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RouthHurwitz

Guides

  • Guide to ZigangPan`RouthHurwitz`

Symbols

  • EmptyMatrixQ
  • FullColumnRankQ
  • FullRowRankQ
  • HurwitzMatrixQ
  • myMatrixQ
  • myNumericMatrixQ
  • myPositiveDefiniteMatrixQ
  • mySymmetricMatrixQ
  • NonDecreasingQ
  • NonNegativeDefiniteMatrixQ
  • NonSingularMatrixQ
  • RouthHurwitzTest
  • StrictIncreasingQ
ZigangPan`RouthHurwitz`
RouthHurwitzTest
​
{np,nn,n0}=RouthHurwitzTest[P,x]
calculates the number of roots of the polynomial
P
(with possibly complex coefficients and independent variable
x
,
P
is a formula rather than a function) that lies in the open right half of the complex plane, the open left half of the complex plane, and on the imaginary axis of the complex plane, which are denoted by
np
,
nn
, and
n0
, respectively. Clearly,
np+nn+n0=n
, where
n
is the degree of P.
​
Examples  
(1)
Basic Examples  
(1)
In[1]:=
p=x1^4+x1^3+x1+1;
In[2]:=
{np,nn,n0}=
RouthHurwitzTest
[p,x1]
Out[2]=
{2,2,0}
In[3]:=
p=(1+I)x1^6+(2-I)x1^5+(1-I)x1^4+(1+I)x1^3+(2+2I)x1^2+(2+3I)x1+1
Out[3]=
1+(2+3)x1+(2+2)
2
x1
+(1+)
3
x1
+(1-)
4
x1
+(2-)
5
x1
+(1+)
6
x1
In[4]:=
{np,nn,n0}=
RouthHurwitzTest
[p,x1]
Out[4]=
{2,4,0}
In[5]:=
p=x1^6+x1^4+x1^2+1
Out[5]=
1+
2
x1
+
4
x1
+
6
x1
In[6]:=
{np,nn,n0}=
RouthHurwitzTest
[p,x1]
Out[6]=
{2,2,2}
SeeAlso
HurwitzMatrixQ
 
▪
myMatrixQ
 
▪
EmptyMatrixQ
 
▪
NonNegativeDefiniteMatrixQ
 
▪
myPositiveDefiniteMatrixQ
 
▪
FullColumnRankQ
 
▪
FullRowRankQ
 
▪
NonSingularMatrixQ
RelatedGuides
▪
Guide to ZigangPan`RouthHurwitz`
""

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