

1)Concerning Interval peeler
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	Interval peeler use constraints projection algotithms to reduce 
	interval domains of variables
	Forward and Backward Propagation (2b consistency) (Waltz algo)


2)Examples
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	a)Ex1
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		Variables and domains definitions
		x1 in [1,2]
		x2 in [3,4]
		x3 in [5,6]
		y in [-oo,+oo]
		Constraints
		y=x1+x2*x3/(x1-2)

	solver gives
		x1 in [1,2]
		x2 in [3,4]
		x3 in [5,6]
		y in [4,75,10]
	
	b)Ex2
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		Variables and domains definitions
		x1 in [1,2]
		x2 in [3,4]
		x3 in [5,6]
		y in [-oo,+oo]
		Constraints
		//u tempory variable
		u=x1+x2*x3/(x1-2)
		y=sin(u)/u

	solver gives
		x1 in [1,2]
		x2 in [3,4]
		x3 in [5,6]
		y in [-0,210377429257974,0,210526315789474]
	
	c)Ex3
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		Variables and domains definitions
		x1 in [1,2]
		x2 in [3,4.5]
		x3 in [5,6]
		y1 in [-oo,+oo]
		y2 in [-oo,+oo]
		y3 in [-oo,+oo]
		Constraints
		//more than one constraint
		y1=sin(x1)/x1
		y2=sin(x2)/x2
		y3=sin(x3)/x3
		y1+y2=y3

	solver gives
		x1 in [1,2]
		x2 in [3,4.5]
		x3 in [5,6]
		y1 in [0,420735492403948,1]
		y2 in [-0,325843372555032,0,0470400026866224]
		y3 in [0,0948921198489159,1,04704000268662]	


3)SOLVER LANGUAGE
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	a)Variables
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		Begin your variables by a letter (A-Za-z) 
		Use all combinaison of digits and letters

		ex: A1 , A456a , test1 , variable4...
		
	b)Interval domain definition
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		x in [ 1 , 2 ]
		x in [ 1 , +oo ]
		x in [ -oo , +oo ]

	c)Constraints definition
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		constraints are written like that
			y=x1+x2+x3
			x1+x2=x3+x4
			y=max(x1,x1*sin(x2))
			...	

		to write constraints you can use :

		i)Arithmetic Operations
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			+	:	a+b
			-	:	a-b
			*	:	a*b
			/	:	a/b
	
		ii)Functions
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			power functions
				sqr(  ) :	sqr(x)=x	
				sqrt(  ) :	sqrt(x)=square root(x)
	
	
			trigonometric functions
				sin(  ) :	sin(x), sin(x+y), sin(sin(x)), ...	
				cos(  ) :	cos(x), cos(x-y), cos(sin(x)), ...
				tan(  ) :	tan(x), tan(x*y), tan(sin(x)), ...
	
			exponential functions
				exp(  ) :	exp(x), exp(x/y), exp(sin(x)), ...	
				ln(  )  :	ln(x), ln(x/y), ln(sin(x)), ...	
				
			MinMax functions	
				max(  ,  ) :	max( a,b ),...
				min(  ,  ) :	min( a,b ),...

			others functions
				abs(  ) :	abs( x )=|x|	
		
		iii)Special constraints
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			bool(x) :	give intersection between [x] and {0,1}	
			int(x) :	give intersection between [x] and {t in Z}	
		

	d)Comments
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		//this ligne is a comment

	

4)USE INTERFACE EDITOR
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	Select constraint or variable
		press return to validate 
		press backspace to delete 

	WARNING in editor windows box, cut copy paste use: 
		x c v Key on Keyboard without CTRL key

5)USE INPUT FILE AND NOTEPAD
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	The file syntaxe is

		Input Variables
		x1 in [1,2]
		x2 in [3,4]
		x3 in [5,6]
		Output Variables
		y1 in [-oo,+oo]
		y2 in [-oo,+oo]
		y3 in [-oo,+oo]
		Constraints
		//more than one constraint
		y1=sin(x1)/x1
		y2=sin(x2)/x2
		y3=sin(x3)/x3
		//redondante constraint
		y1+y2=y3
		End
	
	Use Output Variables when it's possible to calculate yi with xi.
	In the other cases use redondante constraint
	 
WARNING When you use NotePad, SaveAs don't give information to the solveur
you must open the file you just SaveAs !!!! be careful !!!