Texas Instruments TI-92 Owners Manual - Page 80

AUTO Setting When Exact/Approx = AUTO, the TI-89 / TI-92 Plus uses exact rational arithmetic wherever all of the operands are rational numbers. Otherwise, floating-point arithmetic is used after converting any rational operands to floating-point. In other words, floating-point is "infectious." For example: 1/2 − 1/3 transforms to 1/6 but 0.5 − 1/3 transforms to .16666666666667 This floating-point infection does not leap over barriers such as undefined variables or between elements of lists or matrices. For example: (1/2 - 1/3) x + (0.5 − 1/3) y transforms to x/6 + .16666666666667 y and {1/2 - 1/3, 0.5 − 1/3} transforms to {1/6, .16666666666667} In the AUTO setting, functions such as solve determine as many solutions as possible exactly, and then use approximate numerical methods if necessary to determine additional solutions. Similarly, ‰ (integrate) uses approximate numerical methods if appropriate where exact symbolic methods fail. Advantages You see exact results when practical, and approximate numeric results when exact results are impractical. You can often control the format of a result by choosing to enter some coefficients as either rational or floating-point numbers. Disadvantages If you are interested only in exact results, some time may be wasted seeking approximate results. If you are interested only in approximate results, some time may be wasted seeking exact results. Moreover, you might exhaust the memory seeking those exact results. Chapter 3: Symbolic Manipulation 63