loading a program in emu48 - Charles HAMEL

Transcription

Copyright Charles HAMEL aka Nautile 2009 January
PAGE 1
of 7
LOADING A PROGRAM IN EMU48
IFF you have trouble running the EMU48 downloaded from my site you have to instal
your own EMU48 from scratch so just go
http://www.hpcalc.org/search.php?query=EMU48
there download both
*** EMU48 1.47
http://www.hpcalc.org/details.php?id=3644
*** CASEY’s HP48 Graphics http://www.hpcalc.org/details.php?id=3635
Create a folder , say EMU48TEMP
Unzip EMU 1.47
Run the install of EMU48
In the folder of your newly installed EMU48 unzip CASEY’s graphics : this will give
you several rendering of an HP48
The best IMO is UPLIFTER’s GX by MARK CUBBEDGE based on a photo of a
real HP48 ( JEMAC’s)
It only remains to install my programs.
Juts download them from my site and put them as I did in a folder : MyPrograms
that you will create in EMU48
RUN your EMU48 ( read other files such as EMU48 STARTER INSTALLING
YOUR EMU48…… ( remember in the download zone of EMU 48 on my site are a
number of PDF that give you user’s tips )
Now you will install the Uplifter HP as :
PAGE 2
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Now running your own HP Uplifter :
The Goddess is a bit naked !
We will have to dressed her a bit. ( here it is mine so it is already decently attired )
In the MENU OPEN EDIT AND SELECT LOAD OBJECT.
This will give you something like that :
PAGE 4
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As you recall we have put ours programs [ .HP ] files, in MyPrograms, so open this
folder.
There we SELECT the .HP FILE that interest us, say BALG.HP.
Double click on it to save it inside the HP48 emulator.
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The whole file, in this case a DIRECTORY has been put on THE STACK
It remains to STOre it.
For that we need to NAME IT.
SO first use the first key of the third row ( from top ) to put [
the stack as in
‘ ‘
] at the bottom of
Now we have to write the NAME.
Press twice the ALPHA key ( just above the Violet Left Arrow and under the marge
ENTER key. This will put an ALPHA reminder in the uppermost part of the screen.
Now the keys are “loaded ands locked” to gibe ‘letters’.
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Now TYPE THE NAME :
NAME HAVING BEEN ENTERED you still have to UNLOCK the ALPHA by
pressing once on the ALPHA key.
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Now that there is no ALPHA LOCK active you may press STO key ( second one on
the third row from top ).
This put the BALG directory in the MENU at the bottom of the HP48 screen :
You are done with the LOADING OF THE PROGRAM.
INSTALLING YOUR EMU48
In the EMU Folder RUN EMU48.EXE
You should get this result :
Just push the OK button and get that :
Open the lowermost rolling menu where you see Casey’s GX with…….. :
And chose Uplifter’s GX
That will lead you there
Just say OK in the above and you will get the calculator ;
answer NO to the Try To Recover Memory ? question
In the File of Menu open the rolling list menu and make use of « OPEN »
To get this screen
Answer NO to Do You want to save changes ?
THIS IS VERY IMPORTANT or you will destroy the file you are attempting to load !
Activate the MyEMUsiteE48
Answer YES to the Do you want to reload this documents ?
Use the OK button.
You will get :
This is the HP48GX emulation with the programs loaded
EMU48 STARTER
When you are in the download zoen provided by the link in PUBLICATIONS-2 page you
should have these files and folders ( additions will be made )
THE EMULATOR HAS BEEN FULLY INSTALLED BY MYSELF AND IS RUNNING AS IT
IS.
YOU DO NOT HAVE ANYTHING TO DO EXCEPT RUNNING THE PROGRAMS
The PDF files here are as help for you
ROW-BRAINLESS ; ROW-Umanual ; SLIDE-RULE… are for the ROW-CODED KNOTS
SCH PROGRAM USER START TIPS was with the first programs released so it should be
read first it is for COLUMNS and COLUMNS&ROW coded knots
Emu48 is the « heart » of the
download , its engine. Wait a
moment
HP-MANUALS will give you what
you see ------------------------
I suggest that in a first prudent step
you use only the
HP48-QuickMan.pdf it should be
more than enough to gives your the « working » of the calculator HP 48GX I use.
Now you may open the FOLDER Emu 48 ( that is the only part that you have to download in
full )
What you will see then is on the next screen capture :
LEAVE ALONE
EVERY SINGLE
FILE FOR NOW
EXCEPT
EMU48.EXE
(and
EMU48.TXT)
Emu48asc, Macro, Asciibin
are of no interest for you.
MyPrograms is the
container for the programs
that I am sharing for the
moment.
It is theer that you will put
future programs I care to
share and it is from this
folder that you will load
them into the emulator
RUN EMU48.EXE
( third from the bottom
here)
DON’T USE MKE48.EXE
nor any other .EXE filere
by mistake !
Running EMU48.EXE will
give you what is on the
next capture
Just click the OK
button
This will give you THE EMULATOR IN
WORKING ORDER
You see FILES and
FOLDERS ( here only
FOLDERS called
DIRECTORIES IN HP
PARLANCE
SCHR
SCHK
MOBIU ( name can be
longer but only the first
letters are visible . Leran
in HP manual how to put
the full name on the firts
level of the stack : stack
is 1 : 2 : 3 : and so
on ( learn withHP manual how to go in the stack )
A click ( for that the emulator allows the use of the computer mouse put beware many
commands are only possible from the emulator as if it was a real 3D HP48 and ) study the
emulator readin EMU48.TXT that is in the EMU48 folder.
Open SCHR by clicking on it.
You will then have :
Just activate the
program you want
Here PGR ( followed
eventuall by PGR2
when you have the
results of PGR put in
the stack.
VERSION 2008 - DECEMBER 31
Charles HAMEL aka Nautile
page 1 on 6
SCH PROGRAM USER START TIPS
This can be used not only with one of the HP48 calculator still around ( now quite costly on eBay! And
elsewhere) but also with the Windows EMU48 , an emulator of the famous HP48GX using
the HP RPL language ( the acronym stands for Reverse Polish Lisp , a mix of Reverse Polish Notation
and LISP – Lot of Insane Stupid Parenthesis )
Note that an E48
exist for the Mac persons !
This particular program is to be use for knot following
the THK SHADOW ( or THK cordage route ) not
forcibly with the coding of the TRUE THK O1 U1 / U1
O1. ( see my web pages on THK for clarification )
THK are both ROW and COLUMNS ( SCHAAKE
frame of reference : horizontal mandrel with BIGHT
rim in the left and on the right but this is intellectual
myopia as for the vertical cylinder frame of reference
with Bight rim Top and Bottom Row become Column
and Column become Row.
It is QUITE PREFERABLE TO USE A NON
MYOPIC language which will stay constant
between the two frame so I think in terms of
- parallel Bight for Columns on mandrel and
Row on cylinder
- inter-Bight coding for Rows on mandrel and
Columns on cylinder
So SCHAAKE’s Row are for me Inter-Bight code
and Columns are Parallel Bight code and there is
no need to change the words if you go to cylinder
frame of reference.
Back to topic : True THK are BOTH ROW and
COLUMNS coded so this program can do them BUT
only because of the Columns coded and though it
will do knots that are only Column-coded it will not
do knots that are
Only Row coded ( because then the coding
sequence change not only from Odd to Even HalfPeriods but also between Odd Half-Periods and
between Even Half-Periods. I will attempt a program
for them later ( in the midst of clarifying the
mathematics of that )
-
In FOLDER HP-MANUALS :
a quick start manual ( small )
a ‘normal’ user manual a lot more detailed
a “programmer’ user manual explaining USER RPL
(there is a MACHINE RPL)
I will here just give what is strictly necessary to use the EMU48 once the application is opened
In the download you get an already installed EMU48 in full working order but with an ‘arrangement of
the original HP48 aspect to conform with the landscape disposition of computer screen
page 2 on 6
FOLDER EMU48 :
Open this folder
Eventually read FILE EMU48.TXT
To start the application : EMU48.EXE will do that for you after being clicked upon
FOLDER ‘My Programs’ is where I will put my programs
Now the application is opened as under ( my choice of working image, there are other available )
HAVE AN ATTENTIVE LOOK AT THE
KEYBOARD PART
FOR THE MOMENT YOU WILL NEED ONLY A
PART OF IT
DO NOT HESITATE TO HAVE A QUICK LOOK
AT THE SMALLER USER MANUAL IN
FOLDER : HP-MANUALS
page 3 on 6
If you get a message for error following an invalid or illegal entry just key the ON once
{ } : to open this list use the violet left arrow + lowest right corner of keyboard key
you are inside the { } now enter your code ( of for the MOEBIUS the number of Stands )
using 0 ( zero not letter “o” ) for UNDER , LOW crossing and 1 for OVER , HIGH crossing with an
empty space between each digit ( space key is fourth on lowest row in keyboard )
example given { 1 0 0 1 1 ……1}
NOTE : the coding of crossings is the one seen by the SPart-Wend VECTOR on the
FIRST HALF-PERIOD in the FINISHED knot that is coming from the Left / Bottom
BIGHT rim towards the Right/Top BIGHT rim on the first half-period laid to make the
knot.
