_i

_i

_i

$i$

_i

_i

ffi.new("complex", 0, 1)

{0,1}

ii

_i|0+1i

symmath.i

e

e

e

$e$

e

e

e

e

e

e

var("e")

π

π

π

$π$

M_PI

Math.PI

math.pi

pi

π

π|3.1415926535898

symmath.pi

inf

∞

∞

$\infty$

INFINITY

Infinity

math.huge

inf

inf

inf|inf

symmath.inf

Invalid

nan

nan

$¿$

NAN

(0/0)

Invalid

(0/0)

¿

Invalid

symmath.invalid

x

x

x

$x$

x

x

x

x

x

x

var("x")

y

y

y

$y$

y

y

y

y

y

y

var("y")

+

x + y

x + y

${x} + {y}$

x + y

x + y

x + y

x + y

x + y

+[x, y]

(
	var("x") +
	var("y")
)

+

x-y

x - y

${x}{-{y}}$

x + -y

x + -y

x + -y

x + -y

x + -y

+[x, unm(y)]

(
	var("x") +
	-(
		var("y")
	)
)

*

x * y

x * y

${{x}} {{y}}$

x * y

x * y

x * y

x * y

x * y

*[x, y]

(
	var("x") *
	var("y")
)

/

 x 
╶─╴
 y 

x / y

${\frac{1}{y}} {x}$

x / y

x / y

x / y

x / y

x / y

/[x, y]

(
	var("x") /
	var("y")
)

%

x % y

x % y

${x} \mod {y}$

x % y

x % y

x % y

x % y

x % y

%[x, y]

(
	var("x") %
	var("y")
)

^

 y
x 

x^y

${x}^{y}$

pow(x, y)

Math.pow(x, y)

x ^ y

(x ** y)

(x ^ y)

^[x, y]

(
	var("x") ^
	var("y")
)

unm

-x

-x

$-{x}$

-x

-x

-x

-x

-x

unm(x)

-(
	var("x")
)

/

 x 
╶─╴
 2 

x / 2

${\frac{1}{2}} {x}$

x / 2.

x / 2

x / 2

x / 2.

x / 2

/[x, 2]

(
	var("x") /
	Constant(2)
)

*

 1     
╶─╴ * x
 2     

1 / 2 * x

${{\frac{1}{2}}} {{x}}$

1. / 2. * x

1 / 2 * x

1 / 2 * x

1. / 2. * x

1 / 2 * x

*[/[1, 2], x]

(
	(
		Constant(1) /
		Constant(2)
	) *
	var("x")
)

*

2 * x

2 * x

${{2}} {{x}}$

2. * x

2 * x

2 * x

2. * x

2 * x

*[2, x]

(
	Constant(2) *
	var("x")
)

*

2 * (x + 1)

2 * (x + 1)

${{2}} {{\left({{x} + {1}}\right)}}$

2. * (x + 1.)

2 * (x + 1)

2 * (x + 1)

2. * (x + 1.)

2 * (x + 1)

*[2, +[x, 1]]

(
	Constant(2) *
	(
		var("x") +
		Constant(1)
	)
)

^

 2
x 

x^2

${x}^{2}$

(x * x)

Math.pow(x, 2)

x ^ 2

(x ** 2.)

(x ^ 2)

^[x, 2]

(
	var("x") ^
	Constant(2)
)

^

       2
(1 + x) 

(1 + x)^2

${\left({{1} + {x}}\right)}^{2}$

((1. + x) * (1. + x))

Math.pow(1 + x, 2)

(1 + x) ^ 2

(1. + x ** 2.)

(1 + x ^ 2)

^[+[1, x], 2]

(
	(
		Constant(1) +
		var("x")
	) ^
	Constant(2)
)

^

       (1 + y)
(1 + x)       

(1 + x)^(1 + y)

${\left({{1} + {x}}\right)}^{{1} + {y}}$

pow(1. + x, 1. + y)

Math.pow(1 + x, 1 + y)

(1 + x) ^ (1 + y)

(1. + x ** 1. + y)

(1 + x ^ 1 + y)

^[+[1, x], +[1, y]]

(
	(
		Constant(1) +
		var("x")
	) ^
	(
		Constant(1) +
		var("y")
	)
)

^

 (1 + y)
2       

2^(1 + y)

${2}^{{1} + {y}}$

pow(2., 1. + y)

Math.pow(2, 1 + y)

2 ^ (1 + y)

(2. ** 1. + y)

(2 ^ 1 + y)

^[2, +[1, y]]

(
	Constant(2) ^
	(
		Constant(1) +
		var("y")
	)
)

^

 (1 + y)
e       

e^(1 + y)

${e}^{{1} + {y}}$

pow(e, 1. + y)

Math.pow(e, 1 + y)

e ^ (1 + y)

(e ** 1. + y)

(e ^ 1 + y)

^[e, +[1, y]]

(
	var("e") ^
	(
		Constant(1) +
		var("y")
	)
)

abs

│x│

|x|

$\left| x\right|$

abs(x)

Math.abs(x)

math.abs(x)

abs(x)

abs[x]

abs[x]

abs(
	var("x")
)

sqrt

√(x)

√(x)

$\sqrt{x}$

sqrt(x)

Math.sqrt(x)

math.sqrt(x)

sqrt(x)

sqrt[x]

sqrt[x]

sqrt(
	var("x")
)

cbrt

cbrt(x)

cbrt(x)

$\sqrt[3]{x}$

cbrt(x)

Math.cbrt(x)

x ^ (1 / 3)

cbrt(x)

cbrt[x]

cbrt[x]

cbrt(
	var("x")
)

^

  x
_e 

_e^x

$\exp\left( x\right)$

exp(x)

Math.exp(x)

math.exp(x)

(exp(x))

exp[x]

^[_e|2.718281828459, x]

(
symmath.e ^
	var("x")
)

log

log(x)

log(x)

$\log\left(  x\right)$

log(x)

Math.log(x)

math.log(x)

log(x)

log[x]

log[x]

log(
	var("x")
)

Heaviside

Heaviside(x)

Heaviside(x)

$\mathcal{H}\left(  x\right)$

(x >= 0 ? 1 : 0)

(x >= 0 ? 1 : 0)

((x >= 0) and 1 or 0)

(x >= 0.)

