ring_elem SchurRing::mult_monomials(const int *m, const int *n)
{
int i;
exponents a_part = ALLOCATE_EXPONENTS(sizeof(int) * (nvars_ + 1));
exponents b_part = ALLOCATE_EXPONENTS(sizeof(int) * (nvars_ + 1));
exponents lambda = ALLOCATE_EXPONENTS(2 * sizeof(int) * (nvars_ + 1));
exponents p = ALLOCATE_EXPONENTS(2 * sizeof(int) * (nvars_ + 1));
// First: obtain the partitions
to_partition(m, a_part);
to_partition(n, b_part);
// Second: make the skew partition
int a = b_part[1];
for (i=1; i <= nvars_ && a_part[i] != 0; i++)
{
p[i] = a + a_part[i];
lambda[i] = a;
}
int top = i-1;
for (i=1; i <= nvars_ && b_part[i] != 0; i++)
{
p[top+i] = b_part[i];
lambda[top+i] = 0;
}
p[top+i] = 0;
lambda[top+i] = 0;
// Call the SM() algorithm
return skew_schur(lambda, p);
}
ring_elem SchurRing2::mult_terms(const_schur_partition a, const_schur_partition b)
{
int maxsize = (a[0] - 1 + b[0] - 1) + 1; // this is the max number of elements in the output partition, plus one
schur_partition lambda = ALLOCATE_EXPONENTS(sizeof(schur_word) * maxsize);
schur_partition p = ALLOCATE_EXPONENTS(sizeof(schur_word) * maxsize);
// Second: make the skew partition (note: r,s>=1)
// this is: if a = r+1 a1 a2 ... ar
// b = s+1 b1 b2 ... bs
// p is:
// (r+s+1) b1+a1 b1+a2 ... b1+ar b1 b2 ... bs
// lambda is:
// (r+1) b1 b1 ... b1 0 0 ... 0
int r = a[0]-1;
int s = b[0]-1;
int c = b[1];
assert(r+s+1 == maxsize);
for (int i=1; i<=r; i++)
{
assert(i < maxsize);
p[i] = c + a[i];
lambda[i] = c;
}
for (int i=r+1; i<r+s+1; i++)
{
assert(i < maxsize);
p[i] = b[i-r];
lambda[i] = 0;
}
p[0] = r+s+1;
lambda[0] = r+1;
return skew_schur(lambda, p);
}