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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.

Puiab:[Pk=abs(ak)^2-abs(bk)^2,Uk=(ak+bk)*sqrt(Z0k), Ik=(ak-bk)/sqrt(Z0k)];
abUI:[ak=(Uk+Z0k*Ik)/(2*sqrt(Z0k)),bk=(Uk-Z0k*Ik)/(2*sqrt(Z0k))];
spoj:[U1=(a1+b1)*sqrt(Z01),  U2=(a2+b2)*sqrt(Z02),I1=(a1-b1)/sqrt(Z01),  I2=(a2-b2)/sqrt(Z02),U1=U2, I1+I2=0];
spoj1:[eliminate(spoj,  [U1, U2, I1, I2])];

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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