more Lie algebras

[selpoG]

We support few Lie algebras now, but in principle, we can construct any irreps of a simple Lie algebra.

[selpoG]

SU(4) support has begun.
prod is embedded by hand, and could be insufficient.
In case you see such as "Oops! We need prod of v[4,2,1] and v[3,1,0]!", you have to execute f([4,2,1],[3,1]) in SageMath after loading following python code, and insert the output into 386th line in grouplie.m.

import functools
from collections import defaultdict
from sage.combinat.partition import Partitions
import sage.libs.lrcalc.lrcalc as lrcalc

# SU(rank + 1)
rank = 3

def my_get(t, i): return t[i] if i < len(t) else 0

def comp_part(x, y):
	t = sum(x) - sum(y)
	if t != 0: return t
	for i in range(rank - 1):
		t = my_get(y, i) - my_get(x, i)
		if t != 0: return t
	return 0

def as_prod(ans):
	cnt = defaultdict(int)
	for p, n in ans.items():
		l = reduce(list(p))
		if l is not None: cnt[tuple(l)] += n
	for t in sorted(cnt.keys(), key=functools.cmp_to_key(comp_part)):
		l = list(t)
		if cnt[t] > 1: print("{0} appears {1} times!".format(get_v(l), cnt[t]))
		for _ in range(cnt[t]): yield l

def reduce(x):
	if len(x) > rank + 1: return None
	if len(x) <= rank: return [a for a in x if a > 0]
	return [b for a in x[:-1] for b in [a - x[-1]] if b > 0]

def get_parts(n): return list(map(list, Partitions(n, max_length=rank).list()))

def calc_mult(x, y): return list(as_prod(lrcalc.mult(x, y, maxrows=rank + 1)))

def get_v(p): return "v[{0}]".format(", ".join(my_get(p, i) for i in range(rank)))

def to_mathematica(x): return "{" + ", ".join(map(get_v, x)) + "}"

def f(x, y): print ("G[prod[{0}, {1}]] = {2};".format(get_v(x), get_v(y), to_mathematica(calc_mult(x, y))))

[selpoG]

SU(4) support has completed.
The workaround above is not needed now.