Supported Functions and Operators

Corca supports a wide range of mathematical functions, operators, relations, brackets, and symbolic notation across different areas of mathematics.

In most cases, you can simply type naturally and Corca will recognize the notation automatically. But when you need to check whether a specific function exists, look up a symbol, or explore less common notation, this page serves as a complete reference.

The reference is organized by area — arithmetic, algebra, calculus, trigonometry, logic, set theory, geometry, analysis, and others — so you can quickly jump to the part you need instead of searching through everything manually.

Each entry includes the name of the function or operator together with the notation used inside Corca expressions. Some are familiar operations such as +, (log_)(x), or (∫_^)(x*d(x)). Others are more specialized symbols used in areas like functional analysis, group theory, or mathematical logic.

Use this page while writing mathematics, importing LaTeX, or checking which notation Corca understands directly.

Arithmetics

Function Name	Symbol
Plus	+
Divide By	/
Subtraction	-
Division	÷
Multiplication	⋅
Multiplication	×
Plus Minus	±
Logarithm	(log_)()
Logarithm Base 10, Lg	lg()
Logarithm Base 2	(log_2)()
Logarithm Base 2, Lb	lb()
Natural Logarithm, Ln	ln()
Greatest Common Divisor	gcd(,)
Least Common Multiple	lcm(,)
Omega Function	ω()
Capital Omega Function	Ω()
Euler Totient Function	𝜙()
Dirichlet Function	D()
Riemann Function	R()
Modulo	mod(,)
Arithmetic Mean	AM()
Average	AM()
Geometric Mean	GM()
Arithmetic-Geometric Mean	AGM(,)
Min	min()
Max	max()

Relations

Name	Symbol
Not Equal	≠
Not Yet Demonstrated To Be Equal	≟
Equal To By Definition	≝
Delta Equal To	≜
Ring In Equal To	≖
Ring Equal To	≗
Corresponds To	≘
Estimates	≙
Equiangular to	≚
Star Equals	≛
Precedes	≺
Not Precedes	⊀
Less Than	<
Less Than With Dot	⋖
Greater Than With Dot	⋗
Less Than Or Equal To	≤
Greater Than Above Double Line Equal Above Less Than	⪌
Succeeds Not Equal	⪊
Greater Than and Single Line Not Equal To	⪈
Greater Than or Approximate	⪆
Less Than Above Double Line Equal Above Greater Than	⪋
Less Than and Not Approximate	⪉
Less Than and Single Line Not Equal To	⪇
Less Than or Approximate	⪅
Precedes Above Almost Equal To	⪷
Precedes Above Not Almost Equal To	⪹
Precedes Above Not Equal To	⪵
Precedes Above Single Line Equals	⪯
Slanted Equal To or Greater Than	⪖
Slanted Equal To or Less Than	⪕

Groups

Name	Symbol
Parenthesis	()
Square Brackets	[]
Braces	{}
Double Braces	⦃⦄
Bar Brackets	\|\|
Double Bar Brackets	‖‖
Angle Brackets	<>
Bra Brackets	<\|
Ket Brackets	\|>
Open Interval Brackets	]][[
Ceiling Brackets	⌈⌉
Floor Brackets	⌊⌋
Moustache Brackets	⎰⎱
Double Stroke Brackets	⟦⟧

Geometry

Name	Symbol
Ratio	∶
Ring Equal To	≗
Corresponds To	≘
Estimates	≙
Equiangular to	≚
Star Equals	≛
Congruent	≅
Parallel	∥
Equal And Parallel To	⋕
Not Parallel To	∦
Perpendicular	⟂
Perpendicular Angle	⊾
Angle	∠
Measured Angle	∡
Excess	∹
Geometric Proportion	∺
Right Angle	∟
Triangle	△
Circle	○
Geometrically Equal	≑
Geometrically Equivalent	≎
Spherical Angle	∢
Rightwards Arrow	→
Leftwards Arrow	←
Upwards Arrow	↑
Downwards Arrow	↓
Upper Right Arrow	↗
Lower Left Arrow	↙
Left Right Arrow	↔
Up Down Arrow	↕
Tri-Pointed Upwards Arrow	⇵
North West Arrow	↖
South East Arrow	↘
Distance Between Two Points	dist(,)

