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I'm trying to use the function binary_cubic_coefficients_from_invariants from sage.rings.invariants.reconstruction. I tried the example at the documentation for Reconstruction of Algebraic Forms (top of page), which works as shown, and produces the cubic form (0, 1, -1, 0) as shown. However, using any other discriminant (other that 0) in the function call produces the same form. So for example

sage: binary_cubic_coefficients_from_invariants(4)

(0, 1, -1, 0)

sage: binary_cubic_coefficients_from_invariants(-4)

(0, 1, -1, 0)

sage: binary_cubic_coefficients_from_invariants(108)

(0, 1, -1, 0)

I tried in Sage 10.2 for Mac OS x86 and in SageCell, with the same results in both.

I'm trying to use the function binary_cubic_coefficients_from_invariants binary_cubic_coefficients_from_invariants from sage.rings.invariants.reconstruction. sage.rings.invariants.reconstruction. I tried the example at the documentation for Reconstruction of Algebraic Forms (top of page), which works as shown, and produces the cubic form (0, 1, -1, 0) as shown. However, using any other discriminant (other that 0) in the function call produces the same form. So for example

sage: binary_cubic_coefficients_from_invariants(4)
 
binary_cubic_coefficients_from_invariants(4)
(0, 1, -1, 0)0)
  
sage: binary_cubic_coefficients_from_invariants(-4)
 
binary_cubic_coefficients_from_invariants(-4)
(0, 1, -1, 0)0)
  
sage: binary_cubic_coefficients_from_invariants(108)
 
binary_cubic_coefficients_from_invariants(108)
(0, 1, -1, 0)0)