Heaviside[x]

Heaviside[x]

Heaviside(
	var("x")
)

sin

sin(x)

sin(x)

$\sin\left(  x\right)$

sin(x)

Math.sin(x)

math.sin(x)

sin(x)

sin[x]

sin[x]

sin(
	var("x")
)

cos

cos(x)

cos(x)

$\cos\left(  x\right)$

cos(x)

Math.cos(x)

math.cos(x)

cos(x)

cos[x]

cos[x]

cos(
	var("x")
)

tan

tan(x)

tan(x)

$\tan\left(  x\right)$

tan(x)

Math.tan(x)

math.tan(x)

tan(x)

tan[x]

tan[x]

tan(
	var("x")
)

asin

asin(x)

asin(x)

$asin\left(  x\right)$

asin(x)

Math.asin(x)

math.asin(x)

asin(x)

asin[x]

asin[x]

asin(
	var("x")
)

acos

acos(x)

acos(x)

$acos\left(  x\right)$

acos(x)

Math.acos(x)

math.acos(x)

acos(x)

acos[x]

acos[x]

acos(
	var("x")
)

atan

atan(x)

atan(x)

$atan\left(  x\right)$

atan(x)

Math.atan(x)

math.atan(x)

atan(x)

atan[x]

atan[x]

atan(
	var("x")
)

atan2

atan2(x)

atan2(x)

$atan2\left(  x\right)$

atan2(x)

Math.atan2(x)

math.atan2(x)

atan2(x)

atan2[x]

atan2[x]

atan2(
	var("x")
)

sinh

sinh(x)

sinh(x)

$\sinh\left(  x\right)$

sinh(x)

Math.sinh(x)

math.sinh(x)

sinh(x)

sinh[x]

sinh[x]

sinh(
	var("x")
)

cosh

cosh(x)

cosh(x)

$\cosh\left(  x\right)$

cosh(x)

Math.cosh(x)

math.cosh(x)

cosh(x)

cosh[x]

cosh[x]

cosh(
	var("x")
)

tanh

tanh(x)

tanh(x)

$\tanh\left(  x\right)$

tanh(x)

Math.tanh(x)

math.tanh(x)

tanh(x)

tanh[x]

tanh[x]

tanh(
	var("x")
)

asinh

asinh(x)

asinh(x)

$asinh\left(  x\right)$

asinh(x)

Math.asinh(x)

math.asinh(x)

asinh(x)

asinh[x]

asinh[x]

asinh(
	var("x")
)

acosh

acosh(x)

acosh(x)

$acosh\left(  x\right)$

acosh(x)

Math.acosh(x)

math.acosh(x)

acosh(x)

acosh[x]

acosh[x]

acosh(
	var("x")
)

atanh

atanh(x)

atanh(x)

$atanh\left(  x\right)$

atanh(x)

Math.atanh(x)

math.atanh(x)

atanh(x)

atanh[x]

atanh[x]

atanh(
	var("x")
)

=

x = y

x = y

${x} = {y}$

x == y

x == y

x == y

x == y

x == y

=[x, y]

(
	var("x")
):eq(
	var("y")
)

≠

x ≠ y

x ≠ y

${x} \ne {y}$

x != y

x != y

x ~= y

x != y

x != y

≠[x, y]

(
	var("x")
):ne(
	var("y")
)

<

x < y

x < y

${x} \lt {y}$

x < y

x < y

x < y

x < y

x < y

<[x, y]

(
	var("x")
):lt(
	var("y")
)

≤

x ≤ y

x ≤ y

${x} \le {y}$

x <= y

x <= y

x <= y

x <= y

x <= y

≤[x, y]

(
	var("x")
):le(
	var("y")
)

>

x > y

x > y

${x} \gt {y}$

x > y

x > y

x > y

x > y

x > y

>[x, y]

(
	var("x")
):gt(
	var("y")
)

≥

x ≥ y

x ≥ y

${x} \ge {y}$

x >= y

x >= y

x >= y

x >= y

x >= y

≥[x, y]

(
	var("x")
):ge(
	var("y")
)

≈

x ≈ y

x ≈ y

${x} \approx {y}$

x == y

x == y

x == y

x == y

x == y

≈[x, y]

(
	var("x")
):approx(
	var("y")
)

Limit

     
lim  
    y
x→0  
     

lim_x→0 y

${\underset{ x\rightarrow 0}{\lim}}{{y}}$

limit([](double* out, double x) {
	double out1 = y;
	out[0] = out1;
}, 0.)

limit(function(x) {
	var out1 = y;
	return out1;
}, 0)

limit(function(x)
	local out1 = y
	return out1
end, 0)

limit((x) =
	out1 = y
	return out1, 0.)

limit([x_] :=
	out1 = y;
	out1;, 0)

Limit{y, x, 0, {}}

Limit(
	var("y"),
	var("x"),
	Constant(0),
	(

	)
)

Limit

      
 lim  
     y
x→0+  
      

lim_x→0+ y

${\underset{ x\rightarrow{ 0{}^+}}{\lim}}{{y}}$

limit_plus([](double* out, double x) {
	double out1 = y;
	out[0] = out1;
}, 0.)

limit_plus(function(x) {
	var out1 = y;
	return out1;
}, 0)

limit_plus(function(x)
	local out1 = y
	return out1
end, 0)

limit_plus((x) =
	out1 = y
	return out1, 0.)

limit_plus([x_] :=
	out1 = y;
	out1;, 0)

Limit{y, x, 0, +{}}

Limit(
	var("y"),
	var("x"),
	Constant(0),
	+(

	)
)

Limit

      
 lim  
     y
x→0-  
      

lim_x→0- y

${\underset{ x\rightarrow{ 0{}^-}}{\lim}}{{y}}$

limit_minus([](double* out, double x) {
	double out1 = y;
	out[0] = out1;
}, 0.)

