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allroots-float-plot2d-realroots-solve
plot2d(f(x),[x,-5,5]);

f(x):=x^3 -8*x - 2;

solve(f(x));

float(%);

Calculate

allroots-solve

f:8/3*x^4+4/3*x^3+x^2...

allroots(f);

solve(f,x)[1]*solve(f...

Calculate

allroots-factor-solve

f:x^2-4;

solve(f,x);

root(f,x,0,10);

Calculate

allroots-create_list-diff-ev-exp-log-numer-ratsimp

/*p(x) is the polynom...

/* so f(x) sfould be ...

g:diff(f(x),x);

Calculate

allroots-expand

L2(x):=(x-0.6)*(x-0.8...

L3(x):=(x-0.4)*(x-0.8...

L4(x):=(x-0.4)*(x-0.6...

Calculate

allroots

allroots(s^3=0);

allroots(s*(s+1)*(s+1...

Calculate

allroots-at-charpoly-float-lambda-matrix-solve

mat: matrix([F1*gamma...

cp: charpoly(mat,%lam...

sol: substitute([F1=8...

Calculate

allroots-factor-solve

f:x^2-4;

solve(f,x);

root(f,x,0,10);

Calculate

allroots-factor

allroots(s^3=0);

allroots(s*(s+1)*(s+1...

factor(s^4+s);

Calculate

allroots-create_list-diff-ev-exp-log-numer-ratsimp

/* p(x) is the polyno...

p(x):=x*(x-1)*(x-2);

f(x):=p(x)*exp(-x*log...

Calculate

allroots

Run Example
(%i1)a:5;
(%o1)                                  5
(%i2) b:5;
(%o2)                                  5
(%i3) F:13;
(%o3)                                 13
(%i4) s:(a+b+c)/2;
                                    c + 10
(%o4)                               ------
                                      2
(%i5) g:F^2=s*(s-a)*(s-b)*(s-c);
                                   c + 10     2  c + 10
                         (c + 10) (------ - 5)  (------ - c)
                                     2             2
(%o5)              169 = -----------------------------------
                                          2
(%i6) allroots(g);
(%o6) [c = 1.00000000000001 %i + 7.14142842854285, 
c = 7.14142842854285 - 1.00000000000001 %i, 
c = 0.99999999999999 %i - 7.14142842854285, 
c = - 0.99999999999999 %i - 7.14142842854285]
(%i7) 
Run Example
load("log10");
(%o1)          /usr/share/maxima/5.21.1/share/contrib/log10.mac
(%i2) dB(x):= 20*log10(x);
(%o2)                        dB(x) := 20 log10(x)
(%i3) f_to_w(x):= 2*%pi*x;
(%o3)                        f_to_w(x) := 2 %pi x
(%i4) allroots(x^2 -1.99004745483398*x + 0.99007225036621);
(%o4) [x = 1.79564500253386E-4 %i + 0.99502372741699, 
                                 x = 0.99502372741699 - 1.79564500253386E-4 %i]
(%i5) allroots(x^2 -1.69065929318241*x + 0.73248077421585);
(%o5) [x = 0.13378551046297 %i + 0.84532964659121, 
                                    x = 0.84532964659121 - 0.13378551046297 %i]
(%i6) float(solve(exp(-x/48000) = 0.99502372741699,x)/(2*%pi));

rat: replaced -0.995023727417 by -8598/8641 = -0.995023724106
(%o6)               [0.1591549430919 x = 38.11085142032302]
(%i7) float(solve(exp(-x/48000) = 0.84532964659121,x)/(2*%pi));

rat: replaced -0.8453296465912 by -9783/11573 = -0.8453296465912
(%o7)               [0.1591549430919 x = 1283.644051295943]
(%i8) float(solve(exp(-x/48000) = 0.13378551046297,x)/(2*%pi));

