RootSum
RootSum[
f
,
form
] represents the sum of form
[
x
] for all x that satisfy the polynomial equation f
[
x
]
==
0.
f must be a Function object such as (#^5

2
#
+
1)&. form need not correspond to a polynomial function. Normal[
expr
] expands RootSum objects into explicit sums involving Root objects. f and form can contain symbolic parameters. RootSum[
f
,
form
] is automatically simplified whenever form is a rational function. RootSum is often generated in computing integrals of rational functions. See the Mathematica book: Section 3.4.3. See also: Root. Related package: Algebra`SymmetricPolynomials`.
Further Examples
This gives the sum of the seventh powers of the roots of the quintic.
In[1]:=
Out[1]=
Here is the sum of the logarithms.
In[2]:=
Out[2]=
The sum of exponentials is not evaluated explicitly, but we can get its numerical value with N.
In[3]:=
Out[3]=
In[4]:=
Out[4]=
In[5]:=
In this polynomial the coefficients of the linear term is symbolic. We can get numerical results by substitution.
In[6]:=
Out[6]=






