unsigned long staticity( method const& m )
{
unsigned long s = 0ul; //1ul;
for ( int i=0, b=m.bells(); i!=b-1; ++i)
{
int j=0, l=m.size();
while ( j!=l && ( m[j].findswap(i) ||
m[j].findplace(i) && m[j].findplace(i+1) ) )
++j;
if (j==l)
return static_cast<unsigned long>(-1);
for ( int k=j; k<j+l; ++k )
{
int k0=k;
while ( k!=j+l && ( m[k%l].findswap(i) ||
m[k%l].findplace(i) && m[k%l].findplace(i+1) ) )
++k;
if (k!=k0) {
// s *= ipower( 2, k-k0-1 );
s += k-k0-1;
}
}
}
return s;
}
bool has_mirror_symmetry( const method& m )
{
const int n( m.size() );
for ( int i=0; i<n; ++i )
if ( m[i] != m[i].reverse() )
return false;
return true;
}
bool has_glide_symmetry( const method& m )
{
const int n( m.size() );
if ( n % 2 == 1 ) return false;
for ( int i=0; i<n/2; ++i )
if ( m[i] != m[(i + n/2) % n].reverse() )
return false;
return true;
}
bool has_conventional_symmetry( const method& m )
{
const int n( m.size() );
for ( int i=0; i < (n%2==0 ? n/2 : n); ++i )
{
// try m[i] as the sym point
bool ok(true);
for ( int j=1; ok && j<(n%2==0 ? n/2 : n/2+1); ++j )
if ( m[(i+j) % n] != m[(i-j+n) % n] )
ok = false;
if (ok) return true;
}
return false;
}
bool has_rotational_symmetry( const method &m )
{
const int n( m.size() );
{
// Rotational symmetry about a change
for ( int i=0; i<n/2+1; ++i )
{
// Try m[i] as the rotational symmetry point
bool ok = true;
for ( int j=0; j<n/2+1 && ok; ++j )
if ( m[ (i+j)%n ] != m[ (n+i-j)%n ].reverse() )
ok = false;
if (ok)
return true;
}
}
{
// Rotational symmetry about a row
for ( int i=0; i<n/2+1; ++i )
{
// Try m[i] / m[(i+1)%n] as the rotational symmetry point
bool ok = true;
for ( int j=0; j<n/2 && ok; ++j )
if ( m[ (i+j+1)%n ] != m[ (n+i-j)%n ].reverse() )
ok = false;
if (ok)
return true;
}
}
return false;
}