# [R] Summary Orthogonal Polynomials

Peter Dalgaard BSA p.dalgaard at biostat.ku.dk
Wed Oct 9 16:56:39 CEST 2002

```Douglas Bates <bates at stat.wisc.edu> writes:

> Bill.Venables at CMIS.CSIRO.AU writes:
>
> > In fact I find fractions() useful for a lot of things, somewhat to my
> > surprise.
>
> I did try fractions() on the example that Paul gave, poly(1:4, 3), and
> the result is hard to interpret.
>
> > fractions(poly(1:4, 3))
>      1                2                3
> [1,] -5494877/8191279              1/2    -98209/439204
> [2,]    -98209/439204             -1/2    208010/310083
> [3,]    208010/930249             -1/2 -5494877/8191279
> [4,]    208010/310083              1/2    208010/930249

It gets nicer if you square them to get rid of the sqrt(5) factor:

> fractions(poly(1:4, 3)^2)
1    2    3
[1,] 9/20  1/4 1/20
[2,] 1/20  1/4 9/20
[3,] 1/20  1/4 9/20
[4,] 9/20  1/4 1/20

(Anyone want to extend fractions() to deal with square roots as well?)

--
O__  ---- Peter Dalgaard             Blegdamsvej 3
c/ /'_ --- Dept. of Biostatistics     2200 Cph. N
(*) \(*) -- University of Copenhagen   Denmark      Ph: (+45) 35327918
~~~~~~~~~~ - (p.dalgaard at biostat.ku.dk)             FAX: (+45) 35327907
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```