limit_minus(function(x) {
	var out1 = y;
	return out1;
}, 0)

limit_minus(function(x)
	local out1 = y
	return out1
end, 0)

limit_minus((x) =
	out1 = y
	return out1, 0.)

limit_minus([x_] :=
	out1 = y;
	out1;, 0)

Limit{y, x, 0, -{}}

Limit(
	var("y"),
	var("x"),
	Constant(0),
	-(

	)
)

Limit

        
 lim  1 
     ╶─╴
x→0-  x 
        

lim_x→0- 1 / x

${\underset{ x\rightarrow{ 0{}^-}}{\lim}}{{\frac{1}{x}}}$

limit_minus([](double* out, double x) {
	double out1 = 1. / x;
	out[0] = out1;
}, 0.)

limit_minus(function(x) {
	var out1 = 1 / x;
	return out1;
}, 0)

limit_minus(function(x)
	local out1 = 1 / x
	return out1
end, 0)

limit_minus((x) =
	out1 = 1. / x
	return out1, 0.)

limit_minus([x_] :=
	out1 = 1 / x;
	out1;, 0)

Limit{/[1, x], x, 0, -{}}

Limit(
	(
		Constant(1) /
		var("x")
	),
	var("x"),
	Constant(0),
	-(

	)
)

Limit

         
 lim   1 
     ╶──╴
x→0-   2 
      x  

lim_x→0- 1 / x^2

${\underset{ x\rightarrow{ 0{}^-}}{\lim}}{{\frac{1}{{x}^{2}}}}$

limit_minus([](double* out, double x) {
	double out1 = 1. / (x * x);
	out[0] = out1;
}, 0.)

limit_minus(function(x) {
	var out1 = 1 / (x * x);
	return out1;
}, 0)

limit_minus(function(x)
	local out1 = 1 / (x * x)
	return out1
end, 0)

limit_minus((x) =
	out1 = 1. / (x * x)
	return out1, 0.)

limit_minus([x_] :=
	out1 = 1 / (x * x);
	out1;, 0)

Limit{/[1, ^[x, 2]], x, 0, -{}}

Limit(
	(
		Constant(1) /
		(
			var("x") ^
			Constant(2)
		)
	),
	var("x"),
	Constant(0),
	-(

	)
)

Limit

             
 lim   ╭ -1 ╮
       │╶──╴│
x→0-   ╰  x ╯
     _e      

lim_x→0- _e^(-1 / x)

${\underset{ x\rightarrow{ 0{}^-}}{\lim}}{{\exp\left({\frac{-1}{x}}\right)}}$

limit_minus([](double* out, double x) {
	double out1 = exp(-1. / x);
	out[0] = out1;
}, 0.)

limit_minus(function(x) {
	var out1 = Math.exp(-1 / x);
	return out1;
}, 0)

limit_minus(function(x)
	local out1 = math.exp(-1 / x)
	return out1
end, 0)

limit_minus((x) =
	out1 = (exp(-1. / x))
	return out1, 0.)

limit_minus([x_] :=
	out1 = exp[-1 / x];
	out1;, 0)

Limit{^[_e|2.718281828459, /[-1, x]], x, 0, -{}}

Limit(
	(
symmath.e ^
		(
			Constant(-1) /
			var("x")
		)
	),
	var("x"),
	Constant(0),
	-(

	)
)

Limit

           
lim        
    (1 + x)
x→0        
           

lim_x→0 1 + x

${\underset{ x\rightarrow 0}{\lim}}{{\left({{1} + {x}}\right)}}$

limit([](double* out, double x) {
	double out1 = 1. + x;
	out[0] = out1;
}, 0.)

limit(function(x) {
	var out1 = 1 + x;
	return out1;
}, 0)

limit(function(x)
	local out1 = 1 + x
	return out1
end, 0)

limit((x) =
	out1 = 1. + x
	return out1, 0.)

limit([x_] :=
	out1 = 1 + x;
	out1;, 0)

Limit{+[1, x], x, 0, {}}

Limit(
	(
		Constant(1) +
		var("x")
	),
	var("x"),
	Constant(0),
	(

	)
)

Limit

        
lim     
    (-x)
x→0     
        

lim_x→0 -x

${\underset{ x\rightarrow 0}{\lim}}{{\left( -{x}\right)}}$

limit([](double* out, double x) {
	double out1 = -x;
	out[0] = out1;
}, 0.)

limit(function(x) {
	var out1 = -x;
	return out1;
}, 0)

limit(function(x)
	local out1 = -x
	return out1
end, 0)

limit((x) =
	out1 = -x
	return out1, 0.)

limit([x_] :=
	out1 = -x;
	out1;, 0)

Limit{unm(x), x, 0, {}}

Limit(
	-(
		var("x")
	),
	var("x"),
	Constant(0),
	(

	)
)

Derivative

 ∂y 
╶──╴
 ∂x 

∂/{∂x}[y]

$\frac{\partial y}{\partial x}$

dy_dx

dy_dx

dy_dx

dy_dx

dy_dx

Derivative{y, x}

Derivative(
	var("y"),
	var("x")
)

TotalDerivative

 dy 
╶──╴
 dx 

d/{dx}[y]

$\frac{d y}{d x}$

Dy_dx

Dy_dx

Dy_dx

Dy_dx

Dy_dx

TotalDerivative{y, x}

TotalDerivative(
	var("y"),
	var("x")
)

Derivative

 ∂^2 y 
╶─────╴
  ∂x^2 

∂^2/{∂x^2}[y]

$\frac{\partial^ 2 y}{\partial x^ 2}$

d2y_dx_dx

d2y_dx_dx

d2y_dx_dx

d2y_dx_dx

d2y_dx_dx

Derivative{y, x, x}

Derivative(
	var("y"),
	var("x"),
	var("x")
)

TotalDerivative

 d^2 y 
╶─────╴
  dx^2 

d^2/{dx^2}[y]

