Opened 13 years ago

Closed 10 years ago

#172 closed proposed feature (fixed)

Announcement: new library decomp.lib

Reported by: gorzel Owned by: hannes
Priority: minor Milestone: 3-1-5 and higher
Component: singular-libs Version: 3-1-4
Keywords: Cc:


For the next release I will provide

LIBRARY: decomp.lib  Functional Decomposition of Polynomials
AUTHOR:  Christian Gorzel, University of Muenster

 Implements functional decomposition of multivariate polynomials. 

 D. Kozen, S. Landau: Polynomial Decomposition Algorithms,
                       J. Symb. Comp. (1989), 7, 445-456 
 J. von zu Gathen: Functional Decomposition of Polynomials: the Tame Case, 
                       J. Symb. Comp. (1990), 9, 281-299 

 decompose(f[,1]);           [complete] functional decomposition of poly f
 is_composite(f);            predicate, is f a composite polynomial?
 chebyshev(n);               the nth Chebyshev polynomial of the first kind
 compose(I);                 compose entries of ideal

 Decomposes, if possible,  multivariate polynomials as
    f = h o g, where h is univariate and g is multivariate



  • alg.number theory: intermediate fields k < k(f)
  • simplified solving of univariate polynomial equations
  • polynomial mapping: affine Stein factorization


The implementation is much faster than

Maple's compoly or MUPAD's polylib::decompose


Attachments (3)

decomp.pdf (76.9 KB) - added by gorzel 12 years ago.
decomp.lib (45.7 KB) - added by gorzel 11 years ago.
decomp.2.lib (45.7 KB) - added by gorzel 11 years ago.

Download all attachments as: .zip

Change History (8)

Changed 12 years ago by gorzel

Attachment: decomp.pdf added

Changed 11 years ago by gorzel

Attachment: decomp.lib added

Changed 11 years ago by gorzel

Attachment: decomp.2.lib added

comment:1 Changed 10 years ago by gorzel

Milestone: 3-1-13-1-5 and higher
Owner: gorzel deleted
Version: 3-1-03-1-4

comment:2 Changed 10 years ago by gorzel

Could somebody have a look at it?

See also the examples at the end of the library, and compare with REDUCE's command decompose.

comment:3 Changed 10 years ago by gorzel

Owner: set to somebody

comment:4 Changed 10 years ago by ren

Owner: changed from somebody to hannes

comment:5 Changed 10 years ago by hannes

Resolution: fixed
Status: newclosed

added decomp.lib as experimental

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