Background

Basics for setting up equations and extracting solutions.

Terminologies

lhs : Left Hand Side

rhs : Right Hand Side

p = q : an identity

Equational Expression: expr1 = expr2 e.g. expr1 = a*x+b and expr2 = cos[b-c]

copy: when an object is duplicated, byte by byte so to say, into a facsimile.

This definition of copy is the simplest to grasp the concept. In due places, more sophisticated definitions will be produced.

Structure: a structure is that which permitting Similarity to other Similars.

Example: Circular is a structure since it permits similarity to anything that is round.

Example: Red is a structure since it permits similarity to anything that is red.

Example: Numeral is a structure since it permits similarity to anything that is a number.

ff calls a list e.g. {1,2,3} as a structure, or a function e.g. cos[ ] a structure or an algebraic structure e.g. x^2-1.

Symbols

In Free Form Programming Language (ff) the concept of Symbol is more than one:

  1. Individual alphabet in a language e.g. x in English , ω in Greek
  2. Composite of individual symbols e.g. dara that while it is the concatenation of four alphabets ff treats it as a single symbol
  3. Mathematical symbols e.g. ⨂
  4. Glyph (Unicode) e.g. 🌊 , 💬
  5. Glyph a raster image (this option is currently unavailable for HTML use)

The mathematical symbols in many cases have particular syntax and semantics in an expression which cannot be altered or ignored.

The mathematical symbol single space or " " is interpreted multiplication in mathematical textbooks. Additionally in ff often " " is assigned the functionality of separator in a list of items.

o be more general ff defines a Symbol as follows:

An atomic or indivisible structure with no discerning programmable components is called a Symbol.


Constants

In Free Form Programming Language (ff) the concept of a Constant is an immutable structure.

Examples : 5, 𝝅 .

Operators

=

+

-

*

/

{}

()

;

""

->

<

>

<=

⋂

⋃

⊕

✕

∂

∈

∉

⊂

→

and



==

value to rhs. What do we mean equal by value? Example: 3 = 6/2 in spite of the fact that lhs and rhs are made from very different expressions but their values are Identical or the same, hence the Identity term.

= : copies stores the rhs into lhs;

// = stores the rhs into lhs;
x1  = 5;

x2 = 2 * x1;

show x2;

// == creates an equations between lsh and rhs;
x3 = (x1 == 5);

show x3;


x4 = (x2 == 10);

show x4;

// lhs and rhs with different variables;
x5 = (x2 == 2*x1);

show x5;

save as equations;

Expressions

Algebraic

a*(c-u)

Free Form

solve a*x +b == 0 for x

Words

"I am a word"

Phrases

The highlighted are the phrases

pts = evaluate l2 in the -1 to 3 range at increments of (1/4);

Part of a sentence, have a meaning in and of itself, but often has no procedural meaning alone.


Sentences

pts = evaluate l2 in the -1 to 3 range at increments of (1/4);

FIXME: line cannot be even be used as a subphrase;

l2 := l[v,t,{0,b}];