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

Algebra Calculator

#### Resultant

Function: resultant (<p_1>, <p_2>, <x>) -- Variable: resultant Computes the resultant of the two polynomials <p_1> and <p_2>, eliminating the variable <x>. The resultant is a determinant of the coefficients of <x> in <p_1> and <p_2>, which equals zero if and only if <p_1> and <p_2> have a non-constant factor in common.

If <p_1> or <p_2> can be factored, it may be desirable to call `factor` before calling `resultant`.

The variable `resultant` controls which algorithm will be used to compute the resultant. `subres` for subresultant prs, `mod` for modular resultant algorithm, and `red` for reduced prs. On most problems `subres` should be best. On some large degree univariate or bivariate problems `mod` may be better.

The function `bezout` takes the same arguments as `resultant` and returns a matrix. The determinant of the return value is the desired resultant.

```(%o1)                                true
(%i2) ```

### Related Examples

##### resultant

eq1:x-x^2-y+y^2;

eq2:y^2-z^2;

resultant(eq1,eq2,y);

Calculate

##### resultant

g1:z^4+4*a*z+b ;

g2:z^3+p*z^2+q*z+r+3*a ;

h:resultant(g1,g2,z) ;

Calculate

##### resultant

eq1:a*x^2+b*x+c;

eq2:2*a*x+b;

resultant(eq1,eq2,x);

Calculate

##### resultant

eq1:a*x^2+b*x+c;

eq2:2*a*x+b;

resultant(eq1,eq2,x);

Calculate

##### resultant

eq1:x^5-x+1;

eq2:(z-x)^5-(z-x)+1;

resultant(eq1,eq2,x);

Calculate

##### resultant

A:u^4+p*u+q;

B:v^4+a*v^3+b*v^2+c*v...

C:v^4-k;

Calculate

##### resultant

eq1:x^4-x^3+2*x^2-6*x...

eq2:x^2-10*x+25;

resultant(eq1,eq2,x);

Calculate

##### resultant

A:x^4+4*a*x^2+b*x+c;

B:p0*y^2+p1*y+p2-x*(q...

C:resultant(A,B,x);

Calculate

##### resultant

f: 4*x^3-6*y*x+3-a;

g: 2*x^4-4*y*x^2+2*x+...

r: resultant(f,g,x);

Calculate

##### resultant

eq1:x^2*2-1+2*y^2;

eq2:z^2*2-1-2*y^2;

resultant(eq1,eq2,y);

Calculate