A problem when wrongly using Dot command in Mma

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?

than开发者_C百科ks!

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.

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!

It can be informative to view an expression under Hold and FullForm:

a = 1; b = 2;
SameQ[Dot[a, b], a.b]] //Hold //FullForm

    Hold[SameQ[Dot[a, b], Dot[a, b]]]

With this combination of commands, Mathematica parses but does not evaluate the expression (Hold), and then shows the long pseudo-internal form of the expression (FullForm).

In this case, you can see that the second term a.b is parsed as Dot[a, b] before any evaluation happens.

When . appears with numerals as in 1.2 it is interpreted specially as a decimal point. This is similar to other numeric entry formats such as: 1*^6 which is recognized directly as 1000000:

1*^6 //Hold //FullForm

Compare trying to enter:

a = 1;

a*^6