Why does poly() not evalp

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?

Answer 1

[Walter Roberson]

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?

[Billy]

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]

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]

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]

The P function is here: http://www.mathworks.com/matlabcentral/answers/9485-how-do-i-specify-m-for-orthpoly-legendre