Robert M. Corless
Department of Applied Mathematics
University of Western Ontario
London, Canada

Copyright 2001 by Robert M. Corless
All rights reserved

Useful one-word commands 

Использование монокоманд

Solving equations

  Решение уравнений

fsolve

Команда fsolve

> restart;
> Digits := 20;

Digits := 20
> p := x^5-x+1;

p := x^5-x+1
> r := fsolve( p, x );

r := -1.1673039782614186843
> subs( x=r, p );

-.4e-18
> pseudozeros := fsolve( p, x, complex );
> map( evalf[1],[seq( abs(eval( p, x=z)), z=pseudozeros )]);

[.4e-18, .1e-18, .1e-18, .1e-19, .1e-19]
> Digits := trunc(evalhf(Digits));

Digits := 14
> X := fsolve( x*tan(x) - 1, x );

X := -.86033358901938
> X*tan(X)-1;

0.
> plot( [x*tan(x),1], x=-10..10, y=-5..5, discont=true, colour=black );

> X := fsolve( x*tan(x)-1, x=3);

X := 3.4256184594817
> X*tan(X);

.99999999999990
> X := fsolve( x*tan(x)-1, x=6);

X := 6.4372981791719
> X*tan(X);

.99999999999966
> Digits := 20;

Digits := 20
> r := fsolve( x*tan(x)-1, x=1000*Pi );

r := 3141.5929718996364202
> r*tan(r);

.99999999999994046653
> r - evalf(1000*Pi);

.3183098431817e-3
> 1/%;

3141.5930780034739225
> assume(n,integer);
> T := subs( x=(n*Pi+delta), x*tan(x) );

T := (n*Pi+delta)*tan(n*Pi+delta)
> T := series( T, delta );

T := series(n*Pi*delta+1*delta^2+1/3*n*Pi*delta^3+1...
> solve( T=t, delta );

> asympt( eval( convert( %, polynom ), t=1 ), n, 7 );

1/(n*Pi)-4/3*1/(n^3*Pi^3)+O(1/(n^5))
> restart;
> sys := {x^2+y^2-1,25*x*y-12};

sys := {x^2+y^2-1, 25*x*y-12}
> fsolve( sys, {x,y} );

{x = -.6000000000, y = -.8000000000}
> fsolve( sys, {x=-1..0,y=0..1} );

fsolve({x^2+y^2-1, 25*x*y-12},{x, y},{x = -1 .. 0, ...
> fsolve( sys, {x=0.2..1.2, y=0.2..1.2} );

{x = .8000000000, y = .6000000000}
> fsolve( sys, {x=-1.2..-0.2, y=-1.2..-0.2} );

{x = -.6000000000, y = -.8000000000}

С официального разрешения                    © 2002 Waterloo Maple, Inc

 
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