For operators f and g there exists an operator $R$ such that the solution space of $R$ is the intersection of the solution spaces of f and g. This procedure finds this operator $R$. Like the gcd for polynomials, this $R$ is a combination $R=af+bg$ for some operators a and b.

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 will be used. If this environment variable is not set then the argument domain may not be omitted.

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

$\mathrm{GCRD}\left({\mathrm{Dx}}^4\,{\mathrm{Dx}}^2-\frac{18x}{1+2x+3x^3}\,\left[\mathrm{Dx}\,x\right]\right)$

$\mathrm{Dx}-\frac{9x^2+2}{3x^3+2x+1}$