Texas Instruments voyage 200 User Manual - Page 893

zeros( ) MATH/Algebra menu zeros(expression, var) ⇒ list zeros(aù x^2+bù x+c,x) ¸ { } Returns a list of candidate real values of var that make expression=0. zeros() does this by ë( bñ-4øaøc-+b) bñ-4øaøc-b 2øa 2øa computing exp8list(solve(expression=0,var),var). aù x^2+bù x+c|x=ans(1)[2] ¸ 0 For some purposes, the result form for zeros() is more convenient than that of solve(). However, the result form of zeros() cannot express implicit solutions, solutions that require inequalities, or solutions that do not involve var. Note: See also cSolve(), cZeros(), and solve(). exact(zeros(aù (e^(x)+x) (sign (x)ì 1),x)) ¸ {} exact(solve(aù (e^(x)+x) (sign (x)ì 1)=0,x)) ¸ ex + x = 0 or x>0 or a = 0 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}) ¸ r 2 r 2 Extract row 2: ans(1)[2] ¸ r2 3ør  2 ë 3ør 2  ë 23ør Appendix A: Functions and Instructions 895