Since Astralica is based on Logic and Computer Science as well, Astralica has its own set of mathematical symbols, some of them are easy one by one substitution, some of them requires a bit of explanation because some symbols work in a slightly different way than how we normally would use them.
And here are the list of them :
You may notice that some of them would share the same symbol, because in some way, they are connected.
Power, roots, logarithm and natural logarithm share the same symbol.
Factorial, nPr, nCr share the same symbol because they are almost the same.
You might think addition , subtraction, multiplication, division, modulation is simple substitution, but it also can be used in a story-like behavior.
Soon we will direct each group and understand how are the symbols made, and how to use them.
Addition, Subtraction, Multiplication, Division, & Modulation.
These 5 operations are the 5 basic operators, they modify the quantity of an environment. So here are the concept of each of them.
Addition | adding a number into a box |
Subtraction | taking a number out of the box |
Multiplication | a stronger version of Addition |
Division | a stronger version of Subtraction |
Modulation | a modified version of Division |
if you look at the symbols, they all share the "┐" part， which represents the box,
when you add things into it, it goes in from the top,
that's why the "+" symbol has the "⌠" part to show something is going inside from the top.
when you minus things from it, it drops from the bottom,
that's why the "-" symbol has the "⌡" part to show something is dropping outside from the bottom.
multiplication is the slight superior version of addition,
if you compare the add symbol and the multiply symbol, you can find that the multiply symbol has an extra stroke, that stroke is used to say "this is the superior version of it".
A similar concept goes for division,
by comparing the minus symbol and divide symbol, we can see that the divide symbol has one more stroke than the minus symbol.
Modulation is a modification of division,
that is why the symbol is derived from the divide symbol and an extra stroke is given to say "this is the modified version of division."
EG01:
as you can see, there are 2 ways to use the symbols, either we can use it as a string, or we can use "Story Script".
From the 1st example,
we can see that 3 is being added to the box with 2 sitting inside the box, and the result is 5.
From the 2nd example,
we can see that 4 is taken away from the box which has 7 inside of it before, and the result is 3.
From the 3rd example,
we can combine the number with the same operation and separate the numbers with a "math comma", which is something like a lighting bolt.
From the 4th example,
we can combine both addition and subtraction together as well.
EG02:
here we can see a similar pattern exists.
still, Astralica follows the "MultiplyDivision first, then AdditionSubtraction" rule, that's why sometimes we need parenthesis.
we also can use the "Story Script" for multiplication and division.
we can interpret multiplication as : it will scale the box upwards by how many times.
we can also interpret division as : it will slice the box downwards into several pieces.
you can notice that when we are writing negative numbers, we don't use the minus symbol to represent the negativity, instead, we have its specific symbol for that, and since we have the symbol for negativity, we also have the symbol to represent the positivity of a number, but most of the time, we don't use it.
Power, Root, Logarithm.
here we have a slightly complicated situation,
let's say we have a magical triangle,
the left corner will be a slot for the base,
the slot on the right would be the slot for a power,
and the slot on the top would be the slot for a product.
the main idea for this symbol is it acts like a function that takes 2 inputs,
and the output is the missing corner.
base on the different output, the triangle will act as different operations or functions
here we have a table for the inputs and the outputs of the different operations:
| base | power | product | basically asking |
power | input | input | output | what is the product |
root | output | input | input | what is the root ? |
log | input | output | input | what is the power required to let the base become the product |
we can also choose to use the string script, let's say we use "Δ" to represent the triangle, and "," to represent the "math comma", and "_" to represent "empty space"
the main syntax would be: Δ(base, power, product)
it will be something like this :
| syntax | written in normal math | written in Astralica |
power | Δ(i,i,_) | 2^3 | Δ(2,3,_) |
root | Δ(_,i,i) | sqrt(4) | Δ(_,2,4) |
log | Δ(i,_,i) | log(base:2)8 | Δ(2,_,8) |
EG03:
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