void MalcevSet::makeNormalClosure() {
if(isNormal == yes) return;
const BasicCommutators& BC = theCollector.commutators();
int nilClass = BC.nilpotencyClass();
int upper_i = BC.theFirstOfWeight(nilClass);
for(int i = 1; i <= upper_i; i++) {
if( ! theSet.bound( Generator(i) ) ) continue;
PolyWord Wi = theSet.valueOf( Generator(i) );
PolyWord WiInv = Wi.inverse();
// trying generators of the group
for(int j = 1; j <= BC.numberOfGenerators(); j++) {
Generator g(j);
PolyWord comm = collect( Wi * Letter(g,-1) * WiInv * Letter(g,1) );
addWord(comm);
}
// trying basis elements
int upper_j = BC.theFirstOfWeight(nilClass - BC.weightOf(i) + 1);
if(upper_j > i) upper_j = i;
for(int j = 1; j < upper_j; j++) {
if( ! theSet.bound( Generator(j) ) ) continue;
PolyWord Wj = theSet.valueOf( Generator(j) );
PolyWord comm = collect( Wi * Wj * WiInv * Wj.inverse() );
addWord(comm);
}
}
isBasis = true;
isNormal = yes;
}
bool MalcevSet::reduceWords(PolyWord& pw1, PolyWord& pw2) const {
if(pw1.isEmpty() || pw2.isEmpty())
error("MalcevSet::reduceWords: empty argument");
bool firstChanged = false;
int power1 = absPower(pw1);
int power2 = absPower(pw2);
// make both PolyWords to be of distinct signs
if( sign(pw1) ^ sign(pw2) == 0) // if they have the same sign
pw2 = pw2.inverse();
// in fact, this is Euclid algorithm for finding GCD
do {
if( power1 > power2 ) {
// swapping two words
PolyWord tmp = pw1;
pw1 = pw2;
pw2 = tmp;
int t = power1;
power1 = power2;
power2 = t;
firstChanged = true;
}
power2 -= power1;
pw2 = theCollector.multiply(pw1, pw2);
} while(power2 != 0);
return firstChanged;
}