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KSS.SIF
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***************************
* SET UP THE INITIAL DATA *
***************************
NAME KSS
* Problem :
* *********
* The KSS system whose root at zero has exponential multiplicity
* as a function of dimension.
* Source: problem 8.1 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
* Problem dimension
*IE N 4 $ original value
*IE N 10
*IE N 100
IE N 1000
* Define useful parameters
IE 1 1
RI RN N
RA RN-1 RN -1.0
VARIABLES
DO I 1 N
X X(I)
ND
GROUPS
DO I 1 N
IA I-1 I -1
IA I+1 I 1
DO II 1 I-1
XE E(I) X(II) 1.0
OD II
XE E(I) X(I) -3.0
DO II I+1 N
XE E(I) X(II) 1.0
OD II
OD I
CONSTANTS
DO I 1 N
Z KSS E(I) RN-1
ND
BOUNDS
FR KSS 'DEFAULT'
START POINT
X KSS 'DEFAULT' 1000
ELEMENT TYPE
EV SQ X
ELEMENT USES
DO I 1 N
XT S(I) SQ
ZV S(I) X X(I)
ND
GROUP USES
DO I 1 N
XE E(I) S(I)
ND
OBJECT BOUND
* no objective
LO KSS 0.0
* Solution
*LO SOLTN 0.0
ENDATA
***********************
* SET UP THE FUNCTION *
* AND RANGE ROUTINES *
***********************
ELEMENTS KSS
INDIVIDUALS
* square elements
T SQ
F X * X
G X X + X
H X X 2.0
ENDATA