If the multiplication sign * is absent ( say by mistake!) what is SAGE
evaluating?
For example:
x=var('x');f=1/((x-1)(x-3));
f.limit(x=1) returns -1/3
diff(f,x) returns -1/(x - 4)^2
plot(f,(x,0,10)) plots a smooth curve going through -1/3.
It is clear it is evaluating f =1/(x-4). How? Why is not pointing to
the possible error?
Of course with
x=var('x');f=1/((x-1)*(x-3));
diff(f,x) returns -1/((x - 3)*(x - 1)^2) - 1/((x - 3)^2*(x - 1))
f.limit(x=1) returns +Infinity etc.
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