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sum with indexed variable

asked 2022-03-06 20:46:48 +0200

mahmood gravatar image

updated 2022-03-06 20:47:21 +0200

how do i write a symbolic expression/function to calculate this sum based on the given value of the variable 'k'?

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answered 2022-03-07 08:30:25 +0200

Emmanuel Charpentier gravatar image

updated 2022-03-07 18:26:07 +0200

Define a as a function of i. Possible use :

a = function("a")
d = var("d")
# I don't like to scratch Sage's predefined identifiers...
j, k = var("j, k", domain="integer")
S = sum(a(j)*d, j, 1, k+1)

EDIT : If you want to fiddle with output cosmetics, you might try :

a = function("a", nargs=1,
                   print_func=lambda self, *args: r"%s[%s]"%(self, args[0]),
                   print_latex_func=lambda self, *args: r"%s_{%s}"%(self, args[0]))
d = SR.var("d")
j, k = SR.var("j, k", domain="integer")

which allows for :

sage: sum(a(j)*d(), j, 0, k + 1)
d*sum(a[j], j, 0, k + 1)

and latex(sum(a(j)*d(), j, 0, k + 1)) gets interpreted as :

$$d {\sum_{j=0}^{k + 1} a_{j}}$$

HTH,

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makes sense, tysm

mahmood gravatar imagemahmood ( 2022-03-07 11:39:15 +0200 )edit

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Asked: 2022-03-06 20:46:48 +0200

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Last updated: Mar 07