Quantity Operators

the "magic" begins

01:Basic

02:ForLoop

03:Array

04:Exponantial

05:Permutations

01:Basic

Basic

Glyphs

These symbols shares the "┐" part as their radical, which represents a box. The "⌠" part and "⌡" part represents the movements of content into or out of the box, which represents "increase" or "decrease"

something going into the box

Addition : +

something dropping out of the box

Subtraction : -

a stronger version of addition

Multiplication : *

a stronger version of subtraction

Division : /

a modified version of division

Modulation : %

String Script

the First Operand (Left) is the passive operand,

and the Second (Right) is the active operand.

In other words,

the first operand is the one which accepts the action,

and the second operand is the one which describes the action/operation

Here the orange is added to the apple.

another way to understand this is : the number on the right of the operator is used to describe the operation/action.

so in the example above, the addition operator should be paired with the orange, not the apple.

and here's how we can make a box of fruits

we can interpret this as "we have a box, we then put an apple in it, then an orange, then a lemon"

Algebraic Omittion

when an expression only contains multiplication, the multiplication sign can be omitted as long as all operands can be identified.

Algebraic Omittion Example :

the term "3 * 4 * 5 * x * y * z" can be rearranged as "3 * x * 4 * y * 5 * z",

so it can be simplified to "3x4y5z", which is also equivalent to "60xyz"

Story Board Script

the "⌠" part or/and the "⌡" part should be on the same side as the second operand. the other side can be interpret as "inside the box (┐) ", which is where the first operand should be.

02:ForLoop

For Loop Term Generation

Glyphs

These symbols acts just like the big Sigma or big Pi, which generates the term, and sum or multiply all the terms together.

a forLoop version of addition

Sum : Σ

a forLoop version of multiplication

Product : Π

For Loop ? What is that ?

In Computer Science, a for loop is a mechanism to repeat a number of actions for a specific amount of iterations. Below is the basic structure of a for Loop in C++

for(int i = start ; i < end ; i++)

{

// action to be repeated

}

it runs like this :

step 1 : create a counter out of nowhere, let it contain a starting value

step 2 : check if the current situation full fills the given criterion, if yes, go to step 3, else, done

step 3 : do the list of actions to be repeated

step 4 : do some alterations to the counter, in this case, add 1 to it, and go back to step 2

Just like the for loop mentioned above, it needs 5 parts :

counter glyph

what glyph are you using to represent the counter ?

counter starting value

what value should the counter hold initially ?

term generation criterion

a boolean expression, if the expression gives a true, then the term will be generated, else, the for loop is done

term expression

the term to be generated which will be a function which will take the counter as an input

counter manipulation expression

what should the value of the counter be for the next iteration

String Script

Listing all the parts in a bracket, separated by comas, with the glyph at the front

counter glyph

counter starting value

term generation criterion

term expression

counter manipulation expression

Story Board Script

Almost like the Big Sigma / Big Pi we know, but keep in mind the slot is a bit different, plus, Big Sigma and Big Pi omits the counter manipulation expression and assumes that the counter just increments by 1 for every iteration. Here Astralica allows the user to manipulate how is the next value for the counter is generated.

OK I JUST WANT A NORMAL FOR LOOP

if the counter manipulation expression is omitted,

then it will be treated as "counter++"

Say we want Big Sigma of 3i+1 where i starts with =1 as long as I < 10 (//here "i" is used as a counter, not sqrt(-1)), and the next i is i*1.5 we can have :

So the generated terms would be :

when I = 1, 1 < 10,

term = 3 * (1) + 1 = 4, next i = 1 * 1.5 = 1.5

when I = 1.5, 1.5 < 10,

term = 3 * (1.5) + 1 = 5.5, next i = 1.5 * 1.5 = 2.25

when I = 2.25, 2.25 < 10,

term = 3 * (2.25) + 1 = 7.75, next I = 2.25 * 1.15 = 3.375

when I = 3.375, 3.375 < 10

term = 3 * (3.375) + 1 = 11.125, next I = 3.375 * 1.5 = 5.0625

when I = 5.0625, 5.0625 < 10

term = 3 * (5.0625) + 1 = 16.1875, next I = 5.0625 * 1.5 = 7.59375

when I = 7.59375, 7.59375 < 10

term = 3 * (7.59375) + 1 = 23.78125, next I = 7.59375 * 1.5 = 11.390625

when I = 11.390625, 11.390625 < 11 is false, halt

so this for loop will end up with the result :

