How to make homework more fun, MATLAB to Ruby

I wanted to liven up my ElectroMagnetism homework this past week which required us to do some MATLAB. Unfortunately, I don't have MATLAB because it's not OS and I didn't want to go to the school to use a computer, so I did some monkey patching to make my Ruby code look like MATLAB. Now I can just copy in the MATLAB code, make a few changes and run it. Only a few changes necessary at this point to convert the MATLAB to Ruby:

[1 2 3] -> [1, 2, 3]  # arrays
x^2     -> x**2       # exponents
%       -> #          # comments

Update: ^ has lesser precedence than ** which is why I stuck with **. Comment if you know how to change operator precedence. I couldn't find much.

Here is the file I require:

#matlab_helper.rb
$VERBOSE = nil # surpress constant redefinition warnings
include Math

def norm(vector)
  sqrt vector.map{ |x| x**2 }.inject(0, &:+)
end

class Array
  def +(op)
    self.zip(op).map { |a, b| a + b }
  end

  def -(op)
    self.zip(op).map { |a, b| a - b }
  end

  def /(op)
    self.map { |a| a / op }
  end
end

class Float
  alias_method :mult, :*

  def *(op)
    if op.is_a? Array
      op.map { |a| self * a }
    else
      mult op
    end
  end
end

class Fixnum
  alias_method :mult, :*

  def *(op)
    if op.is_a? Array
      op.map { |a| self * a }
    else
      mult op
    end
  end
end

def pi
  PI
end

And my converted MATLAB homework:

#hw.rb
require './matlab_helper'

# clc #clear the command line
# clear #remove all previous variables
Q1 = 8e-9 #charges on Q1
Q2 = 8e-9 #charges on Q2
pL = 2e-9 #charge density of the line
Epsilon_o = 8.8419e-12 #Permitivity of free space

P = [2, 3, 4] #coordinates of observation point
A = [0, 0, 1] #coordinates of Q1
B = [0, 0, -1] #coordinates of Q2
C = [2, 0, 0] #coordinates of the center of the line charge

Number_of_L_Steps = 100000 #the steps of L

##the following routine calculates the electric fields at the
##observation point generated by the point charges
R1 = P - A #the vector pointing from Q1 to the observation point
R2 = P - B #the vector pointing from Q2 to the observation point

R1Mag = norm(R1) #the magnitude of R1
R2Mag = norm(R2) #the magnitude of R1
E1 = Q1 / (4 * pi * Epsilon_o * R1Mag**3) * R1 #the electric field generated by Q1
E2 = Q2 / (4 * pi * Epsilon_o * R2Mag**3) * R2 #the electric field generated by Q2

##the following routine calculates the electric field at the
##observation point generated by the line charge
d = norm(P - C) #the distance from the observation point to the center of the line
length = 100 * d #the length of the line
dL_V = length / Number_of_L_Steps * [1, 0, 0] #vector of a segment
dL = norm(dL_V) #length of a segment

EL = [0, 0, 0] #initialize the electric field generated by EL
C_segment = C - (Number_of_L_Steps / 2 * dL_V - dL_V / 2) #the center of the first segment

for i in (1..Number_of_L_Steps)
  R = P - C_segment #the vector seen from the center of the first segment to the observation point
  RMag = norm(R) #the magnitude of the vector R
  EL = EL + dL * pL / (4 * pi * Epsilon_o * RMag**3) * R #get contibution from each segment
  C_segment = C_segment + dL_V #the center of the i-th segment
end

E = E1 + E2 + EL # the electric field at P

puts "E = #{E}"

# $ ruby hw.rb                                                 
# E = [2.010238790127288, 7.334514610377015, 9.388970095358529]

It runs in about 2 seconds with 100,000 steps, but it's Ruby!

Note: I only included the operators necessary to complete my homework, so there are quite a few combinations left out.