Sun 2018-06-03 11:33:16 UTC, Simon King:
>
> For symbolics, "==" only does trivial checks and leaves the equality
> unevaluated otherwise, so that you need an explicit evaluation as a
> bool in order to force a non-trivial computation.
>
> Such as:
>
> sage: (x+1)^2 == x^2+2*x+1
> (x + 1)^2 == x^2 + 2*x + 1
> sage: bool(_)
> True
Actually, for symbolics, "==" always creates an equation,
and never tries to evaluate it!
A lot of confusion stems from the fact that what "==" does
depends on whether both sides are symbolic:
- if neither side is symbolic, it tests equality
- if either side is symbolic, it creates an equation
Once an equation has been created, to evaluate
whether the equation holds, one can use "bool".
Compare:
sage: 0 == 1
False
sage: SR(0) == 1
0 == 1
sage: 0 == SR(1)
0 == 1
sage: SR(0) == SR(1)
0 == 1
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