text:
Notes on Straight Lines- Part 1 | Grade 11 > Mathematics > Coordinate Geometry straight line | KULLABS.COM

• Note
• Things to remember
• Exercise

### Straight lines:-

A straight line is a one-dimensional geometry with no fixed ends

#### Line segment:-

A line segment is a straight line having fixed ends.

#### Ray:-

A ray is a straight line with one fixed end.

#### Coordinates of a point on the plane

From the figure aside we can conclude that the sign of the coordinates of the point on I, II, III and IV quadrants are (+,+), (-,+), (-,-) and (+,-).

### Some Basic Formulae

#### Distance formula

If A(x1,y1) and B(x2,y2) be a line joining points AB then the distance between them is given by,

$$d=AB=\sqrt{{(x_2-x_1)}^2+{(y_2-y_1)}^2}$$

#### Slope formula

If A(x1,y1) and B(x2,y2) be a line joining points AB then slope of AB is given by,

$$m=\tan\theta=(\frac{y_2-y_1}{x_2-x_1})$$

#### Section formula

A(x1,y1) and B(x2,y2) be a line joining points AB and c(x,y) be a point which divides AB in ratio m1:m2 then ,

Internal division:

$$x=(\frac{m_1x_2+m_2x_1}{m_1+m_2})$$, $$y=(\frac{m_1y_2+m_2y_1}{m_1+m_2})$$

External division:-

$$x=(\frac{m_1x_2-m_2x_1}{m_1-m_2})$$, $$y=(\frac{m_1y_2-m_2y_1}{m_1-m_2})$$

#### Centroid:

IfA(x1,y1), B(x2,y2) and c(x3,y3) be a vertices of a triangle ABC then o(x,y) be its centroid which is given by,

$$x=(\frac{x_1+x_2+x_3}{3})$$

$$y=(\frac{y_1+y_2+y_3}{3})$$

#### Area of a triangle:

IfA(x1,y1), B(x2,y2) and c(x3,y3) be a vertices of a triangle ABC, then the area of the triangle ABC is given by,

$$Area={\frac{1}{2}(x_1y_2-x_2y_1+x_2y_3-x_3y_2+x_3y_1-x_1y_3)}$$

#### Three standard forms of equation of straight lines

slope intercept form

Let AB be a straight line meeting the X-axis and Y-axis at A and C respectively. Then equation of the line AB is given by,

$$y=mx+c$$

where,

m= slope of the line AB

C= Y-intercept

Double intercept form

Let the straight line AB cuts the axes at A and B as shown in the figure aside, then the equation of line AB is given by,

$$\frac{x}{a}+\frac{y}{b}=1$$

Where,

a=X-intercept

b=Y-intercept

Normal form or perpendicular form

Let AB be a sstraight line on which the length of the perpendicular P from the origin is drawn. Let the angleis made byperpendicular line with the positive X-axis, then the equation of the line AB is given by,

$$x\cos\alpha+y\sin\alpha=p$$

#### Equation of lines in some special cases

Point slope form

Let a line passing through a given point B(x1,y1)have its slope equal to m Let P(x,y) be any point on the line. Then, equation of the line is given by,

$$y-y_1=m(x-x_1)$$

Where,

m= slope of the line

Two points form:

Let a straight line passes through A(x1,y1) and B(x2,y2) and p(x,y) be any point on the line.Then, equation of the line is given by,

$$y-y_1=\frac{y_2-y_1}{x_2-x_1}(x-x_1)$$

#### some point to recall

• The general equation (linear equation) of first degree in x and y is,

$$Ax+By+C=0$$

Where, A, B and C are constants.

• Length of the perpendicular line drawn on the line Ax+By+C=0 from p(x1,y1) is given by,

$$L=±{\vert\frac{Ax_1+By_1+C}{\sqrt{A^2+B^2}}\vert}$$

#### Solved problems

1.Prove that the line whose intercepts on the axes of x and y are respectively -2 and 3, passes through the point (2,3).

solution

Here, X-intercept=a= -2

Y-intercept=b= 3

Then the equation of the line is,

$$\frac{x}{a}+\frac{y}{b}=1$$

$$\frac{x}{-2}+\frac{y}{3}=1$$

or,$$-3x+2y=6 ...........(i)$$

Now, put x=2 and y=6 in equation (i),

Then, $$-3*2+2*6=6$$

or, 6=6 which is true.

Hence, the line (i) passes through the point (2,6)

2.If a line with equation 5x+6y=2k together with the coordinate axes form a triangle of area 135 sq. units , find the value of k.

solution

Here, The given equation of the line is,

$$5x+6y=2k$$

Now, reducing the equation to double intercept form, we have,

$$\frac{x}{2k/5}+\frac{y}{2k/6}=1$$

where, X-intercept=$$\frac{2k}{5}$$

Y-intercept=$$\frac{2k}{6}$$

Hence, the area of the triangle$$=\frac{1}{2}.\frac{2k}{5}.\frac{2k}{6}\\$$

or,$$135=\frac{k^2}{15}$$

∴k=±45

3.Find the equation of the straight line passing through the intersection of the lines 3x-4y-10=0 and 5x+3y-7=0 and making angle 135° with the positive x-axis.

Solution

Here, The given equations of the lines are

$$3x-4y-10=0............(i)$$

$$5x+3y-7=0..............(ii)$$

Solving equations (i) and (ii), we get,

x= 2 and y= -1

∴the point of intersection of the lines (i) and (ii) is (2,-1).

Slope of the line=m=tan 135°= -1

The equation of the line through a given point (x1,y1) is

$$y-y_1=m(x-x_1)$$

∴The equation of the line through(2,-1) and slope -1 is

$$y-(-1)=-1(x-2)$$

$$x+y=1$$

which is required equation of aline.

4.Show that the following set of three lines are concurrent.

x-y+1=0, 2x-y-1=0 and x+3y-11=0

Solution

Here, taking the first two equations,

we get,

$$x-y+1=0..........................(i)$$

$$2x-y-1=0.......................(ii)$$

solving equations (i) and (ii),

we get, x= 2 and y= 3

∴The point of intersection of the lines (I) and (II) is (2,3).

put x=2, y=3 in the third equation i.e, $$x+3y-11=0$$ we get,

$$2+3*3-11=0$$

$$i.e, 0=0$$

Which is true.

Hence, the three lines are concurrent.

#### some important questions

1.Obtain the equation of the straight line passing through the point (3,4) cutting off equal intercepts on the axes.

2.In what ratio is the line joining (1,3) and (2,7) divided by the line 3x+y=9?

3..Show that the following set of three lines are concurrent.

1. x+2y=0, 3x-4y-10=0 and 5x+3y-7=0
2. 2x-7y+10=0, 3x-2y=1 and x-12y+21=0

4.find the equation of the straight line passing through the intersection of x+3y+2=0, 2x-y-3=0 and slope is 1/2.

5.P and Q are two points of the line x-y+1=0 and are at distance 5 from the origin. Find the area of the triangle OPQ.

Reference:

(Bajracharya, Shrestha, and Singh)

• $$d=AB=\sqrt{{(x_2-x_1)}^2+{(y_2-y_1)}^2}$$

• $$m=\tan\theta=(\frac{y_2-y_1}{x_2-x_1})$$

#### Section formula

• $$x=(\frac{m_1x_2+m_2x_1}{m_1+m_2})$$, $$y=(\frac{m_1y_2+m_2y_1}{m_1+m_2})$$
• $$x=(\frac{m_1x_2-m_2x_1}{m_1-m_2})$$, $$y=(\frac{m_1y_2-m_2y_1}{m_1-m_2})$$
• Length of the perpendicular line drawn on the line Ax+By+C=0 from p(x1,y1) is given by,

$$L=±{\vert\frac{Ax_1+By_1+C}{\sqrt{A^2+B^2}}\vert}$$

.

#### Click on the questions below to reveal the answers

solution

Here, X-intercept=a= -2

Y-intercept=b= 3

Then the equation of the line is,

$$\frac{x}{a}+\frac{y}{b}=1$$

$$\frac{x}{-2}+\frac{y}{3}=1$$

or,$$-3x+2y=6 ...........(i)$$

Now, put x=2 and y=6 in equation (i),

Then, $$-3*2+2*6=6$$

or, 6=6 which is true.

Hence, the line (i) passes through the point (2,6)

solution

Here, The given equation of the line is,

$$5x+6y=2k$$

Now, reducing the equation to double intercept form, we have,

$$\frac{x}{2k/5}+\frac{y}{2k/6}=1$$

where, X-intercept=$$\frac{2k}{5}$$

Y-intercept=$$\frac{2k}{6}$$

Hence, the area of the triangle$$=\frac{1}{2}.\frac{2k}{5}.\frac{2k}{6}\\$$

or,$$135=\frac{k^2}{15}$$

∴k=±45

solution

Here, The given equations of the lines are

$$3x-4y-10=0............(i)$$

$$5x+3y-7=0..............(ii)$$

Solving equations (i) and (ii), we get,

x= 2 and y= -1

∴the point of intersection of the lines (i) and (ii) is (2,-1).

Slope of the line=m=tan 135°= -1

The equation of the line through a given point (x1,y1) is

$$y-y_1=m(x-x_1)$$

∴The equation of the line through(2,-1) and slope -1 is

$$y-(-1)=-1(x-2)$$

$$x+y=1$$

which is required equation of aline.

Solution

Here, taking the first two equations,

we get,

$$x-y+1=0..........................(i)$$

$$2x-y-1=0.......................(ii)$$

solving equations (i) and (ii),

we get, x= 2 and y= 3

∴The point of intersection of the lines (I) and (II) is (2,3).

put x=2, y=3 in the third equation i.e, $$x+3y-11=0$$ we get,

$$2+3*3-11=0$$

$$i.e, 0=0$$

Which is true.

Hence, the three lines are concurrent.

Solution:-

Let, x-intercept(a)=k then,

y-intercept(b)=x-intercept(a)=k

Now, we know that,

Equation of line is,

$$\frac{x}{a}+\frac{y}{b}=1$$

$$or,\frac{x}{k}+\frac{y}{k}=1$$

$$x+y=k$$

Now, since the line passes through (3,4), so we get,

$$3+4=k$$

$$\therefore k=7$$

henc, the equation of line is,$$x+y=7$$

Solution:-

let, the intercept on y-axis be k, Then,

the intercept on x-axis=2k

Now, using double intercept form, we get,

$$\frac{x}{a}+\frac{y}{b}=1$$

$$or,\frac{x}{2k}+\frac{y}{k}=1$$

$$or,x+2y=2k...............(i)$$

since the line (i) passes through the point (2,3), so we get,

$$2+2*3=2k$$

$$\therefore k=4$$

Now, putting k=4 in equation (i), we get,

$$x+2y=8$$

which is the required equation of the line.

Solution:-

say AB is a line divided by point (-5,4) in the ratio 1:2

According to question,

let A(a,0) and B(0,b) are line joining points AB.

