I used the following code to generate a list of pythagorean triples followed by the difference of a and b:
Do[Print[m^2 - n^2, ",", 2 m n, ",", m^2 + n^2, ";",
m^2 - n^2 - 2 m n], {n, 100}, {m, n + 1, 100}]
I want to be able to check if a certain list of rules apply to any four sets of triples. For example to generate a list of triples of which a^2+b^2=c^2 applies, which would be all of them, except I have a series of rules of all which would need to be met to qualify. I have no clue as to how to do this. If more information is required, demand and I will supply. (Note that if required, I do have excel available if I need to import it into a table & that I am an absolute newbie to mathematica)
Thanks in advance!
Update:
The rules are the following:
a12+b12=c12
a22+b22=c22
a32+b32=c32
a42+b42=c42
a1=b4
b1=a2
b2=a3
b3=a4
a1+b2=L
b1+a4=L
a2+b3=L
a3+b4=L
When all values for a, b, c, and L are whole numbers. Obviously were using m & n to determine the triplets and not a, b, and c, but do I need to define a, b & c from the table? What you gave me is really helpful, but I dont know how to test with different triples simultaneously. Sorry if Im incoherent. Thanks once again!
P.S.
the last four equations/rules just want to determine that a+b is an integer, otherwise L doesnt matter
Here I make an array (still have zeros, haven't thought a way around that for this one yet):
PythagArrayAn = Array[
If[#3 == 1, 1, 0] (#1^2 - #2^2) +
If[#3 == 2, 1, 0] (2 #1 #2) +
If[#3 == 3, 1, 0] (#1^2 + #2^2) +
If[#3 == 4, 1, 0] (#1^2 - #2^2 - 2 #1 #2)
&, {10, 10, 4}, 1]
(*Pardon The Pun*)
Here is the code that was generously given by Sean Clarke (I only added in Abs[ ] aka absolute value to find the distance between a & b):
generateValues[m_, n_] := {m^2 - n^2, 2 m n, m^2 + n^2,
Abs[m^2 - n^2 - 2 m n]};
Table[generateValues[m , n], {n, 1, 20}, {m, n + 1, 20}]
(*Makes a table of generated pythagorean triplets*)
and
isItPythagorean[list_] := (list[[1]]^2 + list[[2]]^2 == list[[3]]^2);
Table[isItPythagorean[generateValues[m, n]], {n, 1, 20}, {m, n + 1,
20}]
(*This simply is testing if it is pythagorean or not as an example as how one might test if a rule applies. Thanks Sean!*)