[Tutor] Calculating a math formula and finding errors

[Jens Kubieziel]

On Fri, Jan 10, 2003 at 04:03:49PM +0100, Michael Janssen wrote:
> On Thu, 9 Jan 2003, Jens Kubieziel wrote:
> 
> {n-1 \choose i}   =2 \left\lfloor \frac{n+2}{2} \right\rfloor

"choose" is much better here. Thanks for this.

> > def MBrechts(n):
> >   b=0
> >   for i in range(0,n):
> >     for j in range(0,n-i):
> >       betrag = n + 1 - (2*i) - (2*j)
> >       if betrag < 0:
> >         betrag = betrag * -1
> >       prod = betrag * perm(n-i,j)
> 
> MBrechts is the left side, isn't it? It must be perm(n-1, i) to represent

You're right, my fault.

> latex: ${n-1 \choose i}$ (which is the binominalcoeffizient of n-1 and i)
> But this won't make the output equal.

Did you look at my note? The original formula has an "i" there, but it
doesn't make much sense to mee. I assume that it must be a "j".

> the "sigma-ranges" might (must? I don't know much about math notation) be
> range(0,n+1) and range(0,n-i+1)  (both zeros aren't neccessary in python
> but provided for the readers convenience).  (From the rest of the code I

Yep, right.
But when I add this, I get a runtime error:

Traceback (most recent call last):
  File "Projekte/Python/MB-Wurzel.py", line 30, in ?
    print "n = %d, Formel rechts = %d, Formel links = %d" % (erg,MBrechts(erg),MBlinks(erg))
  File "Projekte/Python/MB-Wurzel.py", line 22, in MBrechts
    prod = betrag * perm(n-i,j)
  File "Projekte/Python/MB-Wurzel.py", line 9, in facul
    return z*facul(z-1)
RuntimeError: maximum recursion depth exceeded

So I guess I have to change my "facul"-code.

> guess, you're familar with "range" so this typo needn't be explained)

No, it doesn't. I corrected this within my "perm", but forgot it in
"MBrechts".

> In case this doesn't already solve your problem, could you repost a
> patched version (perhaps with english var-names to give the rest of
> tutor-list a better chance :) and clean from rechts/links mess) so that
> we can restart from a coherent version?

#v+
#! /usr/bin/python

import math

def factorial(z):
  if z == 1 or z == 0:
    return 1
  else:
    return z*factorial(z-1)

def binomial(x,y):
  w = 1
  for i in range(y+1,x+1):
      w = w * i
  return w/factorial(x-y)

def MBleft(n):
  b=0
  for i in range(0,n+1):
    for j in range(0,n-i+1):
      betrag = abs(n + 1 - 2*(i+j))
      prod = betrag * binomial(n-i,j)
      b = b + prod
  return b

def MBright(n):
  return 2 * math.floor((n+2)/2) * binomial(n+1,math.floor((n+1)/2)) - n - 1

for erg in range(1,6):
  print "n = %d, Formel rechts = %d, Formel links = %d" % (erg,MBrechts(erg),MBlinks(erg))
#v-

I have to think about the factorial function. Because it seems that the
recursion doesn't work with the correction in MBleft.
-- 
Jens Kubieziel                                  mailto:jens@kubieziel.de
The study of non-linear physics is like the study of non-elephant biology.