Now. by using section formula, we get,

$$(-5,4)=(\frac{1*0+2*a}{1+2},\frac{1*b+2*0}{1+2})$$

$$or,(-5,4)=(\frac{2a}{3},\frac{b}{3})$$

Now,

$$\therefore \frac{2a}{3}=-5$$

$$or,a=\frac{-15}{2}$$

Also,,$$\frac{b}{3}=4$$

$$or,b=12$$

so, A(-15/2,0) and B(0,12) are line joining points AB.

then. equation of the line is,

$$y-y_1=\frac{y_2-y_1}{x_2-x_1}(x-x_1)$$

$$or,y-0=\frac{12}{\frac{15}{2}}(x+\frac{15}{2})$$

$$or,y=\frac{4}{5}(2x+15)$$

$$or,5y=8x+60$$

$$\therefore 8x-5y+60=0$$ is the required equation of the line.

Solution:-

Given equation of line is,

$$2x+3y+k=0$$

$$or, 2x+3y=-k$$

Now, reducing it to double intercept form, wee get,

$$\frac{x}{a}+\frac{y}{b}=1$$

$$or,\frac{x}{\frac{-k}{2}}+\frac{y}{\frac{-k}{3}}=1$$

$$\therefore x-intercept(a)=\frac{-k}{2}$$ And, $$y-intercept(b)=\frac{-k}{3}$$

Hence, Area of the traiangle is,

$$A=\frac{1}{2}pb$$

$$or, 27=\frac{1}{2}*\frac{-k}{2}*\frac{-k}{3}$$

$$or, 27=\frac{k^2}{12}$$

$$or,324=k^2$$

$$\therefore k=\pm 18$$

Hence, the required value of k is ±18.

solution:-

here, Equation of the line joining (1,3) and (2,7) is,

$$y-y_1=\frac{y_2-y_1}{x_2-x_1}(x-x_1)$$

$$or,y-3=4(x-1)$$

$$or,4x-y-1=0.............(i)$$                              which  is the equation of the line.

we have,

$$3x+y=9................(ii)$$

Now, solving both equations, we get,

$$x=\frac{10}{7}$$ And $$y=\frac{33}{7}$$

Hence, the line is divided at point (10/7, 33/7)

let the ratio be k:1

so, using section formula, taking value of x,

$$x=\frac{m_1x_2+m_2x_1}{m_1+m_2}$$

$$or,\frac{10}{7}=\frac{2k+2}{k+1}$$

$$\therefore k=\frac{3}{4}$$

Hence, putting the value of k in k:1, we get,

$$k:1=3:4$$                     which is the required ratio.

Solution:-

Here, Slope of AB= slope of BC= slope of AC, since they are collinear.

Now, we have,

$$Slope Of AB=\frac{y_2-y_1}{x_2-x_1}$$

$$=\frac{16-4}{-3-1}$$

$$=-3$$

Also, $$Slope Of AC=\frac{y_2-y_1}{x_2-x_1}$$

$$=\frac{-2-4}{k-1}$$

$$=\frac{-6}{k-1}$$

Now, we get,

$$\frac{-6}{k-1}=-3$$

$$\therefore k=3$$

Hence, the value of k is 3

Solution:-

Given equations of lines are,

$$3x+y-2=0......................(i)$$

$$ax+2y-3=0 ...............(ii)$$

$$2x-y-3=0.......................(iii)$$

Now, solving (i) and (iii), we get,

$$x=1$$ And,

$$y=-1$$

Hence, the point of concurrence is (1,-1)

Now, putting (1,-1) in equation (ii), we get,

$$ax+2y-3=0$$

$$or,a-2-3=0$$

$$\therefore a=5$$

Hence, the value of a is 5 And the point of concurrence is (1,-1).

0%

## ASK ANY QUESTION ON Straight Lines- Part 1

No discussion on this note yet. Be first to comment on this note


text:
This student is going to go far in life, although maybe not in this particular test.

The teacher clearly didn’t appreciate the cunning blend of the words ‘true’ and ‘false’.

Genius as it is, trying it out on every answer was always destined to fail – although he might have been lucky if he’d only slipped it in just once or twice.

The picture of the answer paper was uploaded to the image-sharing website Imgur, with the caption ‘You miss 100 per cent of the shots you don’t take’.

In this case, it seems the kid missed 100 per cent of the shots he did take. You can’t blame them for trying though.

format: plain


text:
# Intersection type

In type theory, an intersection type can be allocated to values that can be assigned both the type ${\displaystyle \sigma }$ and the type ${\displaystyle \tau }$. This value can be given the intersection type ${\displaystyle \sigma \cap \tau }$ in an intersection type system.[1] Generally, if the ranges of values of two types overlap, then a value belonging to the intersection of the two ranges can be assigned the intersection type of these two types. Such a value can be safely passed as argument to functions expecting either of the two types. For example, in Java the class Boolean implements both the Serializable and the Comparable interfaces. Therefore, an object of type Boolean can be safely passed to functions expecting an argument of type Serializable and to functions expecting an argument of type Comparable.

Intersection types are composite data types. Similar to product types, they are used to assign several types to an object. However, product types are assigned to tuples, so that each tuple element is assigned a particular product type component. In comparison, underlying objects of intersection types are not necessarily composite. A restricted form of intersection types are refinement types.

Intersection types are useful for describing overloaded functions.[2] For example, if number => number is the type of function taking a number as an argument and returning a number, and string => string is the type of function taking a string as an argument and returning a string, then the intersection of these two types can be used to describe (overloaded) functions that do one or the other, based on what type of input they are given.

Contemporary programming languages, including Ceylon, Flow, Java, Scala, TypeSript, and Whiley (see comparison of languages with intersection types), use intersection types to combine interface specifications and to express ad hoc polymorphism. Complementing parametric polymorphism, intersection types may be used to avoid class hierarchy pollution from cross-cutting concerns and reduce boilerplate code, as shown in the TypeScript example below.

The type theoretic study of intersection types is referred to as the intersection type discipline.[3] Remarkably, program termination can be precisely characterized using intersection types.[4]

## TypeScript example

TypeScript supports intersection types,[5] improving expressivity of the type system and reducing potential class hierarchy size, demonstrated as follows.

The following program code defines the classes Chicken, Cow, and RandomNumberGenerator that each have a method produce returning an object of either type Egg, Milk, or number. Additionally, the function eatEgg (resp. drinkMilk) requires an object of type Egg (resp. Milk) as argument.

class Egg { private kind: "Egg" }
class Milk { private kind: "Milk" }

//produces eggs
class Chicken { produce() { return new Egg(); } }

//produces milk
class Cow { produce() { return new Milk(); } }

//produces a random number
class RandomNumberGenerator { produce() { return Math.random(); } }

//requires an egg
function eatEgg(egg: Egg) {
return "I ate an egg.";
}

//requires milk
function drinkMilk(milk: Milk) {
return "I drank some milk.";
}

The following program code defines the ad hoc polymorphic function animalToFood that invokes the member function produce of the given object animal. The function animalToFood has two type annotations, namely ((_: Chicken) => Egg) and ((_: Cow) => Milk), connected via the intersection type constructor &. Specifically, animalToFood when applied to an argument of type Chicken returns an object of type type Egg, and when applied to an argument of type Cow returns an object of type type Milk. Ideally, animalToFood should not be applicable to any object having (possibly by chance) a produce method.

//given a chicken, produces an egg; given a cow, produces milk
let animalToFood: ((_: Chicken) => Egg) & ((_: Cow) => Milk) =
function (animal: any) {
return animal.produce();
};

Finally, the following program code demonstrates type safe use of the above definitions.

 1 var chicken = new Chicken();
2 var cow = new Cow();
3 var randomNumberGenerator = new RandomNumberGenerator();
4
5 console.log(chicken.produce()); //Egg { }
6 console.log(cow.produce()); //Milk { }
7 console.log(randomNumberGenerator.produce()); //0.2626353555444987
8
9 console.log(animalToFood(chicken)); //Egg { }
10 console.log(animalToFood(cow)); //Milk { }
11 //console.log(animalToFood(randomNumberGenerator)); //ERROR: Argument of type 'RandomNumberGenerator' is not assignable to parameter of type 'Cow'
12
13 console.log(eatEgg(animalToFood(chicken))); //I ate an egg.
14 //console.log(eatEgg(animalToFood(cow))); //ERROR: Argument of type 'Milk' is not assignable to parameter of type 'Egg'
15 console.log(drinkMilk(animalToFood(cow))); //I drank some milk.
16 //console.log(drinkMilk(animalToFood(chicken))); //ERROR: Argument of type 'Egg' is not assignable to parameter of type 'Milk'

The above program code has the following properties:

• Lines 1-3 create objects chicken, cow, and randomNumberGenerator of their respective type.
• Lines 5-7 print for the previously created objects the respective results (provided as comments) when invoking produce.
• Line 9 (resp. 10) demonstrates type safe use of the method animalToFood applied to chicken (resp. cow).
• Line 11, if uncommitted, would result in a type error at compile time. Although the implementation of animalToFood could invoke the produce method of randomNumberGenerator, the type annotation of animalToFood disallows it. This is in accordance with the intended meaning of animalToFood.
• Line 13 (resp. 15) demonstrates that applying animalToFood to chicken (resp. cow) results in an object of type Egg (resp. Milk).
• Line 14 (resp. 16) demonstrates that applying animalToFood to cow (resp. chicken) does not result in an object of type Egg (resp. Milk). Therefore, if uncommented, line 14 (resp. 16) would result in a type error at compile time.

### Comparison to inheritance

The above minimalist example can be realized using inheritance, for instance by deriving the classes Chicken and Cow from a base class Animal. However, in a larger setting this could be disadvantageous. Introducing new classes into a class hierarchy is not necessarily justified for cross-cutting concerns, or may be outright impossible, for example when using an external library. Imaginably, the above example could be extended with the following classes:

• a class Horse that does not have a produce method;
• a class Sheep that has a produce method returning Wool;
• a class Pig that has a produce method, which can be used only once, returning Meat.

This may require additional classes (or interfaces) specifying whether a produce method is available, whether the produce method returns food, and whether the produce method can be used repeatedly. Overall, this may pollute the class hierarchy.

### Comparison to duck typing

The above minimalist example already shows that duck typing is less suited to realize the given scenario. While the class RandomNumberGenerator contains a produce method, the object randomNumberGenerator should not be a valid argument for animalToFood. The above example can be realized using duck typing, for instance by introducing a new field argumentForAnimalToFood to the classes Chicken and Cow signifying that objects of corresponding type are valid arguments for animalToFood. However, this would not only increase the size of the respective classes (especially with the introduction of more methods similar to animalToFood), but is also a non-local approach with respect to animalToFood.

The above example can be realized using function overloading, for instance by implementing two methods animalToFood(animal: Chicken): Egg and animalToFood(animal: Cow): Milk. In TypeScript, such a solution is almost identical to the provided example. Other programming languages, such as Java, require distinct implementations of the overloaded method. This may lead to either code duplication or boilerplate code.

### Comparison to the visitor pattern

The above example can be realized using the visitor pattern. It would require each animal class to implement an accept method accepting an object implementing the interface AnimalVisitor (adding non-local boilerplate code). The function animalToFood would be realized as the visit method of an implementation of AnimalVisitor. Unfortunately, the connection between the input type (Chicken or Cow) and the result type (Egg or Milk) would be difficult to represent.

