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CYCLIC3.SIF
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***************************
* SET UP THE INITIAL DATA *
***************************
NAME CYCLIC3
* Problem :
* *********
* The cyclic cubic system whose root at zero has exponential multiplicity
* as a function of dimension.
* Source: problem 8.2 in
* Wenrui Hao, Andrew J. Sommese and Zhonggang Zeng,
* "An algorithm and software for computing multiplicity structures
* at zeros of nonlinear systems", Technical Report,
* Department of Applied & Computational Mathematics & Statistics,
* University of Notre Dame, Indiana, USA (2012)
* SIF input: Nick Gould, Jan 2012.
* classification NOR2-AN-V-0
* dimension parameter
*IE N 4 $ original value
*IE N 10
*IE N 100
*IE N 1000
*IE N 10000
IE N 100000
* Problem dimension
IA N+2 N 2
* Define useful parameters
IE 1 1
IE 2 2
IA N+1 N 1
VARIABLES
DO I 1 N+2
X X(I)
ND
GROUPS
DO I 1 N
XE E(I)
ND
XE E(N+1) X(N+1) 1.0 X(1) -1.0
XE E(N+2) X(N+2) 1.0 X(2) -1.0
BOUNDS
FR CYCLIC3 'DEFAULT'
START POINT
X CYCLIC3 'DEFAULT' 1000.0
ELEMENT TYPE
EV CUBE X
EV PROD X
EV PROD Y
ELEMENT USES
DO I 1 N
XT C(I) CUBE
ZV C(I) X X(I)
IA I+1 I 1
IA I+2 I 2
XT P(I) PROD
ZV P(I) X X(I+1)
ZV P(I) Y X(I+2)
ND
GROUP USES
DO I 1 N
XE E(I) C(I) 1.0 P(I) -1.0
ND
OBJECT BOUND
* no objective
LO CYCLIC3 0.0
* Solution
*LO SOLTN 0.0
ENDATA
***********************
* SET UP THE FUNCTION *
* AND RANGE ROUTINES *
***********************
ELEMENTS CYCLIC3
INDIVIDUALS
* cubic elements
T CUBE
F X ** 3
G X 3.0 * X ** 2
H X X 6.0 * X
* product elements
T PROD
F X * Y
G X Y
G Y X
H X Y 1.0
ENDATA