Changeset 979c4c in git


Ignore:
Timestamp:
Jul 24, 2006, 4:06:06 PM (18 years ago)
Author:
Hans Schönemann <hannes@…>
Branches:
(u'spielwiese', '17f1d200f27c5bd38f5dfc6e8a0879242279d1d8')
Children:
d420d9b1a7dfa526eb758fc647450e545bb219f8
Parents:
79c8130c7014f76030430c9596e3175a30699670
Message:
*hannes: Santiagos changes


git-svn-id: file:///usr/local/Singular/svn/trunk@9343 2c84dea3-7e68-4137-9b89-c4e89433aadc
Location:
Singular/LIB
Files:
3 edited

Legend:

Unmodified
Added
Removed

  • Singular/LIB/algebra.lib

    r79c813 r979c4c  
    11///////////////////////////////////////////////////////////////////////////////
    2 version="$Id: algebra.lib,v 1.14 2006-07-18 15:48:09 Singular Exp $";
     2version="$Id: algebra.lib,v 1.15 2006-07-24 14:06:05 Singular Exp $";
    33category="Commutative Algebra";
    44info="
    … …  
    3939         - k=1 : a list, say l, of size 2, l[1] integer, l[2] ring, satisfying
    4040           l[1]=1 if p is in the subalgebra K[A[1],...,A[m]] and then the ring
    41            l[2] contains poly check = h(y(1),...,y(m)) if p=h(A[1],...,A[m])
     41           l[2]: ring, contains poly check = h(y(1),...,y(m)) if p=h(A[1],...,A[m])
    4242           l[1]=0 if p is not in the subalgebra K[A[1],...,A[m]] and then
    4343           l[2] contains the poly check = h(x,y(1),...,y(m)) if p satisfies
    … …  
    441441         If, moreover, a string s is given, the algorithm creates, in the
    442442         preimage ring pr the kernel of phi with name s.
    443          Three differnt algorithms are used depending on c = 1,2,3.
    444          If c is not given or c=0, a heuristically best method is choosen.
    445          (alogrithm 1 uses the preimage command)
     443         Three different algorithms are used depending on c = 1,2,3.
     444         If c is not given or c=0, a heuristically best method is chosen.
     445         (algorithm 1 uses the preimage command)
    446446NOTE:    Since the kernel of phi lives in pr, it cannot be returned to the
    447447         basering. If s is given, the user has access to it in pr via s.
    … …  
    511511
    512512proc is_injective( map phi, pr,list #)
    513 "USAGE:   is_injective(phi[,c,s]); phi map, pr reimage ring, c int, s string
     513"USAGE:   is_injective(phi,pr[,c,s]); phi map, pr preimage ring, c int, s string
    514514RETURN:
    515515@format
    … …  
    614614         defining phi. Hence, if the basering has local or mixed ordering
    615615         or if the preimage ring is a quotient ring (in which case the map
    616          may not be well defined) then the return value 1 means
    617          \"surjectivity\" in this sense.
     616         may not be well defined) then the return value 1 means \"surjectivity\"
     617         in this sense.
    618618EXAMPLE: example is_surjective; shows an example
    619619"
    … …  
    675675
    676676proc is_bijective ( map phi, pr )
    677 "USAGE:   is_bijective(phi); phi map to basering, pr preimage ring
     677"USAGE:   is_bijective(phi,pr); phi map to basering, pr preimage ring
    678678RETURN:  an integer,  1 if phi is bijective, 0 if not
    679679NOTE:    The algorithm checks first injectivity and then surjectivity
    … …  
    776776RETURN:
    777777@format
    778          a list l two ideals, say I,J:
     778         a list l of two ideals, say I,J:
    779779         - I is generated by a subset of the variables with size(I) = dim(id)
    780780         - J defines a map (coordinate change in the basering), such that:
    … …  
    897897         - l[1] = 1 if var(v1),...,var(vr) are in l[2] and 0 else
    898898         - l[2] (resp. l[3]) contains those variables which occur,
    899            (resp. occur not) as pure power in the leading term of one of the
     899           (resp. do not occur) as pure power in the leading term of one of the
    900900           generators of J,
    901901         - l[4] contains those J[i] for which the leading term is a pure power

