AbelianGroup MalcevSet::mapToQuotient(int k) const {
if( ! isBasis )
error("MalcevSet::mapToQuotient: the set must be full");
// The generators of the quotient are basic commutators of weight k.
const BasicCommutators& bc = theCollector.commutators();
int numGen = bc.numberOfWeight(k);
int firstGen = bc.theFirstOfWeight(k) - 1;
// The relators are Malcev basis words of weight k
SetOf<Word> relsForAbelian;
QuickAssociationsIterator< Generator, PolyWord > iter(theSet);
for( ; ! iter.done(); iter.next() ) {
// take a word from Malcev basis
PolyWord pw = iter.value();
Letter first = pw.firstLetter();
if( ord(first.gen) != firstGen ) continue;
//Ok, this is a word from the quotient. Abelianize it.
ConstPolyWordIterator iter( pw );
Word w;
for(iter.startFromLeft(); ! iter.done(); iter.stepRight() ) {
Letter s = iter.thisLetter();
int newgen = ord(s.gen) - firstGen;
if( newgen > numGen ) break;
s.gen = Generator( newgen );
w *= Word(s);
}
relsForAbelian.adjoinElement(w);
}
// make the abelian quotient
AbelianGroup abel( FPGroup(numGen, relsForAbelian) );
abel.computeCyclicDecomposition();
return abel;
}
main()
{
int i,n=N;
float f[N],g[N],e[N],a,r,k,dr,dk;
void *at;
a = 1.0;
dr = dk = 1.0/n;
for (i=0,r=0.0; i<n; ++i,r+=dr) {
f[i] = a-r;
}
at = abelalloc(n);
abel(at,f,g);
for (i=0,k=0.0; i<n; ++i,k+=dk) {
g[i] *= dr;
e[i] = (k!=0.0 ? a*sqrt(a*a-k*k)-k*k*acosh(a/k) : a*a);
}
abelfree(at);
fwrite(g,sizeof(float),n,stdout);
fwrite(e,sizeof(float),n,stdout);
}
