Simplification of expressions involving radicals
Journal of Symbolic Computation
Mechanical geometry theorem proving
Mechanical geometry theorem proving
The parallel numerical method of mechanical theorem proving
Theoretical Computer Science
The CLP( R ) language and system
ACM Transactions on Programming Languages and Systems (TOPLAS)
Simplification of nested radicals
SIAM Journal on Computing
Naive solving of non-linear constraints
Constraint logic programming
Mechanical theorem proving in geometries
Mechanical theorem proving in geometries
QUAD-CLP(R): Adding the Power of Quadratic Constraints
PPCP '94 Proceedings of the Second International Workshop on Principles and Practice of Constraint Programming
Constraint based automatic construction and manipulation of geometric figures
IJCAI'93 Proceedings of the 13th international joint conference on Artifical intelligence - Volume 1
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ConstraintLogic Programming can be advantageously used to deal with quadraticconstraints stemming from the verification of planar geometrytheorems. A hybrid symbolic-numeric representation involvingradicals and multiple precision rationals is used to denote theresults of quadratic equations. A unification-like algorithmtests for the equality of two expressions using that representation.The proposed approach also utilizes geometric transformationsto reduce the number of quadratic equations defining geometricconstructions involving circles and straight lines. A large number(512) of geometry theorems has been verified using the proposedapproach. Those theorems had been proven correct using a significantmore complex (exponential) approach in a treatise authored byChou in 1988. Even though the proposed approach is based on verification—ratherthan strict correctness utilized by Chou—the efficiencyattained is polynomial thus making the approach useful in classroomsituations where a construction attempted by student has to bequickly validated or refuted.