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How to define function with indexed variables and sum

asked 2023-03-10 15:56:02 +0200

I would like to define a function f(n)=sum(x[k]*x[k+1], k= 1..n) so that it produces expressions like this:

f(1)= x[1]*x[2],
f(2)=x[1]*x[2]+x[2]*x[3]
f(3)=x[1]*x[2]+x[2]*x[3]+x[3]*x[4]

How to do this in sage? I tried to generate indexed variable with the following:

class VariableGenerator(object):
      def __init__(self, prefix):
          self.__prefix = prefix
      @cached_method
      def __getitem__(self, key):
          return SR.var("%s%s"%(self.__prefix,key))

x=VariableGenerator('x')
k, n = var('k,n')
f(n)=sum(x[k], k, 1, n)

Unfortunately this does not work. Any ideas?

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Comments

Would defining f as a Python function work for you?

f = lambda n: sum( x[k] for k in range(1,n+1) )

Max Alekseyev gravatar imageMax Alekseyev ( 2023-03-14 03:24:00 +0200 )edit

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answered 2023-03-13 22:37:31 +0200

tmonteil gravatar image

updated 2023-03-13 22:38:14 +0200

Would something like the following help ?

def f(n):
    return sum(SR.var('x_{}'.format(k))*SR.var('x_{}'.format(k+1)) for k in range(1,n+1))

f(3)
x_1*x_2 + x_2*x_3 + x_3*x_4
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Comments

This solution does create the necessary variables, but does not inject them in the global namespace (which can be done later with sage.misc.misc.inject_variable).

Alternatively, one can use var rather than SR.var to the same effect...

Emmanuel Charpentier gravatar imageEmmanuel Charpentier ( 2023-03-14 10:13:49 +0200 )edit

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Asked: 2023-03-10 15:56:02 +0200

Seen: 52 times

Last updated: Mar 13 '23