IMPORTANT : When asked for an input : coding sequence, choice for mandrel of
cylinder….etc the program HALT.
Make your entry, eventually make a correction then use key ENTER to enter your input
You may still make a correction, program is still HALT ( indication at the top of the
calculator screen ) to make it resume you have to use the function CONT which is
activated by Violet Left Arrow + Key ON ( lowest key in keyboard left corner). The
program will continue.
RESULTS will be put in the STACK
KNOT IS MADE CCW ( counter-clockwise )
page 4 on 6
TO ACCESS THE STACK ABOVE THE 4 LINES ON THE SCREEN : use the UP arrow which is on
the uppermost row of keyboard Fifth key they continue with either the UP or DOWN arrow to circulate
in the STACK
To get out of the STACK just ON once
CAREFULL the White Left arrow : last key on the fifth row from top will drop the item in level 1 of the
STACK. ( in case of false manoeuvre : Immediately use Green Right Arrow + UNDO which is the
EVAL key o : third on the third row from Top )
TO READ ENTIRELY A LONG ENTRY IN STACK put the index on it and use Violet left arrow + EDIT
in +/- key (the one on the immediate right side of the big ENTER key )
Then ENTER to send it back on the STACK
NOW FOR THE PROGRAMS :
To OPEN a FOLDER or a data FILE or to RUN a program FILE or : put the mouse on it and left click
OPEN FOLDER THK
Inside , among other, are :
READ ( use arrow to make it down and up ) will give you sketchy tips
DO NOT USE ( for the moment at least , till you are well use to the emulator which is set to
AUTOMATICALLY save its last configuration on shut down ) ANY OTHER FILE THAN READ /
PGR3 PGR2 PGR
BE ATTENTIVE HERE
FIRST to BE RUN MUST BE EITHER PGR OR PGR3
PGR
WILL DO ONLY TRUE O1-U1 THK
Ask you for LEAD and BIGHT NUMBER
Ask for choice MANDREL OR CYLINDER : This DOES NOT CHANGE THE CODING OF
CROSSING as in any case we will use 1 for OVER and 0 for UNDER instead of / and \
Had we used / and \ it would have been necessary to keep in mind that
/ means UNDER in a CYLINDER frame of reference and OVER in a MANDREL frame of reference
\ means OVER in a CYLINDER frame of reference and UNDER in a MANDREL frame of reference
This is an unnecessary complication and 1 and 0 are more practical ( the more so because ther are
the only available coding for ROW coded knots as the / \ cannot be used.
OVER stay 1 and UNDER stay 0 in any case ! I have just left / and \ in the result for the fum but
providing and automated changing using the choice given in mandrel/cylinder and will only be valid for
the frame you have chosen while the coding in O and 1 will allow use in any frame.
IN THE STACK THE RESULTS WILL BE : ( 7L 5B
LEVEL 5 :
LEVEL 4 :
LEVEL 3 :
LEVEL 2 :
Cylinder)
{ / \ / \ / } coding in / & \ terms ( should be at level 2.5 ! )
{ 0 1 0 1 0 1 } coding for LEFT/BOTTOM
{ 2 4 1 3 0 2 } complementary periodic bight order
{ 2 0 3 1 4 2 } periodic bight order
{ 1 0 1 0 1 0 } coding for RIGHT/TOP
LEVEL 1 :
STRICTLY ( to be ‘in phase’ with what SCHAAKE wrote. ) IT SHOULD HAVE BEEN
LEVEL 3 :
LEVEL 2 :
{0241302}
{2031420}
page 5 on 6
PGR3
WILL DO A THK SHADOW / CORDAGE ROUTE COMPLYING KNOT BUT WILL ALLOW YOU TO
ENTER YOUR OWN CODING.
You may now used that with pencil and paper and work yourself the coding for each b * 2 Half Periods
or make it easy and now running directly after
PGR2
TAKING THE RESULTS EITHER FROM PGR OR PGR3 DIRECTLY IT WILL COMPUTETHE
CODING FOR EACH OF THE B * 2 HALF-PERIOD
PUT AS RESULTS IN THE STACK
LEVEL 1 : you get the PIN STEPS already computed as
{ A ; B ] a and B may be equal or not
For 7L you get PINS STEP : { 3 ; 4 } ( for an EVEN number of LEAD A and B will be equal )
My preference is to put the largest on the Top Bight rim ( Left rim on mandrel ) and the lowest on the
Bottom Bight rim ( Right rim on mandrel) but it will be equivalent to do it the other way except that
( 7L 5B Cylinder) L>B L-B=2
BOTTOM TOP
will be
BOTTOM TOP
Pin 1
Pin 5
Pin 1
Pin 4
Pin 3
Pin 2
Pin 3
Pin 1
Pin 5
Pin 4
Pin 5
Pin 3
Pin 2
Pin 1
Pin 2
Pin 5
Pin 4
Pin 3
Pin 4
Pin 2
Pin 1
Pin 1
th
LEVEL 2 ( LEVEL 1 if you DROP the PINS STEPS ) will have the B*2th ( 10 ) Half-Period coding
th
LEVEL 2 will have the B*2-1th ( 9 here ) coding and so on in going up
So still for ( 7L 5B Cylinder) L>B L-B=2
LEVEL 11 : HALF-TURN WRAP : 1 ( give you the number of 180° wrap in the first Half-Period )
LEVEL 10 : { 0 } SECOND Half Period one UNDER crossing
LEVEL 9 : { 0 } Third H-P
LEVEL 8 : { 0 0 } Fourth H-P
LEVEL 7 : { 0 0 } Fifth H-P
LEVEL 6 : { 0 0 0 1} Sixth H-P
LEVEL 5 : { 0 0 0 1} Seventh H-P
LEVEL 4 : { 0 0 1 0 1 } Eighth H-P
LEVEL 3 : { 0 0 1 0 1} Ninth H-P
LEVEL 2 : { 0 1 0 1 0 1} TENTH and last Haf-Period ( ORIGINAL CODING ENTERED )
LEVEL 1 : PINS STEP: [(3 ; 4 )
Now to clarify a bit the Number of Wrap notion and Free run another example
Cylinder 13L 4 B L>B L-B=9
PGR RESULTS :
LEVEL 5: { / \ / \ / \ / \ / \ / \ }
LEVEL 4: { 0 1 0 1 0 1 0 1 0 1 0 1 }
LEVEL 3: { 3 2 1 0 3 2 1 0 3 2 1 0 }
LEVEL 2: { 0 1 2 3 0 1 2 3 0 1 2 3 }
LEVEL 1: { 1 0 1 0 1 0 1 0 1 0 1 0 }
page 6 on 6
PGR2 RESULTS :
LEVEL 9: HALF-TURN WRAP: 3 FIRTS H-P : FREE RUN with 3 ( 180° * 3 ) half turn before reaching
nd
the pin. LEVEL 8: { 1 1 1 } 2 H-p
rd
LEVEL 7: { 1 1 1 } 3 H-P
th
LEVEL 6: { 0 1 0 1 0 1 } 4 H-P
th
LEVEL 5: { 0 1 0 1 0 1 } 5 H-P
th
LEVEL 4: { 1 0 1 1 0 1 1 0 1 } 6 H-P
th
LEVEL 3: { 1 0 1 1 0 1 1 0 1 } 7 H-P
th
LEVEL 2: { 0 1 0 1 0 1 0 1 0 1 0 1 } 8 and last H-P
LEVEL 1: PINS STEP: (6;7) it also means a FREE RUN
If you happen to find as result an EMPTY LIST such as { }
EXAMPLE 5L 6B L<B B-L=1
PGR RESULTS
LEVEL 5:
LEVEL 4:
LEVEL 3:
LEVEL 2:
LEVEL 1:
{ /\/\}
{0101}
{1234}
{4321}
{1010}
PGR2 RESULTS :
LEVEL 13: HALF-TURN WRAP: 0 ( the cordage goes directly form the bottom pin to the top pin
without even making a half-turn around the cylinder FIRST H-P Pin 1 bottom to Pin 4 top
LEVEL 12 : { } no crossing ; FREE RUN SECOND H-P
rd
LEVEL 11: { } no crossing ; FREE RUN 3 H-P
th
LEVEL 10: { 0 } first crossing UNDER ) is only in the 4 H-P
th
LEVEL 9: { 0 } 5 H-P
LEVEL 8: { 0 1 }
LEVEL 7: { 0 1 }
LEVEL 6: { 0 1 0 }
LEVEL 5: { 0 1 0 }
LEVEL 4: { 0 1 0 1 }
LEVEL 3: { 0 1 0 1 }
LEVEL 2: { 0 1 0 1 }
LEVEL 1: PINS STEP! ( 2 ; 3 )
Pin 4 top to Pin 6 bottom
Pin 6 bottom to Pin 3 top
Pin 3 top to Pin 5 bottom
Don’t hesitate to propose amelioration for this “starting document” or even writing one and give it to me
!
