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https://issues.apache.org/jira/browse/MATH-683?page=com.atlassian.jira.plugin.system.issuetabpanels:comment-tabpanel&focusedCommentId=13119273#comment-13119273
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Sébastien Brisard commented on MATH-683:
----------------------------------------

I think you might want to specify whether or not you would like at some point 
to be able to retrieve the coefficients of {{P2}}. In other words, do you need 
{{P2}} to be a {{PolynomialFunction}} or do you merely need to be able to 
compose {{P1}} and a shifter, which would return {{P2}} as a 
{{UnivariateRealFunction}}, e.g
{code}
final PolynomialFunction p1 = PolynomialsUtils.createLegendrePolynomial(10);
final double a = 1.;
UnivariateRealFunction p2 = new UnivariateRealFunction(){
  public double value(final double x){
    return p1.value(x+a);
  }
}
{code}
I suspect the answer is the first option, since you also requested for the 
Pascale Triangle...
Sébastien
                
> Create a method shift in the PolynomialFunction class
> -----------------------------------------------------
>
>                 Key: MATH-683
>                 URL: https://issues.apache.org/jira/browse/MATH-683
>             Project: Commons Math
>          Issue Type: New Feature
>    Affects Versions: 3.0
>         Environment: All
>            Reporter: DI COSTANZO
>            Priority: Trivial
>
> Create a method shift to transform a polynomial P(k) in P(k + a) where a is 
> any double value.
> The polynomial sum(ai * k^i) turns into sum(ai * (k+a)^i)

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