Geodesic
Involutive Gr\"obner walk
Fundamentalʹnaâ i prikladnaâ matematika, Tome 7 (2001) no. 4, pp. 993-1001.

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An algorithm that transforms an involutive basis of a polynomial ideal with respect to one monomial ordering into an involutive basis with respect to another ordering is proposed. The algorithm is based on the Gröbner walk method of transformation of Gröbner bases of polynomial ideals. 
@article{FPM_2001_7_4_a2,
     author = {O. D. Golubitsky},
     title = {Involutive {Gr\"obner} walk},
     journal = {Fundamentalʹna\^a i prikladna\^a matematika},
     pages = {993--1001},
     publisher = {mathdoc},
     volume = {7},
     number = {4},
     year = {2001},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/FPM_2001_7_4_a2/}
}
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O. D. Golubitsky. Involutive Gr\"obner walk. Fundamentalʹnaâ i prikladnaâ matematika, Tome 7 (2001) no. 4, pp. 993-1001. http://geodesic.mathdoc.fr/item/FPM_2001_7_4_a2/