rat: replaced -0.133785510463 by -1361/10173 = -0.1337855106655
(%o8)               [0.1591549430919 x = 15366.86120660835]
(%i9) H(s):= ((s^2)/(f_to_w(38.11085142032302)^2))/((s^2)/(f_to_w(38.11085142032302)^2) + s/(0.5*f_to_w(38.11085142032302)) + 1);
                                             2
                                            s
                                --------------------------
                                      2
                                f_to_w (38.11085142032302)
(%o9) H(s) := --------------------------------------------------------------
                           2
                          s                              s
              -------------------------- + ----------------------------- + 1
                    2                      0.5 f_to_w(38.11085142032302)
              f_to_w (38.11085142032302)
(%i10) H2(s):= (1.52*(s^2)/(f_to_w(1283.644051295943)^2) + s/(0.13378551046297*f_to_w(1283.644051295943)) + 1)/((s^2)/(f_to_w(1283.644051295943)^2) + s/(0.5*f_to_w(1283.644051295943)) + 1);
(%o10) H2(s) := 
                   2
             1.52 s                                  s
    -------------------------- + ------------------------------------------ + 1
          2                      0.13378551046297 f_to_w(1283.644051295943)
    f_to_w (1283.644051295943)
    ---------------------------------------------------------------------------
                       2
                      s                              s
          -------------------------- + ----------------------------- + 1
                2                      0.5 f_to_w(1283.644051295943)
          f_to_w (1283.644051295943)
(%i11) plot2d([dB(cabs(H(%i*f_to_w(f)))),dB(cabs(H2(%i*f_to_w(f))))],[f,10,24000],[logx,true]);
plotplot2d([dB(cabs(H(%i*f_to_w(f)))),dB(cabs(H2(%i*f_to_w(f))))],[f,10,24000],[logx,true]);
Run Example
allroots((X^5)-(5*X^2)+2);
(%o1) [X = 0.65062919143939, X = - 0.61803398874989, 
X = 1.546868887231396 %i - 0.82531459571969, 
X = - 1.546868887231396 %i - 0.82531459571969, X = 1.618033988749895]
(%i2) 
[allroots,args,create_list,diff,ev,exp,log,numer,ratsimp,solve] [allroots,at,charpoly,float,lambda,matrix,solve] [allroots,at,charpoly,lambda,matrix,solve] [allroots,at,charpoly,lambda,matrix] [allroots,cabs,exp,float,load,plot2d,solve] [allroots,cabs,exp,float,plot2d,solve] [allroots,cos,diff,ev,factor,integrate,kill,numer,solve] [allroots,cos,diff,integrate,plot2d,sin] [allroots,cos,ev,expand,find_root,numer,ratsimp,solve] [allroots,cos,sin,solve] [allroots,create_list,diff,ev,exp,first,log,numer,ratsimp,solve] [allroots,create_list,diff,ev,exp,log,numer,ratsimp,solve] [allroots,create_list,diff,ev,exp,log,numer,ratsimp] [allroots,create_list,diff,ev,exp,log,numer,xthru] [allroots,create_list,diff,ev,exp,log,numer] [allroots,create_list,diff,exp,log,map,numer] [allroots,diff,ev,expand,factor,find_root,ic1,numer,ode2,ratsimp,solve] [allroots,diff,ev,factor,kill,numer,solve] [allroots,diff,exp,expand,log,true] [allroots,diff,exp,log,numer,realpart,rectform,solve] [allroots,diff,exp,log,numer] [allroots,diff,exp,log,true] [allroots,diff,factor,find_root,ic2,ode2,sin,solve] [allroots,diff,factor,find_root,ic2,ode2,solve] [allroots,diff,numer,realroots,solve] [allroots,diff,plot2d] [allroots,diff] [allroots,ev,expand,factor,find_root,numer,ratsimp,solve] [allroots,ev,expand,find_root,numer,ratsimp,solve] [allroots,ev,find_root,numer,solve] [allroots,exp,float,pi,solve] [allroots,exp,float,solve] [allroots,exp,solve] [allroots,expand,factor] [allroots,expand,integrate] [allroots,expand,solve] [allroots,expand] [allroots,factor,find_root,solve] [allroots,factor,plot2d,plot3d,sin,solve] [allroots,factor,solve] [allroots,factor] [allroots,false,numer,ratprint,realroots,solve] [allroots,find_root,solve] [allroots,float,plot2d,realroots,solve] [allroots,gcd] [allroots,load] [allroots,map,solve] [allroots,numer,realroots,solve] [allroots,solve] [allroots]

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