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The Maxima on-line user's manual

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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.

f:x^4+a*x+b ;
g:x^2+(p+y)*x+k*y ;
                                      h:resultant(f,g,x);
 j:coeff(h,y,1);

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

f: 8*x^6+(-8*a^2-24*a...

g: 256*x^12+(-256*b-3...

r: resultant(f,g,x);

Calculate

resultant

eq1: y^2+a*x^3+b*x^2;

eq2: y+c*x^2+d;

resultant(eq1,eq2,y);

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

? resultant;

Calculate

resultant

eq1: ut-6*b*u*ux+6*v*...

eq2: vt+3*u*vx+v3x;

resultant(eq1,eq2,v);

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

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

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

g: x-1;

r: resultant(f,g,x);

Calculate

resultant

f: x^4+2*x^3+1*x^2+7*...

g: x^5+2*x+1 ;

r: resultant(f,g,x);

Calculate

resultant

eq1: y^10+a*x^3+b*x^2;

eq2: y^3+c*x^2+d;

resultant(eq1,eq2,x);

Calculate