Polynômes et matrices
Jean-Michel Sarlat (jm-sarlat@melusine.eu.org) - 25 mars 20031 | Énoncé | |
2 | Calculs |
1 - Énoncé
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Les calculs qui suivent répondent aux questions posées ou viennent appuyer les démonstrations.
2 - Calculs
(C2) load("polymat.mc")$
(C3) A:matrix([0,0,1],[1,0,1],[0,1,-1]);
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(C4) P:X^3+X^2-X-1$
(C5) P1:factor(P);
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(C6) polymat(P,A);
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(C7) block(A1:polymat(part(P1,1),A),A2:polymat(part(P1,2),A),[A1,A2]);
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(C8) A1 . A2;
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(C9) Q:1/4*(X^2+2*X+1)$
(C10) B:polymat(Q,A);
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(C11) R:-1/4*(X^2+2*X-3)$
(C12) C:polymat(R,A);
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(C13) S:-1/4*(X^3+3*X^2-X-3)$
(C14) D:polymat(S,A);
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(C15) B-C+D;
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(C16) B^^2;
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(C17) C^^2;
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(C18) D^^2;
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(C19) B . C;
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(C20) C . D;
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(C21) D . B;
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(C22) load("ordpoly.mc")$
(C23) block([a1,b1,c1],ordpoly((a1+b1+c1)*Q+(a1-b1+c1)*R+(-2*a1+b1)*S-(a1/2-b1/4)*P));
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Autres réalisations de ce document : index.pdf, index.ps.
Source index.txt mouliné par petitParseur(Z+B) le mardi 25 mars 2003.