| Yellow Label | | | Yellow Function
|
| M|P|R | |
| Each tap advances MAINview from Mixed Fractions to Pure
Fractions to Residues then starts over at Mixed Fractions. |
| XCH | |
| Exchanges field F1 and field F2 if the active fCell
contains an integer or residue; or exchanges just the active fCell with its mate if they
are a decimal pair. |
| APRX | | |
Approximates the active fraction by a simpler fraction. If the active
fCell has a decimal point, the approximating stack exactly matches all the given
decimal digits, accurate within 1 in the last given digit (up to 7 digits).
Otherwise the approximation is the best "kitchen fraction" with
denominator 2,3,4,6,8,or 16. |
| DUP | | |
Duplicates the active number (copies it to its mate). If the active fCell
is an integer then its whole field gets duplicated; if the active fCell and
its mate are a decimal pair then just the single active Fcell gets
duplicated. |
MAX | | | Loads
the active fCell with the largest integer that 32-bit computers natively
represent, alternating between pMAX (largest positive) and nMAX (largest
negative). |
| PROG | | |
Switches from the MAIN to the programming view; brings up the system
keyboard so you can edit the frrrNOTE. The note can contain an applet that
interacts with all the MAIN subviews (hInfo, hShow, etc.) using CF
operations. The PROG view also gives access to the frrrFile system via a
filePicker that plants a file command into a button that performs the created
command when you tap it. The file commands are : ?|n| peek, <|n| get, >|n|
save, and -|n| zap (delete). The Get and Save operations handle the numeric
fCells and the main storage registers (the first hundred of the up-to-2000
hpNumber registers (hp s-registers)), but none of the hpString
registers. |
| EXEC | | |
Executes the active Composite Function operation closest to the top of
frrrNote and may continue from there, depending on the CF {{bracket}}
decorations. |
| WEB | | |
Opens a web view into Frrraction's website http://www.frrraction.com
to keep you up-to-date with the App. |
| B|O|Z | | |
Loads simple numbers into the active fraction. With each touch it cycles
from Blank=0+0/0 to One=0+1/1 to Zero=0+0/1 then back to Blank. |
| GCD | | |
Shows the greatest common divisor of the active numerator and denominator.
Also shows the decimal forms of both fields if Frrraction is displaying Mixed
fractions. Alternates greenly with the RDC function. |
| RDC | | |
Cancels all common factors between the active numerator and denominator
to reduce the active stack to lowest form. Alternates greenly with the GCD
function. |
| D|F | | |
Converts between fractions and decimals. If the active number field is a
fraction (all integers) then it converts the field to a decimal in F.active.i
with 0's in F.active.n and F.active/d. If the active fCell is decimal, it
converts it into a fraction using the standard inefficient conversion to fill
the whole active field. |
| TIK | | |
Stops|Restarts the key-click sound. (The sound itself is licensed
from: http://www.freesound.org/forum/profile.php?mode=register) |
| CHS | | |
Changes the sign of the integer, decimal, or residue in the currently
active fCell. |
| INV | | |
Calculates the inverse (the reciprocal, 1 over the numeric value) of
the fraction in the currently active field, or of the decimal or residue
in the currently active fCell. |
| STO | | |
Stores the active fraction into rational storage Register Rn (if active
fCell is integer) or active decimal into decimal storage register Dn (if the
active fCell is decimal) with n specified by the next digit-key
tapped. |
| RCL | | |
Recalls rational storage Register Rn into the active field (if active
fCell is integer) or decimal storage register Dn into only the active fCell
(if the active fCell is decimal) with n specified by the next digit-key
tapped. Empty registers contain 0+0/1. |
Each of the three parts of a mixed fraction can be
independently positive or negative, but there is always an implied
addition+sign between the integer part and the stack. Frrraction's
preferred sign combinations are: integer and numerator should have the same
sign and the denominator should always be positive. It gets to that condition
at its first opportunity—certainly after y-tapping M|P|R. The only
exception is a pathological case called "the Nemesis". More about
that fascinating case later.
