The Modular[GCRD](Ore1, Ore2, p, A) calling sequence returns the GCRD of Ore1 and Ore2 modulo the prime p.

The Modular[LCLM](Ore1, Ore2, ..., Orek, p, A) calling sequence returns the GCRD of Ore1, Ore2, ..., Orek modulo the prime p.

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

$A≔\mathrm{SetOreRing}\left(n\,'\mathrm{differential}'\right)$

$A≔\mathrm{UnivariateOreRing}\left(n\,\mathrm{differential}\right)$

$\mathrm{Ore1}≔'\mathrm{OrePoly}'\left(-n\,n+6\right)$

$\mathrm{Ore1}≔\mathrm{OrePoly}\left(-n\,n+6\right)$

$\mathrm{Ore2}≔'\mathrm{OrePoly}'\left(-n\,n-1\right)$

$\mathrm{Ore2}≔\mathrm{OrePoly}\left(-n\,n-1\right)$

$\mathrm{Ore3}≔'\mathrm{OrePoly}'\left(n+1\,n-1\right)$

$\mathrm{Ore3}≔\mathrm{OrePoly}\left(n+1\,n-1\right)$

$\mathrm{Poly1}≔\mathrm{Modular}\left[\mathrm{Multiply}\right]\left(\mathrm{Ore1}\,\mathrm{Ore3}\,541\,A\right)$

$\mathrm{Poly1}≔\mathrm{OrePoly}\left(540n^2+6\,9n+12\,\left(n+6\right)\left(n+540\right)\right)$

$\mathrm{Poly2}≔\mathrm{Modular}\left[\mathrm{Multiply}\right]\left(\mathrm{Ore2}\,\mathrm{Ore3}\,541\,A\right)$

$\mathrm{Poly2}≔\mathrm{OrePoly}\left(540n^2+540\,2n+539\,{\left(n+540\right)}^2\right)$

$\mathrm{Modular}\left[\mathrm{GCRD}\right]\left(\mathrm{Poly1}\,\mathrm{Poly2}\,541\,A\right)$

$\mathrm{OrePoly}\left(\frac{n+1}{n+540}\,1\right)$

$\mathrm{Modular}\left[\mathrm{LCLM}\right]\left(\mathrm{Poly1}\,\mathrm{Poly2}\,\mathrm{Ore1}\,541\,A\right)$

$\mathrm{OrePoly}\left(\frac{540n^6+531n^5+37n^4+227n^3+468n^2+95n+456}{n^6+24n^5+187n^4+511n^3+177n^2+181n+1}\,\frac{2n^6+38n^5+168n^4+405n^3+438n^2+101n+195}{n^6+24n^5+187n^4+511n^3+177n^2+181n+1}\,\frac{519n^5+169n^4+97n^3+68n^2+439n+267}{n^6+24n^5+187n^4+511n^3+177n^2+181n+1}\,\frac{539n^5+523n^4+88n^3+396n^2+200n+510}{n^5+18n^4+79n^3+37n^2+496n+451}\,1\right)$

Abramov, S.A.; Le, H.Q.; and Li, Z. "OreTools: a computer algebra library for univariate Ore polynomial rings." Technical Report CS-2003-12. School of Computer Science, University of Waterloo, 2003.

Li, Z., and Nemes, I. "A modular algorithm for computing greatest common right divisors of Ore polynomials." Proc. of ISSAC'97, pp. 282-289. Edited by W. Kuechlin. ACM Press, 1997.