An Application of Gro ̈bner Basis

Vimala Ramani

International Journal of Scientific Research in Science and Technology, 2024, vol. 11, issue 6, 455-460

Abstract: We prove that the height of x_1 is 16 in A=Q[x_1,x_2,y_1,…,y_8 ]/I, where deg(x_i)=deg(y_i )=2i, and I is the ideal generated by the relation (1+x_1 +x_2 )(1 +y_1+⋯+y_8 )=1, using a Gro ̈bner basis technique. We discuss the topological implication and significance of computing the height of x_1.

Keywords: Multivariate polynomial; monomial order; Gro ̈bner basis; height of an element; ideal membership problem (search for similar items in EconPapers)
Date: 2024
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DOI: 10.32628/IJSRST24114309

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