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### Polynomial roots

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```I'm trying to find the roots of 100 random polynomials of degree 5 and I need help with finding the roots. I know that I can gernerate 100 polynomials by using
>> x=rand([100 6])
I know that I can't do
>> roots(x)
because the the input must be a vector. Is there anyway to to find all the roots of 100 random polynomials without generating each polynomial one by one.
```
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```Mark wrote:
> I'm trying to find the roots of 100 random polynomials of degree 5 and I
> need help with finding the roots. I know that I can gernerate 100
> polynomials by using
>                                          >> x=rand([100 6])
> I know that I can't do                                          >> roots(x)
> because the the input must be a vector. Is there anyway to to find all
> the roots of 100 random polynomials without generating each polynomial
> one by one.

Not for degree 5. For degree 4, there would be exact solutions you could
plug the coefficients into, but for degree 5 unless you are lucky enough
to be able to factorize, you need to use something like a binary search
for sign changes over a hypothesized interval.

I'm not saying that it would not be possible to build a routine that did
this kind of search in parallel, but it isn't the way the built-in
routines are set up.
```
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```"Mark " <bobbb909@yahoo.com> wrote in message
news:hrcsta\$g22\$1@fred.mathworks.com...
> I'm trying to find the roots of 100 random polynomials of degree 5 and I
> need help with finding the roots. I know that I can gernerate 100
> polynomials by using
>                                          >> x=rand([100 6])
> I know that I can't do >> roots(x)
> because the the input must be a vector. Is there anyway to to find all the
> roots of 100 random polynomials without generating each polynomial one by
> one.

Loop over the rows of x and call ROOTS on each row, storing the roots back
into rows or columns of another matrix or into a cell array (depending on
how you need them.)

--
Steve Lord
slord@mathworks.com
comp.soft-sys.matlab (CSSM) FAQ: http://matlabwiki.mathworks.com/MATLAB_FAQ

```
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```"Mark " <bobbb909@yahoo.com> wrote in message <hrcsta\$g22\$1@fred.mathworks.com>...
> I'm trying to find the roots of 100 random polynomials of degree 5 and I need help with finding the roots. I know that I can gernerate 100 polynomials by using
>                                           >> x=rand([100 6])
> I know that I can't do
>                                           >> roots(x)
> because the the input must be a vector. Is there anyway to to find all the roots of 100 random polynomials without generating each polynomial one by one.

a hint:

help num2cell;
help cellfun;

us
```
 0

```"Steven Lord" <slord@mathworks.com> wrote in message <hrcuhl\$1r6\$1@fred.mathworks.com>...
>
> "Mark " <bobbb909@yahoo.com> wrote in message
> news:hrcsta\$g22\$1@fred.mathworks.com...
> > I'm trying to find the roots of 100 random polynomials of degree 5 and I
> > need help with finding the roots. I know that I can gernerate 100
> > polynomials by using
> >                                          >> x=rand([100 6])
> > I know that I can't do >> roots(x)
> > because the the input must be a vector. Is there anyway to to find all the
> > roots of 100 random polynomials without generating each polynomial one by
> > one.
>
> Loop over the rows of x and call ROOTS on each row, storing the roots back
> into rows or columns of another matrix or into a cell array (depending on
> how you need them.)
>
> --
> Steve Lord
> slord@mathworks.com
> comp.soft-sys.matlab (CSSM) FAQ: http://matlabwiki.mathworks.com/MATLAB_FAQ
>
How would I wrtie the for loop? Here is what I got so far

N=100;
x=zeros(100, 6);    % cretes an empty 100 x 6 matrix

for k=1:N
x(k)=roots(rand([1 6]));
end

x
I know that this won't work so how can I get it to work.
```
 0

```"Mark " <bobbb909@yahoo.com> wrote in message <hri8s0\$gjm\$1@fred.mathworks.com>...
> "Steven Lord" <slord@mathworks.com> wrote in message <hrcuhl\$1r6\$1@fred.mathworks.com>...
> >
> > "Mark " <bobbb909@yahoo.com> wrote in message
> > news:hrcsta\$g22\$1@fred.mathworks.com...
> > > I'm trying to find the roots of 100 random polynomials of degree 5 and I
> > > need help with finding the roots. I know that I can gernerate 100
> > > polynomials by using
> > >                                          >> x=rand([100 6])
> > > I know that I can't do >> roots(x)
> > > because the the input must be a vector. Is there anyway to to find all the
> > > roots of 100 random polynomials without generating each polynomial one by
> > > one.
> >
> > Loop over the rows of x and call ROOTS on each row, storing the roots back
> > into rows or columns of another matrix or into a cell array (depending on
> > how you need them.)
> >
> > --
> > Steve Lord
> > slord@mathworks.com
> > comp.soft-sys.matlab (CSSM) FAQ: http://matlabwiki.mathworks.com/MATLAB_FAQ
> >
> How would I wrtie the for loop? Here is what I got so far
>
> N=100;
> x=zeros(100, 6);    % cretes an empty 100 x 6 matrix
>
> for k=1:N
>     x(k)=roots(rand([1 6]));
> end
>
> x
> I know that this won't work so how can I get it to work.
-----------
You're almost there.  Just add a colon.  And use 100 x 5 size.

N=100;
x=zeros(100, 5);    % creates an empty 100 x 5 matrix
for k=1:N
x(k,:) = roots(randn([1 6]));
end

Roger Stafford
```
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