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We present a computer simulator of semiconductor optical amplifiers. The nonlinear input-output response of the device is characterized in terms of a complex gain, representing the accumulated gain and wavevector change of the propagating field across the active waveguide. We account for the gain saturation induced by stimulated recombination and by the perturbation of the carrier quasi-equilibrium distribution within the bands. A rigorous elimination of the spatial coordinate allows us to reduce the description of the amplifier dynamics to the solution of a set of ordinary differential equation for the complex gain. If the waveguide internal loss is negligible, the spatial inhomogeneity of the complex gain is implicitly yet exactly taken into account by the reduced model. The accuracy of the reduced model is the same for models based on the direct solution of the set of partial differential equations describing the interaction between the optical field and the active semiconductor waveguide, but the model is computationally much simpler. To preserve the input-output characteristics of the model, we include the amplified spontaneous emission noise in the device description by an equivalent signal applied to the device input and amplified by the saturated gain. At the expense of a minor increase of the program complexity, the waveguide internal loss may also be included. We report on the comparison between the output of the simulator and the results of four-wave mixing experiments in various pump-signal configurations. Good agreement is obtained.