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The Maxima on-line user's manual

Algebra Calculator

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Eliminate Calculator

Eliminate

Function: eliminate ([<eqn_1>, ..., <eqn_n>], [<x_1>, ..., <x_k>]) 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.

spojJednacine:[U1 = (a1+b1)*sqrt(Z0), I1 = (a1-b1)/sqrt(Z0),U2 = (a2+b2)*sqrt(Z0), I2 = (a2-b2)/sqrt(Z0),U1 = cos(Teta)*U2+%i*Z0*sin(Teta)*I2, I1 = %i*sin(Teta)*U2/Z0+cos(Teta)*I2];
spojJednacineab:eliminate(spojJednacine, [I1,I2,U1,U2]);
spojJednacineb:solve(spojJednacineab, [b1,b2]);

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]

(%o1)                                true
(%i2) 

Eliminate Example

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