discovers and preserves significantly more factors,.doesn't unnecessarily force common denominators,. ![]() In contrast to the distributed Altran representation, this recursive partially-factored semi-fraction form: Although motivated by computer algebra, many of the goals are also applicable to manual simplification, indicating what transformations are necessary and sufficient for good simplification when no particular canonical result form is required.Īfter motivating the ten goals, the article then explains how the Altran partially-factored form for rational expressions was extended for Derive and the computer algebra in Texas Instruments products to help fulfill the goals. These goals can also help users recognize and partially circumvent some limitations of their current computer-algebra systems. This article provides goals for the design and improvement of default computer-algebra expression simplification. Almost everyone who uses or should use mathematical software can benefit from acquaintance with several such programs, because these programs differ in the sets of constants that they can return. This article describes some of these programs, how they work, and how best to use each of them. Moreover, candidates that are not the exact limit can be provable bounds, or convey qualitative insight, or suggest series that they truncate, or provide sufficiently close efficient approximations for subsequent computation. Therefore these program results are candidates for proving an exact result that you could not otherwise compute or conjecture without the program. ![]() Usefully often such a result is the exact limit as the float is computed with increasing precision. Examples include AskConstants, Inverse Symbolic Calculator, the Maple identify function, MESearch, OEIS, RIES, and WolframAlpha. There are now several comprehensive web applications, stand-alone computer programs and computer algebra functions that, given a floating point number such as 6.518670730718491, can return concise nonfloat constants such as \,3\arctan2 \ln9 1\, that closely approximate the float.
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