# Entering Two-Dimensional Input

When

*Mathematica* reads the text

, it interprets it as

raised to the power

.

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In a notebook, you can also give the two-dimensional input

directly.

*Mathematica* again interprets this as a power.

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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

.

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Here the whole expression

is in the superscript.

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Pressing

Ctrl+Space takes you down from the superscript.

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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.

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Here is the usual one-dimensional

*Mathematica* input that gives the same output expression.

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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

.

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Here the whole

goes into the denominator.

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But pressing

Ctrl+Space takes you out of the denominator, so the

does not appear in the denominator.

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*Mathematica* automatically interprets a built-up fraction as a division.

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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.

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Ctrl+Space takes you out of the square root.

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Here is the usual one-dimensional

*Mathematica* input that gives the same output expression.

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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

.

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Here is another way to enter the same expression.

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The same procedure can be used to enter a definite integral.

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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.

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