CoCalc -- 3339.sagews

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T = CartanType(['A', 5]); #Imput the Cartan Type here
Lambda = RootSystem(T).weight_lattice().fundamental_weights();

def isPerp(x):             #Checks if x+rho is perpendicular to any root
    rho = sum(x.parent().fundamental_weights()); 
    for y in RootSystem(x.parent().cartan_type()).coroot_lattice().roots():                                        
        if (x+rho).scalar(y) == 0:                                
            return [True,y];
            break
    else:
        return [False,y]

def isCaseC(x):          #computes w so that w(x+rho) - rho is dominant
    rho = sum(x.parent().fundamental_weights());
    for w in RootSystem(x.parent().cartan_type()).weight_lattice().weyl_group():
        if (w.action(x+rho)-rho).is_dominant() == True:
            return [(w^-1).length(), w.action(x+rho)-rho];
            break
    else:
            pass

def BWB(x):
    if x.is_dominant():
        print '%s is in the fundamental chamber, so \n H^0(G/B, %s) !=0 and H^j(G/B, %s) is zero for j >0' % (x, x, x)        
    elif isPerp(x)[0]:
        print '%s is perp to \n %s + rho = \n %s, so \n H^j(G/B, %s) = 0 for all j' % (isPerp(x)[1], x, x + sum(x.parent().fundamental_weights()), x)
    else:
        print 'H^i(G/B, %s ) = 0 for i != %s, and \n H^%s(G/B, %s )  = H^0(G/B, %s ) != 0' % (x, isCaseC(x)[0], isCaseC(x)[0], x, isCaseC(x)[1])

BWB(8*Lambda[4]-8*Lambda[1])

H^i(G/B, -8*Lambda[1] + 8*Lambda[4] ) = 0 for i != 3, and 
 H^3(G/B, -8*Lambda[1] + 8*Lambda[4] )  = H^0(G/B, 4*Lambda[3] + 3*Lambda[4] ) != 0

H^i(G/B, -8*Lambda[1] + 8*Lambda[4] ) = 0 for i != 3, and 
 H^3(G/B, -8*Lambda[1] + 8*Lambda[4] )  = H^0(G/B, 4*Lambda[3] + 3*Lambda[4] ) != 0

L = (-4)*Lambda[1];
rho = sum(Lambda);
W = RootSystem(T).weight_lattice().weyl_group();
for w in W:
    if w.action(L + rho) - rho == L and w != W.one():
        w.reduced_word();
        break
    else:
        M = 0

[1, 2, 3, 4, 3, 2, 1]

M = 0;
n = len(Lambda);
i = -2*n +3;
rho = sum(Lambda);
W = RootSystem(T).weight_lattice().weyl_group();
while (i <= 0):
    L = (2*n-2+i )*Lambda[1]-Lambda[5]-Lambda[4];
    for w in W:
        if w.action(L + rho) - rho == L and w != W.one():
            M = 1;
            print M, i;
            i=i+1;
            break
        else:
            M = 0;
            print M, i;
            i=i+1;

WARNING: Output truncated!

full_output.txt