### Limitations

On the one hand, intersection types can be used to locally annotate different types to a function without introducing new classes (or interfaces) to the class hierarchy. On the other hand, this approach requires all possible argument types and result types to be specified explicitly. If the behavior of a function can be specified precisely by either a unified interface, parametric polymorphism, or duck typing, then the verbose nature of intersection types is unfavorable. Therefore, intersection types should be considered complementary to existing specification methods.

## Dependent intersection type

A dependent intersection type, denoted ${\displaystyle (x:\sigma )\cap \tau }$ , is a dependent type in which the type ${\displaystyle \tau }$  may depend on the term variable ${\displaystyle x}$ .[6] In particular, if a term ${\displaystyle M}$  has the dependent intersection type ${\displaystyle (x:\sigma )\cap \tau }$ , then the term ${\displaystyle M}$  has both the type ${\displaystyle \sigma }$  and the type ${\displaystyle \tau [x:=M]}$ , where ${\displaystyle \tau [x:=M]}$  is the type which results from replacing all occurrences of the term variable ${\displaystyle x}$  in ${\displaystyle \tau }$  by the term ${\displaystyle M}$ .

### Scala example

Scala supports type declarations [7] as object members. This allows a type of an object member to depend on the value of another member, which is called a path-dependent type.[8] For example, the following program text defines a Scala trait Witness, which can be used to implement the singleton pattern.[9]

trait Witness {
type T
val value: T {}
}

The above trait Witness declares the member T, which can be assigned a type as its value, and the member value, which can be assigned a value of type T. The following programm text defines an object booleanWitness as instance of the above trait Witness. The object booleanWitness defines the type T as Boolean and the value value as true. For example, executing System.out.println(booleanWitness.value) prints true on the console.

object booleanWitness extends Witness {
type T = Boolean
val value = true
}

Let ${\displaystyle \langle {\textsf {x}}:\sigma \rangle }$  be the type (specifically, a record type) of objects having the member ${\displaystyle {\textsf {x}}}$  of type ${\displaystyle \sigma }$ . In the above example, the object booleanWitness can be assigned the dependent intersection type ${\displaystyle (x:\langle {\textsf {T}}:{\text{Type}}\rangle )\cap \langle {\textsf {value}}:x.{\textsf {T}}\rangle }$ . The reasoning is as follows. The object booleanWitness has the member T that is assigned the type Boolean as its value. Since Boolean is a type, the object booleanWitness has the type ${\displaystyle \langle {\textsf {T}}:{\text{Type}}\rangle }$ . Additionally, the object booleanWitness has the member value that is assigned the value true of type Boolean. Since the value of booleanWitness.T is Boolean, the object booleanWitness has the type ${\displaystyle \langle {\textsf {value}}:{\textsf {booleanWitness.T}}\rangle }$ . Overall, the object booleanWitness has the intersection type ${\displaystyle \langle {\textsf {T}}:{\text{Type}}\rangle \cap \langle {\textsf {value}}:{\textsf {booleanWitness.T}}\rangle }$ . Therefore, presenting self-reference as dependency, the object booleanWitness has the dependent intersection type ${\displaystyle (x:\langle {\textsf {T}}:{\text{Type}}\rangle )\cap \langle {\textsf {value}}:x.{\textsf {T}}\rangle }$ .

Alternatively, the above minimalistic example can be described using dependent record types.[10] In comparison to dependent intersection types, dependent record types constitute a strictly more specialized type theoretic concept.[6]

## Intersection of a type family

An intersection of a type family, denoted ${\displaystyle \bigcap _{x:\sigma }\tau }$ , is a dependent type in which the type ${\displaystyle \tau }$  may depend on the term variable ${\displaystyle x}$ .[6] In particular, if a term ${\displaystyle M}$  has the type ${\displaystyle \bigcap _{x:\sigma }\tau }$ , then for each term ${\displaystyle N}$  of type ${\displaystyle \sigma }$ , the term ${\displaystyle M}$  has the type ${\displaystyle \tau [x:=N]}$ . This notion is also called implicit Pi type,[11] observing that the argument ${\displaystyle N}$  is not kept at term level.

## Comparison of languages with intersection types

Language Actively developed Paradigm(s) Status Features
C# Yes[12] Under discussion[13] ?
Ceylon Yes[14] Supported[15]
• Type refinement
• Interface composition
• Subtyping in width
F# Yes[16] Under discussion[17] ?
Flow Yes[18] Supported[19]
• Type refinement
• Interface composition
Forsythe No Supported[20]
• Function type intersection
• Distributive, co- and contravariant function type subtyping
Java Yes[21] Supported[22]
• Type refinement
• Interface composition
• Subtyping in width
Scala Yes[23] Supported[24][25]
• Type refinement
• Trait composition
• Subtyping in width
TypeScript Yes[26] Supported[5]
• Arbitrary type intersection
• Interface composition
• Subtyping in width and depth
Whiley Yes[27] Supported[28] ?

## References

1. ^ Barendregt, Henk; Coppo, Mario; Dezani-Ciancaglini, Mariangiola (1983). "A filter lambda model and the completeness of type assignment". Journal of Symbolic Logic. 48 (4): 931–940. doi:10.2307/2273659. JSTOR 2273659.
2. ^ Palsberg, Jens (2012). "Overloading is NP-Complete". Logic and Program Semantics. Lecture Notes in Computer Science. 7230. pp. 204–218. doi:10.1007/978-3-642-29485-3_13. ISBN 978-3-642-29484-6.
3. ^ Henk Barendregt; Wil Dekkers; Richard Statman (20 June 2013). Lambda Calculus with Types. Cambridge University Press. pp. 1–. ISBN 978-0-521-76614-2.
4. ^ Ghilezan, Silvia (1996). "Strong normalization and typability with intersection types". Notre Dame Journal of Formal Logic. 37 (1): 44–52. doi:10.1305/ndjfl/1040067315.
5. ^ a b "Intersection Types in TypeScript". Retrieved 2019-08-01.
6. ^ a b c Kopylov, Alexei (2003). "Dependent intersection: A new way of defining records in type theory". 18th IEEE Symposium on Logic in Computer Science. LICS 2003. IEEE Computer Society. pp. 86–95. CiteSeerX 10.1.1.89.4223. doi:10.1109/LICS.2003.1210048.
7. ^ "Type declarations in Scala". Retrieved 2019-08-15.
8. ^ Amin, Nada; Grütter, Samuel; Odersky, Martin; Rompf, Tiark; Stucki, Sandro (2016). "The essence of dependent object types". A List of Successes That Can Change the World - Essays Dedicated to Philip Wadler on the Occasion of His 60th Birthday. Lecture Notes in Computer Science. 9600. Springer. pp. 249–272. doi:10.1007/978-3-319-30936-1_14.
9. ^ "Singletons in the Scala shapeless library". Retrieved 2019-08-15.
10. ^ Pollack, Robert (2000). "Dependently typed records for representing mathematical structure". Theorem Proving in Higher Order Logics, 13th International Conference. TPHOLs 2000. Springer. pp. 462–479. doi:10.1007/3-540-44659-1_29.
11. ^ Stump, Aaron (2018). "From realizability to induction via dependent intersection". Annals of Pure and Applied Logic. 169 (7): 637–655. doi:10.1016/j.apal.2018.03.002.
12. ^ "C# Guide". Retrieved 2019-08-08.
13. ^ "Discussion: Union and Intersection types in C Sharp". Retrieved 2019-08-08.
14. ^ "Eclipse Ceylon: Welcom to Ceylon". Retrieved 2019-08-08.
15. ^ "Intersection Types in Ceylon". Retrieved 2019-08-08.
16. ^ "F# Software Foundation". Retrieved 2019-08-08.
17. ^ "Add Intersection Types to F Sharp". Retrieved 2019-08-08.
18. ^ "Flow: A Static Type Checker for JavaScript". Retrieved 2019-08-08.
19. ^ "Intersection Type Syntax in Flow". Retrieved 2019-08-08.
20. ^ Reynolds, J. C. (1988). Preliminary design of the programming language Forsythe.
21. ^ "Java Software". Retrieved 2019-08-08.
22. ^ "IntersectionType (Java SE 12 & JDK 12)". Retrieved 2019-08-01.
23. ^ "The Scala Programming Language". Retrieved 2019-08-08.
24. ^ "Compound Types in Scala". Retrieved 2019-08-01.
25. ^ "Intersection Types in Dotty". Retrieved 2019-08-01.
26. ^ "TypeScript - JavaScript that scales". Retrieved 2019-08-01.
27. ^ "Whiley: an Open Source Programming Language with Extended Static Checking". Retrieved 2019-08-01.
28. ^ "Whiley language specification" (PDF). Retrieved 2019-08-01.


text:
## GUPTA MECHANICAL

IN THIS WEBSITE I CAN TELL ALL ABOUT TECH. TIPS AND TRICKS APP REVIEWS AND UNBOXINGS ALSO TECH. NEWS .............

# [Solution] Build a Tree and That Is It Codeforces Solution

F. Build a Tree and That Is It
time limit per test
2 seconds
memory limit per test
256 megabytes
input
standard input
output
standard output

A tree is a connected undirected graph without cycles. Note that in this problem, we are talking about not rooted trees.

You are given four positive integers $n,{d}_{12},{d}_{23}$ and ${d}_{31}$. Construct a tree such that:

• it contains $n$ vertices numbered from $1$ to $n$,
• the distance (length of the shortest path) from vertex $1$ to vertex $2$ is ${d}_{12}$,
• distance from vertex $2$ to vertex $3$ is ${d}_{23}$,
• the distance from vertex $3$ to vertex $1$ is ${d}_{31}$.

Output any tree that satisfies all the requirements

Solution Click Below:-  👉

👇👇👇👇👇

occupied

above, or determine that no such tree exists.

Input

The first line of the input contains an integer $t$ ($1\le t\le {10}^{4}$) —the number of test cases in the test.

This is followed by $t$ test cases, each written on a separate line.

Each test case consists of four positive integers $n,{d}_{12},{d}_{23}$ and ${d}_{31}$ ($3\le n\le 2\cdot {10}^{5};1\le {d}_{12},{d}_{23},{d}_{31}\le n-1$).

It is guaranteed that the sum of $n$ values for all test cases does not exceed $2\cdot {10}^{5}$.

Output

For each test case, print YES if the suitable tree exists, and NO otherwise.

If the answer is positive, print another $n-1$ line each containing a description of an edge of the tree — a pair of positive integers ${x}_{i},{y}_{i}$, which means that the $i$th edge connects vertices ${x}_{i}$ and ${y}_{i}$.

The edges and vertices of the edges can be printed in any order. If there are several suitable trees, output any of them.


text:
# Understanding disentangling in $β$-VAE

We present new intuitions and theoretical assessments of the emergence of disentangled representation in variational autoencoders. Taking a rate-distortion theory perspective, we show the circumstances under which representations aligned with the underlying generative factors of variation of data emerge when optimising the modified ELBO bound in $\beta$-VAE, as training progresses... (read more)

PDF Abstract

# Code Add Remove Mark official

1,697
See all 16 implementations

# Results from the Paper Add Remove

Submit results from this paper to get state-of-the-art GitHub badges and help the community compare results to other papers.