ENLARGEMENT(S) OF THK
WITH HP-RPL AND HP48GX or EMUlator48
I have now enhanced the first program with a second one
PGR
For the « price of entering your « starting » THK
LEAD NUMBER and BIGHT NUMBER you will get in the HP stack ( explore it
bottom to top ) the resulting first enlargement available that for :
ENLARGEMENT PROCESS
TYPE I or RIGHT OF THE SPart-WEnd vector
ENLARGEMENT PROCESS
TYPE II or LEFT OF THE SPart-WEnd vector
The only control of entry is for G.D.C = 1
PGR2 or the reeling backward of the THK
Still for the modest price of entering
LEAD NUMBER and BIGHT NUMBER don’t do under “3” as entry
You will get on the stack ( explore it )
-
the original THK LEAD and BIGHT numbers
the LEAD and BIGHT numbers of the « ROOT » THK from what it can be made
and the type of the enlargement E1 or E2
REMEMBER : the entry put the progran on HALT and you have to make it CONT by
pushing « violet left arrow » and « ON » see HP manual
Copyright Ch HAMEL aka nautile ( much inspired by SCHAAKE & TURNER
Page 1 of 6
2009 Jan 8th
V61-0
THE BRAILESS RECIPE
(missing all the intelligent and articulate reasoning and justification given by SCHAAKE & TURER.)
How to prepare your slide-rule without having the first understanding of
the “why” of the “how”
Doing here what I heartily hate : giving a half-baked idiot recipe : “ do that and don’t think about
why”
Page 2 of 6
2009 Jan 8th
V61-0
Still that seems to be much in demand as it avoid painfully engaging brain gears to follow good minds
as SCHAAKE & TURNER’s as many seem loath to do !
*** On the mobile part of the slide rule put a number of round marks in line :
L round marks followed by 2 * REP –1 marks. ( for a 17L 14B and 7 as REP as in the example it
will be 17 + ( 7 * 2 – 1 ) ( recall priority of computing moves µ is done before - ) == 17 + 13 = 30
Now two round marks will be transformed in STAR marks.
The second ( read from L to R ) round mark become a star and the round mark at the Lth position also.
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
then
.
*
. . . . . . . . . . . . . .
*
. . . . . . . . . . . . .
*** Take the coding pattern of the very first half-period ( HP ) in the FIISHED knot or diagram.
This is your Coding Sequence ( CS)
U - U - O - O - U - O - U - O – O - U – U- O -U- O- U- U
For computing I used
0 - 0 - 1 - 1 - 0 - 1 - 0 - 1 - 1 - 0 – 0- 1 - 0 – 1 - 0 - 0
*** From this CS extract the Repeating Coding Sequence ( always, absolutely always keep in
mind the modular mathematics of clockwork mathematics ).
To do that the REPEAT (REP) number will be use.
This REP number is not computed but simply read on the diagram of the finished knot.
It is the Pattern or ‘motif’ grand period, the number of step after which you fall on a HP with the same
sequence of coding .
So using a (2 * REP) length extract from the CS, commencing at the very first left position, a
2*REP long Repeating Coding Sequence ( RCS )
U - U - O - O - U - O - U - O – O - U – U- O -U*** Below this RCS set REP vertical lines at the even positions for the marks line or from the
RCS frame of reference every two step starting at the first code
either from the mark line frame of reference
.
*
. . . . . . . . . . . . . .
*
. . . . . . . . . . . .
U - U -O - O -U - O - U - O – O -U U- U -O- U
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or from the RCS frame of reference
U - U - O - O - U - O - U - O – O - U – U- U -O- U
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The number of vertical line to be put is REP vertical lines
*** Now come back to the REP * 2 –1 round marks on the right of the right side star (the last one
will not be actively use, only REP * 2 – 2 will get a coding)
Using as many RCS as are necessary for doing that put a coding under every mark in the marks
line except the very last one.
.
*
. . . . . . . . . . . . . .
*
. . . . . . . . . . . . .
Page 3 of 6
2009 Jan 8th
V61-0
U - U - O - O - U - O -U - O – O –U -U- O - U- O – U -U - O - O - U - O - U - O – O - U – U- O U- O
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This line of U-O above is written on the upper edge of the lower fixed part of the slide rule.
*** Now reading in the usual Left to Right and starting at the second round mark after the right side
star till the last available coding ( under the before last right side round mark ) take the Coding
Sequence ( CS )
.
*
. . . . . . . . . . . . . .
*
. . . . . . . . . . . . .
U - U - O - O - U - O -U - O – O –U -U- O - U- O – U -U - O - O - U - O - U - O – O - U – U- O U- O
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*** Now search this CS *inside the whole coding starting at the left side star.
.
*
. . . . . . . . . . . . . .
*
. . . . . . . . . . . . .
U - U - O - O - U - O -U - O – O –U -U- O - U- O – U -U - O - O - U - O - U - O – O - U U-O- U - O
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O - U - O - U -O – O -U –U- O U- O
the starting position of this CS inside the coding is the fourth after the left side star mark.
Once you have identified the starting point of this searched for sequence between the 2 stars it becomes
the start of another sequence.
From this point we now take Left to Right a sequence of 2 * REP length
O - U - O -U - O – O –U -U- O - U- O – U -U – O
Then change the coding of this “echoing” sequence for their opposite ( easier with and using modulo 2
after adding 1 to each )
U - O - U - O- U -U - O - O - U – O - U - O - O- U
We have the New Repeating Coding Sequence
Read it Left to Right but write down what is read from Right to left beginning at the right side star mark
on the lower edge of the upper fixed part.
U-O-O-U-O-U-O-O-U-U-O-U-O–U
We get this :
U - O - O - U -O - U -O- O -U - U- O - U - O – U
.
*
. . . . . . . . . . . . . .
*
. . . . . . . . . . . . .
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We have to put in coding in the places missing them and this is done according to the NRCS and the
direction of writing : this is written on the lower edge of the upper fixed part of the slide rule.
O -U -U - O - O - U -O - U -O- O -U - U- O - U - O – U
.
*
. . . . . . . . . . . . . .
*
U - O - O - U - O - U -O- O -U - U- O - U
. . . . . . . . . . . . .
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Page 4 of 6
2009 Jan 8th
V61-0
What is ABOVE the marks line is for EVE HP and what is BELOW is for ODD HP.
Important reminder : BELOW the sequence of crossing is read Left to Right as Westerners do
ABOVE the sequence of crossing is read Right to Left as in Arabic.
*** Now starting from the right side star mark put in progressing Left to Right “REPEAT”
vertical lines , one above every other mark.
|
.
. . . . . . . . . . . . . .
*
*
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U - O - O - U - O - U -O- O -U - U- O - U
. . . . . . . . . . . . .
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*** We need to recall that Row-coded ( mandrel frame of reference ) do not have ( REPEAT oblige )
the same coding for every successive odd HP or for every successive even HP.
There is a “cadenza”, or better but in technical parlance a phase shift to be observed and obeyed.
In order to get the correct phase shift we need to start each HP, whether odd or even, at the appropriate
place. To be able to determine this appropriate place in each case a set of numbers will be given to
each of the different starting points ( a REP number of them for each fixed part of slide rule ) in each
of the two series : odd and even.
So for each odd and each even set of HP 1 to REP “coupled” numbers are attributed.
Coupled because made with two numbers somehow usefully and meaningfully linked together.
First number is Bight and second is HP number. Ex :10/4 or 7/2
The numbering of each of the two vertical lines (Left to Right in both case ) segments start with
the first HP in its series. ( 1 for odd and 2 for even ) and goes on periodically ( again modular
mathematics ) the ‘step’ for this ‘periodical line marking’ is given by |Lead| modulo REP.
In the 17L/14B REP = 7 example the “stepping” pace will be |17|MOD7 that is == 3
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1
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1
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3
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1
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1
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3
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7
3
5
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5
and so on
Page 5 of 6
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1
11
7
3
13
9
5
2009 Jan 8th
V61-0
HP number are now to be added to make ‘coupled’ numbers
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1/-1 11
7
3/0
13
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9
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|
|
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1/-1 11
7
3/0
13
9
5/1
|
|
|
|
|
|
7/2
3/0
|
1/-1 11
13
THE FIRST WILL BE ATTRIBUED (-1)
5
9
5/1
13/5 9/3
5/1
till we have
|
|
1/-1 11/4
|
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7/2
3/0
but we are missing 15/
|
|
|
17/…..27/
so the easy way is to add 2REP* to the first member of a couple
and REP to the second ( this is where the –1 given is useful )
so we get
|
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|
|
|
|
|
1/-1 11/4 7/2
3/0 13/5 9/3
5/1
15/8 25/11 21/9 17/7 27/12 23/10 19/8
27/12 is 27th HP and Bight number 12
we have to stop adding row of coupled numbers when 2*B-1 has been attained for ODD and 2*B for
EVEN
we have to do the same process for the upper fixed part of the slide rule
2
|
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2
|
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4
|
2
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8
4
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6
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Page 6 of 6
2009 Jan 8th
V61-0
till we have an almost finished slide rule
2/0 6/2 10/4
16/7 20/9 24/11
|
.