$\frac{d^ 2 y}{d x^ 2}$

D2y_dx_dx

D2y_dx_dx

D2y_dx_dx

D2y_dx_dx

D2y_dx_dx

TotalDerivative{y, x, x}

TotalDerivative(
	var("y"),
	var("x"),
	var("x")
)

Derivative

 ∂^2 y 
╶─────╴
 ∂x ∂y 

∂^2/{∂x ∂y}[y]

$\frac{\partial^ 2 y}{\partial y\partial x}$

d2y_dx_dy

d2y_dx_dy

d2y_dx_dy

d2y_dx_dy

d2y_dx_dy

Derivative{y, x, y}

Derivative(
	var("y"),
	var("x"),
	var("y")
)

TotalDerivative

 d^2 y 
╶─────╴
 dx dy 

d^2/{dx dy}[y]

$\frac{d^ 2 y}{d y d x}$

D2y_dx_dy

D2y_dx_dy

D2y_dx_dy

D2y_dx_dy

D2y_dx_dy

TotalDerivative{y, x, y}

TotalDerivative(
	var("y"),
	var("x"),
	var("y")
)

Derivative

  ∂      
╶──╴╭  x╮
 ∂x ╰_e ╯

∂/{∂x}[_e^x]

${\frac{\partial}{\partial x}}\left({\exp\left( x\right)}\right)$

d([](double* out, double x) {
	double out1 = exp(x);
	out[0] = out1;
})

d(function(x) {
	var out1 = Math.exp(x);
	return out1;
})

d(function(x)
	local out1 = math.exp(x)
	return out1
end)

d((x) =
	out1 = (exp(x))
	return out1)

d([x_] :=
	out1 = exp[x];
	out1;)

Derivative{^[_e|2.718281828459, x], x}

Derivative(
	(
symmath.e ^
		var("x")
	),
	var("x")
)

Derivative

  ∂          
╶──╴ ╭     2╮
 ∂x √╰1 - x ╯

∂/{∂x}[√(1 - x^2)]

${\frac{\partial}{\partial x}}\left({\sqrt{{1}{-{{x}^{2}}}}}\right)$

d([](double* out, double x) {
	double out1 = sqrt(1. + -x * x);
	out[0] = out1;
})

d(function(x) {
	var out1 = Math.sqrt(1 + -x * x);
	return out1;
})

d(function(x)
	local out1 = math.sqrt(1 + -x * x)
	return out1
end)

d((x) =
	out1 = sqrt(1. + -x * x)
	return out1)

d([x_] :=
	out1 = sqrt[1 + -x * x];
	out1;)

Derivative{sqrt[+[1, unm(^[x, 2])]], x}

Derivative(
	sqrt(
		(
			Constant(1) +
			-(
				(
					var("x") ^
					Constant(2)
				)
			)
		)
	),
	var("x")
)

Integral

⌠     
⌡ y dx

∫(y, x )

$\int{{y}}d x$

integrate([](double* out, double x) {
	double out1 = y;
	out[0] = out1;
})

integrate(function(x) {
	var out1 = y;
	return out1;
})

integrate(function(x)
	local out1 = y
	return out1
end)

integrate((x) =
	out1 = y
	return out1)

integrate([x_] :=
	out1 = y;
	out1;)

Integral{y, x}

Integral(
	var("y"),
	var("x")
)

Integral

⌠1     
│  y dx
⌡0     

∫(y, x, 0, 1 )

$\int\limits_{{0}}^{{1}}{{y}}d x$

integrate([](double* out, double x) {
	double out1 = y;
	out[0] = out1;
}, 0., 1.)

integrate(function(x) {
	var out1 = y;
	return out1;
}, 0, 1)

integrate(function(x)
	local out1 = y
	return out1
end, 0, 1)

integrate((x) =
	out1 = y
	return out1, 0., 1.)

integrate([x_] :=
	out1 = y;
	out1;, 0, 1)

Integral{y, x, 0, 1}

Integral(
	var("y"),
	var("x"),
	Constant(0),
	Constant(1)
)

Integral

⌠1              
│    ╭     2╮   
⌡-1 √╰1 - x ╯ dx

∫(√(1 - x^2), x, -1, 1 )

$\int\limits_{{-1}}^{{1}}{{\sqrt{{1}{-{{x}^{2}}}}}}d x$

integrate([](double* out, double x) {
	double out1 = sqrt(1. + -x * x);
	out[0] = out1;
}, -1., 1.)

integrate(function(x) {
	var out1 = Math.sqrt(1 + -x * x);
	return out1;
}, -1, 1)

integrate(function(x)
	local out1 = math.sqrt(1 + -x * x)
	return out1
end, -1, 1)

integrate((x) =
	out1 = sqrt(1. + -x * x)
	return out1, -1., 1.)

integrate([x_] :=
	out1 = sqrt[1 + -x * x];
	out1;, -1, 1)

Integral{sqrt[+[1, unm(^[x, 2])]], x, -1, 1}

Integral(
	sqrt(
		(
			Constant(1) +
			-(
				(
					var("x") ^
					Constant(2)
				)
			)
		)
	),
	var("x"),
	Constant(-1),
	Constant(1)
)

Integral

⌠1      
│  -x dx
⌡0      

∫(-x, x, 0, 1 )

$\int\limits_{{0}}^{{1}}{{\left( -{x}\right)}}d x$

integrate([](double* out, double x) {
	double out1 = -x;
	out[0] = out1;
}, 0., 1.)

integrate(function(x) {
	var out1 = -x;
	return out1;
}, 0, 1)

integrate(function(x)
	local out1 = -x
	return out1
end, 0, 1)

integrate((x) =
	out1 = -x
	return out1, 0., 1.)

integrate([x_] :=
	out1 = -x;
	out1;, 0, 1)

Integral{unm(x), x, 0, 1}

Integral(
	-(
		var("x")
	),
	var("x"),
	Constant(0),
	Constant(1)
)

Integral

⌠1         
│  1 + x dx
⌡0         

∫(1 + x, x, 0, 1 )

$\int\limits_{{0}}^{{1}}{{\left({{1} + {x}}\right)}}d x$

integrate([](double* out, double x) {
	double out1 = 1. + x;
	out[0] = out1;
}, 0., 1.)