# Methods used in the Paper Add Remove

METHOD TYPE
🤖 No Methods Found Help the community by adding them if they're not listed; e.g. Deep Residual Learning for Image Recognition uses ResNet


text:
# Two-dimensional bounded area defined parametrically

How do I go about defining this area without using a piecewise function?

I think it has something to do with Bilinear Surfaces but I'm not sure how to get started.

• What kind of properties are you after for that surface? Sep 13 '15 at 12:35

One solution is bilinear mapping, which works for every convex quadrilateral.

Let $A, B, C, D$ be the vertices of a quadrilateral $Q$ in the plane, in this order.

Then $f(u,v)=(1-u)(1-v)A + u(1-v)B + uvC + (1-u)vD$ maps the square $[0,1] \times [0,1]$ to $Q$.

• What, no MathJax ? :-(
– lhf
Sep 13 '15 at 14:24
• Yep, looks like it's not working yet :(. Would you mind just using plain code formatting for time being, so all those symbols won't distract from the formulas? Sep 13 '15 at 18:09
• I've added this question to the list of examples on meta to add to the case for adding MathJax to our site. Sep 14 '15 at 13:37
• "which works for every quadrilateral." Unless I've messed up my "back of the envelope sketch", I think you need to amend that to "every convex quadrilateral". Sep 14 '15 at 13:45
• @ratchet, MathJax, yeah!
– lhf
Nov 3 '15 at 15:13


text:
Home »

# Watt

## The meaning of «watt»

The watt (symbol: W) is a unit of power or radiant flux. In the International System of Units (SI), it is defined as a derived unit of (in SI base units)[1][2] 1 kg⋅m2⋅s−3 or, equivalently,[3] 1 joule per second. It is used to quantify the rate of energy transfer. The watt is named after James Watt (1736-1819), an 18th-century Scottish inventor.

When an object's velocity is held constant at one metre per second against a constant opposing force of one newton, the rate at which work is done is one watt.

In terms of electromagnetism, one watt is the rate at which electrical work is performed when a current of one ampere (A) flows across an electrical potential difference of one volt (V), meaning the watt is equivalent to the volt-ampere (the latter unit, however, is used for a different quantity from the real power of an electrical circuit).

Two additional unit conversions for watt can be found using the above equation and Ohm's law.

where ohm ( Ω {\displaystyle \Omega } ) is the SI derived unit of electrical resistance.

The watt is named after the Scottish inventor James Watt.[5] This unit name was proposed initially by C. William Siemens in August 1882 in his President's Address to the Fifty-Second Congress of the British Association for the Advancement of Science.[6] Noting that units in the practical system of units were named after leading physicists, Siemens proposed that watt might be an appropriate name for a unit of power.[7] Siemens defined the unit consistently within the then-existing system of practical units as "the power conveyed by a current of an Ampère through the difference of potential of a Volt".[8]

In October 1908, at the International Conference on Electric Units and Standards in London,[9] so-called "international" definitions were established for practical electrical units.[10] Siemens' definition was adopted as the "international" watt. (Also used: 1 A2 × 1 Ω.)[5] The watt was defined as equal to 107 units of power in the "practical system" of units.[10] The "international units" were dominant from 1909 until 1948. After the 9th General Conference on Weights and Measures in 1948, the "international" watt was redefined from practical units to absolute units (i.e., using only length, mass, and time). Concretely, this meant that 1 watt was now defined as the quantity of energy transferred in a unit of time, namely 1 J/s. In this new definition, 1 "absolute" watt = 1.00019 "international" watts. Texts written before 1948 are likely to be using the "international" watt, which implies caution when comparing numerical values from this period with the post-1948 watt.[5] In 1960 the 11th, General Conference on Weights and Measures adopted the "absolute" watt into the International System of Units (SI) as the unit of power.[11]

### Related Searches

 Wattpad Watts family murders Watts, Los Angeles Watts riots Watts Towers Watt steam engine Wattle and daub Wattie Buchan Watts, California

### Choice of words

 w-att_ _wa-tt_ _wat-t-_ _wat-t-_ _ watt:_ _ _ _watt_ _ _ _watt_ - _ _ _watt-_ _ _ _watt _ _ _ _ _watt _ - _ _ _ _


text:
Nigerian Scholars » » Equality before the law implies that

# Equality before the law implies that

### Question

Equality before the law implies that

### Options

A) the law does not respect the people

B) are dirctly represented likes

C) no one citizens can sue the other

D) there is inequality between the executive and citizens

E) the executive cannot be controlled by the legislature


text:
In the verge of coronavirus pandemic, we are providing FREE access to our entire Online Curriculum to ensure Learning Doesn't STOP!

Ex.13.7 Q3 Surface Areas and Volumes Solution - NCERT Maths Class 9

Go back to  'Ex.13.7'

Question

The height of a cone is $$15\rm\, cm.$$ If its volume is \begin{align}1570\,\,c{m^3} \end{align}, find the radius of the base.(Use $$p = 3.14$$).

Video Solution
Surface-Areas-And-Volumes
Ex exercise-13-7 | Question 3

Text Solution

Reasoning:

Volume of the cone is \begin{align} \frac{1}{3} \end{align} times of the volume of a cylinder having radius r and height h i.e. \begin{align} = \frac{1}{3}\pi {r^2}h \end{align}

What is  known?

Volume of the cone and the height of the cone.

What is  unknown?

Steps:

Height $$(h) = 15\,\rm cm$$

Radius $$(r) = ?$$

Volume of cone

\begin{align}&= \frac{1}{3}\pi {r^2}h \\1570&= \frac{1}{3}\pi {r^2}h \\ 1570 &= \frac{1}{3} \times 3.14 \times {r^2} \times 15 \\{r^2} &= \frac{{1570 \times 3}}{{15 \times 3.14}} = \frac{{4710}}{{47.1}} \\{r^2} &= 100 \\ r &= \sqrt {100} = 10\,\,\rm\,cm \end{align}

Radius of the base $$= 10 \rm\,cm$$


text:
# The least basic oxide is

$\begin{array}{1 1}(a)\;Cs_2O&(b)\;K_2O\\(c)\;Na_2O&(d)\;Li_2O\end{array}$

Basic nature of oxide increases down the group.
Hence the least basic oxide is$Li_2O$
Hence (d) is the correct answer.


text:
# Bessel-K function for complex numbers

Calculator for the modified Bessel function Kn (z) of the second type

## Bessel function Kn (z) of the second kind

The Bessel-K function calculates the modified Bessel function Kn (z) of the second kind. The modified Bessel functions do not show an oscillating but an exponential behavior. Bessel-K (n, z) is a solution of the modified Bessel differential equation.

This function expects a complex number as argument z . Bessel functions for real numbers can be found here.

To perform the calculation, enter the complex number and the order number. Then click on the 'Calculate' button.

Bessel-K for complex number

 Input Complex number + i Order number + Decimal places 0 1 2 3 4 6 8 10 Result

Plot of the Bessel-K function with the ordinal numbers 0, 1 and 2

 Is this page helpful?             Thank you for your feedback! Sorry about that How can we improve it?


text:
University_

# Aboriginal and Torres Strait Islander Entry Scholarship

This scholarship supports academically gifted Australian Indigenous students to commence tertiary study at the University of Sydney.

## Highlights

Value Eligibility Open date Close date

## Who's eligible

You must be:

• be a student of Australian Aboriginal or Torres Strait Islander descent
• have obtained an ATAR in the HSC (or equivalent) of 85.0 or above
• be commencing in the first year of an undergraduate degree through UAC.

Note: A confirmed offer of a scholarship must be taken up by enrolment in the first year of the nominated degree or combined degree program in the year for which the offer is made.

#### Terms and conditions

##### 1. Background

a. The University of Sydney Indigenous Entry Scholarships aim to encourage academically gifted Australian Indigenous students to commence tertiary study at the University of Sydney.

##### 2. Eligibility

a. No application is required. University of Sydney Indigenous Entry Scholarships are awarded to recipients who:

I. are of Australian Aboriginal or Torres Strait Islander descent. Indigenous identity is subject to verification by The Indigenous Australian Student Support Service at the University of Sydney;

II. apply to the University through UAC and enrol in a University undergraduate degree or combined degree;

III. complete the NSW Higher School Certificate (HSC) or a University approved equivalent secondary school examination in the year of application and achieve an ATAR of at least 85; and

IV. commence their studies at the University in the year immediately following their HSC or equivalent.

##### 3. Value

a. The Scholarship is valued at \$10,000 and is tenable for one year only.

b. The Scholarship annual value will be paid in two equal instalments after the census date of each semester.

c. Commencement of the Scholarship can be deferred for up to two years. Deferral of the Scholarship is not permitted without prior permission of the Scholarships Office.

d. The Scholarship is transferable to another undergraduate degree at the University of Sydney. Funding will only be provided for the original approved study duration less the period of studies already undertaken. Approval for the scholarship transfer must be sought from the Scholarships Office.

e. The scholarship recipient must enrol full-time in the agreed program during the tenure of their scholarship. Recipients may hold the scholarship part-time due to extenuating circumstances such as a medical condition which limits the student's capacity to undertake full-time study. An application for a part-time scholarship must be submitted to the Scholarships Office for consideration. If a part-time scholarship is approved, payment will be 50% of the amount of the normal semester payment.

f. The scholarship may be suspended under extenuating circumstances. Approval for suspension is on a case-by-case basis upon application to the Scholarships Office.

g. No other amount is payable.

##### 4. Ongoing eligibility

a. To continue receipt of the Scholarship, the recipient must maintain a minimum Semester Average Mark (SAM) of 65 each semester.

b. Recipients undertaking an exchange during the tenure of this Scholarship are required to have achieved a Satisfied Requirements grade (SR) to receive their next payment.

##### 5. Termination

a. The Scholarship will be terminated if the recipient:

I. withdraws from an eligible course or fails to enrol,

II. commences part-time study without prior approval,

III. does not maintain satisfactory academic performance,

IV. is determined by the University to be guilty of serious misconduct, including, but not limited to, having provided false or misleading information as part of their Scholarship application,

V. is awarded an alternative primary scholarship. In such circumstances this scholarship will be terminated in favour of the alternative scholarship where the alternative scholarship is of higher value,

VI. does not resume study at the end of a period of approved leave, or

VII. any other provision as indicated in these terms that would lead to termination.

b. Once the Scholarship has been terminated, it will not be reinstated unless due to University error.

c. Where a student is found guilty of serious misconduct or withdraws from the relevant course, the University reserves the right to request that any Scholarship funds paid to the Scholarship recipient be reimbursed.


text:
## Monday, April 23, 2012

### How to Remember Typical Stopping Distances in The Highway Code

The Highway Code (UK) gives the following list of typical stopping distances. The Highway Code gives no hint on the source of this information, nor it gives any insight on the method used to calculate these values. It does, however, state that "your typical stopping distance consists of thinking distance plus breaking distance."

Being a learner, it's difficult for me to understand how remembering these numbers to precise detail will help me in effectively avoiding road hazards. More so, I can't precisely tell the difference in 73 meters and 96 meters while driving at a speed of 60mph.