*
. . . . . . . . . . . . . .
*
|
|
14/6 4/1 8/3 12/5
28/13 18/8 22/10 26/12
|
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|
|
U - O - O - U - O - U -O- O -U - U- O - U
. . . . . . . . . . . . .
|
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|
|
|
|
1/-1 11/4 7/2
3/0 13/5 9/3
5/1
15/8 25/11 21/9 17/7 27/12 23/10 19/8
*** The slide rule is almost ready for use for this particular knot 17l 14b REP 7 row code ( mandrel
frame)
There remain only to add the COMPLEMETARY PERIODIC and PERIODIC BIGHT SEQUECES that
are computed exactly as for the Column coded Knots .
Periodic goes on the lower edge of mobile part and complementary on the upper edge of mobile part.
2/0 6/2 10/4
16/7 20/9 24/11
|
|
|
14/6 4/1 8/3 12/5
28/13 18/8 22/10 26/12
|
|
|
|
U - O - O - U - O - U -O- O -U - U- O - U
____________________________________________
4 9 0 5 10 1 6 11 2 7 12 3 8
13 4
.
*
. . . . . . . . . . . . . .
0
9
4 13 8 3 1 2 7 2 11 6 1 10 5 0
9 0
*
. . . . . . . . . . . . .
9 4
_______________________________________________________________________________________
|
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|
|
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|
1/-1 11/4 7/2
3/0 13/5 9/3
5/1
15/8 25/11 21/9 17/7 27/12 23/10 19/8
note that with the star mark goes a non zero digit
Slide rule is now ready to be use and had you been given something more than a BRAINLESS
RECIPE and been given the full works you would not need of any more instruction to use it, you
would know how to go on alone, self-reliant on your knowledge.
May that teach you a lesson about BRAINLESS RECIPE : one cannot be self reliant with them
because one have to rely on the source going on giving brainless, unreasoned and unjustified “orders’”
Don’t worry a brainlesss : HOW TO USE THE COMPLETED SLIDE RULE IS COMING SOON
.
Copyright Charles Hamel aka Nautile – January 2009 V1.0
page 1 of 7
ROW-CODED*** KNOTS FOLLOWING A THK SHADOW
( shadow = cordage route and no nature of crossing given )
said by Schaake & Turner « regular knot s»
*** I strongly object to this myopic nomenclature.
It is attached to Schaake horizontal mandrel reference but will become a ‘column-coding” for a vertical
( frequent and mine in particular) cylinder frame of reference.
It has never seem to me a good idea to use frame of reference dependent nomenclature.
This is building a huge entry door for misunderstanding.
Inter-Bight coded is much better as it goes for row-coded ( mandrel) and column-coded ( cylinder)
Parallel-Bight coded is much better as it goes for column-coded ( mandrel and row-coded ( cylinder)
Better look at my pages on httt://charles.hamel.free.fr/knots-and-cordages for explanation on THK or
NOT THK and SHADOW or cordage route and many other notions such as frame of reference.
CAVEAT : the HP-RPL code, the making of the PVC slide-rule
IDEA OF THE SLIDE-RULE IS SCHAAKE & TURNER ALONE.
are mine alone but the BRILLIANT
User-Tip : better be used to the SCHK program that do the ROW-AND-COLUMN coded and
COLUMN-CODED or even HALL’s book and the Algorithm before tackling this one.
This present one is some steps above SCHK and several stairs cases above this present
program will be the one tackling so called PINEAPPLE or better said STANDARD HERRRINGBONEPINEAPPLE ( nested bight knot of which they are but only one type ! )
My personal slide rule :
From this idea ( I modified Schaake’s illustration to gain clarity for the not abstract minded.) :
page 2 of 7
The UPPER FIXED part is to be “DAER” or READ FROM RIGHT TO LEFT ( RIGHT BIGHT RIM on
mandrel or BOTTOM RIM on cylinder when starting at those rims)
The LOWER FIXED part is to be READ AS USUAL FOR US FROM LEFT TO RIGHT.
The numbers on the mobile part are the bight algorithms. ( DO NOT enter more than 26
BIGHT , more than 25 LEAD in the program )
On this mobile part are several marks : round points and TWO stars
Between the two stars there are ( limits included) L-1 marks.
So the right side star is at Lth position
The round mark on the left of the left side star is a BIGHT RIM (left / bottom) and the round
mark immediately adjacent to the right of the right side star is the other BIGHT RIM (right / top).
The sliding part is used in this way : Use HALF-PERIOD NUMBER TO “ALIGN” on halfperiod being studied and BIGHT NUMBER TO READ THE CROSSINGS RETAINED for it.
The sequence of code for the crossing to be entered is THE CROSSINGS AS SEEN IN THE
FINISHED KNOT FOLLOWING THE VECTOR ( arrow : so from the start bight rim to the
arrival on the other bight rim at the end of the first half-period) Spart-Wend along the FIRST
HALF-PERIOD.
For ODD half-periods : use the lower fixed part, the left side star is then aligned with the
vertical blue line corresponding to the half-period studied (0 1 2 3 …..2B) and bight-number
ex (1 / or 1/-1____27/12___14/6…)
READING is from LEFT TO RIGHT
Using the bight-number (ex : the 12 in 27/12 ) read the nature of crossings and RETAIN ONLY
THE ONE corresponding to bight number as read under the marks BEING LESS OR EQUAL to the
‘12’ and stop at the next star.
So 27th half period gives : O U O U O U U O O U O U O O U or O-U-O-U-O-U2-O2- U-O-U-O2U
For the EVEN half-periods : use the upper fixed part, the right side star is aligned with the
vertical blue line corresponding to the half-period considered.
GNIDAER ( reading) is from RIGHT TO LEFT there
Using the Bight number you note the crossing corresponding to the bight number written just
above the marks on the mobile part so for 12/5 (the 12th half-period with bight-number 5)
you note, going TO the LEFT till the left side star, all the crossings that correspond to bight
number LESS OR EQUAL to 5 so 5, 4 , 3 , 2 , 1 , 0
That is O O O O U O O or O4-U-02
In fact the REPEAT is the number of “move” for alignment of the mobile part for each series
of EVEN and ODD half-periods.
There is :
--- one only round mark on the left of the left side star
--- on the right side of the right side star there are Twice the Repeat less one ( 2 * REP – 1 )
round dots.
You mark the right side star with pencil.
All the other round and star marks are with permanent ink.
Above / Under this line of marks and starting at a star mark you have to inscribe :
UNDER and from LEFT TO RIGHT beginning at the left side star is the cyclic Bight sequence
ABOVE and from RIGHT TO LEFT beginning at the right side star is the complementary cyclic
Bight sequence
They are built in exactly the same manner as in the Column-coded knot.
page 3 of 7
The 7 ( NUMBER OF REPEAT in fact ) BLUE VERTICAL LINES on each fixed part correspond to
the REPEAT of 7 ( change with each knot )
The (Bight / Repeat) row of number x/y are == ( half-cycle number / Bight number )
The REPEAT is simply read from the diagram of the knot, it is not computed by the program:
Staring at the left side star ( second mark from the beginning of the line of marks ) and under
EVERY TWO STEPS from the very first left mark progressing from LEFT TO RIGHT a vertical
line is drawn
Staring at the right side star and under every two step from this star progressing LEFT TO
RIGHT a vertical line is drawn
Because the best program I know ( http://data.oreilly.com/jallwine/knots/ ) can manage
‘only’ Column-coded and RowAND-Column code knots I
decided to write a program in
HP-RPL to be run on HP48
calculator on one of the
emulator for the afore
said.(EMU48 for Windows and
E48 for Mac ).
The easy part with Columns (at
least, can be Row AND
Columns) coded knot is that
the pattern of crossings along
the cordage route being a
constant it is simple to work
how to read it depending on the
even of odd half-period
considered.
BUT in row-coded the pattern is
changing because it obey a
Grand Pattern Period which is
the REPEAT.
You may not use / and \ and
have to use ( as I did with the
Column-coded on my program
) O-U ( symbolised by digit 1
and 0 )
It has been at least 6 years since I last coded in HP-RPL but I wrote so many statistical
applications, and epidemiology simulations with my much loved HP48G and later HP48GX
for years that it came back rather astonishingly quickly.
Code is ugly as I wrote it (not to be recommended mind you) mostly directly on the keyboard
while deciphering Schaake & Turner idea and had only a bit of tweaking to do but a rather
extensive period of testing to be sure.
DO NOT ATTEMPT TO RUN ANY OTHER PROGRAM THAT THE FOLLOWING TWO
before you are well acquainted with the HP48G(X) or its emulator ( I will not answer any
question that have its answer in one of HP USER MANUAL that I have given for download.
You may run without risking damages run NET and NET2 that are cleaning all the used
variables. It is best to clean before closing down.
page 4 of 7
IN THE SCHR ( for Schaake-Row) FOLDER :
PGR will give you all that is necessary to « write » your slide rule.
You will still have to make a slide-rule with PVC strips ( cheap –relatively ) or with paper if
you like.
