Texas Instruments TI-92 Owners Manual - Page 537

zeros({expression1, expression2}, {varOrGuess1, varOrGuess2 matrix Returns candidate real zeros of the simultaneous algebraic expressions, where each varOrGuess specifies an unknown whose value you seek. Optionally, you can specify an initial guess for a variable. Each varOrGuess must have the form: variable - or - variable = real or non-real number For example, x is valid and so is x=3. If all of the expressions are polynomials and if you do NOT specify any initial guesses, zeros() uses the lexical Gröbner/Buchberger elimination method to attempt to determine all real zeros. For example, suppose you have a circle of radius r at the origin and another circle of radius r centered where the first circle crosses the positive x-axis. Use zeros() to find the intersections. As illustrated by r in the example to the right, simultaneous polynomial expressions can have extra variables that have no values, but represent given numeric values that could be substituted later. Each row of the resulting matrix represents an alternate zero, with the components ordered the same as the varOrGuess list. To extract a row, index the matrix by [row]. zeros({x^2+y^2ì r^2, (xì r)^2+y^2ì r^2},{x,y}) ¸ Extract row 2: r 3ør  2 2  r ë 3ør 2 2  ans(1)[2] ¸ r2 ë 23ør 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 @k, where k is an integer suffix from 1 through 255. The suffix resets to 1 when you use ClrHome or ƒ 8:Clear Home. 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 520 Appendix A: Functions and Instructions