Comandos Úteis e Simples

Seção 2.1: Simplificação

>

restart;

>	with(LinearAlgebra):

>	A := Matrix( [[-149,-50,-154], [537,180,546], [-27,-9,-25]] );

>	E := Matrix( [[130, -390, 0], [43, -129, 0], [133,-399,0]] );

>	AtE := simplify( A + t*E );

>	p := CharacteristicPolynomial(AtE,x);

>	d := discrim( p, x );

>	alfs := [fsolve( d, t, complex )];

>	map(abs,alfs);

>	realroot( d, 10^(-14) );

>

evalf(%);

>

>

>	alias( t[0]=RootOf( d, t ) );

>	As := eval( AtE, t=t[0] );

>	eigs := Eigenvalues( As );

>	evalf( % );

>	pf := eval( p, t=t[0] );

>	factor( pf );

>	p2 := eval( p, t=t/1.0e6 );

>	algcurves[plot_real_curve]( p2, x, t, view=[1..3,0..1.0] );

>

restart;

>	with(LinearAlgebra):

>	Yee := Matrix( 8,8,     [[1/e, 1/e, 1/e, 1/e, 1/e, 1/e, 1/e, 0],      [1, 1, 1, 1, 1, 1, 0, 1],      [1, 1, 1, 1, 1, 0, 1, 1],      [1, 1, 1, 1, 0, 1, 1, 1],      [1, 1, 1, 0, 1, 1, 1, 1],      [1, 1, 0, 1, 1, 1, 1, 1],      [1, 0, 1, 1, 1, 1, 1, 1],      [0, e, e, e, e, e, e, e]]);

>	p := CharacteristicPolynomial( Yee, lambda );

>	factor(p);

>	quad_factor := normal( e*p/(lambda-1)^3/(lambda+1)^3 );

>	d := discrim( quad_factor, lambda );

>	factor( d );

>	alias( alpha=RootOf(d,e) );

>	pe := eval( p, e=alpha );

>	factor( pe );

>	r := resultant(quad_factor,lambda-1,lambda);

>	factor( r );

>	r := resultant( quad_factor, lambda+1, lambda );

>	factor( r );

>	alias( beta=RootOf(r,e) );

>	factor( eval(p, e=beta) );

>

>