### The Maxima on-line user's manual

Algebra 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.

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) ```

### Related Examples

##### eliminate-facsum-ratsimp

mix(x0, x1, t) := x0*...

bez2(x0,x1,x2, t):= m...

bez3(x0,x1,x2,x3,t):=...

Calculate

##### eliminate-ratsimp

mix(x0, x1, t) := x0*...

bez2(x0,x1,x2, t):= m...

bez3(x0,x1,x2,x3,t):=...

Calculate

##### eliminate-false-logexpand-logsimp

logexpand: false;

logsimp: false;

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Ie00:(Id*pa_dd+Ic*pa_...

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Ie02:(Id*pa_bd+Ic*pa_...

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##### eliminate

eq1:mka*o1/100+mko=o2;

eq2:mka+mko=100;

eliminate([eq1,eq2],[...

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##### eliminate

expr1: x * (a + c) + ...

expr2: x * (a + c) + ...

eliminate ([expr2, ex...

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##### eliminate

expr1: x*(a+b)+y*a+z*...

expr2: y*a+z*b=n;

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##### eliminate

expr1: x*(a+b)+y*a+z*b;

expr2: y*a;

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##### eliminate

eq1:x=z+y;

eq2:z^2=x+1;

eliminate([eq1,eq2],[...

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##### eliminate-linsolve-sqrt

a:[U1 = (a1 + b1)*sqr...

b:eliminate(a,[I1,I2,...

jednacina1:b2 - b1 + ...

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