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sage: a_1, a_2, b_1, b_2 = var('a_1 a_2 b_1 b_2')
sage: eq1 = a_1 * a_2^2 - a_2 * a_1^3 == 0
sage: eq2 = 2a_1a_2b_2 + b_2a_2^2 - 3a_2a_1^2b_1 - a_1b_2
sage: eq3 = a_2^3 - a_2^2a_1^2
sage: eq4 = 3a_2^2b_2 - 2a_2a_1^2b_2 - 2a_2^2b_1
sage: solve([eq1, eq2, eq3, eq4], a_1, a_2, b_1, b_2)
[[a_1 == 0, a_2 == 0, b_1 == c2439, b_2 == c2440], [a_1 == c2441, a_2 == 0, b_1 == c2442, b_2 == 0], [a_1 == c2443, a_2 == c2443^2, b_1 == 0, b_2 == 0]]

im getting these weird c2439 and c2440 solutions, are they just arbitrary complex numbers? Shouldn't they rather be prefixed with 'r' in that case? Can anyone tell me what these c-values are?

Here is the issue:

sage: a_1, a_2, b_1, b_2 = var('a_1 a_2 b_1 b_2') 
 
sage: eq1 = a_1 * a_2^2 - a_2 * a_1^3 == 0 
 
sage: eq2 = 2a_1a_2b_2 2*a_1*a_2*b_2 + b_2a_2^2 - 3a_2a_1^2b_1 - a_1b_2 
b_2*a_2^2 - 3*a_2*a_1^2*b_1 - a_1*b_2               
sage: eq3 = a_2^3 - a_2^2a_1^2 
a_2^2*a_1^2                                                 
sage: eq4 = 3a_2^2b_2 - 2a_2a_1^2b_2 - 2a_2^2b_1 
3*a_2^2*b_2 - 2*a_2*a_1^2*b_2 - 2*a_2^2*b_1                         
sage: solve([eq1, eq2, eq3, eq4], a_1, a_2, b_1, b_2) 
 
[[a_1 == 0, a_2 == 0, b_1 == c2439, b_2 == c2440], [a_1 == c2441, a_2 == 0, b_1 == c2442, b_2 == 0], [a_1 == c2443, a_2 == c2443^2, b_1 == 0, b_2 == 0]]
0]]

im getting these weird c2439 and c2440 solutions, are they just arbitrary complex numbers? Shouldn't they rather be prefixed with 'r' in that case? Can anyone tell me what these c-values are?