As a network engineer I need to explain some mathematical stuff to my fellow coleagues. Particularly, I need to explain the fact the the Groebner Basis will create an equivalent system. One particular coleague of mine seems to be very skeptical about it as he thinks it is too good to be true.
I also showing him that the solution of the original system and the GB are similar but he still remain a bit skeptical.
For example: (B) is a GB of (A). Note that this result is obtained by using Mathematica so I guess it is a reduced GB.
$\left\{ {\begin{array}{*{20}{c}}{{x^2} - 2xy = 0}\\{{x^2} + 10x + 3{y^2} = 0}\end{array}\left( A \right) \to } \right.\left\{ {\begin{array}{*{20}{c}}{20{y^3} + 7{y^4} = 0}\\{50x + 15{y^2} - 7{y^3} = 0}\end{array}} \right.\left( B \right)$
Is there a simple way to show an algebraic manipulation that turn (A) into (B) ?
I try to express equation 1 and equation 2 of (A) as some kind of linear combination of the equation in (B) but I fail.
Please help me with this
Thank you for your enthusiasm !