The black marks are made with permanent marker and the rest is made with pencil so as to
be erased as it change with each knot
Here illustrated is the case of the 14L 10 B with a PATTERN GRAND PERIOD OF 7
Program puts the results on the STACK and in the order shown on the slide rule
SPGR will give you the coding of crossings for each half-period.
In case of doubt consult the User Tips for the SCHK program and the HP user’ manualS that
come in three flavours (simple – normal-detailed : 3 types )
Results are put on the STACK
Now some 6 examples by SCHAAKE & TURNER for you to work out with this program.(
which has been verifier to give exactly the same results as Schaake & Turner si it is
“guaranteed” at least for those knots ! ;-)
page 5 of 7
The results ( once again pillage from Schaake & Turner ! so as to assure user of a valid
way to control this program ) are :
page 6 of 7
page 7 of 7
Page 1 of 3
2009 Jan 8th
V61-0
USIG THE SLIDE RULE
We have completed our slide rule and we are as they say in French “ comme une poule qui vient de
trouver un couteau” / “like a hen that just found a knife” a bit embarrassed.
2/0 6/2 10/4
16/7 20/9 24/11
|
|
|
14/6 4/1 8/3 12/5
28/13 18/8 22/10 26/12
|
|
|
|
U - O - O - U - O - U -O- O -U - U- O - U
____________________________________________
4 9 0 5 10 1 6 11 2 7 12 3 8
13 4
.
*
. . . . . . . . . . . . . .
0
9
4 13 8 3 1 2 7 2 11 6 1 10 5 0
9 0
*
. . . . . . . . . . . . .
9 4
_______________________________________________________________________________________
|
|
|
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|
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|
1/-1 11/4 7/2
3/0 13/5 9/3
5/1
15/8 25/11 21/9 17/7 27/12 23/10 19/8
Page 2 of 3
2009 Jan 8th
V61-0
This is the start position : this is for the first HP ( first of the ODD HP and firts of all the 2*B HP )
Easy as pie : mark it as HP 1 : { } Free Run
WOW , how intelligent and sure of us we are now.
Yes we can because we don’t have anything special to get the HP 2 : ( the first of the EVEN HP )
We are fortunate that SCHAAKE & TURNER made it so by astute thinking:
The right side star is already in alignment with 2/0 second HP and Bight number 0
2/0 6/2 10/4
16/7 20/9 24/11
|
|
|
14/6 4/1 8/3 12/5
28/13 18/8 22/10 26/12
|
|
|
|
U - O - O - U - O - U -O- O -U - U- O - U
____________________________________________
4 9 0 5 10 1 6 11 2 7 12 3 8
.
*
13 4
. . . . . . . . . . . . . .
9 0
*
. . . . . . . . . . . . .
Now reading RIGHT TO LEFT ( remember that ? ) starting at the alignment right side star vertical
line with 2/0 above and going leftward we read the
4 9 0 5 10 1 6 11 2 7 12 3 8 13 4 9 0
stopping at numbers equal or less than the second member of the ‘coupled’ number : here ‘ 0 ‘
it happen that above this ‘ 0 ‘ is a ‘ U ‘ so HP é : { U }
Second HP has only one crossing : an Under
Now for the tricky part, almost rocket science ;-) how do we get the HP 3 ?
AH ! UMH !
Why do you think this is called a slide rule with a mobile part ?
because we slide the mobile part ! Is that enough clarity for Readers ?
U - O - O - U - O - U -O- O -U - U- O - U
____________________________________________
4 9 0 5 10 1 6 11 2 7 12 3 8
.
13 4
9 0
. . . . . . . . . . . . . .
*
0 9 4 13 8 3 12 7 2 11 6 1 10 5 0 9
4
*
. . . . .
_______________________________________________________________________________________
|
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|
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|
1/-1 11/4 7/2
3/0 13/5 9/3
5/1
15/8 25/11 21/9 17/7 27/12 23/10 19/8
Now we aligned the left side star on the lower 3/0 and we read LEFT TO RIGHT the
(zero is not but is still useful so don’t suppress it unthinkingly ! )
9 4 13 8 3 1 2 7 2 11 6 1 10 5 0 9 4 under the only number equal or less that the
second member of the ‘coupled’ 3/0 is a “U so HP 3: { O } one Over in third HP
Page 3 of 3
2009 Jan 8th
V61-0
Are you beginning to understand how you need to go on ?
I certainly hope so. We need to do HP 4 :
That is so EVEN so on the UPPER fixed part of the slide rule
We align the right side star with the ‘coupled’ numbers we need 4/1
2/0 6/2 10/4
16/7 20/9 24/11
|
|
O -U -U - O - O -U -O U -O- O -U - U- O - U - O –U
|
14/6 4/1 8/3 12/5
28/13 18/8 22/10 26/12
|
|
|
|
U - O - O - U - O U -O- O -U - U- O - U
____________________________________________
.
4
9 0
5 10 1 6 11 2 7 12 3 8 13 4 9 0
*
. . . . . . . . . . . . . .
Reading RIGHT TO LEFT the
4 9 0 5 10 1 6 11 2 7 12 3 8 13 4
we find two that are equal or less that 1
. . . . .
*
9
so HP 4 : { O O } or { 2 O] or {O2} two Over crossings
Now for HP 5 : well just do it yourself : go to lower fixed part and align left side star with 5 / 1
And so on
Now a last exercise HP 22 : say
So EVEN so upper fixed par so right side star
Align right side star with 22/10
2/0 6/2 10/4
16/7 20/9 24/11
|
|
|
-U -U - O - O - U -O - U -O- O - U - U- O -U- O U U - O - O - U- O
14/6 4/1 8/3 12/5
28/13 18/8 22/10 26/12
|
|
|
|
U -O- O - U - U- O - U
____________________________________________
0 4 9 0 5 10 1 6 11
.
*
Bonne route
8 13 4
. . . . . . . . . . . . . .
So this should be HP 22 : {U2 O U2 O U2
Now you are alone.
2 7 12 3
O U O U2 }
9 0 4
*
. . .
JOAT or Jack Of All Trades HP48GX RPL PGR for
Page 1 of 4
NEITHER ROW NOR COLUMN CODED KNOTS ( but it can manage ROW coded, COLUMN coded
Row AND Colum coded ones )
LE PROGRAMME A TOUT FAIRE :
THE JACK OF ALL TRADES PROGRAM
This does the calculations giving you
FOR EACH HALF-PERIOD THE NUMBER OF THE COLUMNS
where a given half-period cross over or under the previously laid half-periods.
( mind you this IS NOT the code as known : this DOES NOT gives you the nature,
the type OVER or UNDER of said crossing in a given COLumn )
With the COLumns NUMbers attached to the studied half-period the
USER THEN WILL READS ON THE PREPARED DIAGRAM OF THE KNOT THE
TYPE OF THE CROSSING AND WRITES HIMSELF THE CODE FOR THIS
PARTICULAR HALF-PERIOD.
THIS WORKS WITH KNOTS MADE ON A THK SHADOW.
WHETHER THEY ARE
- COLUMN-CODED
- ROW-CODED
- BOTH ROW AND COLUMN CODED
- NEITHER ROW NOR COLUMN CODED
HOW TO USE THAT ?
FIRST : PREPARE THE DIAGRAM. Here HORIZONTAL MANDREL FRAME of
REFERENCE. Just make an anti-clockwise rotation of Pi/2 or 90° to get the vertical
cylinder frame of reference.
Page 2 of 4
You first need to have a completed diagram of your projected knot with all the
crossing clearly identifiable just as in the illustration just seen.
We will lay the cordage route CLOCKWISE
That is from BOTTOM LEFT TO TOP RIGHT for the ODD half-periods
and BOTTOM RIGHT TO TOP LEFT for the EVEN half-periods.
Then you have to number ( number is to be put at the starting point for the
considered half-period on the rim.) :
LEFT VERTICAL SIDE ( BIGHT RIM ) the ODD half-period beginning with 1.
EACH ODD half-period commence their cordage route on the l LEFT bight rim and
goes till meeting with the right bight rim their end point and where immediately
commence the FOLLOWING EVEN half-period.
When ALL the HALF-PERIODS ODD AS WELL AS EVEN HAVE BEEN
NUMBERERD you will have to number the COLumns using the horizontal limits.
UPPER LIMIT IS FOR THE ODD half-period and as these ODD half periods run
LEFT to RIGHT the numbering is done LEFT TO RIGHT
LOWER LIMIT IS FOR THE EVEN half-period and as these EVEN half periods run
RIGHT TO LEFT the numbering is done RIGHT TO LEFT .
NEXT : USING THE HP48GX PROGRAM
- Open folder JOAT on the EMU48.
- Run PGR
You will have to enter number of LEAD and number of BIGHT and that is all.
In the stack you will get all the half-period with their COLumns where the crossings
are made.
ONCE AGAIN : those are THE NUMBER IDENTIFYING THE COLUMNS NOT THE
CODING OF CROSSING.
Results will be on the stack : explore bottom to top
{ } empty list is == FREE RUN
{ 3 6 10 } refers to COLumns N° 3 , N°6 and N° 10
Now knowing for each half-period the columns where a crossing exist you return to
your diagram.
