Mathematica doesn't seem to have any problem with these commands:
Simplify[x y, x == 0 && y == 0]
Simplify[x y, x == 0 && y == 10]
Simplify[x y, x == 1 && y == 5]
But when it comes to this command:
Simplify[x y, x == 0 \[Or] y == 0]
it just returns xy
back. I know that for general cases like Simplify[x y, x == 5 \[Or] y == -8]
there isn't any good simplification. Even so, an output like 5y||-8x
can be returned. (Please tell if there's any command to do so). But for the command Simplify[x y, x == 0 \[Or] y == 0]
, the result is pretty obvious which is zero.
I want to know if there's any method to get the output as zero directly. Also, I don't want an output like {0,0}
doing the substitutions alternately.
Thank You.
ClearAll[or]; or /: Refine[a_, or[b__]] := Or @@ (Refine[a, #] & /@ {b}); Refine[x y, or[x == 5, y == -8]]
? $\endgroup$ClearAll[or]; or /: Refine[a_, or[b__]] := Or @@ (Refine[a, #] & /@ {b}); Refine[x y, or[x == 0, y == -0]]
returns0||0
whereas I wanted it simplified to0
only. $\endgroup$