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!

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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.

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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!

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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