Superscripts and Subscripts

Subscripts and superscripts are obtained using the special characters _ and ^ respectively. Thus the identity

[GIF Image]
is obtained by typing
\[ ds^2 = dx_1^2 + dx_2^2 + dx_3^2 - c^2 dt^2 \]
It can also be obtained by typing
\[ ds^2 = dx^2_1 + dx^2_2 + dx^2_3 - c^2 dt^2 \]
since, when a superscript is to appear above a subscript, it is immaterial whether the superscript or subscript is the first to be specified.

Where more than one character occurs in a superscript or subscript, the characters involved should be enclosed in braces. For example, the polynomial [GIF Image] is obtained by typing $x^{17} - 1$.

One may not type expressions such as $s^n^j$ since this is ambiguous and could be interpreted either as [GIF Image] or as [GIF Image]. The first of these alternatives is obtained by typing $s^{n j}$, the second by typing $s^{n^j}$. A similar remark applies to subscripts. Note that one can obtain in this way double superscripts (where a superscript is placed on a superscript) and double subscripts.

It is sometimes necessary to obtain expressions in which the horizontal ordering of the subscripts is significant. One can use an `empty group' {} to separate superscripts and subscripts that must follow one another. For example, the identity

[GIF Image]
can be obtained by typing
\[ R_i{}^j{}_{kl} = g^{jm} R_{imkl}
   = - g^{jm} R_{mikl} = - R^j{}_{ikl} \]