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==

Solvers Background

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...

Expressions

Solvers Background

Algebraic a*(c-u) Free Form solve a*x +b == 0 for x

Symbols

Solvers Background

In Free Form Programming Language (ff) the concept of Symbol is more than one: Individual alphabet in a language e.g. x in English , ω in GreekComposite of individual symbols e.g. dara that while it is the concatenation of four alphabets ff treats it as a sin...

Constants

Solvers Background

In Free Form Programming Language (ff) the concept of a Constant is an immutable structure. Examples : 5, 𝝅 .

Operators

Solvers Background

= + - * / {} () ; "" -> < > <= ⋂ ⋃ ⊕ ✕ ∂ ∈ ∉ ⊂ → and

Terminologies

Solvers Background

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 sim...

Phrases

Solvers Background

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

Solvers Background

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}];

solve[ ]

Solvers

solve [ ] function

solve a*x + b = 0

Solvers solve[ ]

sol = solve[ a*x + b == 0, {x}]; show sol; save as solve4; Output "sol" → {-(b/a)}

instance [ ]

Solvers solve[ ]

radius=norm[{x,y}]; linear = 3*x+2*y; pts = instance [linear <= 3 and 0.5<=radius <=1 , 300]; //show pts; pointplot pts; save as cropped_anulus; Ouput

Sides of Equations

Solvers

Applying same operations on both sides of =

Right hand side vs. Left hand side

Solvers Sides of Equations

What: Different sides to an operator e.g. == Why: Proper treatment of the sides of an operator e.g. == results in much functionality Time To Complete: 3 hours .left and .right In Free Form Programming Language (ff) the dot operator, namely the dot on you...

Subtract from Sides

Solvers Sides of Equations

What: Subtract the same expression from the both sides of == Why: Such side-wise subtraction is an essential computation for solving equations Time to Complete: 3 hours eq = (x -3 == 17*y + 9); lhs = eq.left - 9; rhs = eq.right - 9; eq2 = (lhs == rhs)...

Add to Sides

Solvers Sides of Equations

What: Add the same expression to the both sides of == . Why: Such side-wise addition is an essential computation for solving equations. Time to Complete: 3 hours. eq = (x -3 == 17*y - 9); lhs = eq.left + 9; rhs = eq.right + 9; eq2 = (lhs == rhs); show ...

Divide both Sides

Solvers Sides of Equations

What: Divide both sides of == by the same expression. Why: Such side-wise division is an essential computation for solving equations. Time to Complete: 3 hours. eq = (x - 3 == 17*y); lhs = eq.left / 17; rhs = eq.right /17; eq2 = (lhs == rhs); show eq2;...

Multiply both Sides

Solvers Sides of Equations

What: Multiply both sides of == by the same expression. Why: Such side-wise multiplication is an essential computation for solving equations. Time to Complete: 4 hours. eq = (x - 3 == y / 13); lhs = eq.left * 13; rhs = eq.right * 13; eq2 = (lhs == rhs);...

Preface

Solvers

This mostly live-code computational Wiki book addresses two audiences: STEM high school students to undergraduate college level students Programmers' and computer scientists' learning habitat to freely experiment with new concepts in programming languages On...