On 28.02.2013 19:02, Raymond Toy wrote:
>>>>>> "Adam" == Adam <adammaj1 at o2.pl> writes:
>
> Adam> Hi,
> Adam> What is the best method to find multiplicity of the root ?
>
> Adam> For example equation :
>
> Adam> z^4-z=z
>
> Doesn't this have 4 distinct roots?
>
> Anyway, the variable multiplicities is supposed to have the
> multiplicities.
>
> solve(z^3*(z-1)) -> [z = 0, z = 1]
> multiplicities -> [3, 1]
>
> Ray
>
OK. Thx,
my errors :
====================
(%i1) z:x+y*%i;
(%o1) %i*y+x
(%i2) f:z^4-z;
(%o2) (%i*y+x)^4-%i*y-x
(%i3) solve(f=z,[x,y]);
(%o3)
[[x=%r1,y=sqrt(-2*%r1^2-(-6*%r1^2-3*4^(1/3))/3+2^(5/3))/2+%i*%r1+%i/2^(2/3)],[x=%r2,y=-sqrt(-2*%r2^2-(-6*%r2^2-3*4^(1/3))/3+2^(5/3))/2+%i*%r2+%i/2^(2/3)],[x=%r3,y=sqrt(-2*%r3^2-(-6*%r3^2-3*4^(1/3))/3-2^(5/3))/2+%i*%r3-%i/2^(2/3)],[x=%r4,y=-sqrt(-2*%r4^2-(-6*%r4^2-3*4^(1/3))/3-2^(5/3))/2+%i*%r4-%i/2^(2/3)]]
(%i4) multiplicities;
(%o4) []
/*
===================
(%i5) solve(z^4-z=z,z);
(%o5) []
(%i6) solve(z^4-2*z,z);
(%o6) [%i*y+x=0]
(%i7) multiplicities;
(%o7) [1]
Adam