integrate(function(x) {
	var out1 = 1 + x;
	return out1;
}, 0, 1)

integrate(function(x)
	local out1 = 1 + x
	return out1
end, 0, 1)

integrate((x) =
	out1 = 1. + x
	return out1, 0., 1.)

integrate([x_] :=
	out1 = 1 + x;
	out1;, 0, 1)

Integral{+[1, x], x, 0, 1}

Integral(
	(
		Constant(1) +
		var("x")
	),
	var("x"),
	Constant(0),
	Constant(1)
)

Array

┌ ┐
│x│
│ │
│y│
└ ┘

[x, y]

$\left[\begin{matrix} x \\ y\end{matrix}\right]$

{x, y}

[x, y]

{x, y}

{x, y}

{x, y}

Array{x, y}

Array(
	var("x"),
	var("y")
)

Matrix

┌ ┐
│x│
│ │
│y│
└ ┘

[[x], [y]]

$\left[\begin{array}{c} x\\ y\end{array}\right]$

{{x}, {y}}

[[x], [y]]

{{x}, {y}}

{{x}, {y}}

{{x}, {y}}

Matrix{Matrix{x}, Matrix{y}}

Matrix(
	Matrix(
		var("x")
	),
	Matrix(
		var("y")
	)
)

Matrix

┌    ┐
│x  y│
└    ┘

[[x, y]]

$\left[\begin{array}{cc} x& y\end{array}\right]$

{{x, y}}

[[x, y]]

{{x, y}}

{{x, y}}

{{x, y}}

Matrix{Matrix{x, y}}

Matrix(
	Matrix(
		var("x"),
		var("y")
	)
)

Matrix

┌    ┐
│a  b│
│    │
│c  d│
└    ┘

[[a, b], [c, d]]

$\left[\begin{array}{cc} a& b\\ c& d\end{array}\right]$

{{a, b}, {c, d}}

[[a, b], [c, d]]

{{a, b}, {c, d}}

{{a, b}, {c, d}}

{{a, b}, {c, d}}

Matrix{Matrix{a, b}, Matrix{c, d}}

Matrix(
	Matrix(
		var("a"),
		var("b")
	),
	Matrix(
		var("c"),
		var("d")
	)
)

Tensor

_i↓
┌ ┐
│a│
│ │
│b│
└ ┘

[a, b]

$\overset{i\downarrow}{\left[\begin{matrix} a \\ b\end{matrix}\right]}$

{a, b}

[a, b]

{a, b}

{a, b}

{a, b}

Tensor{a, b}_i

Tensor(
	{
Tensor.Index{lower=true, symbol="i"}
	},
	var("a"),
	var("b")
)

Tensor

_i↓_j→
┌    ┐
│a  b│
│    │
│c  d│
└    ┘

[[a, b], [c, d]]

$\overset{i\downarrow j\rightarrow}{\left[\begin{array}{cc} a& b\\ c& d\end{array}\right]}$

{{a, b}, {c, d}}

[[a, b], [c, d]]

{{a, b}, {c, d}}

{{a, b}, {c, d}}

{{a, b}, {c, d}}

Tensor{Tensor{a, b}_j, Tensor{c, d}_j}_i_j

Tensor(
	{
Tensor.Index{lower=true, symbol="i"},
Tensor.Index{lower=true, symbol="j"}
	},
	Tensor(
		{
Tensor.Index{lower=true, symbol="j"}
		},
		var("a"),
		var("b")
	),
	Tensor(
		{
Tensor.Index{lower=true, symbol="j"}
		},
		var("c"),
		var("d")
	)
)

Tensor

_i↓[_j↓_k→]
┌      ┐   
│_j↓_k→│   
│┌    ┐│   
││a  b││   
││    ││   
││c  d││   
│└    ┘│   
│      │   
│_j↓_k→│   
│┌    ┐│   
││e  f││   
││    ││   
││g  h││   
│└    ┘│   
└      ┘   

[[[a, b], [c, d]], [[e, f], [g, h]]]

$\overset{i\downarrow[{j\downarrow k\rightarrow}]}{\left[\begin{matrix} \overset{j\downarrow k\rightarrow}{\left[\begin{array}{cc} a& b\\ c& d\end{array}\right]} \\ \overset{j\downarrow k\rightarrow}{\left[\begin{array}{cc} e& f\\ g& h\end{array}\right]}\end{matrix}\right]}$

{{{a, b}, {c, d}}, {{e, f}, {g, h}}}

[[[a, b], [c, d]], [[e, f], [g, h]]]

{{{a, b}, {c, d}}, {{e, f}, {g, h}}}

{{{a, b}, {c, d}}, {{e, f}, {g, h}}}

{{{a, b}, {c, d}}, {{e, f}, {g, h}}}

Tensor{Tensor{Tensor{a, b}_k, Tensor{c, d}_k}_j_k, Tensor{Tensor{e, f}_k, Tensor{g, h}_k}_j_k}_i_j_k

Tensor(
	{
Tensor.Index{lower=true, symbol="i"},
Tensor.Index{lower=true, symbol="j"},
Tensor.Index{lower=true, symbol="k"}
	},
	Tensor(
		{
Tensor.Index{lower=true, symbol="j"},
Tensor.Index{lower=true, symbol="k"}
		},
		Tensor(
			{
Tensor.Index{lower=true, symbol="k"}
			},
			var("a"),
			var("b")
		),
		Tensor(
			{
Tensor.Index{lower=true, symbol="k"}
			},
			var("c"),
			var("d")
		)
	),
	Tensor(
		{
Tensor.Index{lower=true, symbol="j"},
Tensor.Index{lower=true, symbol="k"}
		},
		Tensor(
			{
Tensor.Index{lower=true, symbol="k"}
			},
			var("e"),
			var("f")
		),
		Tensor(
			{
Tensor.Index{lower=true, symbol="k"}
			},
			var("g"),
			var("h")
		)
	)
)

