Geodesic
On Standard Basis and Multiplicity of ( X a – Y b , X c – Y d )
Acta mathematica Universitatis Comenianae, Tome 72 (2003) no. 1 
E. Boda; R. Farnbauer. On Standard Basis and Multiplicity of  ( X a – Y b , X c – Y d ). Acta mathematica Universitatis Comenianae, Tome 72 (2003) no. 1. http://geodesic.mathdoc.fr/item/AMUC_2003_72_1_a1/
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     author = {E. Boda and R. Farnbauer},
     title = {On {Standard} {Basis} and {Multiplicity} of  ( {X} a – {Y} b , {X} c – {Y} d )},
     journal = {Acta mathematica Universitatis Comenianae},
     year = {2003},
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Voir la notice de l'article provenant de la source Comenius University

Let $I=(X^{a}-Y^{b},X^{c}-Y^{d})\cdot k[X,Y]$ be an ideal of dimension zero in polynomial ring in two variables. In this note a formula for standard basis of $I$ with respect of anti-graded lexicographic order is derived. As a consequence the discussion on the common points of the plane curves $V(X^{a}-Y^{b})$ and $V(X^{c}-Y^{d})$ is given.