Changeset f32177 in git
- Timestamp:
- Apr 7, 2009, 11:31:52 AM (14 years ago)
- Branches:
- (u'jengelh-datetime', 'ceac47cbc86fe4a15902392bdbb9bd2ae0ea02c6')(u'spielwiese', 'a800fe4b3e9d37a38c5a10cc0ae9dfa0c15a4ee6')
- Children:
- 0ad81f2c92a459da3968f1add8868540fe570fb8
- Parents:
- 1288efb1bc6f003f059484c99a625cf47c1ed08b
- Files:
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- 7 edited
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Singular/LIB/brnoeth.lib (modified) (5 diffs)
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Singular/LIB/control.lib (modified) (3 diffs)
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Singular/LIB/general.lib (modified) (3 diffs)
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Singular/LIB/inout.lib (modified) (2 diffs)
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Singular/LIB/poly.lib (modified) (5 diffs)
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Singular/LIB/redcgs.lib (modified) (4 diffs)
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doc/examples.doc (modified) (previous)
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Singular/LIB/brnoeth.lib
r1288ef rf32177 1 version="$Id: brnoeth.lib,v 1.2 0 2008-10-07 17:36:30 SingularExp $";1 version="$Id: brnoeth.lib,v 1.21 2009-04-07 09:30:44 seelisch Exp $"; 2 2 category="Coding theory"; 3 3 info=" … … 8 8 OVERVIEW: 9 9 Implementation of the Brill-Noether algorithm for solving the 10 Riemann-Roch problem and applications inAlgebraic Geometry codes.10 Riemann-Roch problem and applications to Algebraic Geometry codes. 11 11 The computation of Weierstrass semigroups is also implemented.@* 12 12 The procedures are intended only for plane (singular) curves defined over … … 15 15 16 16 MAIN PROCEDURES: 17 Adj_div(f) ;computes the conductor of a curve18 NSplaces(h,A) ;computes non-singular places with given degrees19 BrillNoether(D,C) ;computes a vector space basis of the linear system L(D)20 Weierstrass(P,m,C) ;computes the Weierstrass semigroup of C at P up to m21 extcurve(d,C) ;extends the curve C to an extension of degree d22 AGcode_L(G,D,E) ;computes the evaluation AG code with divisors G and D23 AGcode_Omega(G,D,E) ;computes the residual AG code with divisors G and D24 prepSV(G,D,F,E) ;preprocessing for the basic decoding algorithm25 decodeSV(y,K) ;decoding of a word with the basic decoding algorithm17 Adj_div(f) computes the conductor of a curve 18 NSplaces(h,A) computes non-singular places with given degrees 19 BrillNoether(D,C) computes a vector space basis of the linear system L(D) 20 Weierstrass(P,m,C) computes the Weierstrass semigroup of C at P up to m 21 extcurve(d,C) extends the curve C to an extension of degree d 22 AGcode_L(G,D,E) computes the evaluation AG code with divisors G and D 23 AGcode_Omega(G,D,E) computes the residual AG code with divisors G and D 24 prepSV(G,D,F,E) preprocessing for the basic decoding algorithm 25 decodeSV(y,K) decoding of a word with the basic decoding algorithm 26 26 27 27 AUXILIARY PROCEDURES: 28 closed_points(I) ;computes the zero-set of a zero-dim. ideal in 2 vars29 dual_code(C) ;computes the dual code30 sys_code(C) ;computes an equivalent systematic code31 permute_L(L,P) ;applies a permutation to a list28 closed_points(I) computes the zero-set of a zero-dim. ideal in 2 vars 29 dual_code(C) computes the dual code 30 sys_code(C) computes an equivalent systematic code 31 permute_L(L,P) applies a permutation to a list 32 32 33 33 KEYWORDS: Weierstrass semigroup; Algebraic Geometry codes; … … 3345 3345 which represent the numerator, resp. denominator, of a rational 3346 3346 function).@* 3347 The corresponding rational functions form a vector basis of the3347 The corresponding rational functions form a vector space basis of the 3348 3348 linear system L(G), G a rational divisor over a non-singular curve. 3349 3349 NOTE: The procedure must be called from the ring CURVE[1][2], where … … 3943 3943 The intvec G represents a rational divisor (see @ref{BrillNoether} 3944 3944 for more details).@* 3945 The code evaluates the vector basis of L(G) at the rational3945 The code evaluates the vector space basis of L(G) at the rational 3946 3946 places given by D. 3947 3947 WARNINGS: G should satisfy @math{ 2*genus-2 < deg(G) < size(D) }, which is -
Singular/LIB/control.lib
