Click on this image to download the software, see below how to get a panel with working controls.
The Slide Rule Explorer User's Guide
The slide rule explorer (SRE)
let's you explore more than 100,000 mathematical expressions that can
be evaluated on a slide rule. You enter an expression and then click
on Find to identify
slide rule procedures that will evaluate that expression.
One way to view the SRE is as
a device to look up the expressions described on
my slide rule
page and in my article
Many Formulas, Journal of the
Oughtred Society, vol. 18, No. 2, 2009, pp. 18-21. However, it
can also be used to explore more restricted scale combinations and to
analyze the capabilities of existing or newly designed sliderules.
To get started
SRE runs on any computer that supports
java. Download the file
SRE.zip, unzip it, and put the files you'll get into
a suitable directory. To start the software connect to that directory and type
java rule
A panel should appear that looks like the image on the top of this web page. We will refer to it as the Control Panel. Using any of the variables x, y, and z, enter a mathematical expression in the Expression Text Field in the second row of the control window and click on the green button labeled Find (or just click on Find if you wish to know how to compute x*y*z). In the Procedure Text Field in the third row of the Control Panel you will find a short description of how to compute your expression with a slide rule. Click on the button labeled Verbose to see a more detailed description appear in the Command Window.
With the SRE, you can enter
expressions and see if and how you can evaluate these expressions with
your slide rule. You can also see a list of expressions that can be
so evaluated, and you can select the scales that are present on the
slide and body of your slide rule. The remainder of this page
describes how to use the controls in the
Control Panel, what kind of sliderule procedures are available,
how to select what scales you assume are present on your sliderule,
and how to log the results of your investigation.
Available Procedures
Depending on whether an expression has 1, 2, or 3 variables,
the SRE investigates one of four
procedures. These are described here briefly, and more fully on
my
slide rule page.
1 Variable: Table Lookup
You align all scales, find the variable x on Scale 1, and look
up the result on Scale 2.
Examples: If the two scales are the same, you won't be surprised to find x as
the result. If Scale 1 is the C scale and Scale 2 the CF scale you
find pi*x. Reversely, if Scale 1 is the CF scale and Scale 2 the C scale you will find x/pi.
2 Variables: Multiplication or Division
These are modeled after the ordinary multiplication and division
procedures which are probably the most frequently employed
slide rule procedures. However, instead of using the C and D scales
exclusively, the SRE considers
the use of other scales as well. For example, suppose you have a
sliderule with an A (x^2) and D (x) scale on the body,
and a K (x^3) scale on the slide, and you want to compute
x^(1/2)*y^(1/3) or x^(1/2)/y^(1/3). Proceed as follows:
Example, Multiplication: Find x on the A scale, align the index of the K scale with x, move the hairline to y on the K scale, and read the result x^(1/2)*y^(1/3) under the hairline on the D scale.
Example, Division: Find x on the A scale, align
with y on the K scale, move the hairline to the index of the K
scale, and read the result
x^(1/2)/y^(1/3) under the hairline on the D scale.
3 Variables
This procedure is obtained from either of the two 2 variable procedures
by replacing the index of scale 2 with a number on another scale.
Example: To compute the triple product x*y*z you can
save one alignment over the ordinary repeated multiplication procedure
by proceeding as follows: Find x on the D scale, align x
with y on the CI scale, move the hairline over z on the
C scale, and read the expression x*y*z under the hairline on
the D scale.
Available Scales
All scales are referenced to the C (on the slide) and D (on the body)
scales. We refer to these two scales collectively as the CD scale, and to a value on
either of those two scales as x. Those scales are logarithmic, the logarithm
of x is proportional to the distance of x from the index of the scale.
The SRE incorporates a total of
13 scales. They are briefly described here, for more information see
Table 1 on the
slide rule page.
The scale menu in the first row of the control panel, next to the quit button, let's you preselect the following combinations:
The SRE proceeds through all
available scale combinations and identifies those (if any) that work for the
current expression. For the 2 variable expressions it then tries
interchanging x and y. For example, x*y = y*x,
and so you can first enter x and then y, or vice versa,
using the same procedure. Thus, having all scales available on body
and slide, the product x*y can be computed in 42 different
ways. For the 3 variable expressions all 6 permutations of the input
variables are investigated. Thus the product x*y*z can be
evaluated in any of 96 distinct ways.
