Mathematica 9 is now available
Services & Resources / Wolfram Forums
-----
 /
MathGroup Archive
1998
*January
*February
*March
*April
*May
*June
*July
*August
*September
*October
*November
*December
*Archive Index
*Ask about this page
*Print this page
*Give us feedback
*Sign up for the Wolfram Insider

MathGroup Archive 1998

[Date Index] [Thread Index] [Author Index]

Search the Archive

Re: summations!



Rahul Swaminathan wrote:
> 
> guys i am new to mathematica ... and want to do summations... if i have
> 2 nested summations one ranging from say i = 0 to i = N and the inner
> one from j = 0 to j = M , how do i represent it in mathematica for the
> under.
> 
> \sigma{_i = 0}{N} \sigma{_j = 0}{M} [Sin ( \theta{_i,_j} ) * Cos (
> \phi{_i} ) ]
> 
> an early responce would be great:)
> 
> regards,
> -sr

Copy the notation that you have given In[1]:=
Sum[Sum[a[i,j],{j,0,M}],{i,0,N}]

Out[1]=
Sum[Sum[a[i, j], {j, 0, M}], {i, 0, N}]

or sum over two indices (notice that the index for the outer summation
in the previous form comes first)

In[2]:=
Sum[a[i,j],{i,0,N},{j,0,M}]

Out[2]=
Sum[a[i, j], {i, 0, N}, {j, 0, M}]

Numerical version of this:

In[3]:=
Sum[a[i,j],{i,0,2},{j,0,3}]

Out[3]=
a[0, 0] + a[0, 1] + a[0, 2] + a[0, 3] + a[1, 0] + a[1, 1] + 
 
  a[1, 2] + a[1, 3] + a[2, 0] + a[2, 1] + a[2, 2] + a[2, 3]


Limits for inner indices can be functions of outer indices In[4]:=
Sum[Sum[a[i,j],{j,0,i+1}],{i,0,2}]

Out[4]=
a[0, 0] + a[0, 1] + a[1, 0] + a[1, 1] + a[1, 2] + a[2, 0] + 
 
  a[2, 1] + a[2, 2] + a[2, 3]

In the summation over multiple indices version this become: Limits for
later indices can be functions of earlier indices.


In[5]:=
Sum[a[i,j],{i,0,2},{j,0,i+1}]

Out[5]=
a[0, 0] + a[0, 1] + a[1, 0] + a[1, 1] + a[1, 2] + a[2, 0] + 
 
  a[2, 1] + a[2, 2] + a[2, 3]


-- 
Allan Hayes
Training and Consulting
Leicester, UK
hay@haystack.demon.co.uk
http://www.haystack.demon.co.uk
voice: +44 (0)116 271 4198
fax: +44 (0)116 271 8642




  • Prev by Date: SUBSCRIPT WITHIN EXPRESSIONS
  • Next by Date: Re: How to change the argument of a function?
  • Prev by thread: summations!
  • Next by thread: saving styles from notebooks: help, please!