multivariate polynomials
- Subject: multivariate polynomials
- From: Maths Mathematica Geometry Crew
- Date: Tue, 9 Jul 2002 23:44:28 +0200
>From Gosei Furuya, Tue Jul 09, at 17:51:
.
.(C1) load("eigen")$
.(C2) display2d:false $
.(C3) H:matrix([_a,v,0],[v,b,0],[0,v,c])$
.(C4) eigenvalues(H);
.(D5) [[(-SQRT(_a^2-2*b*_a+4*v^2+b^2)+_a+b)/2,
. (SQRT(_a^2-2*b*_a+4*v^2+b^2)+_a+b)/2,c],[1,1,1]]
.please down load diag.mac and jordan.dem from
.cvsroot/maxima/share/contrib
.(C6) load("diag.mac")$
.(C7) jordan(H);
.(D7) [[(-SQRT(_a^2-2*b*_a+4*v^2+b^2)+_a+b)/2,1],
. [(SQRT(_a^2-2*b*_a+4*v^2+b^2)+_a+b)/2,1],[c,1]]
.
Thank you Gosei, but still no luck.
Here enclosed my log file.
A strange question mark appears, as diag.mac file is loaded.
Something wrong in my procedure?
thank you
--
Paolo Pumilia
-- enc. ---------------------------------------------------
(C1) load("eigen");
display2d:false ;
H : matrix( [ e1, V, 0],
[ V, e2-e1, V],
[ 0, V, -e2] );
eigenvalues(H);
load("/usr/local/share/maxima/diag.mac");
Warning - you are redefining the MACSYMA function EIGENVALUES
Warning - you are redefining the MACSYMA function EIGENVECTORS
(D1) /usr/lib/maxima-5.6/share/eigen.mc
(C2)
(D2) FALSE
(C3)
(D3) MATRIX([e1,V,0],[V,e2-e1,V],[0,V,-e2])
(C4)
(D4) [[(-SQRT(3)*%I/2-1/2)*(SQRT(-32*V^6-(21*e2^2+6*e1*e2+21*e1^2)*V^4
-(24*e2^4+6*e1*e2^3-36*e1^2*e2^2
+6*e1^3*e2+24*e1^4)
*V^2-4*e2^6+12*e1*e2^5+3*e1^2*e2^4
-26*e1^3*e2^3+3*e1^4*e2^2+12*e1^5*e2
-4*e1^6)
/(6*SQRT(3))
+(e2*V^2+e1*(-V^2-e2^2)+e1^2*e2)/2)
^(1/3)
+(SQRT(3)*%I/2-1/2)*(2*V^2+e2^2-e1*e2+e1^2)
/(3*(SQRT(-32*V^6-(21*e2^2+6*e1*e2+21*e1^2)*V^4
-(24*e2^4+6*e1*e2^3-36*e1^2*e2^2+6*e1^3*e2+24*e1^4)
*V^2-4*e2^6+12*e1*e2^5+3*e1^2*e2^4-26*e1^3*e2^3
+3*e1^4*e2^2+12*e1^5*e2-4*e1^6)
/(6*SQRT(3))
+(e2*V^2+e1*(-V^2-e2^2)+e1^2*e2)/2)
^(1/3)
+(-SQRT(3)*%I/2-1/2)*(2*V^2+e2^2-e1*e2+e1^2)
/(3*(SQRT(-32*V^6-(21*e2^2+6*e1*e2+21*e1^2)*V^4
-(24*e2^4+6*e1*e2^3-36*e1^2*e2^2+6*e1^3*e2+24*e1^4)
*V^2-4*e2^6+12*e1*e2^5+3*e1^2*e2^4-26*e1^3*e2^3
+3*e1^4*e2^2+12*e1^5*e2-4*e1^6)
/(6*SQRT(3))
+(e2*V^2+e1*(-V^2-e2^2)+e1^2*e2)/2)
^(1/3)),
(SQRT(-32*V^6-(21*e2^2+6*e1*e2+21*e1^2)*V^4
-(24*e2^4+6*e1*e2^3-36*e1^2*e2^2+6*e1^3*e2+24*e1^4)*V^2
-4*e2^6+12*e1*e2^5+3*e1^2*e2^4-26*e1^3*e2^3+3*e1^4*e2^2
+12*e1^5*e2-4*e1^6)
/(6*SQRT(3))
+(e2*V^2+e1*(-V^2-e2^2)+e1^2*e2)/2)
^(1/3)
+(2*V^2+e2^2-e1*e2+e1^2)/(3*(SQRT(
-32*V^6-(21*e2^2+6*e1*e2+21*e1^2)*V^4
-(24*e2^4+6*e1*e2^3-36*e1^2*e2^2
+6*e1^3*e2+24*e1^4)
*V^2-4*e2^6+12*e1*e2^5+3*e1^2*e2^4
-26*e1^3*e2^3+3*e1^4*e2^2
+12*e1^5*e2-4*e1^6)
/(6*SQRT(3))
+(e2*V^2+e1*(-V^2-e2^2)+e1^2*e2)/2)
^(1/3))],[1,1,1]]
(C5)
(D5) ?\/usr\/local\/share\/maxima\/diag\.mac
(C6) load("/usr/local/share/maxima/diag.mac");
(D6) ?\/usr\/local\/share\/maxima\/diag\.mac
(C7) jordan(H);
quotient is not exact
#0: EIGENVECTORS(mat=MATRIX([e1,V,0],[V,e2-e1,V],[0,V,-e2]))
#1: jordan(mat=MATRIX([e1,V,0],[V,e2-e1,V],[0,V,-e2]))(diag.mac line 109)
-- an error. Quitting. To debug this try DEBUGMODE(TRUE);)
(C8)
-- end enc. ---------------------------------------------------