Hello all-
Anne and I are working on merging some code that implements the
Lenart--Postnikov alcove path model into sage. The algorithm needed a
few features that aren't available in the root_system package, so I
implemented (very basic) versions of what I needed in a temporary file
called crystals/alcove_path_util.py.
I'd like to get some advice on whether my implementations can be
merged into the root_system code. Essentially, I need the
associated_coroot() method (that returns the element of the
coroot_space corresponding to a given element of the root_space) in
the root_lattice_realization.py to be implemented. My implementation
(currently residing in alcove_path_util.py) is:
def root_norm(R, root):
V = R.ambient_space()
alpha = V.simple_roots()
v = alpha[Integer(1)] - alpha[Integer(1)]
for i in (ellipsis_range(Integer(0),Ellipsis,len(root.monomials())-
Integer(1))):
simple_root = root.monomials()[i]
coeff = root.coefficients()[i]
for j in R.index_set():
if simple_root == R.root_space().simple_root(j):
v = v + coeff*alpha[j]
return v.scalar(v)
# Return an element of coroot_space that is the coroot of the given
root.
def coroot(R, root):
rcoroot = R.coroot_space().simple_root(Integer(1)) -
R.coroot_space().simple_root(Integer(1))
for i in (ellipsis_range(Integer(0),Ellipsis,len(root.monomials())-
Integer(1))):
simple_root = root.monomials()[i]
coeff = root.coefficients()[i]
for j in R.index_set():
if simple_root == R.root_space().simple_root(j):
rcoroot = rcoroot +
coeff*(Integer(1)/Integer(2))*(root_norm(R,
R.root_space().simple_root(j)))*R.coroot_space().simple_root(j)
return (Integer(2)/root_norm(R, root))*rcoroot
(I wrote this code over 6 months ago when the root_system code was
still being developed, so you may have more efficient ways to
accomplish this, and I welcome your feedback.) Would anyone mind if I
make a patch to move this code into root_lattice_realization.py (using
the appropriate method names, of course)?
Once I do this, I think that the existing reflection() method in
root_lattice_realization.py should be able to replace my method
root_space_reflection() in alcove_path_util.py, and I will be able to
get rid of the alcove_path_util.py file entirely.
Thanks very much for your help.
Regards,
Brant
--
You received this message because you are subscribed to the Google Groups
"sage-combinat-devel" group.
To post to this group, send email to sage-combinat-de...@googlegroups.com.
To unsubscribe from this group, send email to
sage-combinat-devel+unsubscr...@googlegroups.com.
For more options, visit this group at
http://groups.google.com/group/sage-combinat-devel?hl=en.
