Solvers
Solving Equations by programming.
Author: Dara O Shayda
Artwork: The Electrofishers were originally Planters who have splintered off and forgotten their past. They currently reside in an Abandoned Level after their original home was destroyed in a Safeguard Attack.
Preface
This mostly live-code computational Wiki book addresses two audiences: STEM high school students...
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 ...
Symbols
In Free Form Programming Language (ff) the concept of Symbol is more than one: Individual alphab...
Constants
In Free Form Programming Language (ff) the concept of a Constant is an immutable structure. Exa...
Operators
= + - * / {} () ; "" -> < > <= ⋂ ⋃ ⊕ ✕ ∂ ∈ ∉ ⊂ → and
==
value to rhs. What do we mean equal by value? Example: 3 = 6/2 in spite of the fact that lhs and ...
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); ...
Sentences
pts = evaluate l2 in the -1 to 3 range at increments of (1/4); FIXME: line cannot be even be use...
Sides of Equations
Applying same operations on both sides of =
Manual Operations on the Sides
What: Use ff to duplicate the manual ways handling equations as taught in school teachings. Wh...
Right hand side vs. Left hand side
What: Different sides to an operator e.g. == Why: Proper treatment of the sides of an operator e...
Subtract from Sides
What: Subtract the same expression from the both sides of == Why: Such side-wise subtraction is...
Add to Sides
What: Add the same expression to the both sides of == . Why: Such side-wise addition is an essent...
Divide both Sides
What: Divide both sides of == by the same expression. Why: Such side-wise division is an essentia...
Multiply both Sides
What: Multiply both sides of == by the same expression. Why: Such side-wise multiplication is an ...
solve[ ]
solve [ ] function
solve a*x + b = 0
sol = solve[ a*x + b == 0, {x}]; show sol; save as solve4; Output "sol" → {-(b/a)}
solve a*x +b == 0 for x
sol = solve a*x +b == 0 for x; show sol; save as solve4; Output "sol" → {-(b/a)}
instance [ ]
radius=norm[{x,y}]; linear = 3*x+2*y; pts = instance [linear <= 3 and 0.5<=radius <=1 , 300];...