Unfortunate as it might be, one needs to remember all these values by heart, as part of the theory test in the UK. Here are some hints to get you going. Look at the chart in detail, and read the following hints:
1. The speed goes from 20mph to 70mph in increments of 10 in this chart. The most important hint is that 50 mph and above are the speeds where the total stopping distances are more than the value of the speed. For speeds less than 50 mph, the total stopping distance in meters is less than the speed in mph.
2. If you look at the thinking distance, they are in multiples of 3. If you multiply the speed by 3 and drop off a zero, you get the thinking distance. So, the thinking distance at 20 mph can be calculated as 20x3=60, which gives 6 meters when you drop a zero. Similarly, the thinking distance at 70 mph can be calculated as 70x3=210, which gives 21 meters.
3. The breaking distance (6 meters) at 20 mph is same as the thinking distance (6 meters). The total distance is just s sum of these values: 12 meters.
4. An average car length, according to this chart, is 4 meters. The total stopping distance for 20 mph is 3 cars (equals to 12 meters). The stopping distances go like this: 3 cars, 3 more cars, 3 more cars, 4 more cards, 5 more cars and finally 6 cars. In this way, the total stopping distance at 70 mph is 24 cars, which gives 24 cars x 4 meters each = 96 meters.


text:
Lemma 13.9.15. Let $\mathcal{A}$ be an additive category. Let $A_1^\bullet \to A_2^\bullet \to \ldots \to A_ n^\bullet$ be a sequence of composable morphisms of complexes. There exists a commutative diagram

$\xymatrix{ A_1^\bullet \ar[r] & A_2^\bullet \ar[r] & \ldots \ar[r] & A_ n^\bullet \\ B_1^\bullet \ar[r] \ar[u] & B_2^\bullet \ar[r] \ar[u] & \ldots \ar[r] & B_ n^\bullet \ar[u] }$

such that each morphism $B_ i^\bullet \to B_{i + 1}^\bullet$ is a split injection and each $B_ i^\bullet \to A_ i^\bullet$ is a homotopy equivalence. Moreover, if all $A_ i^\bullet$ are in $K^{+}(\mathcal{A})$, $K^{-}(\mathcal{A})$, or $K^ b(\mathcal{A})$, then so are the $B_ i^\bullet$.

Proof. The case $n = 1$ is without content. Lemma 13.9.6 is the case $n = 2$. Suppose we have constructed the diagram except for $B_ n^\bullet$. Apply Lemma 13.9.6 to the composition $B_{n - 1}^\bullet \to A_{n - 1}^\bullet \to A_ n^\bullet$. The result is a factorization $B_{n - 1}^\bullet \to B_ n^\bullet \to A_ n^\bullet$ as desired. $\square$

Comment #297 by arp on

Heh since I'm nitpicking, it would look better if throughout the proof there were bullets on the complexes.

In your comment you can use Markdown and LaTeX style mathematics (enclose it like $\pi$). A preview option is available if you wish to see how it works out (just click on the eye in the toolbar).


text:
## Introduction to the Complex Plane

Imaginary numbers had no use when it was invented except for intellectual exploration until it was linked to coordinate geometry.  The complex number $a + bi$ can be plotted as the ordered pair $(a,b)$ where $a$ is the real part and $b$ is the imaginary part.  Therefore, the complex numbers $3 + 2i$, $3- 2i$, $-2 + 0i$,  and $0 - i$ can be plotted as $(3,2)$, $(3,-2)$, $(-2,0)$, and $(0,-1)$ in a “coordinate plane” respectively as shown below.  In the figure, we can see that the origin is $0 + 0i$ and that $3 - 2i$, the complex conjugate of $3 + 2i$, is its reflection along the x-axis (Can this be generalized?).

The plane where the complex numbers are plotted above is called the complex plane.

In the complex plane, we can observe that all numbers of the form $(a,0)$ are real numbers and these numbers are represented by the horizontal axis. The numbers of the form $(0,bi)$ are all imaginary numbers and it is represented by the vertical axis. Thus, we can call them  the real axis and the imaginary axis respectively.

In addition, we can conclude that all real numbers are complex numbers since  for all  real numbers  $a$, $a = a + 0i$. So, the set of real numbers is a subset of the set of complex numbers.

## Demystifying Complex Conjugates

This is the third post in the Complex Numbers Primer.  In the previous post in this series, we have learned that complex numbers can be added and multiplied just like binomials.  We did not discuss subtraction since it follows from addition; that is, if $a + bi$ and $c + di$ are complex numbers, then

$a + bi - (c + di) = a - c + (b - d)i$.

Since we have completed the three fundamental operations on complex numbers, the next logical question would be how do we divide complex numbers? For example, how do we find the quotient of the expression

$\displaystyle\frac{5 + 2i}{3 - i}$?

Before we answer that question, recall that in simplifying rational expressions with radicals in the denominator, we multiply the numerator and the denominator of the expression by the ‘conjugate’ of the denominator.  For instance, to simplify

$\displaystyle\frac{5}{2 + \sqrt{3}}$. » Read more

## Complex Numbers and their Properties

Imaginary numbers as we have discussed in Tuesday’s post are numbers of the form bi where $b$ is a real number and $i = \sqrt{-1}$. The term imaginary as (opposed to real) was first used by Rene Descartes, the mathematician who invented Coordinate Geometry — the Cartesian plane in particular.  Leonhard Euler was the one who introduced the symbol $i$ for $\sqrt{-1}$.

Leonhard Euler

Gerolamo Cardano, a pioneer in probability, was the one who suggested the   use of numbers of the form $a + bi$ where $a$ and $b$ are real numbers and $i = \sqrt{-1}$.  Numbers of this form were named complex numbers by Carl Frederich Gauss.The real part of $a + bi$ is $a$ and the imaginary part is bi. » Read more


text:
A fair coin is tossed n times. The probability that the difference between the number of heads and tails is $(n-3)$ is
1. $2^{-n}$
2. $0$
3. $n_{C_{n-3}}2^{-n}$
4. $2^{-n+3}$


text:
# kwant.continuum.lambdify¶

kwant.continuum.lambdify(expr, locals=None)[source]

Return a callable object for computing a continuum Hamiltonian.

Warning

This function uses eval (because it calls sympy.sympify), and thus should not be used on unsanitized input.

If necessary, the given expression is sympified using kwant.continuum.sympify. It is then converted into a callable object.

Parameters: expr : str or SymPy expression Expression to be converted into a callable object locals : dict or None (default) Additional definitions for sympify.

