Programmable Multinomial Expansion

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In summary, the conversation discusses how to write a programmable multinomial expansion in Mathematica, specifically the summation over all non-negative integer indices. The formula for this expansion is shown and explained, with the meaning of n_1,n_2,\ldots,n_m=0 and the delta function \delta_{n;n_1+n_2+\cdots+n_m}\left(n;n_1,n_2,\ldots,n_m\right) being clarified. The conversation concludes with a request for further elaboration on how to program this expansion in Mathematica.
  • #1
EngWiPy
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Hello,

How can we write a programmable multinomial expansion? I mean the summation over all non-negative integer indices, is somewhat difficult to program in Mathematica, at least for me. Is there any suggestions, please?


I saw this formula at the Mathematica official website, but I didn't know how to interpret it:

[tex]\left(a_1+a_2+\cdots+a_m\right)^n=\sum_{n_1,n_2,\dots,n_m=0}\delta_{n;n_1+n_2+\cdots+n_m}\left(n;n_1,n_2,\ldots,n_m\right)\prod_{k=1}^ma_k^{n_k}[/tex]

what does it mean [tex]n_1,n_2,\ldots,n_m=0[/tex]? and what is the delta function [tex]\delta_{n;n_1+n_2+\cdots+n_m}\left(n;n_1,n_2,\ldots,n_m\right)[/tex]??

Thanks in advance
 
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  • #2
[tex]n_1,n_2,\ldots,n_m=0[/tex] means start the sum with all ni=0.
[tex]\delta_{n;n_1+n_2+\cdots+n_m}\left(n;n_1,n_2,\ldots,n_m\right)[/tex] =1 when the sum of the ni=n and =0 otherwise.

Note: For some reason I get an s where there should be ... In the checking before I submit it is correct?
 
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  • #3
mathman said:
[tex]n_1,n_2,\ldots,n_m=0[/tex] means start the sum with all ni=0.
[tex]\delta_{n;n_1+n_2+\cdots+n_m}\left(n;n_1,n_2,\ldots,n_m\right)[/tex] =1 when the sum of the ni=n and =0 otherwise.

well, after we start all the indices from 0? Can you elaborate more, because I have no clear idea how to program this expansion in Mathematica.

Thanks in advance
 
  • #4
I don't know anything about mathematica. Also (more important) the description you gave does not indicate what the upper limits of the summations for the m indices. In any case each ni goes from 0 to its upper limit.
 

What is Programmable Multinomial Expansion?

Programmable Multinomial Expansion is a mathematical concept that involves representing a polynomial expression as a sum of terms, where each term consists of a coefficient and a variable raised to a certain power. This expansion can be programmed to calculate the coefficients and powers for any given polynomial expression.

How is Programmable Multinomial Expansion different from traditional polynomial expansion?

Unlike traditional polynomial expansion, where the coefficients and powers are predetermined, Programmable Multinomial Expansion allows for flexibility in calculating these values. This means that the expansion can be used for a wider range of polynomial expressions.

What are some applications of Programmable Multinomial Expansion in science?

Programmable Multinomial Expansion has various applications in fields such as statistics, data analysis, and machine learning. It can be used to model and analyze complex data sets, calculate probabilities, and create predictive models.

What are the limitations of Programmable Multinomial Expansion?

One limitation of Programmable Multinomial Expansion is that it can only be applied to polynomial expressions. It also requires a significant amount of computational power and may not be suitable for complex or large-scale data sets.

How can Programmable Multinomial Expansion be implemented in programming languages?

Programmable Multinomial Expansion can be implemented in programming languages such as Python, Java, and C++. There are also libraries and packages available that can perform the expansion for specific types of polynomial expressions.

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