A problem when wrongly using Dot command in Mma

Question

In[1]:= SameQ[Dot[1, 2], 1.2]
TrueQ[Dot[1, 2] == 1.2]

a = 1; b = 2;
SameQ[Dot[a, b], a.b]
TrueQ[Dot[a, b] == a.b]

Out[1]= False

Out[2]= False

Out[4]= True

Out[5]= True 

I know this uses Dot command wrong. Anybody can give me a clear reson for the above different results?

thanks!

Answer 1

a.b is interpreted as Dot[a,b] and then variables a and b are substituted, meaning Dot[1,2] and thus equality holds. This is not the same as 1.2 where the dot stands for the decimal separator and not for the inline operator of Dot.

Answer 2

When you write 1.2, Mma understands a number (aka 6/5), but if you write {1, 1}.{2, 2} or a.b Mma understands a scalar product, as usual in any book using vectors.

HTH!