r1288ef rf32177 1 version="$Id: control.lib,v 1. 39 2008-10-07 17:55:52 levandovExp $";1 version="$Id: control.lib,v 1.40 2009-04-07 09:30:44 seelisch Exp $"; 2 2 category="System and Control Theory"; 3 3 info=" 4 4 LIBRARY: control.lib Algebraic analysis tools for System and Control Theory 5 5 6 AUTHORS: Oleksandr Iena yena@mathematik.uni-kl.de7 @* Markus Becker mbecker@mathematik.uni-kl.de8 @* Viktor Levandovskyy levandov@mathematik.uni-kl.de6 AUTHORS: Oleksandr Iena, yena@mathematik.uni-kl.de 7 @* Markus Becker, mbecker@mathematik.uni-kl.de 8 @* Viktor Levandovskyy, levandov@mathematik.uni-kl.de 9 9 10 10 SUPPORT: Forschungsschwerpunkt 'Mathematik und Praxis' (Project of Dr. E. Zerz 11 and V. Levandovskyy), Uni Kaiserslautern11 and V. Levandovskyy), University of Kaiserslautern 12 12 13 13 MAIN PROCEDURES: 14 control(R) ;analysis of controllability-related properties of R (using Ext modules)15 controlDim(R) ;analysis of controllability-related properties of R (using dimension)16 autonom(R) ;analysis of autonomy-related properties of R (using Ext modules)17 autonomDim(R) ;analysis of autonomy-related properties of R (using dimension)14 control(R) analysis of controllability-related properties of R (using Ext modules) 15 controlDim(R) analysis of controllability-related properties of R (using dimension) 16 autonom(R) analysis of autonomy-related properties of R (using Ext modules) 17 autonomDim(R) analysis of autonomy-related properties of R (using dimension) 18 18 19 19 COMPONENT PROCEDURES: 20 leftKernel(R) ;a left kernel of R21 rightKernel(R) ;a right kernel of R22 leftInverse(R) ;a left inverse of R23 rightInverse(R) ;a right inverse of R24 colrank(M) ;a column rank of M as of matrix25 genericity(M) ;analysis of the genericity of parameters26 canonize(L) ;Groebnerification for modules in the output of control or autonomy procs27 iostruct(R) ;computes an IO-structure of behavior given by a module R28 findTorsion(R, I) ;generators of the submodule of a module R, annihilated by the ideal I20 leftKernel(R) a left kernel of R 21 rightKernel(R) a right kernel of R 22 leftInverse(R) a left inverse of R 23 rightInverse(R) a right inverse of R 24 colrank(M) a column rank of M as of matrix 25 genericity(M) analysis of the genericity of parameters 26 canonize(L) Groebnerification for modules in the output of control or autonomy procs 27 iostruct(R) computes an IO-structure of behavior given by a module R 28 findTorsion(R, I) generators of the submodule of a module R, annihilated by the ideal I 29 29 30 30 AUXILIARY PROCEDURES: 31 controlExample(s) ;set up an example from the mini database inside of the library32 view() ;well-formatted output of lists, modules and matrices31 controlExample(s) set up an example from the mini database inside of the library 32 view() well-formatted output of lists, modules and matrices 33 33 "; 34 34 … … 659 659 RETURN: list (of strings) 660 660 PURPOSE: determine parametric expressions which have been assumed to be non-zero in the process of computing the Groebner basis 661 NOTE: the output list consists of strings. The first string contains the variables only, whereas each further string contain a single polynomial in parameters. 662 $* We strongly recommend to switch on the redSB and redTail options. 661 NOTE: the output list consists of strings. The first string contains the variables only, whereas each further string contains 662 a single polynomial in parameters. 663 @* We strongly recommend to switch on the redSB and redTail options. 663 664 @* The procedure is effective with the lift procedure for modules with parameters 664 665 EXAMPLE: example genericity; shows an example … … 1415 1416 PURPOSE: set up an example from the mini database by initalizing a ring and a module in a ring 1416 1417 NOTE: in order to see the list of available examples, execute @code{controlExample(\"show\");} 1417 @* To use a bexample, one has to do the following. Suppose one calls the ring, where the example will be activated, A. Then, by executing1418 @* To use an example, one has to do the following. Suppose one calls the ring, where the example will be activated, A. Then, by executing 1418 1419 @* @code{def A = controlExample(\"Antenna\");} and @code{setring A;}, 1419 1420 @* A will become a basering from the example \"Antenna\" with -
Singular/LIB/general.lib
r1288ef rf32177 3 3 //eric, added absValue 11.04.2002 4 4 /////////////////////////////////////////////////////////////////////////////// 5 version="$Id: general.lib,v 1. 59 2009-01-14 16:07:04 SingularExp $";5 version="$Id: general.lib,v 1.60 2009-04-07 09:30:44 seelisch Exp $"; 6 6 category="General purpose"; 7 7 info=" … … 742 742 NOTE: If v is given id may be any simply indexed object (e.g. any list or 743 743 string); if v[i]<0 and i<=size(id) v[i] is set internally to i; 744 entries of v must be pairwise distinct to get a permutation i f id.744 entries of v must be pairwise distinct to get a permutation id. 745 745 Zero generators of ideal/module are deleted 746 746 EXAMPLE: example sort; shows an example … … 1175 1175 type(l[3])=typeof(n) 1176 1176 NOTE: If n is a long integer (of type number) then the procedure 1177 finds primefactors <= min(p,32003) but n may as larger as1177 finds primefactors <= min(p,32003) but n may be as larger as 1178 1178 2147483647 (max. integer representation) 1179 1179 WARNING: the procedure works for small integers only, just by testing all -
