Algorithm for solving system of nonlinear equations

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To solve a system of four nonlinear equations involving variables w, x, y, and z, Gröbner basis algorithms are suggested as a viable method. These algorithms can effectively eliminate variables, simplifying the equations for easier analysis. The equations provided include relationships between the variables and constants a, b, c, and d. Seeking advice on the best algorithm indicates a need for efficient computational techniques. Exploring Gröbner bases could lead to a clearer path to finding solutions for the system.
mooshasta
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I'm trying to find an algorithm to solve a 4 variable system of nonlinear equations.. the variables are named w,x,y,z and a,b,c,d are constants:

a = x - y + z
b = w + x
c = y * z
d = x * y / w


Can anyone offer any advice? Much appreciated...
 
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Gröbner basis algorithms could be used to, for example, eliminate all but one variable.
 
Thread 'How to define a vector field?'

Thread 'How to define a vector field?'

Hello! In one book I saw that function ##V## of 3 variables ##V_x, V_y, V_z## (vector field in 3D) can be decomposed in a Taylor series without higher-order terms (partial derivative of second power and higher) at point ##(0,0,0)## such way: I think so: higher-order terms can be neglected because partial derivative of second power and higher are equal to 0. Is this true? And how to define vector field correctly for this case? (In the book I found nothing and my attempt was wrong...
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