Geometry theorem prover using complex numbers and unit circle

- needed software: scala 2.7.7 and SBT 0.7.5
- to run the program: sbt  run tests/program_name.geom
- output is generated both on screen and in the corresponding file in tests/output/ directory
- the input must follow the grammar (see tests/ for more examples):

problem = description + hypotehsis + conclusion

	description = some text

	hypotehsis = "Hypothesis:" + arbitrary + semiarbitrary + deterministic + (constraint)?   /* constraint between defined elements */

		arbitrary = arbitrary_circle + (arbitrary_point)*

			arbitrary_circle = "Let an arbitrary circle " + circle_name + "(" + point + ", radix)" /* circle(center, radix)*/ 

			arbitrary_point  = "Let an arbitrary point " + point 
	
		semiarbitrary = (semiarbitrary_point)* + (euler_circle)?  /* this is a geometric locus of a point - can be a line, a circle, etc"

			semiarbitrary_point = "Let a semiarbitrary point " + point + " situated on " + equation_hyp_double

			euler_circle = "Let the Euler circle with respect to triangle " + point + point + point + "be " + circle_name + "(omega, radix_E)"  /* each point must be on circle(center, radix) */

		deterministic = (deterministic_point_single | deterministic_point_double)*

			deterministic_point_single = "Let a 1-equation deterministic point " + point + " situated on " + equation_hyp_single
			deterministic_point_double = "Let a 2-equations deterministic point " + point + " situated on " + equation_hyp_double + " and " + equation_hyp_double

		constraint__ = "Constraint: " + constraint

	conclusion = "Conclusion:" + equation_concl

equation_hyp_double = line |
		    = "circle " + circle_name |
		    = line + " perpendicular on " + line |
		    = line + " paralel with " + line |
		    = " perpendicular bisector of " + line |
		    = "tangent at circle " + circle_name + " in point" + point

equation_hyp_single = "centroid of triangle " + point + point + point |
		    = "symmetric point of " + point + " with respect to" + point
		    = "projection of " + point + " on " + line
		    = "midpoint of " + point + point

constraint = " collinear " + point + point + point
	   = " concurrent " + line + line + line
	   = line + " perpendicular on " + line |
	   = line + " parallel with " + line | 

equation_concl = " collinear " + point + point + point
	       = " concurrent " + line + line + line
	       = line + " perpendicular on " + line |
	       = line + " paralel with " + line |  
	       = " triangle is equilateral " + point + point + point|
	       = " concyclic points " + point + point + point + point 
	       = point + " = " + point

line = "line " + point + " " + point

circle_name = "Circ", "Inscr", "Euler"

point = "A" (+ number)?, "B" (+ number)?, .....  + " "

afix_of_point = "a" (+ number)? , "b" (+ number)? , ....

conjugate_of_afix = "a" (+ number)? + "__" , "b" (+ number)? + "__", ....

value = x + iy , where x and y are rational numbers