如何遍历TI-83计算器程序中的列表

Question

I created a set of programs to calculate the area under a graph using various methods of approximation (midpoint, trapezoidal, simpson) for my Calculus class.

Here is an example of one of my programs (midpoint):

Prompt A,B,N
(A-B)/N->D
Input "Y1=", Y1
0->X
0->E
For(X,A+D/2,b-D/2,D)
Y1(x)+E->E
End
Disp E*D

Instead of applying these approximation rules to a function (Y1), I would like to apply them to a list of data (L1). How do I iterate through a list? I would need to be able to get the last index in the list in order for a "For Loop" to be any good. I can't do anything like L1.length like I would do in Java.

Answer 1

You can obtain the length of the list using dim() . That can be found in 2nd->LIST->OPS->dim( . Just make sure that you use a list variable otherwise dim() will complain about the type. You could then index into the list with a subscript.

eg,

{1, 2, 3, 4} -> L1
For (X, 1, dim(L1), 1)
Disp L1(X)
End

Answer 2

The for loop is the simplest way to iterate over a list in TI-Basic, as it is in many languages. Jeff Mercado already covered that, so I'll mention a few techniques that are powerful tools in specialized situation.

Mapping over lists

TI-Basic supports simple mapping operation over lists that have the same effect as a map function in any other language. TI-Basic support for this extends to most basic arithmetic function, and selection of other functions.

The syntax could not be simpler. If you want to add some number X to every element in some list L1 you type X+L1→L1 .

seq(

Most for loops over a lists in TI-Basic can be replaced by cleverly constructed seq( command that will outperform the for loop in time and memory. The exceptions to this rule are loops that contain I/O or storing variables.

The syntax for this command can be quite confusing, so I recommend reading over this documentation before using it. In case that link dies, here's the most relevant information.

Command Summary

Creates a list by evaluating a formula with one variable taking on a range of values, optionally skipping by a specified step.

Command Syntax

seq(formula, variable, start-value, end-value [, step])

Menu Location

While editing a program, press:

2nd LIST to enter the LIST menu RIGHT to enter the OPS submenu 5 to choose seq(, or use arrows.

Calculator Compatibility

TI-83/84/+/SE

Token Size

1 byte

The documentation should do a good job explaining the syntax for seq( , so I'll just provide a sample use case.

If you want the square of every number between 1 and 100 you could do this

For Loop

DelVar L1100→dim(L1
for(A,1,100
A²→L1(A
End

or, this

seq

seq(A²,A,1,100→L1

The drawback of seq( is that you can't do any I/O or store any variables inside the expression.

Predefined list iteration function

Go to the LIST menu and check out all the operations under OPS and MATH . These predefined function are always going to be faster than a for loops or even a seq( expression designed to do the same thing.