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resultant

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

eq2:y-y^2-z+z^2;

resultant(eq1,eq2,y);

Calculate

resultant

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

eq2:y^2-z^2;

resultant(eq1,eq2,y);

Calculate

resultant

resultant(121241,123,4);

Calculate

resultant

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

eq2: y^5+c*x^2+d;

resultant(eq1,eq2,x);

Calculate

resultant

eqlist: [ut-v*vx,vt-u...

resultant(eqlist[5],e...

Calculate

resultant

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

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

resultant(eq1,eq2,x);

Calculate

resultant

f: x^5+a*x+b ;

g: x^4+p*x^3+q*x^2+r*...

r: resultant(f,g,x);

Calculate

resultant

eq1:-x^2+y^2;

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

resultant(eq1,eq2,y);

Calculate

resultant

f: x^3-(A+2)*x^2+B*x-A;

g: 2*x^2+B*x-A*(B+2*A...

resultant(f,g,x);

Calculate

resultant

Run Example
(%i1)1;
(%o1)                                  1
(%i2) 1;
(%o2)                                  1
(%i3) 1;
(%o3)                                  1
(%i4) 1;
(%o4)                                  1
(%i5) 1;
(%o5)                                  1
(%i6) 1;
(%o6)                                  1
(%i7) 1;
(%o7)                                  1
(%i8) 1;
(%o8)                                  1
(%i9) 1;
(%o9)                                  1
(%i10) 1;
(%o10)                                 1
(%i11) 1;
(%o11)                                 1
(%i12) 1;
(%o12)                                 1
(%i13) 1;
(%o13)                                 1
(%i14) 1;
(%o14)                                 1
(%i15) 1;
(%o15)                                 1
(%i16) 1;
(%o16)                                 1
(%i17) 1;
(%o17)                                 1
(%i18) 1;
(%o18)                                 1
(%i19) A:u^4+p*u+q;
                                  4
(%o19)                           u  + p u + q
(%i20) B:a*u^2+b*u*v+c*u+d*v+e;
                                          2
(%o20)                   b u v + d v + a u  + c u + e
(%i21) C:factor(resultant(A,B,u));
        4    4    3      4    4  4        2      3      3      3    3      3
(%o21) b  q v  - b  d p v  + d  v  - 4 a b  d q v  + 4 b  c q v  - b  e p v
          2    3      2        3      3    3        2      2      2  2    2
 + 3 a b d  p v  - 3 b  c d p v  + 4 d  e v  - 4 a b  e q v  + 2 a  d  q v
                2      2  2    2                2      2        2
 - 8 a b c d q v  + 6 b  c  q v  + 6 a b d e p v  - 3 b  c e p v
          2    2        2      2      2  2  2    3              2
 + 3 a c d  p v  - 3 b c  d p v  + 6 d  e  v  - a  b p q v + 4 a  d e q v
                        2              3        3    2            2
 - 8 a b c e q v - 4 a c  d q v + 4 b c  q v + a  d p  v + 3 a b e  p v
                        2          3              3      4  2    3
 + 6 a c d e p v - 3 b c  e p v - c  d p v + 4 d e  v + a  q  - a  c p q
      2  2          2        4      3    2          2      3        4
 + 2 a  e  q - 4 a c  e q + c  q + a  e p  + 3 a c e  p - c  e p + e
(%i22) D1:factor(coeff(C,v));
           3            2                            2            3      3    2
(%o22) - (a  b p q - 4 a  d e q + 8 a b c e q + 4 a c  d q - 4 b c  q - a  d p
                              2                        2        3            3
                     - 3 a b e  p - 6 a c d e p + 3 b c  e p + c  d p - 4 d e )
(%i23) D2:factor(coeff(C,v,2));
               2          2  2                      2  2
(%o23) - (4 a b  e q - 2 a  d  q + 8 a b c d q - 6 b  c  q - 6 a b d e p
                                   2                2          2          2  2
                              + 3 b  c e p - 3 a c d  p + 3 b c  d p - 6 d  e )
(%i24) D3:factor(coeff(C,v,3));
               2          3        3              2        2            3
(%o24) - (4 a b  d q - 4 b  c q + b  e p - 3 a b d  p + 3 b  c d p - 4 d  e)
