1 restart(1);maple_mode(1);cas_setup(0,0,0,1,0,1e-10,10,[1,50,0,25],0,0,0); #radians,pas de cmplx, pas de Sqrt 2/* -------------------Polynome caracteristique et mineurs diagonaux------------------------------------------------------------------------------*/ 3n:=5; In:={seq(i,i=1..n)}; In minus {2,4}; 4 extr:=proc(A,II,JJ) 5 matrix([seq([seq(A[i,j],j=JJ)],i=II)]); 6 end_proc; 7/* Attention, diff(f,x,y) derive en x puis y, alors que diff(f,[x,y])�donne la liste des derive en x et en y.*/ 8diff(x*y,x,y);diff(x*y,[x,y]); 9 purge(a,x); 10 n:=5;A:=matrix(n,n,(i,j)->a[i,j]); 11 d:=diag(seq(x[i],i=1..n)); 12 II:=In minus {1,3};# on essaye (i,j)=(1,3) 13 extr(A,II,II); 14 dij:=diff(det(A-d),x[1],x[3]); 15 normal(det( extr(A,II,II)) - subs(x=[0,0,0,0,0],dij)); 16 II:=In minus {2,3};# on essaye (i,j)=(2,3) 17 extr(A,II,II); 18 dij:=diff(det(A-d),x[2],x[3]); 19 normal(det( extr(A,II,II)) - subs(x=[0,0,0,0,0],dij)); 20 II:=In minus {4,5};# on essaye (i,j)=(4,5) 21 extr(A,II,II); 22 dij:=diff(det(A-d),x[4],x[5]); 23 normal(det( extr(A,II,II)) - subs(x=[0,0,0,0,0],dij)); 24 B:=A-x*identity(n); 25 d:=seq(normal(subs(x=0,diff(det(B),x,i))/i!),i=n..1); 26 P:=charpoly(A); 27 monpolyfaddeev:=proc(A) 28 local a,n,B,P; 29 n:=dim(A)[1];a:=1:B:=identity(n);P:=[a]; 30 for i from n-1 to 0 by -1 do 31 B:=normal(B*A); 32 a:=trace(B)/(i-n); 33 P:=[op(P),a];B:=B+a*identity(n) od; 34 P; 35 end proc: 36 n:=30;A:=matrix(n,n,(i,j)->rand(21)-10): 37 normal(poly2symb(monpolyfaddeev(A),x)); 38 charpoly(A)-monpolyfaddeev(A); 39time(monpolyfaddeev(A)): 40time(charpoly(A)): 41 coeff(3*x^4+2*x^3+y^3,x,3); 42 A:=matrix(3,4,2);matrix(op(dim(A))); 43 cf:=proc(P,k) 44 local i,j; 45 matrix(op(dim(P)),(i,j)->coeff(P[i,j],x,k)); 46 end_proc; 47 P:=matrix[[2*x^4+2*x^3+x^2+4,2*x^4+5*x^2+5*x+3,3*x^2+5],[2*x^4+3*x^3+6*x^2+5*x+5,x^4+4*x^3+2*x^2+x,5*x^4+5*x^3+x^2+6*x+6],[x^4+2*x^3+2*x^2+x+6,6*x^4+x^3+x^2+2,x^4+2*x^3+5*x^2+2*x+5]]; // matrix(3,3,(i,j)->add(rand(7)*x^l,l=0..4)); 48A:=matrix(3,3,(i,j)->a[i,j]); 49cf(P,4); 50R:=P;k:=4;Q:=0; 51R:=normal(R-cf(R,k)*x^(k-1)*(x*identity(3)-A));Q:=cf(R,k)*x^(k-1)+Q:k:=k-1; 52R:=normal(R-cf(R,k)*x^(k-1)*(x*identity(3)-A));Q:=cf(R,k)*x^(k-1)+Q:k:=k-1; 53R:=normal(R-cf(R,k)*x^(k-1)*(x*identity(3)-A));Q:=cf(R,k)*x^(k-1)+Q:k:=k-1; 54R:=normal(R-cf(R,k)*x^(k-1)*(x*identity(3)-A));Q:=cf(R,k)*x^(k-1)+Q:k:=k-1; 55R2:=add(cf(P,i)*A^i,i=0..4):; 56normal(R2-R); 57