Texas Instruments TI-89 User Manual - Page 896

You can also (or instead) include unknowns that do not appear in the expressions. For example, you can include z as an unknown to extend the previous example to two parallel intersecting cylinders of radius r. The cylinder zeros illustrate how families of zeros might contain arbitrary constants in the form ck, where k is an integer suffix from 1 through 255. The suffix resets to 1 when you use ClrHome or ƒ 8:Clear Home. ans(1)[2] ¸ r2 ë 23ør zeros({x^2+y^2ì r^2, (xì r)^2+y^2ì r^2},{x,y,z}) ¸ r 2 3ør 2 @1   r 2 ë 3ør 2 @1 For polynomial systems, computation time or memory exhaustion may depend strongly on the order in which you list unknowns. If your initial choice exhausts memory or your patience, try rearranging the variables in the expressions and/or varOrGuess list. If you do not include any guesses and if any expression is non-polynomial in any variable but all expressions are linear in the unknowns, zeros() uses Gaussian elimination to attempt to determine all real zeros. If a system is neither polynomial in all of its variables nor linear in its unknowns, zeros() determines at most one zero using an approximate iterative method. To do so, the number of unknowns must equal the number of expressions, and all other variables in the expressions must simplify to numbers. Each unknown starts at its guessed value if there is one; otherwise, it starts at 0.0. Use guesses to seek additional zeros one by one. For convergence, a guess may have to be rather close to a zero. zeros({x+e^(z)ù yì 1,xì yì sin(z)},{x,y }) ¸ ezøseizn+(1z)+1 ë (sin(z)ì ez +1 1) zeros({e^(z)ùyì1,ëyìsin(z)}, {y,z}) ¸ [.041... 3.183...] zeros({e^(z)ù yì 1,ë yì sin(z)}, {y,z=2p}) ¸ [.001... 6.281...] ZoomBox CATALOG ZoomBox Displays the Graph screen, lets you draw a box that defines a new viewing window, and updates the window. In function graphing mode: 1.25xù cos(x)! y1(x) ¸ ZoomStd:ZoomBox ¸ Done 1st corner 2nd corner The display after defining ZoomBox by pressing ¸ the second time. 896 Appendix A: Functions and Instructions