Garbage.sagews

avar_string = ""
deg = 4
for i in range(deg): 
    avar_string += "a"
    avar_string += str(i)
    avar_string += ", "
avar_string += "a"
avar_string += str(deg)


R.<A,B,C> = QQ['A,B,C']
RR = R[avar_string]
a = RR.gens()
RRR.<x,y> = RR['x,y']


f = sum([a[i] * x^(deg-i) * y^i for i in range(deg+1)])

QF = A*x^2 + B*x*y + C*y^2
Lap_f = C*derivative(f,x,2) - B * derivative(f,x,y) + A * derivative(f,y,2)


Lap_f.coefficients()
Lap_f.coefficients()[0]
Lap_f.coefficients()[1]

Lap_f.coefficients()[2]

Lap_f.coefficients()[2].coefficients()

print"\n"
Lap_f.coefficient(x^2)
(Lap_f.coefficient(x^2)).change_ring(RR).coefficient(a[0])
print "\n"

[[Lap_f.coefficient(mon).coefficient(a[j]) for mon in [x^2, x*y, y^2]] for j in range(deg+1)]

[12*C*a0 + (-3*B)*a1 + 2*A*a2, 6*C*a1 + (-4*B)*a2 + 6*A*a3, 2*C*a2 + (-3*B)*a3 + 12*A*a4] 12*C*a0 + (-3*B)*a1 + 2*A*a2 6*C*a1 + (-4*B)*a2 + 6*A*a3 2*C*a2 + (-3*B)*a3 + 12*A*a4 [2*C, -3*B, 12*A] 12*C*a0 + (-3*B)*a1 + 2*A*a2

Error in lines 23-23 Traceback (most recent call last): File "/projects/sage/sage-7.6/local/lib/python2.7/site-packages/smc_sagews/sage_server.py", line 995, in execute exec compile(block+'\n', '', 'single') in namespace, locals File "", line 1, in <module> File "/projects/sage/sage-7.6/local/lib/python2.7/site-packages/sage/rings/polynomial/multi_polynomial_element.py", line 866, in coefficient raise ValueError("You must pass a dictionary list or monomial.") ValueError: You must pass a dictionary list or monomial.

f = sum([a[i] * x^(deg-i) * y^i for i in range(deg+1)])

QF = A*x^2 + B*x*y + C*y^2
Lap_f = C*derivative(f,x,2) - B * derivative(f,x,y) + A * derivative(f,y,2)

matrix([[Lap_f.coefficients()[j].coefficient(a[i]) for i in range(deg+1)] for j in range(3)])