False implicit plot

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Sage does not guess the names of the variables (you could have been using any name). As your expression contains a single variable, it assumes that this is the first variable (what you would call "x"). To get what you want, use the more explicit syntax

sage: x = var('x')
sage: y = var('y')
sage: implicit_plot(y==1/2, (x,0,1), (y,0,1))