How Input and Output Work
| Input | convert from a textual form to an expression |
| Processing | do computations on the expression |
| Output | convert the resulting expression to textual form |
Steps in the operation of Mathematica.
When you type something like
x^2 what
Mathematica at first sees is just the string of characters
x,
^,
2. But with the usual way that
Mathematica is set up, it immediately knows to convert this string of characters into the expression
Power[x, 2].
Then, after whatever processing is possible has been done,
Mathematica takes the expression
Power[x, 2] and converts it into some kind of textual representation for output.
Mathematica reads the string of characters x, ^, 2 and converts it to the expression Power[x, 2].
| Out[1]= |  |
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This shows the expression in Fortran form.
Out[2]//FortranForm= |
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| Out[3]= |  |
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It is important to understand that in a typical
Mathematica session
In[n] and
Out[n] record only the underlying expressions that are processed, not the textual representations that happen to be used for their input or output.
If you explicitly request a particular kind of output, say by using
TraditionalForm[expr], then what you get will be labeled with
Out[n]//TraditionalForm. This indicates that what you are seeing is
expr//TraditionalForm, even though the value of
Out[n] itself is just
expr.
Mathematica also allows you to specify globally that you want output to be displayed in a particular form. And if you do this, then the form will no longer be indicated explicitly in the label for each line. But it is still the case that
In[n] and
Out[n] will record only underlying expressions, not the textual representations used for their input and output.
This sets t to be an expression with FortranForm explicitly wrapped around it.
Out[4]//FortranForm= |
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The result on the previous line is just the expression.
| Out[5]= |  |
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Out[6]//FortranForm= |
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| Out[7]= |  |
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