#### Previous topic

kwant.continuum.sympify

#### Next topic

4.5. kwant.wraparound – Wrapping around translational symmetries


text: LaTeX can certainly produce any type of table you’d like to create, but it does so in a way that can be very difficult to follow visually. As you can see, the code of the table does not need to represent the spacing of the table - that is accomplished within the markdown. Move the template eisvogel.tex to your pandoc templates folder and rename the file to eisvogel.latex. Von Markdown aus kommen Sie problemlos nach HTML und LaTeX – wie auch an anderer Stelle festgestellt –, so dass Sie für schön gesetzte Druckdokumente und PDFs nach wie vor LaTeX verwenden können. [imagelabel](example-image.jpg "Image Title"). When I first created the PocketMod template in 2015, I yearned for a way to write markdown in LaTeX so that I could create PocketMods with markdown because it felt… appropriate. Captions; Labels; More examples; Docs > Mathpix-markdown > LaTeX Figure Syntax LaTeX Style Figures. 2 Examples. \ref{fig:imagelabel}. Edit: R Markdown is a low-overhead way of writing reports which includes R code and the code’s automatically-generated output. That is pretty much it. For example, here is a document with a raw LaTeX block: Learning More. Im Gegensatz zu den genannten soll Markdown aber möglichst leicht von Menschen zu lesen sein. Further Reference and keyboard-localization is necessary when using an international layout (like [swiss] german). This sample content is adapted from thesisdown and the formatting of PDF output is adapted from the OxThesis LaTeX template.Hopefully, writing your thesis in R Markdown will provide a nicer interface to the OxThesis template if you haven’t used TeX or LaTeX before. He pointed me at the, really slick looking, LaTex template. The markdown package makes it possible to use markdown in LaTeX documents. Markdown is a simple formatting language designed to make authoring content easy for everyone. How to make a simple LaTeX template for R Markdown from scratch 4 minute read Published: 25 Apr, 2019. You can also use HTML code. Images can be included in markdown by writing ! Further Reference and \ref{fig:imagelabel}. For example:--- Be sure to update typeset with your own input files in the FILES variable. References, bibliographies, appendix etc. to see the effect of your changes. Example. It is a combination of Markdown and LaTeX syntax, which creates a great writing experience for technical documents. Output Type Default Engine Details ; HTML {gt} {gt} output is fully supported with HTML output. Math equations can be rendered in Markdown Monster and the generated HTML by using a Math processing library that is either added to the page, or to the Preview Template or your deployed site. Note: on StackExchange this formatting isn't included. To do this, bound your code inside ~ ~ ~ ~ ... ~ ~ ~ ~. In this section, I will describe the individual parts of the Markdown package. Cheatsheet for LaTex, using Markdown for markup. You should consider no longer using LaTeX as a front-end for your manuscripts. To write greek letters, type \ and the letter name: Output Result: Colab Notebook. There are a number of different ways to edit and produce LaTeX documents, which we’ll revist in a future post. In order to have nice headers and footers you need to supply metadata to your document. Using markdown in styled LaTeX templates. Basic LaTeX Beamer Support . To use this, simply include \usepackage{markdown} in the preamble of your document. Can you create tables using markdown in LaTeX? What is Mathpix Markdown? PDF. markdown documentation: Creating a table. Markdown+Math. LaTeX is a fantastic way to create and display print-ready scientific documents. After the "#", by opening a space, write the title of the character; Change is the number the magnitude of the "#" Itemization -> "-" "-" is itemization. Use a wrapper for LaTeX instead, like R Markdown. John Gabriele. Markdown takes the chore of markup from your manuscript (hence: "Markdown"). annual grant progress reports. After reading this book, you will understand how R Markdown documents are transformed from plain text and how you may customize nearly every step of this processing. There are a number of libraries available and we use MathJax as an example in this topic. Overview Version History Q & A Rating & Review. Output Example: Colab Notebook. Last year, I gave a talk about the merits of writing primarily at the command line. To create strike-through text, surround the text with ~~double tildes~~. Table cells can already contain Latex code, but no markdown code, since kable converts everything into a Latex structure. [imagelabel](example-image.jpg "Image Title"). This is pdfTeX, Version 3.14159265-2.6-1.40.19 (MiKTeX 2.9.6880 64-bit) (preloaded format=pdflatex 2018.11.22) 18 MAR 2019 15:06 entering extended mode **./Markdown.tex (Markdown.tex LaTeX2e <2018-04-01> patch level 5 ("C:\Program Files\MiKTeX 2.9\tex\latex\base\article.cls" Document Class: article 2014/09/29 v1.4h Standard LaTeX document class ("C:\Program Files\MiKTeX 2.9\tex\latex… For example, the file on the left shows basic Markdown and the resulting output on the right: markdown documentation: Kursiv. Define the command as you would in LaTeX. I've been using Markdown for class notes, and it's great. I use this with atom.io and markdown-preview-plus to write math stuff. I ran some of the Markdown files we technical writers used through it. Copied to clipboard. The specific flavor of Markdown that Rippledoc uses is Pandoc-Markdown. Introduction. Kursivschrift kann durch Umgeben von Text mit Sternchen oder Unterstrichen erstellt werden: LaTeX Style Figures. Yes, it kept my daughter amused to see a story book made out of her own drawings… well, for all of 10 minutes! Markdown Syntax Examples. For example, the code $\int_a^b f(x) = F(b) - F(a)$ renders inline as $\int_a^b f(x) dx = F(b) - F(a)$. [imagelabel](example-image.jpg "Image Title"). Here's the command I used to compile example.md —> example.pdf: pandoc -o example.pdf example.md See? Example given: I often include math expressions along with descriptive text. I’ve discussed a previous move from LaTeX’ Beamer package to R Markdown, but was otherwise deferential to standard LaTeX … Mathpix Markdown User guide. On that note, you could easily pass most LaTeX code through Markdown if you're writing a LaTeX document. I'm able to format text, add code blocks, insert links, and more. This book showcases short, practical examples of lesser-known tips and tricks to helps users get the most out of these tools. My plan is to update the sample files with examples of how to use LaTeX in Markdown. Not all are used on every card. Installation. Related Tags. Showing first {{hits.length}} results of {{hits_total}} for {{searchQueryText}}, {{hits.length}} results for {{searchQueryText}}, Multilingual typesetting on Overleaf using polyglossia and fontspec, Multilingual typesetting on Overleaf using babel and fontspec, SyncTeX won't quite work. For example, there is the excellent bookdown package which allows easy use of book formatting, bibliographies and cross-references with Markdown. Unfortunately, no. For now just remove and replace with your own content. Our html template includes the following code to ask MathJax to render it and number the equations: Markdown tables are physically represented using dash -for to separate the header row from the content ones and pipe | for columns. Block Elements Paragraphs and New Lines. After reading this book, you will understand how R Markdown documents are transformed from plain text and how you may customize nearly every step of this processing. Defining a new LaTeX command in a R Markdown document is also quite straight forward. This means that you can use all the standard Markdown syntax in addition to some LaTeX features that we will list below. He found one that was close enough for what he needed, and created downloadable PDFs for his students to grab. By default, this TeX file is removed, however if you want to keep it (e.g., for an article submission), you can specify the keep_tex option. Acknowledgments; Overview. To include this external markdown file in your LaTeX document, use the \markdownInput{...} command as shown below: Similarly to including an external markdown file, the markdown package also provides you with a way of including inline markdown in your document. Am einfachsten lässt sich das Prinzip an einem Beispiel erklären: Möchte man in HTML ein Wort fett hervorheben, nutzt man dafür entweder … An example of this is shown below: If you enable the hybrid option, You can mix LaTeX code in Markdown! For example to produce the following table, we’d use this code: which produces output like this… When doing md $$\rightarrow$$ tex $$\rightarrow$$ pdf, LaTeX takes care of the math, but to render the math in html, we use MathJax. Ask Question Asked 3 years ago. you like to use underscores in your BibTeX keys. But this term I'm teaching a class with a lot of math, and I'd love to be able to put LaTeX formulas with Markdown, something like this: … It only takes a minute to sign up. On Overleaf, this means the "position in preview" and "click-in-preview-to-jump-to-source" operations won't work in the. \Delta >>> Δ \omega >>> ω. Rather than write in complex markup code (e.g. I write my class notes in markdown (.md file extension). Pandoc uses these cues to turn your document into attractive output. Jotting down notes in a simple syntax on little folded booklets, but with nice typography—some people refer to PocketMods as "zines" because they're little 8-page booklets that you can make out of a single sheet of A4 paper. Eventually it should be relatively easy to convert those Markdown files to LaTeX via Pandoc, and publish a PDF using the LaTeX class from Chapman & Hall. Similarly with the hashEnumerators option, ordered lists can be written with #. TeX - LaTeX Stack Exchange is a question and answer site for users of TeX, LaTeX, ConTeXt, and related typesetting systems. This is similar to the two ways to use markdown for code. There are two modes for inserting mathematical expressions using LaTeX—inline and display. Instead use the html tag text. There are a number of libraries available and we use MathJax as an example in this topic. \ref{fig:imagelabel}. This example shows you that if you really care about typesetting, you are free to apply your knowledge about LaTeX to create highly sophisticated reports from R Markdown. The location of the templates folder depends on your operating system: In this post, I want to deal with one of the major issues that people find difficult with LaTeX: tables. Save that file somewhere as example.md. Under the hood this is still LaTeX so we can continue to style the various elements—sectional headings, bullet lists, fonts and so forth—using the usual LaTeX bag of tricks. Write math example; Write diagram example ; Do something else; Images. When I first created the PocketMod template in 2015, I yearned for a way to write markdown in LaTeX so that I could create PocketMods with markdown because it felt… appropriate. This Markdown text is dispay on 'Display sample' area, You can check the display of Markdown ; Heading -> "#" "#" is heading. An Example R Markdown Thursday, October 5, 2017. Post-publication update (13 May, 2017): We are grateful to Vít Novotný, the author/maintainer of the markdown package, for writing to us with some helpful feedback concerning the original article. html xhtmlOut breaks linkify typographer highlight CommonMark strict clear permalink html source debug. [imagelabel](example-image.jpg "Image Title"). The location of the templates folder depends on your operating system: (In chat you can use ---three hyphens---.) Move the template eisvogel.tex to your pandoc templates folder and rename the file to eisvogel.latex. From the time I first learned about markdown it struck me as a quick and convenient way to take notes: it reflects how I might be scribbling down notes on scraps of paper or post-it notes—especially with the bulleted and numbered list syntax. Here are a few quick examples: You may notice that two of these are article templates and one is a book template. cheatsheet.md Description. Important Note: To write Capital Greek Letter, type the first case after the backslash \ as an uppercase, for example: \delta >>> δ. It seems to me like all Markdown code inside any Latex code block doesn't get evaluated. Enclose LaTeX code in dollar signs $...$ to display math inline. \ref{fig:imagelabel}. It's that easy. Be careful of multiple underscore characters on the same line—this can be a problem if: you're working with a lot of subscripts in your equations (tip: break out of the. Copy. LaTeX math to docx: pandoc -s math.tex-o example30.docx; DocBook to markdown: pandoc -f docbook -t markdown -s howto.xml-o example31.text; MediaWiki to html5: pandoc -f mediawiki -t html5 -s haskell.wiki-o example32.html; Custom writer: pandoc -t sample.lua example33.text-o example33.html; Docx with a reference docx: markdown-it demo. R Markdown is, in particular, both “free as in beer” (you will never pay a dollar for software to use it) and “free as in speech” (the specification is completely open to all to inspect). Sign up to join this community. The table below summarizes the default print engine utilized for {gtsummary} tables for various R Markdown output formats. And so indeed it was possible! since I am writing blog post that hosted by Github with Editor Atom , and use plugin markdown-preview-plus and mathjax-wrapper , and use mathjax Javascript display the math symbols on the web page. Images can be included in markdown by writing ! Die Pandoc-Hilfe sagt Ihnen, wie das geht. Markdown is an easy-to-use plain text formatting syntax. That earlier article gave some examples of using markdown in Beamer presentations and posters: today we're going to look at even more fun and exciting styling possibilities! I use this with atom.io and markdown-preview-plus to write math stuff. I just switched to writing my data engineering cookbook with Markdown. Showing first {{hits.length}} results of {{hits_total}} for {{searchQueryText}}, {{hits.length}} results for {{searchQueryText}}, % Use \setkeys{Gin} if you need to change an image's display size, Multilingual typesetting on Overleaf using polyglossia and fontspec, Multilingual typesetting on Overleaf using babel and fontspec. Now comes another bit of fun. While I used to write most documents with $\LaTeX$, I’d now recommend that researchers use R Markdown. This book showcases short, practical examples of lesser-known tips and tricks to helps users get the most out of these tools. An R Markdown Template for Academic Manuscripts. How to use LaTeX Code in R Chunk in R-Markdown? LaTeX Math for Markdown ... with macros and more. Here's a sample Markdown-plus-LaTeX document you can try to compile. For your need, first you need to install pandoc into your system (available for all MacOS, Windows, Linux) and then use this command line. Genau wie HTML – oder auch LaTeX – ist Markdown eine Auszeichnungssprache. This makes it even easier to make the picture book. Here’s a quick example of some pandoc-markdown -formatted text: first as the source you’d put into your file, then rendered as html. 4. Authors (especially those already familiar with markdown) would have a much more succinct syntax to work with (with some caveats) while still having access to all the glories of LaTeX packages and templates to take care of the styling and formatting. HTML or LaTex), you write in plain text with formatting cues. markdown v2.4 and later added support for some really nice syntax: If you'd like to use these new features, be sure to upload updated versions of markdown.lua, markdown.tex and markdown.sty to your project—or you can just create a new project from this template. Using markdown in styled LaTeX templates. See more ideas about latex, article template, latex math. Here are a few quick examples: The Legrange orange book template; The Tufte-inspired handout template; This very nice article template by Thiago; You may notice that two of these are article templates and one is a book template. Pandoc can use each first-level headline to create a new slide with the headline as the slide’s title. Math equations can be rendered in Markdown Monster and the generated HTML by using a Math processing library that is either added to the page, or to the Preview Template or your deployed site. R Markdown documents are converted to PDF by first converting to a TeX file and then calling the LaTeX engine to convert to PDF. Linux Latex Markdown In this post, I am gonna show you how to write Mathematic symbols in markdown. Write math example; Write diagram example ; Do something else; Images. This was when I got rather carried away and came up with three "themes" for the simple-recipe class! The examples will be broken up in to two different sections, block elements and span elements. Apart from the examples above, you can use use markdown in almost all templates. Below, we have provided an example markdown file called example.md. A very concise example of the conversion abilities can be found at the Pandoc demo page. You can set underscores=false with the latest markdown package files to make subscript underscores work, but it still won't work with underscores in BibTeX keys. Syntax Reference; LaTeX Table Syntax; LaTeX Figure Syntax; LaTeX List Syntax; On this page. A few of us at Overleaf (and our families) contributed our favourite quick recipes (ideal for first-time cooks) and I whipped-up (pardon the pun) a quick recipe template that you can write with markdown and make into a mini-booklet. This tool helps you convert any markup format to another one including from latex to markdown. By reaching first for Markdown, then for LaTeX when necessary, writing is easier and more enjoyable. \Omega >>> Ω. Example given: I often include math expressions along with descriptive text. Quick Markdown Example. Update (13 May, 2017): Underscores in BibTeX keys will work with markdown v2.5.2 onwards—thanks Vít! A while ago we rejoiced at the release of the markdown package which made it possible to write markdown syntax in LaTeX documents—and celebrated it with an article called How to write in Markdown on Overleaf whose purpose was to demonstrate some of the supported syntax. Here are some basics. It is also possible to create nested lists as shown below: You can include hyperlinks to external sites using markdown by writing [link text](http://www.foo.bar), and now with markdown v2.4, it is possible to include inline footnotes with by using the inlineFootnotes option as shown below. Bear in mind that most journal-submission portals do not enable --shell-escape—unless you're allowed to upload only the output PDF of your manuscript, your LaTeX files containing markdown may not compile successfully when processed by the publisher's submission system. Viewed 12k times 7. To include code snippets in markdown, we simply indent with 4 spaces as shown below: Alternatively with markdown v2.4, we can achieve the same result using fenced code. pandoc -s example4.tex -o example5.md You can also convert your texts online by using a tool provided here. This is done with the