Singular/LIB/inout.lib
r1288ef rf32177 1 1 // (GMG/BM, last modified 22.06.96) 2 2 /////////////////////////////////////////////////////////////////////////////// 3 version="$Id: inout.lib,v 1.3 2 2009-02-23 12:08:39 SingularExp $";3 version="$Id: inout.lib,v 1.33 2009-04-07 09:30:44 seelisch Exp $"; 4 4 category="General purpose"; 5 5 info=" … … 566 566 567 567 proc showrecursive (@@id,poly p,list #) 568 "USAGE: showrecursive(id,p[,ord]); id =any object of basering, p= product of568 "USAGE: showrecursive(id,p[,ord]); id any object of basering, p= product of 569 569 variables and ord=string (any allowed ordstr) 570 570 DISPLAY: display 'id' in a recursive format as a polynomial in the variables -
Singular/LIB/poly.lib
r1288ef rf32177 1 1 /////////////////////////////////////////////////////////////////////////////// 2 version="$Id: poly.lib,v 1.5 1 2009-02-20 18:50:55 SingularExp $";2 version="$Id: poly.lib,v 1.52 2009-04-07 09:30:44 seelisch Exp $"; 3 3 category="General purpose"; 4 4 info=" … … 259 259 COMPUTE: rank of module presented by M in case it is free. 260 260 By definition this is vdim(coker(M)/m*coker(M)) if coker(M) 261 is free, where m =maximal ideal of the variables of the262 basering and M is considered asmatrix.261 is free, where m is the maximal ideal of the variables of the 262 basering and M is considered to be a matrix. 263 263 (the 0-module is free of rank 0) 264 264 RETURN: rank of coker(M) if coker(M) is free and -1 else; … … 361 361 corresponding component of id, independent of ring ordering 362 362 (maxdeg of each var is 1). 363 Of type int if id is of type poly, of type intmat else 364 NOTE: proc maxdeg1 returns an integer, the absolute maximum; moreover, it has 365 an option for computing weighted degrees 363 Of type int, if id is of type poly; of type intmat otherwise 366 364 SEE ALSO: maxdeg1 367 365 EXAMPLE: example maxdeg; shows examples … … 498 496 (mindeg of each variable is 1) of type int if id of type poly, else 499 497 of type intmat. 500 NOTE: proc mindeg1 returns one integer, the absolute minimum; moreover it 501 has an option for computing weighted degrees. 498 SEE ALSO: mindeg1 502 499 EXAMPLE: example mindeg; shows examples 503 500 " … … 630 627 proc normalize (id) 631 628 "USAGE: normalize(id); id=poly/vector/ideal/module 632 RETURN: object of same type ,s633 each element is normalized to make itsleading coefficient equal to 1629 RETURN: object of same type 630 each element is normalized with leading coefficient equal to 1 634 631 EXAMPLE: example normalize; shows an example 635 632 " -
Singular/LIB/redcgs.lib
r1288ef rf32177 1 1 ////////////////////////////////////////////////////////////////////////////// 2 version="$Id: redcgs.lib,v 1. 4 2009-02-26 14:07:04 SingularExp $";2 version="$Id: redcgs.lib,v 1.5 2009-04-07 09:30:44 seelisch Exp $"; 3 3 category="General purpose"; 4 4 info=" … … 3253 3253 The elements of the list T computed by mrcgs are lists representing 3254 3254 a rooted tree. 3255 Each element has as the two first entries with the following content: 3255 Each element has as the two first entries with the following content:@* 3256 3256 [1]: The label (intvec) representing the position in the rooted 3257 3257 tree: 0 for the root (and this is a special element) … … 3596 3596 The elements of the list T computed by rcgs are lists representing 3597 3597 a rooted tree. 3598 Each element has as the two first entries with the following content: 3598 Each element has as the two first entries with the following content:@* 3599 3599 [1]: The label (intvec) representing the position in the rooted 3600 3600 tree: 0 for the root (and this is a special element) … … 3778 3778 The elements of the list T computed by crcgs are lists representing 3779 3779 a rooted tree. 3780 Each element has as the two first entries with the following content: 3780 Each element has as the two first entries with the following content:@* 3781 3781 [1]: The label (intvec) representing the position in the rooted 3782 3782 tree: 0 for the root (and this is a special element)
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