Why does poly() not evalp

2011 6 14
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I have an example:
evalp( poly( sqrt( 1-x^2 ), [x] ), x=cos(0.5) )
This gives (sqrt(1-x^2)) as the response.
The expected result is only given by
evalp( poly( sqrt( 1-x^2 ), [x] ), x=cos(0.5) ) | x=cos(0.5)
And evalp works as expected with simple expression like
evalp( poly( x, [x] ), x = 1 )
Is this a bug?

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Walter Roberson
Walter Roberson 2011-6-15

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sqrt( 1-x^2 ) is not a polynomial. evalp() is only for evaluating polynomials.
I am not familiar with the way you used "|" in your second expression. I looked through the Standard Library but I do not find any meaning defined for "|" . Could you give a reference on that?

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Billy
Billy 2011-6-15
So can you eval the expression without using |? | can also be used for evaluating any function, I cannot remember where I first saw it, will post a reference when I do.
Walter Roberson
Walter Roberson 2011-6-15
Found the | notation: it is a shortcut for evalAt() http://www.mathworks.com/help/toolbox/mupad/stdlib/evalAt.html
Evaluation:
level(subs(sqrt(1-x^2),x=cos(0.5)),1)
or perhaps the ,1 might need to be ,2 -- that would have to be tested.
I would probably tend to instead use
eval(subs(sqrt(1-x^2),x=cos(0.5))
which is a bit different than the level() version with respect to symbols in the expression that might have been assigned a value. evalp() is defined to *not* evaluate the other symbols indefinitely.
Well... actually what I would probably use myself is
eval(sqrt(1-x^2),x=cos(0.5))
in Maple. This is similar to MuPad's evalAt() .
Is there a specific reason you are using poly() instead of just an expression ? Do you care about the number of levels of evaluation of symbols, for example?
Billy
Billy 2011-6-15
I'm using poly() to simulate the output of my P function I just wrote, which outputs a poly() (in turn because orthpoly::legendre outputs a poly).
Ultimately I'm trying to evaluate the legendre polynomials with cos(t) in the place of x in legendre(n,x).
Billy
Billy 2011-6-15
The P function is here: http://www.mathworks.com/matlabcentral/answers/9485-how-do-i-specify-m-for-orthpoly-legendre

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