First Half-Period ( 1-H-P )
1 to 2
ALWAYS a FREE RUN devoid of any crossing
Page 3 of 4
2-H-P 2 (RIGHT) to 3 (LEFT)
3-H-P 3 (LEFT) to 4 (RIGHT) and so on
till last H-P and EVEN one RIGHT TO LEFT RETURNING TO THE STARTING point
Last -H-P 2B to 1
Suppose that we are as in the illustration under that we are studying the second H-P
(EVEN so RIGHT TO LEFT) with 2-H-p == { 10 }
Then starting from the BOTTOM horizontal line that is to be read RIGHT TO LEFT
when there are more than one number between the { } then staring from the 10 mark
you go up the COLumn till you met the half-period going from RIGHT 2 TO LEFT 3
Then you note the type of the crossing as seen by the cordge making its route from
RIGHT 2 TO LEFT 3 ; it is an UNDER so you now note what will be the CODING
OF CROSSING
H-P-2 :UNDER
And so on half-period after half-period.
Page 4 of 4
Now suppose we are studying the FIFTH hal-Period ( ODD ) going from
LEFT 5 TO RIGHT 6
You are given the COLumn NUMbers for this 5-H-P : { 3 10 13 }
So you will read the TOP horizontal line numbering the COLumns from LEFT TO
RIGHT the same directional arrow than the 5th H-P is following.
On COL 3 you go down till you meet the line figuring the 5th H-P going from LEFT 5
TO RIGHT 6 and you make note of the nature of the crossing that is there : UNDER
TO RIGHT 6 and you make note of the nature of the crossing that is there : OVER
TO RIGHT 6 and you make note of the nature of the crossing that is there : UNDER
You have no more COL-NUM to treat so you now have the CROSSING CODING for
the 5th HP
H-P-5 = UNDER – OVER – UNDER
Of course what you are manually doing it is possible to code as a program.
But it will be much more of a hassle for YOU :
because the sort of entries it will ask for from the user demand the full
understanding and mastery some sophisticated notions and you will have to find
“REPEATING BLOCKS units” in left side, middle and right side of the knot usually.
ALL THIS IS THANKS TO SCHAAKE & TURNER
BINX user tips Copyright Nautile
BINX
or YAJOAT yet another JOAT
BUT MUCH MORE INTERESTING
Page 1 on 6
Version 1.0.0
Click on it to open it.
Now you are inside BINX DIRECTORY as
The computation procedures are different
from those used in JOAT and rest on
Schaake & Turner’s work once again.
Bight Index Numbers ( what I had in my
own quest labelled otherwise in my THK
pages ).
The computation procedures being
different it will allow the untrusting souls to
verify the JOAT results and even those of
the other programs results.
It is till EMU48 for Windows and HP-RPL
language.
can be seen in the uppermost line on the
screen: { HOME BINX }.
You can see ( if not use side arrows ) the
four “staged” programs :
PGR, PGR2, PGR3, PGR4
( a week of pondering and researching
went into the naming so don’t snort
please). PGR is indeed PGR1.
So you “push” on it to RUN the program.
This one will do ROW-coded, COLUMNcoded, ROW&COL-coded, NEITHER
ROW NOR COL-coded.
READ JOAT USER’S TIPS AGAIN PLEASE you
will need that to understand without trouble what is
following and to “plug” the holes I have left in my
explanations.
FIRST OF ALL READ THE ANNEXE AT THE END
OF THIS PAPER BEFORE TACKLING THE MAIN
TEXT.
We are in EMU48 with all the programs
“loaded”.
RESULTS WILL NOT BE CODING
SEQUENCES OF CROSSINGS BUT
IDENTIFYING NUMBER FOR COLUMNS
OR/AND ROWS WHERE CROSSINGS
HAPPEN.
Among the {HOME} DIRectories you will
find BINX’s.
If you cannot see it then use the side
arrows to try and find it.
PGR(1) immediately retaliates for having
been aroused from a pleasant slumber
and asks, no demands that you enter
number of LEAD and number of BIGHT
and makes a HALT (the uppermost part of
the screen).
Do enter what has been ask from you.
You have to KILL the HALT ( equivalent
to FORWARD MARCH, MARCH ) using the
violet Left arrow and the ON keys.
Program runs and puts the results of its
calculations in the STACK.
The results are expressed under the form
of COMPLEX numbers : have no fear they
do not bite and anyway I am using them
here as “label” and not as complex
numbers.
Page 2 on 6
Version 1.0.0
H-P in the knot the number of the
COLumns where a crossing exist for
that Half-Period.
HP4: { 3 10 13 } means
Half-Period N°4 has a crossing in
COLumns N°3, N°10 and N° 13.
You may stop here and make use of those
result on your “prepared diagram”
You get a whole collection of
( SOME_NUMBER_1 , SOME_NUMBER_2)
SOME_NUMBER_1 stands for BIGHT-INDEX
I0, I1, I2 … IB ( whether left or right –
mandrel frame of reference- )
ODD are on the LEFT BIGHT RIM ( left to
right H-P ) and EVEN are on the RIGHT
Bight rim ( right to left H-P).
You may also decide to push you luck with
the HP48GX and run PGR3.
Above “21” flags one that is on the LEFT
BIGHT RIM
and
“20” goes with one that is on the RIGHT
BIGHT RIM.
SOME_NUMBER_2 is the computed BightIndex-Number.
PGR3 will gives you a list of numbers
(empty { } lists are for FREE RUN
remember ?)
that are labelled CROW (for Crossing
ROW)
Now if you don’t want to stop here and
‘manually’ exploit the results obtained you
can run PGR2.
RUNning PGR2 will give you for EACH
For EACH H-P just as before you got the
number identifying the columns where a
crossing existed , here you get the
Page 3 on 6
Version 1.0.0
identifying number of the ROWs where
a crossing exists.
CROW4 is 4th H-P, CROW7 is 7th H-P.
CROW4 or 4th Half-period has a crossing
in ROW N° 14, in ROW N° 1 and in ROW
N°4. ( DO NOT try to make that an ‘ordered
list’ for ease of use as in
{ 1 4 14 } instead of using what directly
resulted from the computation loops.)
Now there only remain to “mix” but in a
carefylly appropriate way the N° identifying
COL and the N° identifying the ROW to
get the intersection where the crossing is :
Now it will only be necessary to read the
TYPE ( HIGH / LOW over/under ) of this
crossing on the diagram prepared prior to
using the programs.
Please remember that the "perspective" on
the TYPE of a crossing depends on the
way the arrow SPart-Wend is going :
LEFT to RIGHT for an ODD Half-Period,
RIGHT to LEFT for an EVEN H-P :
the OVER in the perspective of one will be
the UNDER in the perspective of the other.
Better not forget that .(even when writing a
program : that is why it is much better to use 0 and 1 that
can be easily convert to the opposite just using a 2
MODULO than persisting in the very cumbersome / & \.)
Again COMPLEX numbers ( but for you
they will just be labels )
Those are in fact
COORDINATES for EACH CROSSING in
a given HP ( Half-Period ) first you get
the COLumns ( remember read LEFT to
RIGHT for ODD HP running from left bight
rim to right bight rim and RIGHT to LEFT
for EVEN period running from right bight
rim to left bight rim.
Second number identify the ROW ( again a
reading order has to be complied to : ROW
ZERO is at the SPart in the knot or the
return of the WEnd to the SPart, the
numbering is made upward and “in a
circular fashion” : remember always think
MODULO : look at the row numbering in
the prepared diagram )
Use that manually to get the CODE
for each HP in the
knot you have the diagram of.
SEQUENCE OF CROSSING
RUN PGR4 to get those intersection
coordinates per H-P.
PGR4 gives for each crossing a set of
number identifying COLUMN and ROW
where a crossing happens for the H-P
studied.
Of course a PGR5 asking for extensive
entry of code per row or per columns or for
the whole knot can be written that will write
automatically the coding sequence of
crossings ( may be I will do it but for
NEITHER / NOR coded it will need very
heavy entering of data by user)
Now that you are finished with playing : it
is time to CLEAN the mess you made !
Page 4 on 6
Version 1.0.0
NET ( abbrev NETtoyage ==cleaning in
French) and NET2 ( in whatever order
takes your fancy ) will free the memory
(not important on the computer but really
important on a real HP48GX calculator ).
NET and NET2 are RUN when the
programs RUN if only to avoid bugs due to
pre-existing variables
_________________________________________________________________________
ANNEXE
Instead of putting ALL the H-P in the same layer as in a classical diagram ( see above) they
are “unrolled” as I explained in :
--- http://charles.hamel.free.fr/knots-and-cordages/turksheads_3.html
as it relate to ENLARGEMENT in topic :
UNROLLING OF TIME SEQUENCE COMPARED WITH
SPATIAL SEQUENCE FOR ENLARGEMENT PROCESSES
--- in http://charles.hamel.free.fr/knots-and-cordages/turksheads_4.html
in
BIGHT NUMBER versus BIGHT ORDER
in particular in
HOW TO GET THE ORDER IN WHICH THE BIGHT ARE COMPLETED
IN THE PROCESS OF MAKING A TRUE THK:
Page 5 on 6
Version 1.0.0
HOW TO COMPUTE THE ORDER IN WHICH BIGHT ARE IN FACT LAID
BY THE RUNNING CORDAGE
THEIR TIME SEQUENCE IS UNROLLED IN SPACE and a certain computation is done.