Tensor.Ref

x_a

x_a

${ x} _a$

x_Da

x_Da

x_Da

x_Da

x_Da

Tensor.Ref{x, Tensor.Index{_a}}

Tensor.Ref(
	var("x"),
	Tensor.Index{lower=true, symbol="a"}
)

Tensor.Ref

x^a

x^a

${ x} ^a$

x_Ua

x_Ua

x_Ua

x_Ua

x_Ua

Tensor.Ref{x, Tensor.Index{^a}}

Tensor.Ref(
	var("x"),
	Tensor.Index{lower=false, symbol="a"}
)

Tensor.Ref

x_\mu

x_\mu

${ x} _{\mu}$

x_D\mu

x_D\mu

x_D\mu

x_D\mu

x_D\mu

Tensor.Ref{x, Tensor.Index{_\mu}}

Tensor.Ref(
	var("x"),
	Tensor.Index{lower=true, symbol="\\mu"}
)

Tensor.Ref

x^\mu

x^\mu

${ x} ^{\mu}$

x_U\mu

x_U\mu

x_U\mu

x_U\mu

x_U\mu

Tensor.Ref{x, Tensor.Index{^\mu}}

Tensor.Ref(
	var("x"),
	Tensor.Index{lower=false, symbol="\\mu"}
)

Tensor.Ref

x_ab

x_ab

${{ x} _a} _b$

x_Da_Db

x_Da_Db

x_Da_Db

x_Da_Db

x_Da_Db

Tensor.Ref{x, Tensor.Index{_a}, Tensor.Index{_b}}

Tensor.Ref(
	var("x"),
	Tensor.Index{lower=true, symbol="a"},
	Tensor.Index{lower=true, symbol="b"}
)

Tensor.Ref

x^ab

x^ab

${{ x} ^a} ^b$

x_Ua_Ub

x_Ua_Ub

x_Ua_Ub

x_Ua_Ub

x_Ua_Ub

Tensor.Ref{x, Tensor.Index{^a}, Tensor.Index{^b}}

Tensor.Ref(
	var("x"),
	Tensor.Index{lower=false, symbol="a"},
	Tensor.Index{lower=false, symbol="b"}
)

Tensor.Ref

x_\mu_\nu

x_\mu_\nu

${{ x} _{\mu}} _{\nu}$

x_D\mu_D\nu

x_D\mu_D\nu

x_D\mu_D\nu

x_D\mu_D\nu

x_D\mu_D\nu

Tensor.Ref{x, Tensor.Index{_\mu}, Tensor.Index{_\nu}}

Tensor.Ref(
	var("x"),
	Tensor.Index{lower=true, symbol="\\mu"},
	Tensor.Index{lower=true, symbol="\\nu"}
)

Tensor.Ref

x^\mu^\nu

x^\mu^\nu

${{ x} ^{\mu}} ^{\nu}$

x_U\mu_U\nu

x_U\mu_U\nu

x_U\mu_U\nu

x_U\mu_U\nu

x_U\mu_U\nu

Tensor.Ref{x, Tensor.Index{^\mu}, Tensor.Index{^\nu}}

Tensor.Ref(
	var("x"),
	Tensor.Index{lower=false, symbol="\\mu"},
	Tensor.Index{lower=false, symbol="\\nu"}
)

alpha

alpha

alpha

$alpha$

alpha

alpha

alpha

alpha

alpha

alpha

var("alpha")

beta

beta

beta

$beta$

beta

beta

beta

beta

beta

beta

var("beta")

gamma

gamma

gamma

$gamma$

gamma

gamma

gamma

gamma

gamma

gamma

var("gamma")

delta

delta

delta

$delta$

delta

delta

delta

delta

delta

delta

var("delta")

epsilon

epsilon

epsilon

$epsilon$

epsilon

epsilon

epsilon

epsilon

epsilon

epsilon

var("epsilon")

zeta

zeta

zeta

$zeta$

zeta

zeta

zeta

zeta

zeta

zeta

var("zeta")

eta

eta

eta

$eta$

eta

eta

eta

eta

eta

eta

var("eta")

theta

theta

theta

$theta$

theta

theta

theta

theta

theta

theta

var("theta")

iota

iota

iota

$iota$

iota

iota

iota

iota

iota

iota

var("iota")

kappa

kappa

kappa

$kappa$

kappa

kappa

kappa

kappa

kappa

kappa

var("kappa")

lambda

lambda

lambda

$lambda$

lambda

lambda

lambda

lambda

lambda

lambda

var("lambda")

mu

mu

mu

$mu$

mu

mu

mu

mu

mu

mu

var("mu")

nu

nu

nu

$nu$

nu

nu

nu

nu

nu

nu

var("nu")

xi

xi

xi

$xi$

xi

xi

xi

xi

xi

xi

var("xi")

omicron

omicron

omicron

$omicron$

omicron

omicron

omicron

omicron

omicron

omicron

var("omicron")

pi

pi

pi

$pi$

pi

pi

pi

pi

pi

pi

var("pi")

rho

rho

rho

$rho$

rho

rho

rho

rho

rho

rho

var("rho")

sigma

sigma

sigma

$sigma$

sigma

sigma

sigma

sigma

sigma

sigma

var("sigma")

tau

tau

tau

$tau$

tau

tau

tau

tau

tau

tau

var("tau")

upsilon

upsilon

upsilon

$upsilon$

upsilon

upsilon

upsilon

upsilon

upsilon

upsilon

var("upsilon")

phi

phi

phi

$phi$

phi

phi

phi

phi

phi

phi

var("phi")

chi

chi

chi

$chi$

chi

chi

chi

chi

chi

chi

var("chi")

psi

psi

psi

$psi$

psi

psi

psi

psi

psi

psi

var("psi")

omega

omega

omega

$omega$

omega

omega

omega

omega

omega

omega

var("omega")

Alpha

Alpha

Alpha

$Alpha$

Alpha

Alpha

Alpha

Alpha

Alpha

Alpha

var("Alpha")

Beta

Beta

Beta

$Beta$

Beta

Beta

Beta

Beta

Beta

Beta

var("Beta")

