[PDF] Polynomial Solver Algorithm for the TI Graphing Calculators

Intro to the TI calculator TI-82 - Tech4Mathed

This handout will teach four methods of solving an equation on the TI-82 graphing calculator The methods will include two graphing methods, tables and using the solver To answer the previous question, let y = 900 The new equation is 2900 = 2x + 56 x - 53, where x is the number of years after 1980 Solve the equation for x

Utilisation du solveur de la TI 82 Advanced

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TI-82 STATS

82STAT~2 DOC TI-83 Intl English, Title Page Bob Fedorisko Revised: 10/28/05 11:55 AM Printed: 10/28/05 11:57 AM Page iii of 8 TI-82 STATS

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Polynomial Solver Algorithm for the TI Graphing Calculators

TI-84+ Silver Edition The TI-85 and TI-86 appeared in 1992 and 1997, respectively, and both of these calculators are officially discontinued The screen shots shown here are from its built-in polynomial solver menu used to solve the above polynomial Note that complex numbers on the TI-85 and TI-86 are displayed as ordered pairs TI-86

TI-82 STATS MANUEL D’UTILISATION

de Texas Instruments, quelle que soit la nature de l’action, ne devra pas excéder le prix d’achat du présent équipement En outre, Texas Instruments décline toute responsabilité en ce qui concerne les plaintes d’utilisateurs tiers La TI-82 STATS est conforme à la circulaire N° 99-186 DU 19-11-

FIN 1 : CALCULS FINANCIERS - Texas Instruments

©Texas Instruments 2005/ Photocopie autorisée 1 Jean-Louis Balas FIN 1 : CALCULS FINANCIERS TI-82 STATS − TI-83 Plus − TI-84 Plus Mots-clés : intérêts simples, intérêts composés, fonction affine, suite géométrique 1 Objectifs

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Academic Forum 27 2009-10

57
Polynomial Solver Algorithm for the TI Graphing Calculators

Michael Lloyd, Ph.D.

Professor of Mathematics

Abstract

The history of polynomial solvers for the TI calculators (TI-85 through the TI-nspire), and an explanation of a QR-based polynomial solver algorithm is explained.

TIs with Built-In Polynomial Solvers

The TI-83+ appeared in 1999, and the original TI-83+ polynomial application appeared in

2001. This application also runs on a TI-84+ and the screen shots for a newer version of this

Ez are shown here:

TI-84+ Silver Edition

The TI-85 and TI-86 appeared in 1992 and 1997, respectively, and both of these calculators are officially discontinued. The screen shots shown here are from its built-in polynomial solver menu used to solve the above polynomial. Note that complex numbers on the TI-85 and TI-86 are displayed as ordered pairs. TI-86

Academic Forum 27 2009-10

58
The 89 appeared in 1998 and although it was a computer- algebra system (CAS), a polynomial application for it appeared in 2001, the same year the polynomial application was released for the TI-83+.

TI-89 Titanium

The TI non-CAS and CAS nspires appeared in 2007, and the touch pad nspires appeared in

2010. The screen shot here shows finding the zeros using a CAS nspire.

TI-Touch Pad Nspire

Academic Forum 27 2009-10

59

Basic Polynomial Solver Programs

The TI-83 appeared in 1996 and the first version of the polynomial solver program was written for TI-83 and TI-82 by the author the same year. This program hangs indefinitely if any two pairs of complex zeros have similar moduli. For example, the above polynomial has two such pairs of complex zeros causing the program to run indefinitely without successfully finding all the zeros.

Here are the two zeros with

similar moduli that foiled the program.

The program runs successfully

for the polynomial െ͹ݔହ൅ because the two pair of complex zeros have sufficiently different moduli: TI-83

Each row in the output matrix

gives a complex zero. The following table gives a timeline for the TI graphing calculators and the various polynomial solvers. A = flash application, B = basic program or function, C = built-in command

Year 90 91 92 93 94 95 96 97 98 99 00 01

TI 81 85 82 80,92 83 86 73,89 92+,83+ 83+SE

solver C C B-82,83 C C C A83+,89

Year 02 03 04 05 06 07 08 09 10

Academic Forum 27 2009-10

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TI V200 84+,89T nspires Nspire touch

solver C C-89T C-nspire B-nspire

Basic Polynomial Method using Eigenvalues

The non-CAS TI-nspire does not have a polynomial command, but it does have a built-in command for finding all the eigenvalues of a matrix. This suggests the following method:

1. Divide the polynomial by its leading coefficient.

2. Create an upper Hessenburg matrix whose eigenvalues are the same as the zeros of the

polynomial.

3. Use the eigenvalue command.

Recall that a Hessenburg matrix is almost triangular. Specifically, an upper Hessenburg matrix has zeros below the subdiagonal. The polynomial nn nnnaxaxaxaxp 1 2 2 1 13 has the same eigenvalues as the upper-Hessenburg matrix A shown here. nn naaaa Aquotesdbs_dbs3.pdfusesText_6