/*
carres latins mutuellement orthogonaux
pour q = p^a avec p premier
GF(q) = { l1, l2, ..., l_q-1, lq=0 }
matrices A_i A_2 ... A_k A_q-1 1<= k <= q-1
A_k(x_i,j) = ( li*lk+lj )
(C) 2009 Jean-Paul Davalan
*/
function gcd(x, y) {
var u=x, v=y, w;
while(v!=0) {
w = u%v
u=v
v=w
}
return u
}
//var Alpha ="A B C D E F G H I J K L M N O P Q R S T U V W X Y Z".split(/\s/g)
var alpha ="a b c d e f g h i j k l m n o p q r s t u v w x y z A B C D E F G H I J K L M N O P Q R S T U V W X Y Z".split(/\s/g)
var grec = "α β γ δ ε ζ η θ ϑ ι κ λ μ ν ξ ο π ϖ ρ ς σ τ υ ϒ φ χ ψ ω Α Β Γ Δ Ε Ζ Η Θ &Thetasym; Ι Κ Λ Μ Ν Ξ Ο Π &Piv; Ρ &Sigmaf; Σ Τ Υ &Upsih; Φ Χ Ψ Ω".split(/\s/g)
//alert(Alpha)
var gl=true;
function cgl(q, k0, k1) {
var a, b, u,uu, tb=[]
s = ""
var r=0
var premier=true, test=true
if(isprime(q)==false) {
premier = false
//s += "
"
s += "
"
if(gcd(q, k0) != 1) r++
if(gcd(q, k1) != 1) r++
if(r>0) {
test = false
s += "
"
if(r==2) s += "aucun des deux carrés utilisés n'est un carré latin.
"
}
}
if(k0==k1) {
s += "
"
}
s += "
"
for(var i=0; i 1 ) {
s += "
"
test = false
break;
}
}
if(premier==false && test==true) {
s += "
"
}
return "
"+s+"
"
}
function isprime(n) {
if(n<2 || (n>2 && n%2==0)) return false
var a = Math.sqrt(n)
for(var k=3; k<= a; k+= 2) {
if(n%k==0) return false
}
return true;
}
//alert(cgl(7,3,5))
function calcule() {
var q = parseInt(document.frm.p.value)
var k0 = parseInt(document.frm.k0.value)
var k1 = parseInt(document.frm.k1.value)
gl = (document.frm.ck.checked)
// alert(q+" "+k0+" "+k1)
var s = cgl(q, k0, k1)
// alert(s)
document.getElementById("divCarre").innerHTML = s
}
var prm = [3,5,7,11,13,17,19]
function exmplegl() {
gl=false
var p = prm[Math.floor(prm.length*Math.random())]
var k0 = Math.floor((p-1)*Math.random())
var t = Math.floor((p-2)*Math.random())
var k1 = (k0+t)%(p-1)
//alert(p+" "+k0+" "+k1)
var s = cgl(p, 1+k0, 2+k1)
document.getElementById("carre2").innerHTML = s
}