Gamma

Gamma

Gamma

$Gamma$

Gamma

Gamma

Gamma

Gamma

Gamma

Gamma

var("Gamma")

Delta

Delta

Delta

$Delta$

Delta

Delta

Delta

Delta

Delta

Delta

var("Delta")

Epsilon

Epsilon

Epsilon

$Epsilon$

Epsilon

Epsilon

Epsilon

Epsilon

Epsilon

Epsilon

var("Epsilon")

Zeta

Zeta

Zeta

$Zeta$

Zeta

Zeta

Zeta

Zeta

Zeta

Zeta

var("Zeta")

Eta

Eta

Eta

$Eta$

Eta

Eta

Eta

Eta

Eta

Eta

var("Eta")

Theta

Theta

Theta

$Theta$

Theta

Theta

Theta

Theta

Theta

Theta

var("Theta")

Iota

Iota

Iota

$Iota$

Iota

Iota

Iota

Iota

Iota

Iota

var("Iota")

Kappa

Kappa

Kappa

$Kappa$

Kappa

Kappa

Kappa

Kappa

Kappa

Kappa

var("Kappa")

Lambda

Lambda

Lambda

$Lambda$

Lambda

Lambda

Lambda

Lambda

Lambda

Lambda

var("Lambda")

Mu

Mu

Mu

$Mu$

Mu

Mu

Mu

Mu

Mu

Mu

var("Mu")

Nu

Nu

Nu

$Nu$

Nu

Nu

Nu

Nu

Nu

Nu

var("Nu")

Xi

Xi

Xi

$Xi$

Xi

Xi

Xi

Xi

Xi

Xi

var("Xi")

Omicron

Omicron

Omicron

$Omicron$

Omicron

Omicron

Omicron

Omicron

Omicron

Omicron

var("Omicron")

Pi

Pi

Pi

$Pi$

Pi

Pi

Pi

Pi

Pi

Pi

var("Pi")

Rho

Rho

Rho

$Rho$

Rho

Rho

Rho

Rho

Rho

Rho

var("Rho")

Sigma

Sigma

Sigma

$Sigma$

Sigma

Sigma

Sigma

Sigma

Sigma

Sigma

var("Sigma")

Tau

Tau

Tau

$Tau$

Tau

Tau

Tau

Tau

Tau

Tau

var("Tau")

Upsilon

Upsilon

Upsilon

$Upsilon$

Upsilon

Upsilon

Upsilon

Upsilon

Upsilon

Upsilon

var("Upsilon")

Phi

Phi

Phi

$Phi$

Phi

Phi

Phi

Phi

Phi

Phi

var("Phi")

Chi

Chi

Chi

$Chi$

Chi

Chi

Chi

Chi

Chi

Chi

var("Chi")

Psi

Psi

Psi

$Psi$

Psi

Psi

Psi

Psi

Psi

Psi

var("Psi")

Omega

Omega

Omega

$Omega$

Omega

Omega

Omega

Omega

Omega

Omega

var("Omega")

Tensor.Ref

x_mu

x_mu

${ x} _{mu}$

x_Dmu

x_Dmu

x_Dmu

x_Dmu

x_Dmu

Tensor.Ref{x, Tensor.Index{_mu}}

Tensor.Ref(
	var("x"),
	Tensor.Index{lower=true, symbol="mu"}
)

Tensor.Ref

x^mu

x^mu

${ x} ^{mu}$

x_Umu

x_Umu

x_Umu

x_Umu

x_Umu

Tensor.Ref{x, Tensor.Index{^mu}}

Tensor.Ref(
	var("x"),
	Tensor.Index{lower=false, symbol="mu"}
)

Tensor.Ref

x_mu_nu

x_mu_nu

${{ x} _{mu}} _{nu}$

x_Dmu_Dnu

x_Dmu_Dnu

x_Dmu_Dnu

x_Dmu_Dnu

x_Dmu_Dnu

Tensor.Ref{x, Tensor.Index{_mu}, Tensor.Index{_nu}}

Tensor.Ref(
	var("x"),
	Tensor.Index{lower=true, symbol="mu"},
	Tensor.Index{lower=true, symbol="nu"}
)

Tensor.Ref

x^mu^nu

x^mu^nu

${{ x} ^{mu}} ^{nu}$

x_Umu_Unu

x_Umu_Unu

x_Umu_Unu

x_Umu_Unu

x_Umu_Unu

Tensor.Ref{x, Tensor.Index{^mu}, Tensor.Index{^nu}}

Tensor.Ref(
	var("x"),
	Tensor.Index{lower=false, symbol="mu"},
	Tensor.Index{lower=false, symbol="nu"}
)

alpha

α

α

$\alpha$

alpha

alpha

alpha

alpha

alpha

alpha

var("alpha")

beta

β

β

$\beta$

beta

beta

beta

beta

beta

beta

var("beta")

gamma

γ

γ

$\gamma$

gamma

gamma

gamma

gamma

gamma

gamma

var("gamma")

delta

δ

δ

$\delta$

delta

delta

delta

delta

delta

delta

var("delta")

epsilon

ε

ε

$\epsilon$

epsilon

epsilon

epsilon

epsilon

epsilon

epsilon

var("epsilon")

zeta

ζ

ζ

$\zeta$

zeta

zeta

zeta

zeta

zeta

zeta

var("zeta")

eta

η

η

$\eta$

eta

eta

eta

eta

eta

eta

var("eta")

theta

θ

θ

$\theta$

theta

theta

theta

theta

theta

theta

var("theta")

iota

ι

ι

$\iota$

iota

iota

iota

iota

iota

iota

var("iota")

kappa

κ

κ

$\kappa$

kappa

kappa

kappa

kappa

kappa

kappa

var("kappa")

lambda

λ

λ

$\lambda$

lambda

lambda

lambda

lambda

lambda

lambda

var("lambda")

mu

μ

μ

$\mu$

mu

mu

mu

mu

mu

mu

var("mu")

nu

ν

ν

$\nu$

nu

nu

nu

nu

nu

nu

var("nu")

