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SciMax Toolbox >> eliminate

eliminate

Maxima Function

Calling Sequence

eliminate ([eqn_1, ..., eqn_n], [x_1, ..., x_k])

Description

Eliminates variables from equations (or expressions assumed equal to zero) by taking successive resultants. This returns a list of n - k expressions with the k variables x_1, ..., x_k eliminated. First x_1 is eliminated yielding n - 1 expressions, then x_2 is eliminated, etc. If k = n then a single expression in a list is returned free of the variables x_1, ..., x_k. In this case solve is called to solve the last resultant for the last variable.

Example:

(%i1) expr1: 2*x^2 + y*x + z;
                                      2
(%o1)                    z + x y + 2 x
(%i2) expr2: 3*x + 5*y - z - 1;
(%o2)                  - z + 5 y + 3 x - 1
(%i3) expr3: z^2 + x - y^2 + 5;
                          2    2
(%o3)                    z  - y  + x + 5
(%i4) eliminate ([expr3, expr2, expr1], [y, z]);
             8         7         6          5          4
(%o4) [7425 x  - 1170 x  + 1299 x  + 12076 x  + 22887 x
                                    3         2
                            - 5154 x  - 1291 x  + 7688 x + 15376]
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