Mathematical symbolism

Mathematica offers a full range of possible mathematical symbols - for input and output of data. Mathematica combines the compactness of mathematical symbols with the accuracy of a programming language.

Example 1. In order to calculate an integral we can type in the following command, which uses only ordinary keyboard symbols (standard input):

Integrate[Log[1 + x]/Sqrt[x], x]

-4 x^(1/2) + 4 ArcTan[x^(1/2)] + 2 x^(1/2) Log[1 + x]

The same command can be called by using special symbols. They can be chosen from the palette or directly from the keyboard.

∫Log[1 + ξ]/ξ^(1/2) ξ

-4 ξ^(1/2) + 4 ArcTan[ξ^(1/2)] + 2 ξ^(1/2) Log[1 + ξ]

To input the upper command from the keyboard directly you must first type in the combination of symbols shown below. The symbol  :  is printed by pressing the [ESC] key. For example the combination :int: generates the integral symbol.

int Log[1 + x] / 2 x   dd x

Example 2.  A very helpful thing is the possibility of editing (changing, deleting, copying, etc.) in any part of the notebook - in input or output, or, in other words, in the 'In' or the 'Out' line.

-4 ξ^(1/2) + 4 ArcTan[ξ^(1/2)] + 2 ξ^(1/2) Log[1 + ξ]

-4 ξ^(1/2) + 4 ArcTan[ξ^(1/2)] + 2 ξ^(1/2) Log[1 + ξ]

Example 3. Mathematica can show the result in traditional from, as shown in the mathematical books. The next integral will be calculated and the result will be shown in traditional form.

∫Log[1 + ξ]/ξ^(1/2) ξ // TraditionalForm

4 tan^(-1)(ξ^(1/2)) + 2 ξ^(1/2) log(ξ + 1) - 4 ξ^(1/2)

Look in Formula Gallery for other examples of mathematical formulas.

Example 4. Using abstract markings is not difficult:

Table[⋄Overscript[α_i⊕β_i, _] ⟹Underoverscript[Ϡ, i, arg3], {i, 6}]

{⋄Overscript[α_1⊕β_1, _] ⟹Underoverscript[Ϡ, 1, arg3 ... ], ⋄Overscript[α_6⊕β_6, _] ⟹Underoverscript[Ϡ, 6, arg3]}

Mathematica supports over 700 special symbols for screen or print reproduction. They are located in the palette Complete Characters. There are foreign as well as TeX and SGML symbols.

[Graphics:HTMLFiles/index_12.gif]

[Graphics:HTMLFiles/index_13.gif]


Created by Mathematica  (October 6, 2007)