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This procedure computes products in the differential algebra ${C\left(t\right)}_{\mathrm{Dt}}$. The multiplication in this ring is defined by $\mathrm{Dt}a=\frac{\ⅆa}{\ⅆt}+\mathrm{Dt}a$ for all $a$ in $C\left(t\right)$.

The argument domain describes the differential algebra. If this argument is the list $\left[\mathrm{Dt}\,t\right]$, then the differential operators are notated with the symbols $\mathrm{Dt}$ and $t$. They are viewed as elements of the differential algebra $C\left(t\right)$$\left[\mathrm{Dt}\right]$ where $C$ is the field of constants.

If the argument domain is omitted then the differential specified by the environment variable _Envdiffopdomain is used. If this environment variable is not set then the argument domain may not be omitted.

This function is part of the DEtools package, and so it can be used in the form mult(..) only after executing the command with(DEtools). However, it can always be accessed through the long form of the command by using DEtools[mult](..).

$\mathrm{with}\left(\mathrm{DEtools}\right)\:$

$\mathrm{mult}\left(\mathrm{Dt}\,t\mathrm{Dt}\,\left[\mathrm{Dt}\,t\right]\right)$

$t{\mathrm{Dt}}^2+\mathrm{Dt}$