查看“︁Maple/方程求解”︁的源代码


==二次多项式方程==

<center><math>f:=a*x^2+b*x+c;</math></center>
求解 f=0;

solve(f,x);


<center><math>(1/2)*(-b+\sqrt(b^2-4*a*c))/a, -(1/2)*(b+\sqrt(b^2-4*a*c))/a</math></center>
<center><math></math></center>





==三次多项式方程==
<center><math>f := 5*x^3+6*x^2+7*x+8</math></center>
solve(f，x);

<center><math>-(1/15)*(1971+15*\sqrt(18726))^(1/3)+23/(5*(1971+15*\sqrt(18726))^(1/3))-2/5, </math>

<math>(1/30)*(1971+15*\sqrt(18726))^(1/3)-23/(10*(1971+15*\sqrt(18726))^(1/3))

-2/5+(1/2*I)*\sqrt(3)*(-(1/15)*(1971+15*\sqrt(18726))^(1/3)

-23/(5*(1971+15*\sqrt(18726))^(1/3)))</math>, 

<math>(1/30)*(1971+15*\sqrt(18726))^(1/3)-23/(10*(1971+15*\sqrt(18726))^(1/3))

-2/5-(1/2*I)*\sqrt(3)*(-(1/15)*(1971+15*\sqrt(18726))^(1/3)-23/(5*(1971+15*\sqrt(18726))^(1/3)))</math></center>
<center><math></math></center>
<center><math></math></center>
<center><math></math></center>
<center><math></math></center>
<center><math></math></center>
<center><math></math></center>

==高次多项式方程==
f := x^7+3*x = 7;

solve(f,x);                    
:             RootOf(<math>Z^7  + 3 Z - 7</math>, index = 1),
:             RootOf(<math>Z^7  + 3 Z - 7</math>, index = 2),
:             RootOf(<math>Z^7  + 3 Z - 7</math>, index = 3),
:             RootOf(<math>Z^7  + 3 Z - 7</math>, index = 4),
:             RootOf(<math>Z^7  + 3 Z - 7</math>, index = 5),
:             RootOf(<math>Z^7  + 3 Z - 7</math>, index = 5),
:             RootOf(<math>Z^7  + 3 Z - 7</math>, index =7),

evalf(%);

* (1.1922047171828134), 
*    (0.8658388666792263) + (0.9230818802764879) I, 
*    (0.2099602786426775) + (1.3442579297631496) I, 
*    (1.2519809466279554) + (0.6424819505558892) I, 
*    (1.2519809466279554) - (0.6424819505558892) I, 
*    (0.2099602786426775) - (1.3442579297631496) I, 
*    (0.8658388666792263) - (0.9230818802764879) I

==三角函数方程==
f := sin(x)^3+5*cosh(x) = 0;

                                        
<math>       sin^3(x)  + 5 cosh(x) = 0</math>

> solve(f, x);

                   
RootOf(<math>sin^3(Z) - arccosh(\frac{-1}{5} sin(Z)</math>))

> evalf(%);

:                  0.2873691672 - 1.111497506 I

==方程组==
:> p1 := x*y*z-x*y^2-z-x-y; p2 := x*z-x^2-z-y+x; p3 := z^2-x^2-y^2;
:> sys := {p1, p2, p3};
:> var := {x, y, z};
:                       
:> solve(sys, var);
:：       {x = 0, y = y, z = -y}, {x = 3, y = 4, z = 5}, {x = 1, y = 0, z = -1}

==三角函数方程组==
:> f1 := cos(x)+sin(3*y)+tan(5*z) = 0;
:                
:> f2 := cos(3*z)+tan(3*y^2)-sin(2*z^3) = 33;
:> f3 := tan(4*x+y)-sin(5*y-4*z) = 2*x;
:           
:> sys1 := {f1, f2, f3};
:         > var1 := {x, y, z};
:                           {x, y, z}
:> fsolve(sys1, var1);
:     {x = -10.77771790, y = -2.397849343, z = -7.382158103}