[Tutor] Random equation generator

[Rich Lovely]

Please use the reply-all button when responding, so that your message  
gets sent to the list as well.

If that's the sort of equation you're after, than the easiest way  
would probably to decide on a generalised form:
> y=(2x-1)*4x
y = 4*x**2 - 4x
> y=2+5(x-1)
y = 5*x - 3
> y=(2x+5)+(5x-25)
y = 10*x**2 + 75*x - 125

> y=((x+13)/((x-18))*(2x-1)
y = (2*x**2 - 19*x -13) / (x - 18)

Except for the last equation, they are all of the "general form" ax^2  
+bx + c.

These can be generated using tools from the random module:
(pseudo python)
equation = randint(minimum, maximum) * x ** 2 +  
randint(minimum,maximum) * x + randint(minimum,maximum)

if you want to generate equations in the form of the last one you  
mentioned, it will be a bit more difficult.

You could add a random number of terms with a random power, but  
actually impliementing it might be a bit harder:

import random
def generate_terms(minimum, maximum):
     "generate a list of random terms for an equation of the form  
(a*x)**b + ...  "
     return [(random.randint(minimum, maximum), random.randint(-1,1))  
for x in xrange(random.randint(1, 10))]

class Line(object):
     epsilon = 1e-15
     def __init__(self, equation_terms):
         self._equation_terms = equation_terms
     def is_on_line(self, (x,y)):
         calulated_y = sum((a * x) ** b for a,b in self._equation_terms)
         return abs(y - calculated_y) <= self.epsilon #see message  
from Paul

Then, instead of picking two points, you can do:

line = Line(generate_terms(-25, 25))

then proceed as with my previous message.

getting a nice string representation won't be as easy... unless you're  
happy with seeing x**-1's dotted around.

You'll need to tweak the values within the generate_terms function to  
get exactly what you want.


Alternatively (and I'm probably going to get shouted at for suggesting  
it), you could write something that generates random python equations,  
and use some variety of eval() to get a value out of it...

Does that help?

On 5 Dec 2008, at 13:52, TexasJerky100 at aol.com wrote:

>    Thanks for the response.   This will help me passing the points  
> and compairing the results.
> I however still need to find something that will generate the actual  
> linear equations or similar equations in a
> random fashion.  For instance lets say the program would first  
> generate the actual equations.
>
> y=(2x-1)*4x
> y=2+5(x-1)
> y=(2x+5)+(5x-25)
> y=((x+13)/((x-18))*(2x-1)
>
> Then I could use your program to pass through the values.
>
>
> Frank Hopkins
> Houston, Tx
>
>
>
>
>
>
> In a message dated 12/5/2008 7:29:42 A.M. Central Standard Time, roadierich at googlemail.com 
>  writes:
> When you say linear, I'm assuming fitting y=mx+c, and passing  
> through points?
>
> The line through points (x1, y1) and (x2,y2) is
>
> y - y1 = (y2-y1) / (x2-x1) * (x-x1)
>
> That multiplies out to:
>
> y = (y2-y1)/(x2-x1) * x - (y2-y1)/(x2-x1) + y1
> That gives m = (y2-y1)/(x2-x1) and c =  y1 - (y2-y1)/(x2-x1)
>
> you can then create a class to represent the line:
>
> class Line(object):
>     def __init__(self, (x1,y1), (x2,y2)):
>         "create a line passing through points (x1,y1) and (x2,y2)  
> (inputted as tuples)"
>         self.m = (y2-y1)/(x2-x1)
>         self.c = y1 - self.m
>
>     def is_on_line(self,(x,y)):
>         'Test if point represtented by an (x,y) tuple is on the line"
>         if self. m * x + self.c == y:
>             return True
>         else:
>             return False
>
>     def __str__(self):
>         "returns the equation of the line in the form y=mx+c.  Might  
> be quite long if floats are involved."
>         print "y=%dx + %d" % (self.m, self.c)
>
>
> Then all you have to do is choose a pair of points, then iterate  
> over the list, testing each point in turn, wash, rinse and repeat.
>
> Does that help?
>
> On 4 Dec 2008, at 20:28, TexasJerky100 at aol.com wrote:
>
>>    I am starting out with 7 fixed reference points.  From there I  
>> want  a program that can randomly
>> generate linear equations.  After the equations are generated I  
>> would then like to randomly insert
>> the 7 fixed reference points into the equations and calculate the  
>> results.  I currently have several
>> programs that can generate random string of words from a file that  
>> contains a list of word but is not
>> much help creating random equations.
>>   Do you know if there is such a program that can do what  I am  
>> trying to get accomplished??
>>
>> Thanks
>>
>> Frank Hopkins
>> Houston, Tx
>>
>>
>>
>> Make your life easier with all your friends, email, and favorite  
>> sites in one place. Try it now.
>> _______________________________________________
>> Tutor maillist  -  Tutor at python.org
>> http://mail.python.org/mailman/listinfo/tutor
>
> =
>
>
>
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