  • Singular/LIB/linalg.lib

    r79c813 r979c4c  
    11//GMG last modified: 04/25/2000
    22//////////////////////////////////////////////////////////////////////////////
    3 version="$Id: linalg.lib,v 1.38 2005-05-06 14:38:43 hannes Exp $";
     3version="$Id: linalg.lib,v 1.39 2006-07-24 14:06:05 Singular Exp $";
    44category="Linear Algebra";
    55info="
    … …  
    237237proc sym_gauss(matrix A)
    238238"USAGE:    sym_gauss(A);  A = symmetric matrix
    239 RETURN:   matrix, diagonalisation with symmetric gauss algorithm
     239RETURN:   matrix, diagonalisation of A with symmetric gauss algorithm
    240240EXAMPLE:  example sym_gauss; shows an example"
    241241{
    … …  
    276276//////////////////////////////////////////////////////////////////////////////
    277277proc orthogonalize(matrix A)
    278 "USAGE:    orthogonalize(A); A = constant matrix
     278"USAGE:    orthogonalize(A); A = matrix of constants
    279279RETURN:    matrix, orthogonal basis of the colum space of A
    280280EXAMPLE:   example orthogonalize; shows an example "
    … …  
    313313proc diag_test(matrix A)
    314314"USAGE:          diag_test(A); A = const square matrix
    315 RETURN:   int,  1 if A is diagonalisable, 0 if not
    316                -1 no statement is possible, since A does not split.
     315RETURN:   int,  1 if A is diagonalizable,@*
     316                0 if not@*
     317               -1 if no statement is possible, since A does not split.
    317318NOTE:     The test works only for split matrices, i.e if eigenvalues of A
    318319          are in the ground field.
    … …  
    858859"USAGE:     gaussred_pivot(A);   A any constant matrix
    859860RETURN:    list Z:  Z[1]=P , Z[2]=U , Z[3]=S , Z[4]=rank(A)
    860            gives n row reduced matrix S, a permutation matrix P and a
     861           gives a row reduced matrix S, a permutation matrix P and a
    861862           normalized lower triangular matrix U, with P*A=U*S
    862863NOTE:      with row pivoting
    … …  
    14171418
    14181419proc minipoly(matrix M,list #)
    1419 "USAGE:   minpoly(M); matrix M
     1420"USAGE:   minipoly(M); matrix M
    14201421ASSUME:  eigenvalues of M in basefield
    14211422RETURN:
    … …  
    15961597
    15971598proc spprint(list sp)
    1598 "USAGE:   spprint(sp); list sp
     1599"USAGE:   spprint(sp); list sp (helper routine for spnf, gmssing.lib)
    15991600RETURN:  string s;  spectrum sp
    16001601EXAMPLE: example spprint; shows examples
     1602SEE ALSO: gmssing_lib, spnf
    16011603"
    16021604{

  • Singular/LIB/matrix.lib

    r79c813 r979c4c  
    11///////////////////////////////////////////////////////////////////////////////
    2 version="$Id: matrix.lib,v 1.31 2006-07-20 17:02:38 Singular Exp $";
     2version="$Id: matrix.lib,v 1.32 2006-07-24 14:06:06 Singular Exp $";
    33category="Linear Algebra";
    44info="
    … …  
    743743proc permrow (matrix A, int r1, int r2)
    744744"USAGE:   permrow(A,r1,r2);  A matrix, r1,r2 positive integers
    745 RETURN:  matrix,  A being modified by permuting row r1 and r2
     745RETURN:  matrix,  A being modified by permuting rows r1 and r2
    746746EXAMPLE: example permrow; shows an example
    747747"
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