Entering Two-Dimensional Input
When
Mathematica reads the text
, it interprets it as
raised to the power
.
| Out[1]= |  |
In a notebook, you can also give the two-dimensional input
directly.
Mathematica again interprets this as a power.
| Out[2]= |  |
One way to enter a two-dimensional form such as 
into a Mathematica notebook is to paste this form into the notebook by clicking the appropriate button in the palette.
Here is a palette for entering some common two-dimensional notations.
There are also several ways to enter two-dimensional forms directly from the keyboard.
| x Ctrl+^ y Ctrl+Space | use control keys that exist on most keyboards |
| x Ctrl+6 y Ctrl+Space | use control keys that should exist on all keyboards |
Ways to enter a superscript directly from the keyboard.
You type Ctrl+^ by holding down the Control key, then pressing the ^ key. As soon as you do this, your cursor will jump to a superscript position. You can then type anything you want and it will appear in that position.
When you have finished, press Ctrl+Space to move back down from the superscript position. You type Ctrl+Space by holding down the Control key, then pressing the Space bar.
This sequence of keystrokes enters
.
| Out[3]= |  |
Here the whole expression
is in the superscript.
| Out[4]= |  |
Pressing
Ctrl+Space takes you down from the superscript.
| Out[5]= |  |
You can remember the fact that Ctrl+^ gives you a superscript by thinking of Ctrl+^ as just a more immediate form of ^. When you type 
, Mathematica will leave this one-dimensional form unchanged until you explicitly process it. But if you type 
Ctrl+^ 
then Mathematica will immediately give you a superscript.
On a standard English-language keyboard, the character ^ appears as the shifted version of 6. Mathematica therefore accepts Ctrl+6 as an alternative to Ctrl+^. Note that if you are using something other than a standard English-language keyboard, Mathematica will almost always accept Ctrl+6 but may not accept Ctrl+^.
| x Ctrl+_ y Ctrl+Space | use control keys that exist on most keyboards |
| x Ctrl+- y Ctrl+Space | use control keys that should exist on all keyboards |
Ways to enter a subscript directly from the keyboard.
Subscripts in Mathematica work very much like superscripts. However, whereas Mathematica automatically interprets 
as 
raised to the power 
, it has no similar interpretation for 
. Instead, it just treats 
as a purely symbolic object.
This enters
as a subscript.
| Out[6]= |  |
Here is the usual one-dimensional
Mathematica input that gives the same output expression.
| Out[7]= |  |
| x Ctrl+/ y Ctrl+Space | use control keys |
How to enter a built-up fraction directly from the keyboard.
This enters the built-up fraction
.
| Out[8]= |  |
Here the whole
goes into the denominator.
| Out[9]= |  |
But pressing
Ctrl+Space takes you out of the denominator, so the
does not appear in the denominator.
| Out[10]= |  |
Mathematica automatically interprets a built-up fraction as a division.
| Out[11]= |  |
| Ctrl+@ x Ctrl+Space | use control keys that exist on most keyboards |
| Ctrl+2 x Ctrl+Space | use control keys that should exist on all keyboards |
Ways to enter a square root directly from the keyboard.
This enters a square root.
| Out[12]= |  |
Ctrl+Space takes you out of the square root.
| Out[13]= |  |
Here is the usual one-dimensional
Mathematica input that gives the same output expression.
| Out[14]= |  |
| Ctrl+^ or Ctrl+6 | go to the superscript position |
| Ctrl+_ or Ctrl+- | go to the subscript position |
| Ctrl+@ or Ctrl+2 | go into a square root |
| Ctrl+% or Ctrl+5 | go from subscript to superscript or vice versa, or to the exponent position in a root |
| Ctrl+/ | go to the denominator for a fraction |
| Ctrl+Space | return from a special position |
Special input forms based on control characters. The second forms given should work on any keyboard.
This puts both a subscript and a superscript on
.
| Out[15]= |  |
Here is another way to enter the same expression.
| Out[16]= |  |
The same procedure can be used to enter a definite integral.
| Out[17]= |  |
In addition to subscripts and superscripts, Mathematica also supports the notion of underscripts and overscripts—elements that go directly underneath or above. Among other things, you can use underscripts and overscripts to enter the limits of sums and products.
| x Ctrl+Plus y Ctrl+Space or x Ctrl+= y Ctrl+Space |
| create an underscript  |
| x Ctrl+& y Ctrl+Space or x Ctrl+7 y Ctrl+Space |
| create an overscript  |
Creating underscripts and overscripts.
Here is a way to enter a summation.
| Out[18]= |  |
