Ciro Santilli
OurBigBook.com
$£
Sponsor
中国
独裁统治 China Dictatorship 新疆改造中心、六四事件、法轮功、郝海东、709大抓捕、2015巴拿马文件 邓家贵、低端人口、西藏骚乱
Function by signature
Home
Mathematics
Area of mathematics
Formalization of mathematics
Function (mathematics)
OurBigBook.com
Words: 2k
Articles: 83
In this section we classify some functions by the type of inputs and outputs they take and produce.
Table of contents
2k
83
Functional function
Function by signature
11
1
Convolution
Functional function
Set function
Function by signature
38
2
Cartesian product
Set function
9
Direct product
Set function
19
Numeric function
Function by signature
2k
77
Addition
Numeric function
Subtraction
Numeric function
Multiplication
Numeric function
Division
Numeric function
Exponentiation
(
x
y
)
Numeric function
623
13
nth root
Exponentiation
1
Square root
nth root
Exponentiation functional equation
Exponentiation
20
Exponential function
(
e
x
)
Exponentiation
603
9
Exponential function differential equation
Exponential function
41
Definition of the exponential function
Exponential function
430
2
Taylor expansion definition of the exponential function
Definition of the exponential function
63
Product definition of the exponential function
Definition of the exponential function
367
Gaussian function
(
e
−
x
2
)
Exponential function
Logarithm
Exponential function
Matrix exponential
Exponential function
132
2
Logarithm of a matrix
Matrix exponential
71
1
Existence of the matrix logarithm
Logarithm of a matrix
71
Polynomial
Numeric function
874
56
Degree of a polynomial
Polynomial
Algebraic equation
(Polynomial equation)
Polynomial
149
15
Named algebraic equation
Algebraic equation
7
Quadratic equation
Named algebraic equation
2
Quadratic equation modulo n
(Quadratic equation over a cyclic group)
Quadratic equation
Quadratic formula
Quadratic equation
Cubic equation
Named algebraic equation
Quartic equation
Named algebraic equation
Quintic equation
Named algebraic equation
1
Abel-Ruffini theorem
Quintic equation
Algebraic equation over a field
Algebraic equation
10
Algebraic equation modulo n
Algebraic equation
Algebraic number
(Root of a polynomial)
Algebraic equation
139
4
Algebraic number field
(
Q
)
Algebraic number
106
Algebraic function
(Root of a polynomial)
Algebraic number
2
Transcendental number
Algebraic number
31
1
Transcendental number conjecture
Transcendental number
23
Diophantine equation
Polynomial
263
28
Pythagorean triple
(
a
2
+
b
2
=
c
2
)
Diophantine equation
13
7
Euclid's formula
Pythagorean triple
4
2
There are infinitely many Pythagorean triples
Euclid's formula
4
Euclid's formula generates all Pythagorean triples
Euclid's formula
Classification of Pythagorean triples
Pythagorean triple
Taxicab number
Pythagorean triple
Fermat's last theorem
Pythagorean triple
9
1
Andrew Wiles
Fermat's last theorem
3
Hilbert's tenth problem
(1970, Determine if one Diophantine equation has a solution)
Diophantine equation
87
7
Hilbert's tenth problem variant
Hilbert's tenth problem
38
6
Decidability of Hilbert's tenth problem in modular arithmetic
Hilbert's tenth problem variant
11
Decidability of Hilbert's tenth problem of a given degree and number of variables
Hilbert's tenth problem variant
12
3
Quadratic Diophantine equation
Decidability of Hilbert's tenth problem of a given degree and number of variables
Hilbert's tenth problem is decidable for quadratic equations
Decidability of Hilbert's tenth problem of a given degree and number of variables
6
Undecidable Diophantine equation example
Decidability of Hilbert's tenth problem of a given degree and number of variables
6
Hilbert's tenth problem over other rings
Hilbert's tenth problem variant
15
Additive number theory
Diophantine equation
114
11
Additive basis
Additive number theory
114
10
Additive basis theorem
Additive basis
114
9
Waring's problem
(Every number is a sum of
g
positive numbers to the power of
k
)
Additive basis theorem
114
8
Waring's problem for squares
Waring's problem
25
3
Lagrange's four-square theorem
(Every natural number is a sum of four squares, 1770)
Waring's problem for squares
Legendre's three-square theorem
(iff not of form
4
a
(
8
b
+
7
)
, 1770)
Waring's problem for squares
Sum of two squares theorem
Waring's problem for squares
Waring problem variant
Waring's problem
73
3
Waring problem with negative numbers allowed
Waring problem variant
51
1
Sum of three cubes
(Every number has infinitely many representations as the sum of three cubes)
Waring problem with negative numbers allowed
51
Waring-Goldbach problem
Waring problem variant
22
Named small order polynomial
Polynomial
11
1
Linear polynomial
Named small order polynomial
11
Galois theory
Polynomial
Irreducible polynomial
Polynomial
Multivariate polynomial
Polynomial
44
Domain of a polynomial
Polynomial
396
3
Polynomial over a field
(
F
i
e
l
d
[
X
]
)
Domain of a polynomial
239
Polynomial over a ring
Domain of a polynomial
127
Polynomial over a commutative ring
Domain of a polynomial
30
Polynomial ring
Polynomial
11
Step function
Numeric function
1
Heavyside step function
Step function
Ancestors
(5)
Function (mathematics)
Formalization of mathematics
Area of mathematics
Mathematics
Home
Ciro Santilli
OurBigBook.com