The Magic Encyclopedia ™ DataBase

(by Aale de Winkel)

The spreadsheet "square qualification" (2002.09.29) is my latest effort write general software for the construction and qualification of squares. With Excell the macro language "visual basic for applications" is built in. With it's help I put the added to the mentioned spreadsheet the following macro's, the following table also serves as a short manual to the currently uploaded:

SquareQualification macro's
main instruction: set parameters and hit <ctrl>w to construct, hit <ctrl>q to qualify or <ctrl>p to print also
<ctrl>w (w from window) interpete the input from the main window and create the square
<ctrl>q (q from qualify) qualify the created square
<ctrl>f (f from full) fully qualify the created square
aside from doing a full p-multimagic qualification for p = 1 .. 5 for
the complete square with the theoretical sums, it also runs for p = 1
the qulifying routine for all internal (wrapped around) subsquares with
ordrs 2 till m - 1 (G5 holds m), possibly resulting in a qulification list
the routine halts at. This strings are (not yet) summarized into a compound
qulification string so currently this need to be done manually
<ctrl>p (p from print) print the created square
note this redirect the usual meaning to the neater macro defined printout
NOTE: summation page 0 still need some definition for high order squares
input fields (worksheet: "main display")
E2 and E3 these field is mainly used in the print routine and can be used to identify the square
for your own purposes.
F4 and G4 The field F4 defines the sample set and G4 the sample within the set based on F4 currently:
0: user input
1: use of pasted square in worksheet "paste area"
2: selection of squares in worksheet "sample set 2" (G4 0 .. 5)
3/9: selection of samples in worksheet "sample set 3 to 9" (G4 0 .. depends on set)
E13 and E14 input of "pan-relocation vector"
F13 control over the aspectial variant (values 0 .. 7)
D12 input for the number range shift (1 pe from analitic to regular, -1 the other way)
parameter definition (worksheet: "main display") H3:R14 B15:R16 B17:R18
SUGGEST: walkthrough through samples set 3 .. 9
Q3 defines the type of input parameters, the following are currently defined
kj: input defines knight jump construction
de: input fields for digit equations
pde: input fileds represent p-digital equations
pan: construction of prime order pandiagonal squares
........ yet to be defined
Knight Jump Construction
H5:J6 "prescription field" define the position of the number 1 H5:H6
and the to vectors I5:I6 and J5:J6
Digit Equation Construction
H5:J6 "prescription field" define parameters of J.R. Hendrickses digit equations
the modular equations: H5 x + I5 y + J5 mod G5 and H6 x + I6 y + J6 mod G5 are
combined and incase N4 = '=' the digit changing permutation B15:R16 is applied
dote: x and y in range 1 .. G5 (the squares order)
p-Digital Equation Construction
H5:J6 "prescription field" define parameters of p-digital equations
the p-digital modular equations depend on the value of p (field M3), if field
N4 yields '_' the diagonal permutation B15:R16 is applied, if N4 shows '=' this
permutation yields a digit change on the high component latin square, while the
digit changing permutation B17:R18 is applied on the low component latin square
Field N3 (either 'n' or 't') transposes the low component latin square (iff 't'),
prior to application of the diagonal permutation.
note1: this is the current imlementation which probably change in a future upload
note: the coordinate have analitic range [0 .. G5-1], so 1-digital eqation versus
de need some trivial conversion!
prime order panmagic square
The field J3 serves as the input field for the high component ls(a) parameter
while M3 takes the role as low component parameter ls(b), the corresponding digit
changing parameters are in B15:R16 and B17:R18 respectively. The order field G5
need to be input as well (It is not tested for being a prime number!)
Note: The limit of the spreadsheet is in principle order 256 due to the limit of columns
the permutation field B15:R16 and B17:R18 are limited to order 32, for higher orders they
are filled by the normal "identity digits", currently not changeable. Some minor surgery
needs to be done if you need to input those digit also.

Note: The author of this spreadsheet is still investigating the programming language and check the possibilities, the main display mentioned fields H3:R14 might change on type of input (ie value of Q3 field) as options are added lines between B17 and R22 probably come in use for input of nessecairy permutations "square" "printer" and "calculations" worksheets are working areas for the macros, the paste area can be used to input your own square, but will probably also get in use to hold data for one of the squares involved in multiplication etc.
Mentioned "input fields" are solidly defined, the use of the permutations B15:R16 and B17:R18 with respect to the pde production probably changes in future uploads (since this isn't defined yet. The printroutine still need work since the "production strings" intend to get too long for a single line, and for the new options of the pde-production not solidly defined yet, also the permutations need be output which might need me to delete the square display for the high orders on the summation page 0

Feel free to suggest add-onns to this spreadsheet (or implement them yourself and send me the "module" by pasting in into a simple ascii-text file (shorter up and download)). Already suggested a pattern matching (myself)

Note: for high order square the full qualifier <ctrl>f takes time due to the runthrough of all suborders on all possible positions!
Further: it is possible that given a square which has s1-pan and s2-pan (s2 <> s2) the direction of this is interchanged. In case you have such a square please run a test, and notify me of this result. In case just interchange the statements just below the text "setup qulifying strings" in module 1