(%i25) D4:coeff(C,v,4);
                               4      3        4
(%o25)                        b  q - b  d p + d
(%i26) D5:coeff(C,v,5);
(%o26)                                 0
(%i27) 
Run Example
1;
(%o1)                                  1
(%i2) 1;
(%o2)                                  1
(%i3) 1;
(%o3)                                  1
(%i4) 1;
(%o4)                                  1
(%i5) 1;
(%o5)                                  1
(%i6) 1;
(%o6)                                  1
(%i7) 1;
(%o7)                                  1
(%i8) 1;
(%o8)                                  1
(%i9) 1;
(%o9)                                  1
(%i10) 1;
(%o10)                                 1
(%i11) 1;
(%o11)                                 1
(%i12) 1;
(%o12)                                 1
(%i13) 1;
(%o13)                                 1
(%i14) 1;
(%o14)                                 1
(%i15) 1;
(%o15)                                 1
(%i16) 1;
(%o16)                                 1
(%i17) 1;
(%o17)                                 1
(%i18) 1;
(%o18)                                 1
(%i19) 1;
(%o19)                                 1
(%i20) 1;
(%o20)                                 1
(%i21) 1;
(%o21)                                 1
(%i22) 1;
(%o22)                                 1
(%i23) 1;
(%o23)                                 1
(%i24) 1;
(%o24)                                 1
(%i25) 1;
(%o25)                                 1
(%i26) 1;
(%o26)                                 1
(%i27) 1;
(%o27)                                 1
(%i28) 1;
(%o28)                                 1
(%i29) 1;
(%o29)                                 1
(%i30) 1;
(%o30)                                 1
(%i31) A:u^4+4*p*u+3*q;
                                4
(%o31)                         u  + 4 p u + 3 q
(%i32) B:a*u*u+p*u*v+a*b*u+q*v;
                                           2
(%o32)                    p u v + q v + a u  + a b u
(%i33) C:expand(resultant(A,B,u));
        4  4    4    4      2  3  2       2      2  2      2  2  2    2
(%o33) q  v  - p  q v  + 6 a  q  v  - 12 a  b p q  v  + 6 a  b  p  q v
       3  2  2        3  2          3  3            4  2       4
 - 12 a  b  q  v + 4 a  p  q v + 8 a  b  p q v + 9 a  q  - 12 a  b p q
      4  4
 + 3 a  b  q
(%i34) D0:factor(coeff(C,v,0));
                              4                   4
(%o34)                     3 a  q (3 q - 4 b p + b )
(%i35) D1:factor(coeff(C,v));
                             3       2      2      3
(%o35)                  - 4 a  q (3 b  q - p  - 2 b  p)
(%i36) D2:factor(coeff(C,v,2));
                                  2            2
(%o36)                         6 a  q (q - b p)
(%i37) D3:factor(coeff(C,v,3));
(%o37)                                 0
(%i38) D4:factor(coeff(C,v,4));
                                      3    4
(%o38)                            q (q  - p )
(%i39) E:factor(resultant(expand(0/12/p),expand(D3/8),d));
(%o39)                                 1
(%i40)  F:solve(D2=0,z);
(%o40)                                []
(%i41) G:subst(d=q+sqrt(q^2+p^3),z);
(%o41)                                 z
(%i42) H:expand(G);
(%o42)                                 z
(%i43) J:ratsimp(H);
(%o43)                                 z
(%i44) K:factor(J);
(%o44)                                 z
(%i45) 
Run Example
A:u^4+p*u^2+q*u+r;
                               4      2
(%o1)                         u  + p u  + q u + r
(%i2) B:u^2+a*u+b;
                                  2
(%o2)                            u  + a u + b
(%i3) C:expand(A*B);
       6      5      4      4      3        3      2        2        2
(%o3) u  + a u  + p u  + b u  + q u  + a p u  + r u  + a q u  + b p u  + a r u
                                                                  + b q u + b r
(%i4) D:u^4+k*u+m;
                                  4
(%o4)                            u  + k u + m
(%i5) E:remainder(C,D,u);