xi

ξ

ξ

$\xi$

xi

xi

xi

xi

xi

xi

var("xi")

omicron

ο

ο

$\omicron$

omicron

omicron

omicron

omicron

omicron

omicron

var("omicron")

pi

π

π

$\pi$

pi

pi

pi

pi

pi

pi

var("pi")

rho

ρ

ρ

$\rho$

rho

rho

rho

rho

rho

rho

var("rho")

sigma

σ

σ

$\sigma$

sigma

sigma

sigma

sigma

sigma

sigma

var("sigma")

tau

τ

τ

$\tau$

tau

tau

tau

tau

tau

tau

var("tau")

upsilon

υ

υ

$\upsilon$

upsilon

upsilon

upsilon

upsilon

upsilon

upsilon

var("upsilon")

phi

φ

φ

$\phi$

phi

phi

phi

phi

phi

phi

var("phi")

chi

χ

χ

$\chi$

chi

chi

chi

chi

chi

chi

var("chi")

psi

ψ

ψ

$\psi$

psi

psi

psi

psi

psi

psi

var("psi")

omega

ω

ω

$\omega$

omega

omega

omega

omega

omega

omega

var("omega")

Alpha

Α

Α

$A$

Alpha

Alpha

Alpha

Alpha

Alpha

Alpha

var("Alpha")

Beta

Β

Β

$B$

Beta

Beta

Beta

Beta

Beta

Beta

var("Beta")

Gamma

Γ

Γ

$\Gamma$

Gamma

Gamma

Gamma

Gamma

Gamma

Gamma

var("Gamma")

Delta

Δ

Δ

$\Delta$

Delta

Delta

Delta

Delta

Delta

Delta

var("Delta")

Epsilon

Ε

Ε

$E$

Epsilon

Epsilon

Epsilon

Epsilon

Epsilon

Epsilon

var("Epsilon")

Zeta

Ζ

Ζ

$Z$

Zeta

Zeta

Zeta

Zeta

Zeta

Zeta

var("Zeta")

Eta

Η

Η

$H$

Eta

Eta

Eta

Eta

Eta

Eta

var("Eta")

Theta

Θ

Θ

$\Theta$

Theta

Theta

Theta

Theta

Theta

Theta

var("Theta")

Iota

Ι

Ι

$I$

Iota

Iota

Iota

Iota

Iota

Iota

var("Iota")

Kappa

Κ

Κ

$K$

Kappa

Kappa

Kappa

Kappa

Kappa

Kappa

var("Kappa")

Lambda

Λ

Λ

$\Lambda$

Lambda

Lambda

Lambda

Lambda

Lambda

Lambda

var("Lambda")

Mu

Μ

Μ

$M$

Mu

Mu

Mu

Mu

Mu

Mu

var("Mu")

Nu

Ν

Ν

$N$

Nu

Nu

Nu

Nu

Nu

Nu

var("Nu")

Xi

Ξ

Ξ

$\Xi$

Xi

Xi

Xi

Xi

Xi

Xi

var("Xi")

Omicron

Ο

Ο

$O$

Omicron

Omicron

Omicron

Omicron

Omicron

Omicron

var("Omicron")

Pi

Π

Π

$\Pi$

Pi

Pi

Pi

Pi

Pi

Pi

var("Pi")

Rho

Ρ

Ρ

$P$

Rho

Rho

Rho

Rho

Rho

Rho

var("Rho")

Sigma

Σ

Σ

$\Sigma$

Sigma

Sigma

Sigma

Sigma

Sigma

Sigma

var("Sigma")

Tau

Τ

Τ

$T$

Tau

Tau

Tau

Tau

Tau

Tau

var("Tau")

Upsilon

Υ

Υ

$\Upsilon$

Upsilon

Upsilon

Upsilon

Upsilon

Upsilon

Upsilon

var("Upsilon")

Phi

Φ

Φ

$\Phi$

Phi

Phi

Phi

Phi

Phi

Phi

var("Phi")

Chi

Χ

Χ

$X$

Chi

Chi

Chi

Chi

Chi

Chi

var("Chi")

Psi

Ψ

Ψ

$\Psi$

Psi

Psi

Psi

Psi

Psi

Psi

var("Psi")

Omega

Ω

Ω

$\Omega$

Omega

Omega

Omega

Omega

Omega

Omega

var("Omega")

Tensor.Ref

x_\mu

x_\mu

${ x} _{\mu}$

x_D\mu

x_D\mu

x_D\mu

x_D\mu

x_D\mu

Tensor.Ref{x, Tensor.Index{_\mu}}

Tensor.Ref(
	var("x"),
	Tensor.Index{lower=true, symbol="mu"}
)

Tensor.Ref

x^\mu

x^\mu

${ x} ^{\mu}$

x_U\mu

x_U\mu

x_U\mu

x_U\mu

x_U\mu

Tensor.Ref{x, Tensor.Index{^\mu}}

Tensor.Ref(
	var("x"),
	Tensor.Index{lower=false, symbol="mu"}
)

Tensor.Ref

x_\mu_\nu

x_\mu_\nu

${{ x} _{\mu}} _{\nu}$

x_D\mu_D\nu

x_D\mu_D\nu

x_D\mu_D\nu

x_D\mu_D\nu

x_D\mu_D\nu

Tensor.Ref{x, Tensor.Index{_\mu}, Tensor.Index{_\nu}}

Tensor.Ref(
	var("x"),
	Tensor.Index{lower=true, symbol="mu"},
	Tensor.Index{lower=true, symbol="nu"}
)

Tensor.Ref

x^\mu^\nu

x^\mu^\nu

${{ x} ^{\mu}} ^{\nu}$

x_U\mu_U\nu

x_U\mu_U\nu

x_U\mu_U\nu

x_U\mu_U\nu

x_U\mu_U\nu

Tensor.Ref{x, Tensor.Index{^\mu}, Tensor.Index{^\nu}}

Tensor.Ref(
	var("x"),
	Tensor.Index{lower=false, symbol="mu"},
	Tensor.Index{lower=false, symbol="nu"}
)