Say we have $r$ linear polynomials $p_1,\ldots,p_r\in k[x_1,\ldots,x_n]$ which are linearly independent. How can we establish an automorphism of $k[x_1,\ldots,x_n]$ such that each $p_i$ goes to $x_i$? I know it has something to do with gaussian elimination, but I have no clue on how to proceed.
2026-03-28 06:40:46.1774680046
Automorphism of $k[x_1,\ldots,x_n]$
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