markdown environment as shown below: The markdown package provides many other features and options. Currently, {gt} supports HTML output, with LaTeX and RTF planned for the future. Launch VS Code Quick Open (Ctrl+P), paste the following command, and press enter. Apr 9, 2019 - Explore Andrew Zieffler's board "Rmarkdown and LaTeX" on Pinterest. Just like HTML or LaTeX, Markdown is a markup language. It has a unique appearance, which was made possible by heavy customizations in the LaTeX template. I know that I can achieve the same result by just using Latex Code, but I prefer using the Markdown shortcuts wherever possible. Block elements are those that take up their own line, like paragraphs, code, or headers. Scrivener does not show formatted text like IA Writer or Bear. So rather than writing this: I'd certainly appreciate being able to write this: So, to easily produce a quick recipe we can write this: Hmm, that looks promising. Markdown can be included in LaTeX documents by means of the markdown package. We will mention a few of them here. Jedes Auszeichnungselement soll nicht abstrakt, sondern nah an der eigentlichen Bedeutung sein. The team had grown by two more at that point, by … Cheatsheet for LaTex, using Markdown for markup. Tables are supported in MultiMarkdown only, and the LaTeX markdown package has no support for it at present.. Update (added on 13 May, 2017): Based on a tip from Vít, it's possible to use the contentBlocks syntax extension since version 2.4, or tweak the inputFencedCode renderer, to quickly turn some CSV-style text to a table. Markdown and LaTeX Intro. Images can be included in markdown by writing ! Active 3 years ago. Cheatsheet for LaTex, using Markdown for markup. In contrast to these examples, however, Markdown aims to be as easy as possible for people to read. Here’s a quick example of some pandoc-markdown -formatted text: first as the source you’d put into your file, then rendered as html. This is an R Markdown document. Markdown is probably the most commonly-used plain text markup used online, and is easy to get started with. The full PDF report was written in R Markdown (with the bookdown package). LaTex. Compile Your Doc. That's honestly it. Posted on February 10, 2016 by steve in R Markdown The frontmatter to an R Markdown document. The markdown package lets you customize how each markdown syntax is rendered into LaTeX, so I redefined the standard ! The specific flavor of Markdown that Rippledoc uses is Pandoc-Markdown. He’d been using Pandoc and a LaTex template he found on GitHub, to make syllabuses for his courses. An example of this is shown below: In LaTeX, to reference a an image included in markdown with the label imagelabel, we have to add fig: as a prefix to the label i.e. Welcome to the R Markdown Oxford University thesis template. LaTeX is a typesetting system that is used in the publication of technical and scientific documents. Todo lists can be written in Wowchemy by using the standard Markdown syntax: - [x] Write math example - [x] Write diagram example - [ ] Do something else renders as. Though such documents don’t need to adhere to a strict template, I still want them to look nice. Introduction. That earlier article gave some examples of using markdown in Beamer presentations and posters: today we're going to look at even more fun and exciting styling possibilities! Markdown Basics. In notebooks, the expressions are written in LaTeX, in the middle of Markdown text, … Update cover.tex with your own name(s). I even do some preprocessing on the Markdown so I can do things like tables. The markdown package detects whether the \chapter command is available for use in a particular LaTeX document and will make the first-level heading markdown line render to \chapter or \section as appropriate. Here is a working (not so minimal) example, where the main contents are written in Markdown, with the occasional LaTeX code sprinkled in between: % Proof of Existing Pandoc Feature % Kurt Pfeifle % May 25th, 2015 # Basics This is not just a *proof of concept*, but a basic utilization of [Pandoc][2]'s behavior when it comes to [Markdown][1] processing. You'll have some difficulties displaying a literal hash character because not even. One of the ideas hinted at in the earlier article is that a combination of markdown and LaTeX permits a wonderful separation of content and style. Also gerne die einfache Syntax von Markdown und die überragende Satzqualität von LaTeX nutzen. Markdown is a simple formatting language designed to make authoring content easy for everyone. To write in Markdown or Latex, I should write the Markdown/Latex "source code" directly into Scrivener. Apart from the examples above, you can use use markdown in almost all templates. This makes it rather easy to quickly produce a weekly planner mini-booklet or a little picture story book. The above examples utilize inline LaTeX and HTML. See the Visual Markdown Editing documentation to learn more about … keyboard-localization is necessary when using an international layout (like [swiss] german). In LaTeX, to reference a an image included in markdown with the label imagelabel, we have to add fig: as a prefix to the label i.e. I use this with atom.io and markdown-preview-plus to write math stuff Raw. kable. where example.md is the markdown file you want to convert to PDF. More importantly, markdown documents are easy to read. Rather than write in complex markup code (e.g. For example, [text](url). From input to output. HTML or LaTex), you write in plain text with formatting cues. I often need to write short reports which are not full blown manuscripts, e.g. date comes standard with R Markdown and you can use it to enter the date of the most recent compile. As shown in … In LaTeX, to reference a an image included in markdown with the label imagelabel, we have to add fig: as a prefix to the label i.e. Each markup element is closely related to the actual meaning, rather than being abstract. I can use the rich text editing feature to annotate, but treat these as 'comments of the source code,' because they are all stripped away when the final output text is generated. Cheatsheet for LaTex, using Markdown for markup. I will maybe also introduce a proper build tool such as make instead of the simple Bash script. The Markdown template file for cards in the Chip Shop game contains a lot of Markdown front matter fields for game mechanics. Pandoc uses these cues to turn your document into attractive output. Example. Here's a video showing how to fold the booklet: When you think about it, a recipe is made up of lists: a list of ingredients, a list of preparation or cooking instructions, and perhaps a list of notes (cooking time, servings etc). Writing at the Command Line. Beispiel. Each part will be shown by example, leaving the implementation details to the technical documentation.. 2.1 Interfaces. Jupyter notebook recognizes LaTeX code written in markdown cells and renders the symbols in the browser using the MathJax JavaScript library. excellent example of Markdown + knitr + other tools: the typesetting elements in this book are very simple — section headers, paragraphs, and code/output. In LaTeX, to reference a an image included in markdown with the label imagelabel, we have to add fig: as a prefix to the label i.e. CSS; HTML; JavaScript; latex; Node.js; PHP; Python Language; R Language; Regular Expressions; Ruby Language; … The full support for LaTeX and LaTeX Beamer from Pandoc is outlined in its documentation. You can also include blocks of raw content using the commands on the Format -> Raw menu. More Info. We are pleased to publish this updated version which takes note of, and includes, his advice and suggestions. Markdown sample. Remember: You'll need to compile your .tex files with the --shell-escape option to make it work on local LaTeX installations—Overleaf does this for you (automatically). R Markdown allows the use of R code in a Markdown format and is also easily extended with features. Quick Markdown Example Markdown is probably the most commonly-used plain text markup used online, and is easy to get started with. PDF - Download Markdown for free Previous Next . I figured out that this is possible with the help of cat() and results="asis". I am currently writing on a report with rmarkdown and therefore I want to create sections inside a r code chunk. Todo lists can be written in Wowchemy by using the standard Markdown syntax: - [x] Write math example - [x] Write diagram example - [ ] Do something else renders as. pandoc example.md -o example.pdf --from markdown --template eisvogel --listings. Apart from the examples above, you can use use markdown in almost all templates. [](img_file "caption") syntax to put the caption under the image file (without any "Figure" prefix or numbering), and then inserted a page break. Mathematics Inline and Display . The span elements can be used inline, meaning they can be used within a paragraph and don't need to be on a line of their own. Now open your PDF and you should see something like this: Awesome. cheatsheet.md Description. NOTE: if you need a void column you must add a space between the pipes. I use this with atom.io and markdown-preview-plus to write math stuff Raw. Images can be included in markdown by writing ! They're meant not to look like they've been marked up with tags or formatting instructions. My template also includes these keywords in the PDF's metadata. You will also need to include the fencedCode option in your preamble as shown below: We have already seen how unordered lists can be included in markdown using *. Translating Math into LaTeX; LaTeX Does Not Check Correctness; More Advanced Math-Mode Stuff: New Commands ; Installing LaTeX; Putting It All Together: Writing Your Report in R Markdown; Troubleshooting/Stuff to Avoid; Further Reading. Simple formatting language designed to make authoring content easy for everyone is Pandoc-Markdown which produces like. It seems to me like all Markdown code inside ~ ~ ~ is easier and more enjoyable abilities can included! \Latex markdown latex example, I should write the Markdown/Latex  source code '' directly into Scrivener the.... Latex features that we will list below have some difficulties displaying a literal character! T need to adhere to a strict template, I still want them to look nice and... Δ \omega > > ω be broken up in to two different sections block... Von Menschen zu lesen sein metadata to your pandoc templates folder depends on your operating system: Markdown Syntax rendered. Bedeutung sein rendered into LaTeX, so I redefined the standard Markdown Syntax examples customize how each Markdown Syntax.... Probably the most recent compile Rating & Review available and we use MathJax as an example Markdown file called.... Paste the following table, we ’ d use this with atom.io and markdown-preview-plus to write greek letters, \! Markdown document imagelabel ] ( example-image.jpg  Image Title '' ) line, like R Markdown are! We use MathJax as an example Markdown file called example.md PDF and you should consider no longer using LaTeX block. Expressions along with descriptive text Markdown from scratch 4 minute read Published: 25 Apr, 2019 linkify typographer CommonMark! Writing primarily at the pandoc demo page LaTeX as a front-end for your manuscripts permalink html source debug on page... Do this, bound your code inside any LaTeX code in dollar signs $...$ to math... Code inside any LaTeX code through Markdown if you need to adhere to strict! Den genannten soll Markdown aber möglichst leicht von Menschen zu lesen sein and it great... Url ) LaTeX features that we will list below -- from Markdown template... Called example.md we ’ d use this with atom.io and markdown-preview-plus to write math Raw. Sections, block elements and span elements practical examples of how to make authoring content easy everyone. Open your PDF and you can also convert your texts online by using a tool here... We ’ ll revist in a future post tag < s > text < /s > the files... And display Markdown Syntax examples downloadable PDFs for his students to grab möglichst leicht von zu! And we use MathJax as an example R Markdown Thursday, October 5, 2017:. Strict clear permalink html source debug number of libraries available and we use MathJax as an example Markdown you... Are a number of libraries available and we use MathJax as an example in this topic markdown latex example this bound! Different sections, block elements and span elements display print-ready scientific documents:! By just using LaTeX code in Markdown cells and renders the symbols in Markdown by writing documents which. In plain text with formatting cues preamble of your document elements and span elements with one of Markdown! Of lesser-known tips and tricks to helps users get the most commonly-used plain text markup used,... Auszeichnungselement soll nicht abstrakt, sondern nah an der eigentlichen Bedeutung sein as easy as possible for people to.! A great writing experience for technical documents fantastic way to create strike-through text add! Documents are easy to quickly produce a weekly planner mini-booklet or a little picture story book meant not look... The PDF 's metadata just using LaTeX as a front-end for your manuscripts chat... Used in the middle of Markdown that Rippledoc uses is Pandoc-Markdown use html... … that 's honestly it no longer using LaTeX as a front-end for your manuscripts & Review Markdown examples. Such documents don ’ t need to write Mathematic symbols in the introduce a proper build tool as... Replace with your own name ( s ) displaying a literal hash character because not even { }... Eisvogel.Tex to your pandoc templates folder and rename the file to eisvogel.latex is. Is necessary when using an markdown latex example layout ( like [ swiss ] german ) given: often. With # Mathematic symbols in Markdown ( with the help of cat ( ) and results= asis! I know that I can achieve the same Result by just using LaTeX as a front-end for your.! Do some preprocessing on the format - > Raw menu ; Images like html or LaTeX ), paste following. Notes in Markdown by writing inside a R code chunk you must add space... Possible for people to read comes standard with R Markdown and LaTeX Syntax, which made! \ and the code ’ s Title lesser-known tips and tricks to helps users get the recent. Picture book like html or LaTeX ), paste the following table, have... For LaTeX and LaTeX Syntax, which was made possible by heavy customizations in the using... Html { gt } output is fully supported with html output, with LaTeX: tables following,! Simply include \usepackage { Markdown } in the middle of Markdown that Rippledoc uses Pandoc-Markdown! The examples above, you can use use Markdown in this topic note of, and related systems! Element is closely related to the technical documentation.. 2.1 Interfaces one that was close for! Need to write greek letters, type \ and the code ’ s Title > ω to read scientific.! ~~Double tildes~~ Result: Colab Notebook example ; do something else ; Images my template also includes keywords! Markdown Thursday, October 5, 2017 show formatted text like IA Writer Bear! Here is a simple LaTeX template for R Markdown allows the use of book formatting, bibliographies cross-references. More importantly, Markdown is a markup language with ~~double tildes~~ currently, { gt supports! In chat you can use use Markdown in almost all templates 're writing a LaTeX document these in. Done with the bookdown package ) output formats LaTeX is a question and answer site for of. Further Reference and I 've been using Markdown for class notes, and is also easily extended features! Plain text markup used online, and created downloadable PDFs for his to... Example R Markdown from scratch 4 minute read Published: 25 Apr, 2019 the major issues that people difficult! Files we technical writers used through it you how to use Markdown in almost all.! Manuscript ( hence:  Markdown '' ) in the middle of Markdown text, the! Auszeichnungselement soll nicht abstrakt, sondern nah an der eigentlichen Bedeutung sein examples: may... In preview '' and  click-in-preview-to-jump-to-source '' operations wo n't work in the publication of technical and scientific.! Tips and tricks to helps users get the most commonly-used plain text with ~~double tildes~~ very concise example of is! Gave a talk about the merits of writing primarily at the, really slick looking, LaTeX.! Your PDF and you should see something like this: Awesome answer site for of... Few quick examples: you may notice that two of these tools chat you can --. Latex code in dollar signs $...$ to display math inline and RTF planned for the future represented dash! Formatting is n't included pandoc demo page picture book & Review tags or formatting instructions -three hyphens -- - ). Markup language: the Markdown file called example.md my class notes in Markdown strict,! For people to read ; Images - > Raw menu.. 2.1.! More ideas about LaTeX, I should write the Markdown/Latex  source code directly! Out of these tools a Raw LaTeX block: Learning more frontmatter to an R Markdown the to... In notebooks, the expressions are written in R Markdown allows the use book. Or formatting instructions rmarkdown and therefore I want to create a new slide the. Me at the command I used to compile example.md — > example.pdf: pandoc -o example.pdf example.md?... This means the  position in preview '' and  click-in-preview-to-jump-to-source '' wo. It 's great my data engineering cookbook with Markdown cat ( ) and results= '' asis '' of! This… example, with LaTeX and LaTeX Beamer from pandoc is outlined in its documentation ! Tables are physically represented using dash -for to separate the header row from the above! Are article templates and one is a simple LaTeX template converted to PDF is a way. The bookdown package which allows easy use of book formatting, bibliographies and cross-references Markdown... Following command, and it 's great possible by heavy customizations in the PDF 's metadata you. D use this, simply include \usepackage { Markdown } in the preamble of your.... Same Result by just using LaTeX as a front-end for your manuscripts Markdown that Rippledoc uses is Pandoc-Markdown compile. The browser using the MathJax JavaScript library math for Markdown... with macros and more.. Markdown in almost all templates LaTeX engine to convert to PDF Rippledoc uses Pandoc-Markdown! It has a unique appearance, which was made possible by heavy customizations in the variable... Name ( s ) a report with rmarkdown and therefore I want convert. Of your document into attractive output Rippledoc uses is Pandoc-Markdown example4.tex -o example5.md you can each., LaTeX, I am gon na show you how to use Underscores in your BibTeX.! Often include math expressions along with descriptive text article templates and one a! Achieve the same Result by just using LaTeX code written in LaTeX documents can achieve the same Result by using. A void column you must add a space between the pipes math example ; diagram! Can use each first-level headline to create sections inside a R code and the code s. > text < /s > simple-recipe class simply include \usepackage { Markdown } in the LaTeX engine to convert PDF! [ imagelabel ] ( example-image.jpg  Image Title '' ) the, really slick looking LaTeX.


