Intc - Maple Help

Physics[Intc] - quick input of multiple integrals from -infinity to infinity

 Calling Sequence Intc(f, x1, x2, ..., xn)

Parameters

 f - any algebraic expression; the integrand x1, x2, ..., xn - names representing the integration variables

Description

 • The Intc command facilitates the input of multiple integrals from $-\mathrm{\infty }$ to $\mathrm{\infty }$, frequently used in Physics. The first argument represents the integrand, while the following arguments (one or many) are the integration variables. Note that all integrals built by using Intc use the inert Int instead of int.

Examples

 > $\mathrm{with}\left(\mathrm{Physics}\right):$
 > $\mathrm{Setup}\left(\mathrm{mathematicalnotation}=\mathrm{true}\right)$
 $\left[{\mathrm{mathematicalnotation}}{=}{\mathrm{true}}\right]$ (1)

To enter a two dimensional Integral from -$\mathrm{\infty }$ to $\mathrm{\infty }$, use the following command:

 > $\mathrm{Intc}\left(F\left(\mathrm{x1},\mathrm{x2}\right),\mathrm{x1},\mathrm{x2}\right)$
 ${{\int }}_{{-}{\mathrm{\infty }}}^{{\mathrm{\infty }}}\left({{\int }}_{{-}{\mathrm{\infty }}}^{{\mathrm{\infty }}}{F}{}\left({\mathrm{x1}}{,}{\mathrm{x2}}\right)\phantom{\rule[-0.0ex]{0.3em}{0.0ex}}{ⅆ}{\mathrm{x1}}\right)\phantom{\rule[-0.0ex]{0.3em}{0.0ex}}{ⅆ}{\mathrm{x2}}$ (2)

A typical situation is one in which you want to integrate in a d-volume, where d is the dimension of spacetime. For that purpose, you can either enter all the coordinates as arguments to Intc, or to make the input easier, set an alias for the coordinates, $X=\mathrm{x1},\mathrm{x2},\mathrm{x3},\mathrm{x4}$ (in Physics, the default setting is a Minkowski spacetime with dimension 4 = 3 + 1; you can change this by using Setup), by using the Coordinates command.

 > $\mathrm{Coordinates}\left(X\right)$
 ${}\mathrm{Systems of spacetime coordinates are:}{}\left\{X=\left(\mathrm{x1}{,}\mathrm{x2}{,}\mathrm{x3}{,}\mathrm{x4}\right)\right\}$
 $\left\{{X}\right\}$ (3)
 > $\mathrm{Intc}\left(F\left(X\right),X\right)$
 ${{\int }}_{{-}{\mathrm{\infty }}}^{{\mathrm{\infty }}}\left({{\int }}_{{-}{\mathrm{\infty }}}^{{\mathrm{\infty }}}\left({{\int }}_{{-}{\mathrm{\infty }}}^{{\mathrm{\infty }}}\left({{\int }}_{{-}{\mathrm{\infty }}}^{{\mathrm{\infty }}}{F}{}\left({X}\right)\phantom{\rule[-0.0ex]{0.3em}{0.0ex}}{ⅆ}{\mathrm{x1}}\right)\phantom{\rule[-0.0ex]{0.3em}{0.0ex}}{ⅆ}{\mathrm{x2}}\right)\phantom{\rule[-0.0ex]{0.3em}{0.0ex}}{ⅆ}{\mathrm{x3}}\right)\phantom{\rule[-0.0ex]{0.3em}{0.0ex}}{ⅆ}{\mathrm{x4}}$ (4)