Texas Instruments TI-89 Tip List page 417

factor() function algorithm.
The methods include the well-known factorizations of binomials and quadratics, together with methods
described by Geddes, Czapor and Labahn, "Algorithms for Computer Algebra", Kluwer Academic
Publishers, Boston, 1992. Laguerre's method is used for approximate polynomial factorization. (Press
et. al: "Numerical Recipes" Cambridge University Press, 1986.)
factor( returns the rational number factored into primes and a residual having prime factors that exceed
65521.
I have two TI-92s that simplify the same expression differently.
Why? With slight modifications that have been made to the TI-92 ROM there have been some very
specific examples that do not evaluate the same from version to version. Other problems may
evaluate differently or not at all. A change may not have been made in the TI-92 symbolic
manipulation code to directly correct this example. It most likely was an indirect result of changes
made for other reasons. You will also be able to find examples of problems that will not evaluate on
later TI-92's that would on earlier versions. This is the nature of dealing with CAS software.
limit() function algorithm.
Limits of indeterminate forms are computed by series expansions, algebraic transformations and
repeated use of L-Hopital's rule when all else fails. Limits of determinate forms are determined by
substitution.
Similar expressions simplify differently - why?
The goals of default simplification are to ensure that critical cancellations occur, without unnecessarily
applying drastic transformations that might consume an unacceptable amount of time or exhaust
memory. Simplification is necessarily a compromise between these conflicting goals.
Minor appearing differences between expressions can cause dramatic differences in the default
simplification path. For example, there is an effort to retain most polynomial factoring, but adding a
term to a factored polynomial can cause the polynomial to be expanded. Similarly, there is an effort to
avoid common denominators, unless denominators share a common factor, so some fractions combine
while others don't. As another example, x orders more main than y, so merely changing the names of
variables can affect how much expansion and common denominators occurs.
Also, the default simplification path can depend strongly on the mode settings.
There are so many potentially useful mathematical transformations that it is not feasible to fit them all in
the limited amount of program ROM. Consequently, a useful transformation that you desire might not
be in the TI-92. For example, x*x^n will not simplify to x^(n+1) because this is not one of the rules built
in. Another example is integral(x^(n-1),x) will simplify to x^n/n, but integral(x^(n+1),x) will not simplify.
Simplifications - why are some so slow?
Some operations can be inherently slow for rather simple operands. Examples include factoring,
simplification of fractional powers, and cancelation of hidden factors between non-numeric numerators
and denominators. In some cases, intermediate expressions can become quite large despite modest
inputs and final results.
If a problem is taking an unacceptable amount of time:
1. Try using a different mode, such as diamond-enter versus enter.
2. Try using an appropriate alternate function, such as nSolve() versus solve() or nINT() versus
integral().
B - 6