Entering Expressions
Expressions can be entered in the text fields in the second and third
rows of the control panel, or by selecting scale combinations in the
fourth, fifth, or sixth row. For example, if you wonder what you get when using the C
and D scales exclusively select CD on each of the scale menus in the fourth,
fifth, and sixth row of the control panel. (Select Multiply in
the last menu of the 2 variable row.) The expressions
x , x*y, and x/y*z will appear in the associated
text fields. (You can also use these text fields to store expressions
for later examination. In that case make sure not to touch the
associated scale menus after entering your expressions.) To find more ways to evaluate any of those expressions
click on the pertinent
Transfer button, and then
use the
Find,
All,
and
Verbose
buttons, as desired.
When entering expressions in a text field, note that for your input to be effective it needs to be finalized by pressing the Enter key on the keyboard.
Expressions are of the ordinary algebraic kind. By clicking on the button labeled Syntax you get the following information in the command window.
algebraic expression syntax:
x, y, z: can be used as variables, one or two may be missing
+, -, *, /, **, ^: arithmetic operations, ** or ^ is exponentiation
0, 1, 2, 3, 4, 5, 6, 7, 8, 9, pi: the only pure numbers allowed (no multidigit numbers)
properly matching parentheses, brackets, braces, (), [], {}
white space (blanks and tabs) allowed, and will be ignored
available functions:
sqrt, Sqrt, SQRT: square root
exp: natural exponential
EXP or Exp: base 10 exponential
log or ln: natural logarithm
LOG or Log: base 10 logarithm
sin: sine function
asin or arcsin: inverse sin
tan: tangent function
arctan or atan: inverse tangent function
cos: cosine function
sinh: hyperbolic sine function
cosh: hyperbolic cosine function
tanh: hyperbolic tangent function
asinh: inverse hyperbolic sine function
acosh: inverse hyperbolic cosine function (x > 0)
atanh: inverse hyperbolic tangent function
Examples:
z*sqrt(1-y^2), sin(x*y), EXP(1+x^2), {x/[y/z]}
arctan((x^2-1)^(1/2)/(y^2-1)^(1/2)*(z^2-1)^(1/2))
Note that while you can use the usual notations to input the hyperbolic functions and their inverses, they are represented internally in terms of exponentials and logarithm and will be so displayed on output.
If an expression cannot be interpreted, for example because there is a syntax error, there will be an appropriate message in the command window. If the expression cannot be evaluated with the currently available scales the message
no working scale combos foundis printed in the text field in the third row of the control panel, and in the command window.
You can find the documentation for this software online at www.math.utah.edu/~pa/sliderules/SRE.html The file SRE.html also should have come with this software. You can view it locally with your preferred browser. More information about the context of this software is at www.math.utah.edu/~pa/sliderules direct questions to Peter Alfeld at peteralfeld@gmail.com .You may find it interesting to look at the files table1.data, table2.data, and table3.data which come with this software. They contain tables with available expressions in algebraic form, equivalent versions in reverse polish notation, their scale combinations, and information on how to test whether an expression entered by you is equivalent. Do note that modifying these files in any way may interfere with the proper operation of the SRE software!
On the other hand, you want to enter expressions without unduly
limiting their domain. For example, the software will find 2 scale
combos for the expression
sqrt(1-x^2)/sqrt(1-y^2) but 4 for the seemingly equivalent
expression
sqrt((1-x^2)/(1-y^2)). The reason for this is that the first
expression cannot be evaluated in real arithmetic if the absolute
values of x and y are greater than 1, whereas the second expression
can.
Caveats
The SRE is restricted to the four
procedures described on this page. Of course many, in fact,
infinitely many, others are possible. For example, a product of any
number of factors can be computed in a straightforward fashion, but
the SRE will tell you that it
cannot find a scale combination to compute 2*x*y, and it cannot even
recognize expressions with more than 3 variables (and those 3
would have to be x, y, and z).
It is possible that some valid scale combinations are not recognized by the software because some parts of an equivalent expression cannot be evaluated at the random numbers provided in the data files. It is also possible that the software will deem two expressions equivalent when mathematically they aren't. These cases should be rare.
It is well known
to any slide rule enthusiast that there are many restrictions on the
ranges of the numbers that can be entered and manipulated on the
various scales of a slide rule. Scales may be split into two or more
subscales and it is up to you to figure out which is relevant for a
particular calculation. Scales may not contain information about the
location of the decimal point. In any calculation, slide rule based
or otherwise, you have to understand your problem before you compute
an answer, you need to check your answers, and you need to be vigilant
about the possibility of errors. So don't just identify a procedure,
apply it, and assume you have the right answer!
More Info
You can write to me at peteralfeld@gmail.com.