The Magic Encyclopedia ™ DataBase

General Spreadsheets
(by Aale de Winkel)

Creating general software allowing me to explore the various situations was thus far limited to spreadsheets written for only one order, or programming in high level programming languages. Recently I found manners to dispense with the single order limit of spreadsheets. The software here uploaded are the result of these programming excercise. Within the next month the list will increase steadily with spreadsheets implementing the various construction methods. The result of one spreadsheet will become pastable into another spreadsheet, thus allowing the user rapid access to a wide variety of possibilities for analysis.
The dates given might indicate a new version of the spreadsheet!

General Spreadsheets
square qualification

This spreadsheet superseed most of the other spreadsheet, in that most of the basic
creation methods are implemented in the macro langage "Visual Basic for Applications",
the following keystrokes are implemented:
<ctrl>W (indow) Check main windows input and create square
<ctrl>Q (ualify) Qualify the given square
<ctrl>P (rint) Print the square in neat 16 by 16 portions
note that the last keystroke redirectthe usual excell <ctrl>p to the squareprint macro
currently the spreadsheet implements creation through the following methods (field Q3):
kj: knightjump procedure
de: digit equations (John R. Hendricks)
pde: p-digital equation (implemented for p = 1,2,3,4 and 5
pan: (regular) pandiagonal squares of prime order
sample fields F4 gives the sample set G4 the sample within the set
sample set 0 revers to the manual input fields H3:R14 C15:R16 C17:R18
also in use for the samples
sample set 1 revers to the paste area where one can paste any square one like at A4
sample set 2 revers to the "sample set 1" worksheet with the known trimagic squares
sample set 3 / 9 are defined in the "sample set 2" worksheet with a snapshot of data
for the options kj, de and pde selectable by number

further the pan-reloc E13 E14 field panrelocates and the aspect F13 regulates the
aspectial variant (values: 0..7)

For further details I rever to the spreadsheet manual
More ptions might be built in in some future date (feel free to contribute)

NOTE 1-digital use coordinate 0 .. m-1 while digit equation coordinates 1 .. m, so that
parameters must be converted when one or the other is used
square construction
by p-digital equation
This spreadsheet implement the square construction by p-digital equation
therewith it gives access to the in the encyclopedia database listed order 8 and 9 bimagic
squares obtained by this method (the first 16 are listed in sampleset 2 resp 3), the input-
display D2 is the sampe set, and E2 the sample mumber, if the sampel number is set to 0 the
input midsection becomes active so that the user can experiment with values, any other number
selects a sample from the given sample set

The 1-digital point of view difffers from J.R. Hendrickses digit-equations in the fact that
the latin squares are calculated using coordinates [0..m-1] in the first and [1..m] in the
latter, the spreadsheet allows for this by the imput cel D2 (in the digital tab spreadsheet
(automated in the samples listing by the control section of the tables)
Another diffrence between the two s the use of the permutation, either permuting the main-
diagonal or changing the digits. The spreadsheet allows for inputting the '=' (digit change
on both latin squares), or the '_' (main diagonal permutation of lower latin square only)
field L3 the field L4 allows for transposing the lower latin square by inputting a 't' here

If time permits more data will be added to the sample listings, the reader is free to add
his own sample set to the ones listed (sample handling is completely implemented in its
own tab spreadsheet (contact me if you need help adding such a set).

The spreadsheet is set for manual recalculation <F9> for allow fast parameter input
also the qualifier is valid only for the inputted power, so change to 2 inorder to check
the bimagic propeerty. (PLEASE report to me if inadvertently this check is in error)
square construction
by digit equation
This spreadsheet implement the John R. Hendricks's construction by digit equation
for squares. Next to the input mode (sample 0) it also holds a sample mode, currently
holding merely the samples taken from John R. Hendrickses book "Magic Square to Tesseract
by Computer". Given a sample the "Latin Prescription" might hold a reverse of the intended
digit equation, the ones I verified had merely an aspectial variant of the square the book
lists. Also the litle same description are merely the books pagenumbers according to the copy
I have. (John might augment this lists according to recent versions of his books

The user might easily add his own samples to the sample list, allowing him easy acces
to thesquare by simply typing is its sample number in the main screen. If the list grows
beyond it's current limits just increase the numbers in the first row of the sample page.
panmagic squares
of prime order
This sqpreadsheet implement this authors viewpoint of the construction of prime order
panmagic squares. Input validity is checked here in a limited manner, permutations are
not checked for validity etc. In principle as theory suggest all regular panmagic squares
are obtainable by the method (the spreadsheet is limited to prime order 5 uptill 37 as the
maximum order of ntermediate squres is 40 (also the limit for the DigitEquations spreadsheet)
multi-magic samples
Spreadsheet displaying various trimagic spreadsheets currently around.
It allows for symmetric diagonal permutation of the given squares
powers 1, 2 and 3 can be tested against either the theoretical or the first column sum
higher powers are only testable against the sum result of the first colmn, thereby allowing
the find of higher p-multimagic squares. Currrent the spreadsheet is limmited to order 128
however the reader could stretch the "sample" and "powered" squares to allow higher
order testing

Current mishaps, a hyperlink in a samles accompanying text doesn't remain a hyperlink in
the user-interface (therefore hyperlink are explicity situated in the "samples page")
positions of squares and accompanying texts need be manually canged / added in the
sample control table on top of the sample-page, in case of addition one also need to
increse the table range in the second column control statements. The helptext also need
a mnor alteration in this case.

NOTE statements are rather compex and also the intermediate squares order is
relatively high changing the sample number might therefore take a while to be
calculated. This also applies upon changig one of the other involved parameters.
square multiplication
Square multiplication is a way to combine two square into one by a method simular to
regular number multiplication. Acording to theory when both involved squares are of
certain quality the resulting square is also of that quality, This fact I have proven
for pandiagonality and p-Multimagicness
The spreadsheet implements the multiplication process, the policy page allows to influence
the aspectial variant of the multiplicant into the multiplyers cell (due to the rather
involved expressions this does not go beyond the 4 reflections (N,H,V,R) besides the
Transposition, given the quality of the squares many more possibilities exist)

as the download file show the multilication of two trimagic order 12 (by Walter) gives a
trimagic square order 144, by changing the input to two order 8 bimagic squares you thus
obtain bimagic squares order 64, simular bimagic squares orders 72 and 81 are obtainable

Due to the involved equations this spreadsheet ses "manual recalculation <F9>" for
the entire spreadsheet "shift<F9>" for the current sheet

For the multiplication no definite notation is decided upon (aside from formula)
in case of this spreadsheet one need to specify square1, square2 and placement policy
as stated (far too) many othr possibilities exists

The reader is invited to join me in this programming effort, shortly I'll upload spreadsheet allowing creation of pandiagonal magic squares of prime order and creation of magic square by p-digital equation. The latter two probably also will be complemented by hypercube variations, once I set up the appropriate framework.