 |
M|P|R BackgroundTopic:
We saw M|P|R do sign-corrections in the previous section of the guide,
but actually, in transforming from Pure through Residue to Mixed, M|P|R did two other
things too:
It made F1n smaller, to make F1's stack into a
proper fraction, meaning that its numerator became
smaller than its denominator, so the stack became truly a fractional
number—less than one. Then, to preserve the numeric value of the
fraction while reducing F1n, M|P|R made up for the reduction by
simultaneously increasing F1i — a nice balancing act. Thus, 304/82
became 3 + 58/82.
The other thing M|P|R did is put the stack into reduced
form, which means eliminating all factors shared by the numerator and
denominator. That converted 3 + 58/82 into the final, preferred,
result: 3 + 29/41.
[Editor's note: Internally, Frrraction always begins all
fraction-processing by reducing the involved stacks if possible, then doing
whatever else the task requires. So in the above case it would have first
reduced 304/82 to 152/41, then converted that to 3 + 29/41. By
working with smaller integers when possible, it avoids some numeric
overflows that could occur with larger numerators and denominators.] |
You can abort the HINT operation by tapping YellowKey one more time,
changing the status back to W.
By now you have noticed that every time you tap
YellowKey, Frrraction temporarily covers the Notes area with a brief
description of what to expect next. Here's welcome news about that:
The three consecutive taps Y Y Y which start-then-abort the HINT
operation also serve to stop those repeated YellowKey status reminders for
the rest of this Frrraction session. (The next time you run Frrraction from a
cold start, the reminders will be back, so remember Y Y Y.)
Like several of the other yellow functions,
M|P|R has 'cyclic action': Using it several times
in a row does a repetitive series of actions, like
Mixed-to-Pure-to-Residue-to-Mixed-to-Pure-to... etc. Other such
functions are MAX, GCD, and B|O|Z.
 | TryIt (start in Pure mode with
152/41 in F1):
Y-tap M|P|R (Remember, that means
tap YellowKey then tap the M|P|R-key). Starting in Pure mode,
this switches the display to Residue mode. Notice that Frrraction correctly
keeps F1i and F2i hidden, since modular fields also need only two cells: one
for residue and the other for modulus.
Now yTap CHS and notice F1. Ytap CHS again, notice F1
again. Do DUP CHS +(add) and notice — the residue plus its negative
is indeed zero. Do +(add) again to confirm that 0 plus the original residue
is the original residue. If you're rusty on residue arithmetic, then the
sequence 152 CHS 12 CHS 29 CHS 12 might be disconcerting. It's correct, and
Frraction Guide's HighSchool course on residues will make it all
clear.
If you're new to residues, introductions are readily available on the web and
here's an intermediate
treatment on Frrraction's site.
If you're OK with residues, do this simple example and predict the
results of each step before having Frrraction do it:
Starting in mixed fraction
mode, put the fraction
3 + 10/8 into F1; convert it to a pure fraction; yTap INV,
then MPR into residue mode. Field1 is now a residue, modulo...modulo
what? — any surprises from M|P|R? yTap DUP then INV; then tap x
(residueMultiply) — note that 13 surely was the reciprocal of 4 modulo 17.
ResidueMultiply again — note that 1 surely was a multiplicative identity element
modulo 17. Let's try that again, but with CHS instead of INV:
Staying in residue mode, ytap CHS — reciprocal equals negative!? That's
unusual even for residues, but not impossible; confirm it in this case by
adding the 4 (mod 17) that's still in Field2 (tap + for residueAdd). Then
add again and CHS once more, to restore Field1 to
where we started when we first entered residue mode. Convert Frrraction back to
mixed fraction; ytap INV one last time — any final surprises?
Return to MixedFraction mode with 3+10/8 in F1 and try taking
the INVerse once — then INV again. Repeat INV,INV in Pure mode and
again in Residue mode.
|
There. You passed Frrraction 101. You now know the App's basic
idioms.
