Difference between revisions of "ElemSymPoly"
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|desc=Computes the elementary symmetric polynomial of a given set of numbers. | |desc=Computes the elementary symmetric polynomial of a given set of numbers. | ||
|cat=[[List of functions#Miscellaneous|Miscellaneous]] | |cat=[[List of functions#Miscellaneous|Miscellaneous]] | ||
| − | |upd=August | + | |upd=August 23, 2024 |
|v=0.90}} | |v=0.90}} | ||
<tt>'''ElemSymPoly'''</tt> is a [[List of functions|function]] that computes the ''k''<sup>th</sup> [https://en.wikipedia.org/wiki/Elementary_symmetric_polynomial elementary symmetric polynomial] of a given set of numbers. | <tt>'''ElemSymPoly'''</tt> is a [[List of functions|function]] that computes the ''k''<sup>th</sup> [https://en.wikipedia.org/wiki/Elementary_symmetric_polynomial elementary symmetric polynomial] of a given set of numbers. | ||
==Syntax== | ==Syntax== | ||
| − | * <tt> | + | * <tt>RES = ElemSymPoly(X, K)</tt> |
==Argument descriptions== | ==Argument descriptions== | ||
| − | * <tt> | + | * <tt>X</tt>: A vector of length <tt>n</tt>. |
| − | * <tt> | + | * <tt>K</tt>: An integer denoting the degree of the terms in the elementary symmetric polynomial. Must be between <tt>0</tt> and <tt>n</tt>, inclusive. |
==Example== | ==Example== | ||
| − | This function computes the sum of products of ''k'' distinct elements of a vector ''x''. For example, the 3<sup>rd</sup> elementary symmetric polynomial of the vector [1, 2, 3, 4] is computed by summing the distinct products of 3 elements, these products being | + | This function computes the sum of products of ''k'' distinct elements of a vector ''x''. For example, the 3<sup>rd</sup> elementary symmetric polynomial of the vector [1, 2, 3, 4] is computed by summing the distinct products of 3 elements, these products being 1 x 2 x 3, 1 x 2 x 4, 1 x 3 x 4, and 2 x 3 x 4. |
<syntaxhighlight> | <syntaxhighlight> | ||
>> ElemSymPoly([1, 2, 3, 4], 3) | >> ElemSymPoly([1, 2, 3, 4], 3) | ||
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50 | 50 | ||
</syntaxhighlight> | </syntaxhighlight> | ||
| + | |||
| + | ==Notes== | ||
| + | The 0<sup>th</sup> elementary symmetric polynomial is defined as S<sub>0</sub>(''x'') = 1. | ||
{{SourceCode|name=ElemSymPoly}} | {{SourceCode|name=ElemSymPoly}} | ||
Latest revision as of 14:07, 26 August 2024
| ElemSymPoly | |
| Computes the elementary symmetric polynomial of a given set of numbers. | |
| Other toolboxes required | none |
|---|---|
| Function category | Miscellaneous |
ElemSymPoly is a function that computes the kth elementary symmetric polynomial of a given set of numbers.
Syntax
- RES = ElemSymPoly(X, K)
Argument descriptions
- X: A vector of length n.
- K: An integer denoting the degree of the terms in the elementary symmetric polynomial. Must be between 0 and n, inclusive.
Example
This function computes the sum of products of k distinct elements of a vector x. For example, the 3rd elementary symmetric polynomial of the vector [1, 2, 3, 4] is computed by summing the distinct products of 3 elements, these products being 1 x 2 x 3, 1 x 2 x 4, 1 x 3 x 4, and 2 x 3 x 4.
>> ElemSymPoly([1, 2, 3, 4], 3)
ans =
50Notes
The 0th elementary symmetric polynomial is defined as S0(x) = 1.
Source code
Click here to view this function's source code on github.