Page 6 on 6
Now for SCHAAKE & TURNER perspective on that.
Version 1.0.0
PAGE 1 on 12
PINAPL ( & PINALP2) STANDARD HERRINGBONE PINEAPPLE KNOTS
Lengthy user’s tips but may be you will be rewarded by what the 5 programs can do
for you when you will have learned to correctly use them .
The programs PGR1 …..PGR5 in PINAPL take the load of calculation off your brain.
NONETHELESS you will need to set yourself in ‘BRAIN ENABLED MODE’ when
tackling the coding of those knots.
A POINT MUST BE MADE CLEAR : ALL THIS REST ON SCHAAKE AND TURNER’s
MATHEMATICAL GROUND BREAKING WORK :
No disrespect intended to all grade of ‘expert’ but…… you will be better for having
read THE BRAIDER and the Pamphlets if you want to be anything else than a
spider** making knots, relying on mere ganglia rather than on grey matter, or rather
on handed down recipes not really explained and not fully understood - (at least in
the full meaning usually attributed to those terms.)
**the sort of spider that is “constrained” to specially tailor cores for the knots they know how to make but are
unable to reciprocate and tailor their knots to a given core, those poor souls are “constrained” to remain into a
small “over-trodden” fenced territory.
th
As a 16 century French writer, MONTAIGNE, said “ knowing by rote is not knowing, it is holding what has been
put in the care of one’s memory .
First a small bit of sketchy NOMENCLATURE ( read SCHAAKE & TURNER to get
the full story or a very ‘gauche’ summary in my Turkshead-pages)
Those knots are part of a bigger CLASS : the REGULAR NESTED CYLINDRICAL
KNOTS. ( BUT despite what has always seem to me -- I have met like-thinking in S & T
now ! feel less lonely for it -- to be the too often encountered mistaken usual opinion
, what knot has ‘nested bight’ is NOT necessarily a PINEAPPLE knot.)
The nested bight leads to distinguish BIGHT BOUNDARIES ( I will think PINS LINES
rather ) :
Here 5 Bights in each NEST , so FIVE BOUDARIES on which you put pins to make the
knot. ( note that two adjacent pins lines are separated by 2 columns )
You need to know all about :
*
The NUMBER OF BIGHT NESTS ( B ) on each rim
The NUMBER OF BIGHT PER NEST which leads to the NUMBER OF BIGHT BOUNDARIES (
I prefer to call them pins lines or pins rim as I used the cylinder frame of reference
mostly ).Those boundaries are vital components in the calculation and for
approaching an understanding of the inner nature of those knots.
PAGE 2 on 12
You also need the NUMBER of LEADS in EACH STANDARD THK COMPONENT of the
COMPLETE PINEAPPLE. ( this number of LEADS in each component THK will be
denoted by ‘ S ‘ in the calculation.)
The so-called NUMBER OF PASS (or of STEPS in the making ) will be denoted by
letter “A”.
Note that if A = 5 then there is 5! ways of making the pineapple.
That is factorial, that is 5 * 4 * 3 * 2 * 1 = 120 different ways to make the pineapple.
You already know from using the others HP48GX programs in EMU48 that we can
compute the columns in which a crossing exist.
This is relating to the component THK seen in isolation.
It is what figure the upper part of each illustrations of calculations that will be
following.
When you will be doing the next (immediately following) PASS then the crossings of
the component THK itself will be added to the crossings collection made by the
preceding component(s) installed.
So the “recipe” is to calculate the “base component THK matrix “ and the
“already laid components matrix” , adding the two will give you another matrix
that is indeed quite easy to read to get the code for each H-P ( Half-Period ) in the
PASS.
PAGE 3 on 12
We will from this point work on an example inspired by SCHAAKE AND TURNER and
entirely done ( with some others as verification ) on my HP48GX.
---------------------------------------------------------------------------------------------------
A FIVE PASS HERRINGBONE ¨PINEAPPLE
ALL TOLD 29
LEAD for 20 BIGHT [ (5*3) + (7*2) L (4*5)B
The programs are set for a max of 30L 30B ( GDC permitting ) and 15 PASS
I do believe you will NEVER BE ABLE TO TIE A 15 pass PINEAPPLE of 27L 30B
and 29L 30B component THK ; just imagine 421 L 450 B
{(27*7) + (29*8)= 421 L and the Bight to go with that (30 * 15 ) = 450 B}
THK BASE COMPONENTS IN THIS ONE COME IN TWO GROUPS. THE 2
GROUPS ARE WITH THE SAME NUMBER OF BIGHTS BUT WITH NUMBER OF
LEADS ( the “S” ) THAT ARE SEPARATED BY 2 UNITS (ex : 5 and 7 )
One group of two will be 7 L ( so S=7) and 4 B*
The second group will be 5 L (so S=5) and 4 B*
4 B* mean 4 NESTS PER BIGHT RIM
5 BIGHTS PER NEST so 5 BIGHT BOUNDARIES ( PINS LINES ) on
each border
For each component you will have to enter the
LEFT BIGHT BOUNDARY
and the
RIGHT BIGHT BOUNDARY
-----------------------------------------------------------------------------------------------------------
PAGE 4 on 12
PRACTICAL WORKED EXAMPLE
29 LEAD
20 BIGHT
5 PASS
The order of the FIVE PASS will be chosen as : ( 5! manners to order the passes )
PASS ONE ( one layer added on nothing pre-existing )
5L 4B THK component so
S=5
B* =4
A=1
Left boundary = 1 Right b =1
PASS TWO ( one layer added to ONE pre-existing layer of crossings )
S=7
B* =4
A=2
Left boundary = 1
Right b=1
PASS THREE (one layer added to TWO pre-existing intermingled layers of crossings)
S=5
B* =4
A=3
Left boundary = 3
Right b =2
PASS FOUR ( one layer added to THREE pre-existing layers )
S=7
B* =4
A=4
Left boundary = 2
Right b =1
PASS FIVE ( one layer added to FOUR pre-existing layers )
S=5
B* =4
A=5
Left boundary = 4
Right b =4
After you have understood this page and the following illustration (modified from
SCHAAKE & TURNER for the edification of the not “abstract” minded) we will then
look at how to use the FIVE programs I wrote : PINAPL.HP
«PGR1»
You will have to enter ‘S’ and ‘B*’
( remember to break the HALT with a CONT command)
The calculation will put on the stack ( and STOre in a series of HP1 ……HP(b*2)
variables ) the Columns where a crossing happen. You can exploit it as such with the
aid of a precise diagram of the knot in its finished state.
You have now to RUN PGR2
«PGR2»
PGR2 ask for a digit identifying the LIST that will be made .
PAGE 5 on 12
( remember to break the HALT with a CONT command)
The computation will produce a LINU(index) file STOring a MATRIX that is the result.
This is : the Basic component as seen in isolation.
Now you need to find the resulting CROSSING due to the component THK being
ADDED on ALREADY LAID THK COMPONENT(S)
In fact what you will exploit as matrices is the result of
«PGR1»
«
»
immediately followed by PGR2
I let persist the intermediate step of PGR1 results persist as visible rather that
transparent for the user as they are practically useful in some situations and are good
teaching.
Resulting matrices are STOred in variables named LINU(index) index being the
number identifying the LIST ( that is converted to MATRIX form at the end stage of
PGR2 )
You may decide to make at one go the whole series of ‘THK-component-in-isolation’
matrices for the whole of the number PASS in the intended knot ( so reiterate [PGR1 +
PGR2] as often needed to cover all the PASS )
or
you may decide to immediately follow with doing the calculation for the “reference” or
the already laid layers or PASS then you have to RUN PGR3 ( to do all the PASS you
will do reiteration of PGR1 + PGR2 followed by PGR3 and….)
«PGR3»
You will have to enter ‘S’ and ‘B*’ ( identical to the one entered for PGR1 for the
corresponding PASS, but as I have for didactic reason “disjoined” the use of PGR3
from the preceding calculation phase it must be entered again )
Again the LIST NUMBER ( this is for user’s usage so can be arbitrary as long as you
remember and stay coherent and congruent – better use the real number == pass
number )
Enter NUMBER OF THE PASS ( this must be conform to “reality” as it is an essential part
of the calculation )
ENTER NUMBER OF THE LEFT BOUNDARY
ENTER NUMBER OF THE RIGHT BOUNDARY
THE RESULTS are STOred in LREF(index) files as a MATRIX ( these are easier for
calculation than LIST are ) Later we will add LINU(index) and LREF(index) by
matched PAIRS ( match according to identical (index) the result being STOred in
PASS(index) files
As in : LINU1 + LREF1 = PASS1
NOT as
LINU1 + LREF2 = PASS3
or
LINU2 + LREF4 = PASS5
PAGE 6 on 12
«PGR4»
This one is making the ‘synthesis” : the addition of the calculated matrices to obtain
the final matrix ( in PASSn files) of the considered PASS ( with index n )
Bright users will be rather easily able to directly use on their own the results put in
files.
