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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...

Implicit Line Equation

Vector Algebra Lines

line