Lab 0: Quadratic Equations
==========================
Anthony Stark (1160611) <A01160611@itesm.mx>

This lab report was developed for the _Software Design and Architecture_ course
(_Tc3003_), at the Tecnológico de Monterrey, Campus Estado de México. 
// The institution's name should always be in Spanish. 

:numbered:

== Introduction

The roots of a quadratic equation _ax_^2^ + _bx_ + _c_ = 0 can be computed using
the quadratic formula, which is something you typically learn in high school:

************************************************************************
_x_ = (&#8722;__b__ &#177; sqrt(__b__^2^ &#8722; 4__ac__)) &#247; 2__a__
************************************************************************

[NOTE]
.INTERESTING NOTE
================================================================================
The quadratic formula is known in Mexico as ``el chicharronero'', because even
the guy who sells _chicharrones_ (pork cracklings) knows how to use it.
================================================================================

In this lab report, I will demonstrate how to determine the number of real roots
of a quadratic equation in the Ruby programming language <<Ruby>>. Section
2 consists of the code, section 3 discusses my testing, and lastly there are
some concluding remarks.

== Number of Real Roots of a Quadratic Equation

In this part of the lab, I designed a function to compute how many real roots a
quadratic equation has. This can be determined by computing the discriminant of
the equation and then testing that discriminant <<Baldor>>. I broke the
problem into those two parts:

[source,ruby]
---------------------------------------------------------
# How many real roots does ax^2+bx+c=0 have?
def num_real_roots(a, b, c)
  num_real_roots_from_discriminant(discriminant(a, b, c))
end
---------------------------------------------------------

The two auxiliary routines used by the above code straightforwardly reflect my
memories from high school:

[source,ruby]
---------------------------------------
def discriminant(a, b, c)
  b ** 2 - 4 * a * c
end

def num_real_roots_from_discriminant(d)
  if d < 0
    0
  elsif d == 0
    1
  else
    2
  end
end
---------------------------------------

== Testing

I tested the number of real-roots function using one simple example falling into
each of the three cases. Note that I took care to use examples in which the
three arguments were different from one another, to improve the chances of
catching certain bugs. My function worked in all three cases, as shown below:

[options="header", cols="2<m,1^m", width="50%"]
|====================================
^|Expression                ^|Result
 |num_real_roots(1, 2, 3)    | 0
 |num_real_roots(1, 10, 2)   | 2
 |num_real_roots(2, 16, 32)  | 1
|====================================

== Conclusion

It's a common perception that ``useful'' programs have to be long. Determining
the number of real roots of a quadratic equation is an example of an unusual
category of computations: those that are complex enough to be worth automating,
yet involve only a fixed amount of computation. As this lab demonstrated,
programs which mirror routine mathematical calculations are quite
straightforward to write.

== Acknowledgements

I would like to thank my good friend Thursday Rubinstein for his advice on how
to write cool Ruby method names.

== References

[bibliography]

- [[[Baldor]]] J. Aureliano Baldor. _Álgebra_. Grupo Patria Cultural.
Mexico, 2007. p. 265.

- [[[Ruby]]] The Ruby community. _Ruby Programming Language_
http://www.ruby-lang.org/en/ (Accessed January 22, 2013).