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The problem here is that, since LHS is a symbolic expression, then LHS == a will also be a symbolic expression, not a boolean, see:

sage: LHS.parent()
Symbolic Ring
sage: (LHS == a).parent()
Symbolic Ring

You can try:

sage: bool(LHS == a)
True

The problem here is that, since LHS is a symbolic expression, then LHS == a will also be a symbolic expression, not a boolean, see:

sage: LHS.parent()
Symbolic Ring
sage: (LHS == a).parent()
Symbolic Ring

You can try:

sage: bool(LHS == a)
True

Also, LHS is a yields to False since LHS and a do not point to the same object in memory.