4 + 5.5 + 7.75 + 11.125 + 16.1875 + 23.78125 = 68.34375

03:ArrayConsump

Array Consumption

Glyphs

sometimes, addition and subtraction can be done at the same time, and a list of them,

same goes for multiplication and division.

adding things and substracting things

at the same time

multiplying things and dividing things at the same time

String Script

Here both symbols take a bracket, and the bracket is separated into 2 parts by using a double coma, the left side is the increment list, and the right side is the decrement list.

both the increment list and the decrement list are coma separated lists which contain a list of operands, if these operands were to appear on the left part of the bracket, they were to be used for addition/multiplication, else if they are on the right part, they were to be used for subtraction/division.

to be added

to be subtracted

to be multiplied

to be divided by

Story Board Script

here we have the increment list on the upper part and the decrement list on the lower part, each list now has their own brackets, no more double comas.

to be added

to be subtracted

to be multiplied by

to be divided by

04:Expo

Exponential Relationship

Glyphs

Instead of getting overwhelmed by power, root, and logarithm, here we only have one glyph : the powerTriangle

the powerTriangle has 3 slots :

base

power / exponent

product

such that base ^ power = product

String Script

Let's write out the whole complete string first, just like other compared operators, the expoTriangle also takes a bracket as well

if the base slot is left empty,

then the expoTriangle will act as a root (root is used to find the base of the product when a power is given)

if the power slot is left empty,

the expoTriangle will act as a logarithm (log is used to find the required power to raise the base to the product)

if the product slot is left empty,

the expoTriangle will act as a power operation (power is used to know what is the product when the base is raised to the power given)

√

log

Story Board Script

here the same rule applies, it is just now the slots are in a triangle

05:FctnPrnCr

Permutations and Combinations

Glyphs

Here we have a single symbol to generalize factorial, Permutation, and combination, but based on different inputs, it will behave differently

String Script

Factorial

if a single parameter is given, then the symbol will act is a normal factorial

Permutation

if a bracket with 2 numbers are given, then the left number will be treated as the starting number, and the second number will be treated as the range

Combination

just like Permutation, it accepts a bracket with 2 numbers, but instead of a coma, we have a double coma here

Story Board Script

Having the same rules as the String script, fill in the slot and the glyph will behave differently

Pronunciations

Here, all the operations can be categorized or decomposed into several parts :

Rate of Change and Direction

Rate of Change

Karo

(Ko)

None

Kari

(Ki)

Step

Karæ

(Kæ)

Linear

Kara

(Ka)

Exponential

Direction

KaxiTa

(Ta)

Increase

KaxiTæ

(Tæ)

Decrease

KaxiTaTæ (TaTæ)

Periodic

KaxiTo

(To)

Periodic

with this setup, we can try to assign each operation into the fitting criteria.

Klari

(Kla)

Math Opr.

Karo

(Ko)

None

Kari

(Ki)

Step

Karæ

(Kæ)

Linear

Kara

(Ka)

Exponential

KaxiTa

(Ta)

Increase

KaxiTæ

(Tæ)

Decrease

KaxiTaTæ (TaTæ)

Periodic

KaxiTo

(To)

Undefined

Kla-Ki-Ta

Addition

Kla-Kæ-Ta

Multiplication

Kla-Ka-Ta

Factorials

Kla-Ki-Tæ

Subtraction

Kla-Kæ-Tæ

Division

Kla-Kæ-TaTæ

Modulation

Kla-Ka-To

Power Triangle

Including Waves and Oscilations ?

There is a probability where we may add different waves into the table so such that

SineWave is "Kla - Ka - TaTæ"

TriangleWave is "Kla - Kæ - TaTæ"

SawtoothWave is "Kla - Kæ - TaTæ"

SquareWave is "Kla - Ki - TaTæ"

however, there are some crashes, so this idea is put on hold.