D4=QuadraticForm(Matrix(ZZ,4,4,[2,0,0,-1,0,2,0,-1,0,0,2,-1,-1,-1,-1,2]))
G=D4.global_genus_symbol()
sage.quadratic_forms.genera.genus.is_GlobalGenus(G)
G==copy(G)
sage.quadratic_forms.genera.genus.is_GlobalGenus(G)
Another instance of the same problem:
D4=QuadraticForm(Matrix(ZZ,4,4,[2,0,0,-1,0,2,0,-1,0,0,2,-1,-1,-1,-1,2]))
G=D4.global_genus_symbol()
G._local_symbols[0].excess()
G==copy(G)
G._local_symbols[0].excess()
the second answer is wrong here.
The problem seems to originate somewhere in
sage.quadratic_forms.genera.genus.Genus_Symbol_p_adic_ring.canonical_symbol