I try to solve an equation by using Groebner bases. When I use Maple to find its Groebner basis with plex order, Maple take too long to calculate and the proceed does not terminate. Thus, I try to find with tdeg order and the proceed takes seconds.
Now, I have the Groebner basis with tdeg order. I want to use it to find the Groebner basis with plex order. Can I do it in Maple?
Yes, it is possible. Two options are using Walk and FGLM commands, both from Groebner package. You can read about these two commands and see some examples of using them to convert a Grobner basis from a monomial order to a Grobner basis in another monomial order in the documentation of these commands in Maple's help manual.