«PGR5»
This one is for those feeling like “don’t want to feel my brain work”, it will help the lazy
by directly making the code for each half-period of the PASSn variable studied.
Those coding will be put on the STACK and a LIST of those will be STOred in the
PASSn file
«PGR6»
Will pace you though the FIVE proceeding PGR and let you get the calculation of one
PASS at one go ( you still have to make entries ! ). Another version of PINAPL will be
(may be ; if feedback is given on that ) written allowing to treat a full PASS with entries
to make only at the start.
----------------------------------------------------------------------------------------------------------------DO NOT FORGET TO USE : «CLEAN» to erase the used variables before closing down
the HP48GX or the EMU unless you have a use of them again ( “eat” quite a lot of
memory on a “real” HP48GX )
---------------------------------------------------------------------------------
PINALP2 This one a slight modification of PINALP
«PGR»
This one will SEAMLESSLY ( once you have made the necessary entries ) calculate a
whole PASS.
Of course you will have to COMPLY WITH THE NATURAL ORDER of the PASSes in you
projected knot ( or it will amount to building the third level of a building without having
built the street level, 1 floor, 2 floor )
So you will have to reiterate PGR for PASS 1 , PASS ( 1 + 1 =2) PASS (2+1 = 3)
PASS (3+ 1 = 4)……………PASS ( (n-1) , PASS (n)
Otherwise just refer to the same documentation as for PINAPL
«
»
BEWARE : DO NOT use «CLEAN» BETWEEN RUN of this PGR or you will erase
variables that are necessary for RUN to come, but DO NOT FORGET TO RUN
«CLEAN» when
you are finished and just before the very first RUN of
«PGR»
PAGE 7 on 12
Say you have as “end result for the PASS you intend to lay :
[
[ 3 4 4 4 3 ]…………………………………….correspond to FIRST H-P
[ 3 4 4 5 3 ]…………………………………….correspond to SECOND H-P
[ 3 4 4 5 3 ]…………………………………….correspond to THIRD H-P
[ 3 4 5 5 3 ]…………………………………….
[ 3 4 5 5 3 ]…………………………………….
[ 3 5 5 5 3 ]…………………………………….
[ 3 5 5 5 3 ]…………………………………….
[ 4 5 5 5 3 ]…………………………………….correspond to EIGHTH H-P
]
Remember that the coding is
U – O – U – O …………. U – O – U – O ….
So you have for the Nth PASS
[ 3 4 4 4 3 ] that is HP1 == [ U3 O4 U4 O4 U3 ]
[ 3 4 4 5 3 ] that is HP2 == [ U3 O4 U4 O5 U3 ]
AND SO ON…
and you have all that is needed to put
cordage on the pins !
Now for the suite of PASSes in the WORKED EXAMPLE :
DO THAT FOR PASS ONE, ……,THEN LAST PASS
PAGE 8 on 12
This is simply the coding of the very first THK component laid. No mystery in that.
Now we are doing PASS TWO
so the crossing are piling up
in each columns : those
already there and the one
added.
Upper part is the added THK
component as seen “in
isolation”
The lower part is the addition
of “reference” coding already
laid and the newly added
one in the last PASS done.
Before using the PINAPL you
need to be VERY CLEAR
ABOUT YOUR PROJECT :
you will need a VERY PRECISE
DIAGRAM :
* NUMBER OF NEST
** NUMBER OF BIGHT PER
NEST ==NUMBER OF
BOUNDARY LINES
** *NUMBER OF LEAD IN EACH
COMPONENT THK THAT GIVES
THE ‘S’ parameter.
**** THE PRECISE STARING
LEFT BOUNDARY and
ARRIVING RIGHT BOUNDARY
FOR THE FIRST H-P OF EACH
COMPONENT THK.
***** THE ORDER IN WHICH YOU
WILL PROCEED ( remember ‘A’
means A! ways of going about
doing the knot
A=2
2 * 1 = 2 ways
A=3
3*2*1=6 ways
A=4
4*3*2*1= 24 ways
PASS
A=
5
5*4*3*2*1=120 ways
WITHOUT THOSE
ELEMENTS YOU CANNOT
MEANINGFULLY
COMPUTE THE CODING
EITHER MANUALLY OR
WITH THE PROGRAM
PAGE 9 on 12
PAGE 10 on 12
/…
PAGE 11 on 12
IF YOU WANT SOME TRAINING, in fact you cannot escape it if you want to be proficient ;-) : DO
THE EXERCICE PROPOSED JUST UNDER :
Make the CODE FOR EACH FIVE PASS with PINAPL and then with PINAPL2
PAGE 12 on 12
AS ILLUSTRATIONS HERE UNDER ARE, DIRECT FROM MY HP48GX, PRACTICAL
RESULTS OF THE WORKED EXAMPLE
R5
[[ 3 4 4 4 3 ]
[34443]
[34443]
[34443]
[34443]
[34443]
[34443]
[ 3 4 4 4 3 ]]
R2
[[ 0 1 1 1 1 1 0 ]
[0111110]
[0111110]
[0111110]
[0111110]
[0111110]
[0111110]
[ 0 1 1 1 1 1 0 ]]
N5
[[ 0 0 0 0 0 ]
[00010]
[00010]
[00110]
[00110]
[01110]
[01110]
[ 1 1 1 1 0 ]]
R4
[[ 1 3 3 3 3 3 0 ]
[0333331]
[1333330]
[0333331]
[1333330]
[0333331]
[1333330]
[ 0 3 3 3 3 3 1 ]]
R1
[[ 0 0 0 0 0 ]
[00000]
[00000]
[00000]
[00000]
[00000]
[00000]
[ 0 0 0 0 0 ]]
N3
[[ 0 0 0 0 0 ]
[00010]
[00010]
[00110]
[00110]
[01110]
[01110]
[ 1 1 1 1 0 ]]
R3
[[ 2 2 2 2 1 ]
[12222]
[22221]
[12222]
[22221]
[12222]
[22221]
[ 1 2 2 2 2 ]]
N4
[[ 0 0 0 0 0 0 0 ]
[0001000]
[0001000]
[1001100]
[1001100]
[1101110]
[1101110]
[ 1 1 1 1 1 1 0 ]]
N1
[[ 0 0 0 0 0 ]
[00010]
[00010]
[00110]
[00110]
[01110]
[01110]
[ 1 1 1 1 0 ]]
N2
[[ 0 0 0 0 0 0 0 ]
[0001000]
[0001000]
[1001100]
[1001100]
[1101110]
[1101110]
[ 1 1 1 1 1 1 0 ]]
---------------------------------------------------------------------------------------------------------------
PAGE 13 on 12
To get the “end result” that you want it is only necessary to ADD THE NEW PASS that
you intend to make to ALL THE PREVIOUS LAYERS laid ( PASSes already done ) and this
will lead you to the coding to use in order to do without too much trouble that
intended new PASS.
For example adding N4 & R4
-----------------------N4
[[ 0 0 0 0 0 0 0 ]
[0001000]
[0001000]
[1001100]
[1001100]
[1101110]
[1101110]
[ 1 1 1 1 1 1 0 ]]
SECOND 7L 4B to be
added on…….
THAT WILL DECIPHER AS
R4
[[ 1 3 3 3 3 3 0 ]
[0333331]
[1333330]
[0333331]
[1333330]
[0333331]
[1333330]
[ 0 3 3 3 3 3 1 ]]
RESULT
[[ 1 3 3 3 3 3 0 ]
[0334331]
[1334330]
[1334431]
[2334430]
[1434441]
[2434440]
[ 1 4 4 4 4 4 1 ]]
the already laid PASS
will get you this.
(essential coding is U - O - U - O…U - O - U - O…U - O…)
RESULT for the FOURTH PASS
[[ U1 O3 U3 O3 U3 O3
[ U0 O3 U3 O4 U3 O3
[ U1 O3 U3 O4 U3 O3
[ U1 O3 U3 O4 U4 O3
[ U2 O3 U3 O4 U4 O3
[ U1 O4 U3 O4 U4 O4
[ U2 O4 U3 O4 U4 O4
[ U1 O4 U4 O4 U4 O4
U0 ] [Under One Over Two…….Under NONE]
U1 ] = second Half-Period
U0 ] = third Half-Period
U1 ] = fourth Half-Period
U0 ] = fifth Half-Period
U1 ] = sixth Half-Period
U0 ] = seventh Half-Period
U1 ]] = eighth Half-Period
U0 Under NONE
O0 Over NONE
Those U0 and O0 are there only for the sake of being able to use matrices and
equal length sub-lists inside LIST and have to be discarded when you write down the
coding on a paper.
Happy moments !
I hope you enjoy using this one billionth of what I enjoyed writing those programs on
my old faithful HP48GX and savouring SCHAAKE & TURNER CRISTAL CLEAR THINKING.
You should take to making the effort of reading THE BRAIDER ”

loading a program in emu48 - Charles HAMEL

Transcription

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