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A computer model simulating fractional crystallization at one atmosphere pressure incorporates nine broadly-defined minerals—magnetite, olivine, hypersthene, augite, quartz, plagioclase, orthoclase, leucite, and nepheline. The crystallization temperature of each mineral is considered to be a smooth function of the composition of the magmatic liquid. These mineral temperature equations are obtained by multiple linear regression analysis of information from published silicate systems and rock melting experiments. The nine equations are solved for any primary liquid, within the broad range of common magma types, to select the crystallizing mineral or minerals. Partition ratios from published experiments and analyses of lavas and phenocrysts permit calculation of the composition of the crystallizing mineral assemblage. Subtraction of a small amount of that composition from the primary liquid yields a new liquid, which may be recycled to yield a sequence of liquids during fractional crystallization. The crystallization model handles assemblages of co-precipitating minerals, and can trace progressive saturation in new minerals, substitution of a new mineral for an old mineral, and cessation of crystallization of a mineral. The sequences of minerals and liquids derived from a broad set of primary liquids are geologically realistic, so the model is useful in predicting phenocrysts in volcanic rocks and events during crystallization of shallow intrusions.