PRODUCTS
Products Overview
Mathematica
Mathematica for Students
Mathematica Home Edition
Wolfram
CDF Player
(free download)
Computable Document Format (CDF)
web
Mathematica
grid
Mathematica
Wolfram
Workbench
Mathematica
Add-Ons
Wolfram|Alpha Products
SOLUTIONS
Solutions Overview
Engineering
Aerospace Engineering & Defense
Chemical Engineering
Control Systems
Electrical Engineering
Image Processing
Industrial Engineering
Materials Science
Mechanical Engineering
Operations Research
Optics
Petroleum Engineering
Biotechnology & Medicine
Bioinformatics
Medical Imaging
Finance, Statistics & Business Analysis
Actuarial Sciences
Data Analysis & Mining
Econometrics
Economics
Financial Engineering & Mathematics
Financial Risk Management
Statistics
Software Engineering & Content Delivery
Authoring & Publishing
Interface Development
Software Engineering
Web Development
Science
Astronomy
Biological Sciences
Chemistry
Environmental Sciences
Geosciences
Social & Behavioral Sciences
Design, Arts & Entertainment
Game Design, Special Effects & Generative Art
Education
STEM Education Initiative
Higher Education
Community & Technical College Education
Primary & Secondary Education
Students
Technology
Computable Document Format (CDF)
High-Performance & Parallel Computing (HPC)
See Also: Technology Guide
PURCHASE
Online Store
Other Ways to Buy
Volume & Site Licensing
Contact Sales
Software
Service
Upgrades
Training
Books
SUPPORT
Support Overview
Knowledge Base
Learning Center
Community & Forums
Training & Free Seminars
Does My Site Have a License?
Wolfram User Portal
COMPANY
About Wolfram Research
News & Events
Wolfram Blog
Partnerships
Employment Opportunities
History of
Mathematica
Stephen Wolfram's Home Page
Contact Us
OUR SITES
All Sites
Wolfram|Alpha
Demonstrations Project
MathWorld
Integrator
Wolfram Functions Site
Mathematica Journal
Wolfram Media
Wolfram
Tones
Wolfram Science
Stephen Wolfram
DOCUMENTATION CENTER SEARCH
New to
Mathematica
?
Find your learning path
»
Mathematica
>
Mathematics and Algorithms
>
Formula Manipulation
>
Algebraic Transformations
>
Algebraic Numbers
>
MinimalPolynomial
>
Mathematica
>
Mathematics and Algorithms
>
Number Theory
>
Algebraic Number Theory
>
Algebraic Numbers
>
MinimalPolynomial
>
Mathematica
>
Mathematics and Algorithms
>
Mathematical Functions
>
Number Theoretic Functions
>
Algebraic Number Theory
>
Algebraic Numbers
>
MinimalPolynomial
>
BUILT-IN MATHEMATICA SYMBOL
Algebraic Number Fields
Tutorials »
|
Root
RootReduce
RootApproximant
AlgebraicNumber
See Also »
|
Algebraic Numbers
Algebraic Number Theory
Number Recognition
Number Theory
Polynomial Algebra
New in 6.0: Number Theory & Integer Functions
More About »
MinimalPolynomial
MinimalPolynomial
gives the minimal polynomial in
x
for which the algebraic number
s
is a root.
MORE INFORMATION
MinimalPolynomial
[
s
]
gives a pure function representation of the minimal polynomial of
s
.
MinimalPolynomial
[
s
,
x
,
Extension
->
a
]
finds the characteristic polynomial of
s
over the field
.
EXAMPLES
CLOSE ALL
Basic Examples
(2)
In[1]:=
Out[1]=
In[1]:=
Out[1]=
Scope
(4)
Radical expressions:
Root
objects:
AlgebraicNumber
objects:
MinimalPolynomial
automatically threads over lists:
Generalizations & Extensions
(1)
Express the minimal polynomial as a pure function:
Options
(1)
Find the characteristic polynomial of
over the extension
E
^(
I
Pi
/4)
of
:
Applications
(2)
Construct a polynomial with a root
:
The degree of the number field generated by
(2-
I
)/
Sqrt
[5]
:
Properties & Relations
(1)
Compute the extension that defines the number field
:
Find the characteristic polynomial of
over
:
SEE ALSO
Root
RootReduce
RootApproximant
AlgebraicNumber
TUTORIALS
Algebraic Number Fields
MORE ABOUT
Algebraic Numbers
Algebraic Number Theory
Number Recognition
Number Theory
Polynomial Algebra
New in 6.0: Number Theory & Integer Functions
New in 6