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Question: How to make a variable exchange of quadratic terms in system of equations

Question:How to make a variable exchange of quadratic terms in system of equations

questerion 10 Maple 2018
substitution
December 18 2018
2

Hello,

Suppose we have a set of quadratic equations of the form:

 

U_11 * a * q + U_12 * b * q + U_13 * c * q + U_14 * d * q + U_15 * a * w + U_16 * b * w + U_17 * c * w + U_18 * d * w + .. = C_i

.

.

.

 

Where terms in uppercase means constant while lowercase letters correspond to unknowns.

 

Now, I want to make a change of variable, so instead of having non-linear term `a * q` we would have `s_ij`, meaning i-th equation and j-th unknown after the change was done.

 

I'm trying to do so, because in my case I will be left with a linear system with a small number of unknowns(relative to N) and N equations, and so I could then solve it easily.

 

Any help is appreciated, thank you!
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