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NonlinearCholeskyFactorization

Guides

  • Guide to ZigangPan`NonlinearCholeskyFactorization`

Symbols

  • approximateHJIequation
  • approximatenonlinearCholeskyfactorization
  • backsteppinglocaloptimalmatchingglobalinverseoptimal
  • backsteppinglocaloptimalmatchingglobalinverseoptimalNew
  • backsteppinglocaloptimalmatchingglobalinverseoptimalN
  • backsteppinglocaloptimalmatchingglobalinverseoptimalNNew
  • expandseriesntruncate
  • monomialsofgivenorder
ZigangPan`NonlinearCholeskyFactorization`
monomialsofgivenorder
​
V=monomialsofgivenorder[xc,m]
returns a scalar that is the sum of all monomials of
m
-th order with independent variables that are listed in
xc
.
​
Examples  
(1)
Basic Examples  
(1)
In[1]:=
monomialsofgivenorder
[{x1,x2,x3},10]
Out[1]=
10
x1
+
10
x2
+
9
x2
x3+
8
x2
2
x3
+
7
x2
3
x3
+
6
x2
4
x3
+
5
x2
5
x3
+
4
x2
6
x3
+
3
x2
7
x3
+
2
x2
8
x3
+x2
9
x3
+
10
x3
+
9
x1
(x2+x3)+
8
x1
(
2
x2
+x2x3+
2
x3
)+
7
x1
(
3
x2
+
2
x2
x3+x2
2
x3
+
3
x3
)+
6
x1
(
4
x2
+
3
x2
x3+
2
x2
2
x3
+x2
3
x3
+
4
x3
)+
5
x1
(
5
x2
+
4
x2
x3+
3
x2
2
x3
+
2
x2
3
x3
+x2
4
x3
+
5
x3
)+
4
x1
(
6
x2
+
5
x2
x3+
4
x2
2
x3
+
3
x2
3
x3
+
2
x2
4
x3
+x2
5
x3
+
6
x3
)+
3
x1
(
7
x2
+
6
x2
x3+
5
x2
2
x3
+
4
x2
3
x3
+
3
x2
4
x3
+
2
x2
5
x3
+x2
6
x3
+
7
x3
)+
2
x1
(
8
x2
+
7
x2
x3+
6
x2
2
x3
+
5
x2
3
x3
+
4
x2
4
x3
+
3
x2
5
x3
+
2
x2
6
x3
+x2
7
x3
+
8
x3
)+x1(
9
x2
+
8
x2
x3+
7
x2
2
x3
+
6
x2
3
x3
+
5
x2
4
x3
+
4
x2
5
x3
+
3
x2
6
x3
+
2
x2
7
x3
+x2
8
x3
+
9
x3
)
In[2]:=
monomialsofgivenorder
[{x1,x2},5]
Out[2]=
5
x1
+
4
x1
x2+
3
x1
2
x2
+
2
x1
3
x2
+x1
4
x2
+
5
x2
SeeAlso
expandseriesntruncate
 
▪
approximateHJIequation
 
▪
approximatenonlinearCholeskyfactorization
""

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