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SINGULAR - A Computer Algebra System for Polynomial Computations
Overview
Objects
Functionality
Libraries
Examples
Applications
Availability
History
Contributors
Future
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Sao Carlos, 08/02
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http://www.singular.uni-kl.de
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SINGULAR Examples
Build. Blocks
Comb. Appl.
HCA Proving
Arrangements
Branches
Classify
Coding
Deformations
Equidim Part
Existence
Finite Groups
Flatness
Genus
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Membership
Nonnormal Locus
Normalization
Primdec
Puiseux
Plane Curves
Saturation
Solving
Space Curves
Spectrum
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Sao Carlos, 08/02
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http://www.singular.uni-kl.de
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SINGULAR Applications
| Task: |
Compute M. Saito's endomorphisms
which satisfy:
A1 is semisimple with eigenvalues being the spectral
numbers of f added by 1, and
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ring R=0,(x,y),ds;
poly f=x5+x2y2+y5;
LIB "gaussman.lib";
The command tmatrix(f) returns a list
L :
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L[1] contains
A0 with respect to the basis
matrix(L[4])*L[3] of H''/H'.
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L[2] contains
A1 with respect to the basis
matrix(L[4])*L[3] of H''/H'.
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L[4] contains a monomial vector space basis for
H''/H'.
list L=tmatrix(f);
print(L[1]); // the matrix A_0
0,0,0,0,0,0,0,0,0,0,0,
0,0,0,0,0,0,0,0,0,0,0,
0,0,0,0,0,0,0,0,0,0,0,
0,0,0,0,0,0,0,0,0,0,0,
0,0,0,0,0,0,0,0,0,0,0,
0,0,0,0,0,0,0,0,0,0,0,
0,0,0,0,0,0,0,0,0,0,0,
0,0,0,0,0,0,0,0,0,0,0,
0,0,0,0,0,0,0,0,0,0,0,
0,0,0,0,0,0,0,0,0,0,0,
1,0,0,0,0,0,0,0,0,0,0
print(L[2]); // the matrix A_1
1/2,0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
0, 7/10,0, 0, 0, 0, 0, 0, 0, 0, 0,
0, 0, 7/10,0, 0, 0, 0, 0, 0, 0, 0,
0, 0, 0, 9/10,0, 0, 0, 0, 0, 0, 0,
0, 0, 0, 0, 9/10,0, 0, 0, 0, 0, 0,
0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0,
0, 0, 0, 0, 0, 0, 11/10,0, 0, 0, 0,
0, 0, 0, 0, 0, 0, 0, 11/10,0, 0, 0,
0, 0, 0, 0, 0, 0, 0, 0, 13/10,0, 0,
0, 0, 0, 0, 0, 0, 0, 0, 0, 13/10,0,
0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 3/2
print(matrix(L[4])*L[3]); // the chosen basis of H''/H'
-1+2xy-1445/64y5, 16x+125y4, 16y+125x4, 4x2+5y3, 4y2+5x3, xy+85/8y5, y3, x3, y4, x4, 1/2y5