                     3                              2
(%o5) (q + a p - k) u  + (r + a q + b p - m - a k) u
                        + (a r + b q + k (- p - b) - a m) u + b r + m (- p - b)
(%i6) F:coeff(E,u,3);
(%o6)                             q + a p - k
(%i7) G:resultant(E,F,k);
                 2          2                   2
(%o7) (r + (b - a ) p - m) u  + (a r - p q - a p  - a b p - a m) u + b r - m p
                                                                          - b m
(%i8) H:coeff(G,u,2);
                                        2
(%o8)                         r + (b - a ) p - m
(%i9) J:resultant(G,H,m);
                                   3                2       2    2
(%o9)     - p ((q + a p + 2 a b - a ) u + r + (b - a ) p + b  - a  b)
(%i10) K:expand(J);
                    2                  3                2    2  2    2
(%o10) - p q u - a p  u - 2 a b p u + a  p u - p r - b p  + a  p  - b  p
                                                                          2
                                                                       + a  b p
(%i11) L:coeff(K,u);
                                    2              3
(%o11)                   - p q - a p  - 2 a b p + a  p
(%i12) M:resultant(K,L,b);
                      3     2      2    2  2      4      6
(%o12)             - p  (4 a  r + q  - a  p  - 2 a  p - a )
(%i13) N:resultant(K,L,a);
        6   3         2            2   2     4        3      3      4
(%o13) p  (r  + (- 2 p  - 3 b p - b ) r  + (p  + 2 b p  - 2 b  p - b ) r
       3        2      2      3   2      5      2  4       3  3       4  2
 + (- p  - 3 b p  - 3 b  p - b ) q  + b p  + 5 b  p  + 10 b  p  + 10 b  p
      5      6
 + 5 b  p + b )
(%i14) P:factor(N);
        6   3      2  2          2    2  2    4          3        3        4
(%o14) p  (r  - 2 p  r  - 3 b p r  - b  r  + p  r + 2 b p  r - 2 b  p r - b  r
    3  2        2  2      2    2    3  2      5      2  4       3  3       4  2
 - p  q  - 3 b p  q  - 3 b  p q  - b  q  + b p  + 5 b  p  + 10 b  p  + 10 b  p
      5      6
 + 5 b  p + b )
(%i15) 
[addrow,append,block,copylist,copymatrix,delete,error,hipow,length,makelist,print,resultant,return,row,submatrix] [append,build_info,lambda,map,plot2d,rat,resultant,rhs,solve,sqrt] [append,build_info,map,plot2d,rat,resultant,solve,sqrt] [append,map,plot2d,resultant,solve,sqrt] [coeff,expand,factor,linsolve,remainder,resultant,subst] [coeff,expand,factor,rat,remainder,resultant,subst] [coeff,expand,factor,rat,remainder,resultant] [coeff,expand,factor,rat,resultant,solve,subst] [coeff,expand,factor,rat,resultant,solve] [coeff,expand,factor,rat,resultant] [coeff,expand,factor,ratsimp,resultant,solve,sqrt,subst] [coeff,expand,factor,remainder,resultant,solve] [coeff,expand,factor,remainder,resultant,subst] [coeff,expand,factor,remainder,resultant] [coeff,expand,factor,resultant,subst] [coeff,expand,factor,resultant] [coeff,expand,rat,remainder,resultant] [coeff,expand,rat,resultant,subst] [coeff,expand,rat,resultant] [coeff,expand,remainder,resultant] [coeff,expand,resultant,solve,subst] [coeff,expand,resultant,subst] [coeff,expand,resultant] [coeff,factor,rat,remainder,resultant,subst] [coeff,factor,rat,remainder,resultant] [coeff,factor,rat,resultant,subst] [coeff,factor,rat,resultant] [coeff,factor,remainder,resultant,subst] [coeff,factor,remainder,resultant] [coeff,factor,resultant] [coeff,rat,remainder,resultant] [coeff,rat,resultant,sqrt,subst] [coeff,rat,resultant] [coeff,remainder,resultant,subst] [coeff,remainder,resultant] [coeff,resultant] [diff,expand,factor,rat,realroots,resultant] [diff,factor,false,ratfac,resultant] [do,load,resultant] [expand,factor,map,plot2d,rat,realroots,resultant,solve] [expand,factor,rat,realroots,resultant] [expand,listofvars,resultant] [expand,resultant] [factor,false,ratfac,resultant] [factor,resultant,subst] [factor,resultant] [rat,remainder,resultant] [rat,resultant] [remainder,resultant] [resultant]

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