Algebra

Name	Symbol
Dot Plus	∔
Cartesian Product	⨉
Cross Product	⨯
Triple Tilde	≋
Similar To	~
Not Similar	≁
Difference Between	≏
Almost Equal To	≊
Not Almost Equal To	≉
Approximately Equal To	≒
Image Of Or Approximately Equal To	≓
Approximately Equal	≒
Equal To Or Approximately Equal To	⋍
Equivalent To	≡
Strictly Equivalent To	≣
Not Equivalent	≢
Approximately But Not Actually Equal	≆
Defined As	≔
Not Asymptotically Equal	≄
Not Equivalent	≢
Between	≬
Join	∨
Minus Tilde	≂
Homothetic	∻
Transpose	⊺
Tensor Product	⨂
Direct Sum	⨁
Multimap	⊸
Hadamard Product	⨀
Khatri–Rao Product	∗
Determinant	det()
Trace	tr()
Rank	rank()
Kernel	ker()
Image Of The Function	im()
Metric Signature	sign()
Divide-Times	⋇
Retraction	↩
Inclusion Map	↪
Dot Product	⋅
Direct Sum	⨁

Trigonometry

Name	Symbol
Hyperbolic Sine	sinh()
Hyperbolic Cosine	cosh()
Hyperbolic Tangent	tanh()
Hyperbolic Cotangent	coth()
Hyperbolic Secant	sech()
Hyperbolic Cosecant	csch()
Hyperbolic Arcsine	arcsinh()
Hyperbolic Arccosine	arccosh()
Hyperbolic Arctangent	arctanh()
Hyperbolic Arccotangent	arccoth()
Hyperbolic Arcsecant	arcsech()
Hyperbolic Arccosecant	arccosh()
Atan2	atan2(,)
Versine	versin()
Coversine	cvs()
Exsecant	exsec()
Excosecant	excsc()
Haversine	haversin()
Hacoversine	hacoversin()
Gudermannian	gd()

Calculus

Name	Symbol
Infimum	(inf_)()
Supremum	(sup_)()
Exponential Function	exp()
Limit	(lim_)()
Differential	d()
Second Differential	(d^2)()
Third Differential	(d^3)()
N-Differential	(d^N)()
Partial Differential	∂()
Second Partial Differential	(∂^2)()
Third Partial Differential	(∂^3)()
N-Partial Differential	(∂^N)()
Delta	Δ()
Summation	(∑_^)()
Modulo Two Sum	(⨊_^)()
Product	(∏_^)()
Coproduct	(∐_^)()
Definite Integral	(∫_^)()
Indefinite Integral	∫()
Double Integral	(∬_^)()
Triple Integral	(∭_^)()
Contour Integral	(∮_)()
Clockwise Integral	(∱_)()
Clockwise Contour Integral	(∲_)()
Anticlockwise Contour Integral	(∳_)()
Surface Integral	(∯_)()
Anticlockwise Integral	(∳_)()
Integral Average	(⨏_)()
Integral with Double	(⨎_)()
Finite Part Integral	(⨍_)()
Integral with Union	(⨚_)()
Integral with Intersection	(⨙_)()
Integral with Leftwards Arrow with Hook	(⨗_)()
Integral with Times	(⨘_)()
Integral Around a Point Operator	(⨕_)()
Line Integration Not Including the Pole	(⨔_)()
Quaternion Integral Operator	(⨖_)()
Line Integration with Rectangular Path Around Pole	(⨒_)()
Line Integration with Semicircular Path Around Pole	(⨓_)()
Volume Integral	(∰_)()
Buchstab Function	ω()
Boxcar Function	П()
Exponental Generating Function	EG()
Definite Integral Evaluation	(∣_^)()
Poisson Generating Function	PG()
Boustrophedon Transform	b()
Bourget Function	(J__)()
Summation With Integral	(⨋_^)()