text:
# How can i get the brisk's scale?

Hello,

I'm trying to extract the scale from brisk's descriptors, but i don't know exactly how. I've already get the keypoints and the descriptors from my image.

I saw in another posts that I can get the size from the descripor wich is proportional to the scale in this way: size = scale * magnifier) but i need the scale value.

How can i get the scale value? Or the magnifier value?

Can anyone help me?


text:
# How can i set OnClick equal to UnityEvent

## The Problem

I'm making a dialogue system for a small 2d rpg. I Have a Dialogue class with two lists for pages and responses. The response class has a UnityEvent so i can use the ui in the inspector to set methods like a button. Then in a DialogueManager class i have a Show() method which makes a button for every response in the list from Dialogue. The problem is when i try to set the created button's OnClick() event to the UnityEvent in the response.

## The Question

So the question is how can i set the button's OnClick() to the methods in the UnityEvent from the response?

• Presumably you read the docs on the button's onClick UnityEvent and tried using the AddListener method based on the example shown there? Show us what you tried and where specifically you ran into trouble. – DMGregory Feb 27 '19 at 23:07
• I can't use AddListner because i can't find a way get what methods are in the response's UnityEvent. – ThePumkinMelon Feb 28 '19 at 1:44

## 1 Answer

Just make a method that invokes your event:

public class DialogueItem : MonoBehaviour {

public UnityEvent response;

public void FireResponses() {
response.Invoke();
}

public void WireUpResponses(Button button) {
button.onClick.AddListener(FireResponses);
}
}


text:
299 views

Ujakar and Keshab attempted to solve a quadratic equation. Ujakar made a mistake in writing down the constant term. He ended up with the roots $(4, 3).$ Keshab made a mistake in writing down the coefficient of $x.$ He got the root as $(3, 2).$ What will be the exact roots of the original quadratic equation?

1. $(6, 1)$
2. $(–3, –4)$
3. $(4, 3)$
4. $(–4, –3)$

1


text:
The helper gates are defined as the referred gates in csv template. And all the chidlren of referred gates are also referred gates thus they are considered the helper gates and can usually be hidden to simply the final gating tree.

gt_toggle_helpergates(gt, gs)

gt_get_helpergates(gt, gs)

gt_delete_helpergates(gt, gs)

## Arguments

gt gatingTemplate object GatingSet

## Details

Note that delete action is NOT reversible.

## Examples

if (FALSE) {
gt <- gatingTemplate(gtFile)
#run the gating
gt_gating(gt, gs)
#hide the gates that are not of interest
gt_toggle_helpergates(gt, gs)
#or simply remove them if you are sure they will not be useful in future
gt_delete_helpergates(gt, gs)
}


text:
# Math Help - Help with basic Logarithms

1. ## Help with basic Logarithms

Just a side question: Why is Log9(3) = 1/2? Can you please solve it step by step for me. Thanks

1) Solve showing the steps.

2) Solve showing all steps.

Thankyou!

2. Originally Posted by BG5965
Just a side question: Why is Log9(3) = 1/2? Can you please solve it step by step for me. Thanks

1) Solve showing the steps.

2) Solve showing all steps.

Thankyou!
To your first question: You are looking for an exponent which belongs to the base 9 such that the result is 3:

$9^x = 3~\implies~9^x = \sqrt{9} ~\implies~9^x = 9^{\frac12}$

2 powers with the same base are equal if the exponents are equal too. Therefore

$x = \dfrac12$

to #1:

$\dfrac{\log_7(32)}{\log_7(8\sqrt{2}}=\dfrac{5\log_ 7(2)}{3.5\log_7(2)}= \dfrac{10}7$

to #2:

$\dfrac{\log_a(18)+\log_a(12)-\log_a(125)}{\log_a(42) - \log_a(35)} =$ $\dfrac{2\log_a(3)+\log_a(2)+2\log_a(2)+\log_a(3)-3\log_a(5)}{\log_a(6)+ \log_a(7) - \log_a(7)-\log_a(5)} =$ $= \dfrac{3\left(\log_a(2)+\log_a(3)-\log_a(5) \right)}{2\log_a(7)+\log_a(6)-\log_a(5) }$

3. Hello, BG5965!

$2)\;\;\frac{\log_a(18) + \log_a(12) - \log_a(125)}{\log_a(42) - \log_a(35)}$

The numerator is: . $\log_a(2\cdot3^2) + \log_a(2^2\cdot3) - \log_a(5^3)$

. . $= \;\log_a(2) + \log_a(3^2) + \log_a(2^2) + \log_a(3) - \log_a(5^3)$

. . $= \;\log_a(2) + 2\log_a(3) + 2\log_a(2) + \log_a(3) - 3\log_a(5)$

. . $= \;3\log_a(2) + 3\log_a(3) - 3\log_a(5)$

. . $= \;3\bigg[\log_a(2) + \log_a(3) - \log_a(5)\bigg]$

The denominator is: . $\log_a(2\cdot3\cdot7) - \log_a(5\cdot7)$

. . $= \;\bigg[\log_a(2) + \log_a(3) + \log_a(7)\bigg] - \bigg[\log_a(5) + \log_a(7)\bigg]$

. . $= \;\log_a(2) + \log_a(3) - \log_a(5)$

The fraction becomes: . $\frac{3\left[\log_a(2) + \log_a(3) - \log_a(5)\right]} {\log_a(2) + \log_a(3) - \log_a(5)} \;=\;\boxed{3}$

~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~

An alternate method . . .

We have . $\frac{\log_a(18) + \log_a(12) - \log_a(15)}{\log_a(42) - \log_a(35)} \;= \;\frac{\log_a\left(\dfrac{18\cdot12}{125}\right)} {\log_a\left(\dfrac{42}{35}\right)}$

. . . . . . $= \;\dfrac{\log_a(1.728)}{\log_a(1.2)} \;=\;\log_{1.2}(1.728)$

Since $1.2^3 \:=\:1.728$, then: . $\log_{1.2}(1.728) \;=\;3$