Using Lists
Lists allow multiple numerical values to be used in a single calculation. Lists are also used for the statistical analysis functions on the calculator, and for graphing multiple functions at one time.
Entering Lists "{ }":
Lists are entered by pressing the "{" button at the start of the list, entering all the numerical values, calculations, or functions that are wanted in the list into the stack, and then pressing the "}" button to close the list. The braces may also be entered by using the "{" or "}" keys on the keyboard. Additionally, if the list is to be composed of all previous stack entries, the "}" button may be pressed by itself and all previous stack entries will become part of the list.
It is possible to cut and paste comma separated values into lists (with or without braces), but it is necessary to include spaces after the commas or the calculator confuses the commas with grouping marks or decimals, depending on settings. Also spaces or semi-colons may be used as list separators.
Once a list is closed it becomes a single stack entry. A list may be broken back into individual entries again using the "Split" button.
Ordered Lists "( )": - ordered lists are used specifically when each element of the list is to be treated as a different ordinate (i.e., x, y pairs in linear regression ). For general use the "{ }" buttons are preferred, but the "( )" can be used in lists of lists for readability if preferred.
Using a List in a Calculation
When a list is used as part of a calculation, the calculation will be repeated for each member of the list and the result will be a list. For instance, entering the following:
{3 4 5.5} 2 +
Will generate a result {5, 6, 7.5}.
Entering two lists as part of a calculation will result in the first entry in each list being used from for the first calculation, then the second entry, etc. For example, entering:
{1, 2, 3} {.1, .2, .3} +
Will result in the answer {1.1, 2.2, 3.3}. If two lists of different sizes are used in a calculation, the calculator will return an error (note: commas are optional for list entry as long as there is a space after the comma).
Using Lists with Functions
Lists are especially powerful when used in conjunction with functions. See this link for more details.
Using Lists with Graphing
To graph multiple functions in one graph, enclose the functions in a list before hitting the "graph" button. See this link for details.
Special Functions for Lists
There are a few functions on the calculator designed specifically for use with lists that are worth special mention.
Plus Minus "±" - Entering "±" in a calculation will result in the answer being a list with two values - one where "±" is replaced by a plus operation and one where "±" is replaced with a minus operation. For example, entering:
1 3 ±
Will result in the answer {4, -2}.
seqr(i,f,s) - This operation generates a list of evenly spaced numbers within a given range, starting at i, ending at f, with a step size of s between each entry. The values for i, f, and s are taken from the stack when the "seqr(i,f,s)" button is pressed.
seqn(i,n,s) - This operation generates a list of n evenly spaced numbers starting at i, with a step size of s between each entry. The values for i, n, and s are taken from the stack when the "seqn(i,n,s)" button is pressed.
Sum "Σ" - This operation sums the members of a list.
Programming oriented functions: the following functions are useful for using lists inside of a functional program.
- Indexing([]) to return a list member
- Append to combine lists or add numbers into a list
- Count function to return number of entries in list
If you need more list functionality than this, consider writing the developer at john@linstrum.net and let him know what you need.
Using Lists to Calculate a Series
Let's say you wanted to calculate the value of e using the formula:
1/0! + 1/1! + 1/2! + 1/3! + 1/4! + 1/5!
You could do this by entering the following:
0 5 1 seqr(i,f,s) ! 1/x Σ
The first 4 entries generate the list {0, 1, 2, 3, 4, 5}. The next two entries turn that into {1/0!, 1/1!, etc..}. Finally, using the Σ button causes the whole list to be added together to get the sum of the series.
Statistics
Lists are also used in statistics calculations.