Group Theory

Name	Symbol
Set Difference	∖
Subset Of	⊂
Double Subset	⋐
Not A Subset Of	⊄
Double Superset	⋑
Disjoint Union	⊎
Natural Join	⨝
Multiset Union	⨄
Superset Of	⊃
Not A Superset Of	⊅
Superset Of Or Equal To	⊇
Superset Of With Not Equal To	⊋
Subset Of With Not Equal To	⊊
Not An Improper Superset	⊉
Subset Of Or Equal To	⊊
Not Improper Subset	⊈
Element Of	∈
Not An Element Of	∉
Ring In Equal To	≖
Greater Than Above Double Line Equal Above Less Than	⪌
Greater Than and Single Line Not Equal To	⪈
Greater Than or Approximate	⪆
Less Than Above Double Line Equal Above Greater Than	⪋
Less Than and Not Approximate	⪉
Less Than and Single Line Not Equal To	⪇
Less Than or Approximate	⪅
Subset of Above Equals	⫅
Subset of Above Not Equal To	⫋
Superset of Above Equals	⫆
Superset of Above Not Equal To	⫌
Does Not Succeed	⊁
Precedes Or Equivalent To	≾
Succeeds Or Equivalent To	≿
Wreath Product	≀
Union	∪
Intersection	∩
Intersect Transversally	⋔
Square Image Of Or Equal To	⊑
Square Original Of Or Equal To	⊒
Square Image Of	⊏
Square Original Of	⊐
Disjoint Union	⊎
Add Member	;
Power Set	P()
Union Of Sets	(⋃_^)()
Intersection Of Sets	(⋂_^)()
N-Ary Logical And	(⋀_^)()
N-Ary Logical Or	(⋁_^)()
Disjoint Union	⊎
Double Intersection	⋒
Double Union	⋓
Rightwards Two-Headed Arrow	↠
Leftwards Arrow From Bar	↤
Rightwards Arrow From Bar	↦

Logic

Name	Symbol
Less Than With Dot	⋖
Greater Than With Dot	⋗
Contradiction	⊥
Tautology	⊤
Logical And	∧
Logical Or	∨
Logical Exclusive Or	⊻
Logical Nand	⊼
Logical Nor	⊽
Implies	→
For All	∀
There Exists Exactly One	∃!
There Doesn't Exist	∄
Logical Not	¬
If And Only If	↔
There Exists	∃
Such That	:
Approaches The Limit	≐
Proves	⊦
Entails	⊨
Derivability	⊪
Logical Consequence	⊫
Diamond	◇
Box Operator	◻
Turnstile	⊢
Forces	⊩
Satisfaction	⊧
Does Not Entail	⊭
Because	∵
Not Entailed	⊬
End Of Proof	∎
Therefore	∴
Ellipsis	⋯
3 Dots	⋯
Measured By	≞
Does Not Model	⊯
Then	⇒
If And Only If	⇔
End Of Proof	⊣
Converse Implication	⇐
To	→
Does Not Imply	↛
Is Not Implied By	↚
Upwards Double Arrow	⇑
Downwards Double Arrow	⇓
Long Left Right Arrow	⟷

Order Theory

Name	Symbol
Precedes	≺
Not Precedes	⊀
Succeeds Not Equal	⪊
Precedes Above Almost Equal To	⪷
Precedes Above Not Almost Equal To	⪷
Precedes Above Not Equal To	⪹
Precedes Above Single Line Equals	⪯
Slanted Equal To or Greater Than	⪖
Slanted Equal To or Less Than	⪕
Succeeds Above Almost Equal To	⪸
Succeeds Above Not Almost Equal To	⪺
Succeeds Above Not Equal To	⪶
Succeeds Above Single-Line Equals	⪰
Succeeds	≻
Precedes Or Equal To	≼
Succeeds Or Equal To	≽
Isomorphic To	≃
Join	∨
Bottom Element	⊥
Top Element	⊤
Wedge Product	⋏

Complex & Functional Analysis

Name	Symbol
Gradient	∇
Laplacian	∇
Divergence	div()
Curl	curl()
Argument Of A Complex Number	arg()
Minus-Plus	∓
Proportional To	∝
As	∷
Hamiltonian	H()
Fourier Transform	ℱ()
Fourier Bessel Transform	(ℱ_B)()
Abel Transform	g()
Instrument Function	I()
Large Tensor Product	(⨂_^)()

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