Why does an expression get constants like C1?

[certik]

An example is here, the output [9] has a constant C₁:

In [4]: p = expr_to_holonomic(sqrt(x))

In [5]: q = expr_to_holonomic(sqrt(x**2-x))

In [6]: p
Out[6]: HolonomicFunction((-1/2) + (x)Dx, x), {1/2: [1]}

In [7]: q
Out[7]: HolonomicFunction((-x + 1/2) + (x**2 - x)Dx, x), {1/2: [I]}

In [8]: p+q
Out[8]: HolonomicFunction((x/2 - 3/4) + (-x**2/2 + x)Dx + (x**3 - x**2)Dx**2, x), {1/2: [1 + I]}

In [9]: (p+q).to_expr()
Out[9]: 
   ⎛       ⎛  ________    ⎞        ⎞
√x⋅⎝- 2⋅C₁⋅⎝╲╱ -x + 1  - 1⎠ + 1 + ⅈ⎠

In [10]: p.to_expr()
Out[10]: √x

In [11]: q.to_expr()
Out[11]: 
       ________
ⅈ⋅√x⋅╲╱ -x + 1 

I thought that both p and q is uniquely given here, aren't they?

Also, if the C₁ constant is needed, the user should have a way to specify a generator for these, similarly how the ODE solvers work.