Two Powers/General Commutative Ring
- Difference of Two Squares
- Dimension of Vector Space of Polynomial Functions
- Division Theorem for Polynomial Forms over Field
- Double Root of Polynomial is Root of Derivative
E
- Epimorphism from Polynomial Forms to Polynomial Functions
- Equality of Polynomials
- Equivalence of Definitions of Polynomial Function on Subset of Ring
- Equivalence of Definitions of Polynomial in Ring Element
- Equivalence of Definitions of Polynomial Ring
- Equivalence of Definitions of Polynomial Ring in Multiple Variables
- Equivalence of Definitions of Polynomial Ring in One Variable
- Existence of Real Polynomial with no Real Root
- Existence of Ring of Polynomial Forms in Transcendental over Integral Domain
- Exponential Dominates Polynomial
F
- Factorisation of Quintic x^5 - x + n into Irreducible Quadratic and Irreducible Cubic
- Factors of Polynomial with Integer Coefficients have Integer Coefficients
- Field of Quotients of Ring of Polynomial Forms on Reals that yields Complex Numbers
- Field of Rational Functions is Field
- Formal Derivative of Polynomials Satisfies Leibniz's Rule
- Free Commutative Monoid is Commutative Monoid
- Fundamental Theorem of Algebra
G
I
L
M
P
- Polynomial Addition is Associative
- Polynomial Addition is Commutative
- Polynomial Factor Theorem
- Polynomial Factor Theorem/Corollary
- Polynomial Forms is PID Implies Coefficient Ring is Field
- Polynomial Forms over Field form Integral Domain
- Polynomial Forms over Field form Integral Domain/Formulation 1
- Polynomial Forms over Field form Principal Ideal Domain
- Polynomial Forms over Field is Euclidean Domain
- Polynomial Functions form Submodule of All Functions
- Polynomial is Linear Combination of Monomials
- Polynomial over Field has Finitely Many Roots
- Polynomial over Field is Reducible iff Scalar Multiple is Reducible
- Polynomial Ring is Generated by Indeterminate over Ground Ring
- Polynomial Ring of Sequences is Ring
- Polynomial which is Irreducible over Integers is Irreducible over Rationals
- Polynomial X^2 + 1 is Irreducible in Ring of Real Polynomials
- Polynomials Closed under Addition
- Polynomials Closed under Addition/Polynomial Forms
- Polynomials Closed under Addition/Polynomials over Integral Domain
- Polynomials Closed under Addition/Polynomials over Integral Domain/Proof 1
- Polynomials Closed under Addition/Polynomials over Integral Domain/Proof 2
- Polynomials Closed under Addition/Polynomials over Ring
- Polynomials Closed under Ring Product
- Polynomials Contain Multiplicative Identity
- Polynomials of Congruent Integers are Congruent
- Polynomials of Congruent Ring Elements are Congruent
- Primary Decomposition Theorem
- Product of Polynomials is Polynomial
- Product of Primitive Polynomials is Primitive
- Product of Rational Polynomials
- Properties of Degree
R
S
- Set of Polynomials over Infinite Set has Same Cardinality
- Set of Polynomials over Integral Domain is Subring
- Stabilizer of Polynomial
- Submodule of Module of Polynomial Functions
- Subring of Polynomials over Integral Domain Contains that Domain
- Subring of Polynomials over Integral Domain is Smallest Subring containing Element and Domain
- Sum of Two Odd Powers
- Symmetric Function Theorem
T
U
- Unique Representation in Polynomial Forms
- Unique Representation in Polynomial Forms/General Result
- Unique Representation in Polynomial Forms/General Result/Corollary
- Uniqueness of Polynomial Ring in One Variable
- Units of Ring of Polynomial Forms over Commutative Ring
- Units of Ring of Polynomial Forms over Field
- Units of Ring of Polynomial Forms over Integral Domain
- Universal Property of Field of Rational Fractions
- Universal Property of Polynomial Ring
- Universal Property of Polynomial Ring/Free Monoid on Set