Non-linear constraints over real-valued decision variables

(!****************************************************************
   CP example problems
   ===================
   
   file nlinctr.mos
   ````````````````
   Definition and use of non-linear constraints.

   *** This model cannot be run with a Community Licence ***  

   (c) 2008 Artelys S.A. and Fair Isaac Corporation
       Creation: 2005, rev. Mar. 2013
*****************************************************************!)

model "Non-linear constraints" 
 uses "kalis"

 parameters
  PREC =  1e-10 
 end-parameters

! Setting default precision of continuous variables 
 setparam("KALIS_DEFAULT_PRECISION_VALUE", PREC)
 
 declarations
  ISET = 1..8
  x: array(ISET) of cpfloatvar
 end-declarations
 
 ! Setting variable names
 forall(i in ISET) x(i).name:= "x"+i

 ! Setting variable bounds
 forall(i in ISET) do
  x(i) >= -100; x(i) <= 100
 end-do

 ! Defining and posting non-linear constraints
 x(1) + x(2)*(x(1)+x(3)) + x(4)*(x(3)+x(5)) + x(6)*(x(5)+x(7)) - 
   (x(8)*((1/8)-x(7))) = 0
 x(2) + x(3)*(x(1)+x(5)) + x(4)*(x(2)+x(6)) + x(5)*x(7) -
   (x(8)*((2/8)-x(6))) = 0
 x(3)*(1 + x(6)) + x(4)*(x(1)+x(7)) + x(2)*x(5) - 
   (x(8)*((3/8)-x(5))) = 0
 x(4) + x(1)*x(5) + x(2)*x(6) + x(3)*x(7) - (x(8)*((4/8)-x(4))) = 0
 x(5) + x(1)*x(6) + x(2)*x(7) - (x(8)*((5/8)-x(3))) = 0
 x(6) + x(1)*x(7) - (x(8)*((6/8)-x(2))) = 0
 x(7) - (x(8)*((7/8)-x(1))) = 0
 sum(i in ISET) x(i) = -1

 ! Set the enumeration strategy
 cp_set_branching(split_domain(KALIS_WIDEST_DOMAIN, KALIS_MIDDLE_VALUE,
                               x, true, 0))

 ! Find one solution
 if cp_find_next_sol then
  writeln("Solution number 1" ) 
  cp_show_sol
  cp_show_stats
 end-if

end-model