# Entering Formulas

character | short form | long form | symbol |

EscpEsc | \[Pi] | Pi | |

EscinfEsc | \[Infinity] | Infinity | |

EscdegEsc | \[Degree] | Degree |

Special forms for some common symbols.

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special characters | short form | long form | ordinary characters |

x≤y | x Esc<=Esc y | x \[LessEqual] y | x <= y |

x≥y | x Esc>=Esc y | x \[GreaterEqual] y | x >= y |

x≠y | x Esc!=Esc y | x \[NotEqual] y | x != y |

xy | x EscelEsc y | x \[Element] y | Element[x,y] |

x→y | x Esc->Esc y | x \[Rule] y | x -> y |

Special forms for a few operators. "Operator Input Forms" gives a complete list.

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When you type the ordinary-character form for certain operators, the front end automatically replaces them with the special-character form. For instance, when you type the last three examples, the front end automatically substitutes the character for .

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special characters | short form | long form | ordinary characters |

x ÷ y | x EscdivEsc y | x \[Divide] y | x / y |

x × y | x Esc*Esc y | x \[Times] y | x * y |

x y | x EsccrossEsc y | x \[Cross] y | Cross[x,y] |

x = y | x Esc==Esc y | x \[Equal] y | x == y |

x y | x Escl=Esc y | x \[LongEqual] y | x == y |

x y | x Esc&&Esc y | x \[And] y | x && y |

x y | x Esc||Esc y | x \[Or] y | x || y |

¬ x | Esc!Esc x | \[Not] x | ! x |

x y | x Esc=>Esc y | x \[Implies] y | x => y |

x y | x EscunEsc y | x \[Union] y | Union[x,y] |

x y | x EscinterEsc y | x \[Intersection] y | Intersection[x,y] |

xy | x Esc,Esc y | x \[InvisibleComma] y | x , y |

fx | f Esc@Esc x | f \[InvisibleApplication] x | f @ x or f[x] |

x | x Esc+Esc | x \[ImplicitPlus] | x + y / z |

Some operators with special forms used for input but not output.

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Many of the forms of input discussed here use special characters, but otherwise just consist of ordinary one-dimensional lines of text. *Mathematica* notebooks, however, also make it possible to use two-dimensional forms of input.

two-dimensional | one-dimensional | |

x^y | power | |

x/y | division | |

Sqrt[x] | square root | |

x^(1/n) | root | |

Sum[f,{i,i_{min},i_{max}}] | sum | |

Product[f,{i,i_{min},i_{max}}] | product | |

Integrate[f,x] | indefinite integral | |

Integrate[f,{x,x_{min},x_{max}}] | definite integral | |

D[f,x] | partial derivative | |

D[f,x,y] | multivariate partial derivative | |

Conjugate[x] | complex conjugate | |

Transpose[m] | transpose | |

ConjugateTranspose[m] | conjugate transpose | |

Part[expr,i,j,...] | part extraction |

Some two-dimensional forms that can be used in *Mathematica* notebooks.

You can enter two-dimensional forms using any of the mechanisms discussed in "Entering Two-Dimensional Input". Note that upper and lower limits for sums and products must be entered as overscripts and underscripts—not superscripts and subscripts.

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short form | long form | |

EscsumEsc | \[Sum] | summation sign |

EscprodEsc | \[Product] | product sign |

EscintEsc | \[Integral] | integral sign |

EscddEsc | \[DifferentialD] | special for use in integrals |

EscpdEsc | \[PartialD] | partial derivative operator |

EsccoEsc | \[Conjugate] | conjugate symbol |

EsctrEsc | \[Transpose] | transpose symbol |

EscctEsc | \[ConjugateTranspose] | conjugate transpose symbol |

Esc[[Esc | \[LeftDoubleBracket] | part brackets |

Some special characters used in entering formulas. "Mathematical and Other Notation" gives a complete list.

You should realize that even though a summation sign can look almost identical to a capital sigma it is treated in a very different way by *Mathematica*. The point is that a sigma is just a letter; but a summation sign is an operator which tells *Mathematica* to perform a Sum operation.

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Much as *Mathematica* distinguishes between a summation sign and a capital sigma, it also distinguishes between an ordinary , the "partial d" that is used for taking derivatives, and the special "differential d" that is used in the standard notation for integrals. It is crucial that you use the differential —entered as EscddEsc—when you type in an integral. If you try to use an ordinary , *Mathematica* will just interpret this as a symbol called —it will not understand that you are entering the second part of an integration operator.

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