ALGORITMOS PROBABILISTICOS BERTINI THEOREMS GEOMETRIC SOLUTIONS PROBABILISTIC ALGORITHMS PUNTOS RACIONALES RATIONAL POINTS SOLUCION GEOMETRICA STRAIGHT-LINE PROGRAMS TEOREMAS DE BERTINI TEORIA DE ELIMINACION EFECTIVO VARIEDADES SOBRE CUERPOS FINITOS VARIETIES OVER FINITE FIELDS Varieties over finite fields Matemáticas Rational points Chebyshev Polynomials Computational geometry Conformal mapping Cryptography Effective elimination theory Effective first Bertini theorem Energy of Graphs Estadística y Probabilidad Estimation Finite element method Finite fields First Bertini theorem Geometric solutions Graph theory Graphs