Changeset b4a463 in git

Timestamp:

Jul 18, 2006, 2:17:36 PM (18 years ago)

Author:

Hans Schönemann <hannes@…>

Branches:

(u'spielwiese', 'fe61d9c35bf7c61f2b6cbf1b56e25e2f08d536cc')

Children:

c89c574998a1ffa7816eb2b5e388287e16b1a4b0

Parents:

f04aafa3db2b15cf551661055b7cfbce72c3d342

Message:

*hannes: format, typos in docu


git-svn-id: file:///usr/local/Singular/svn/trunk@9312 2c84dea3-7e68-4137-9b89-c4e89433aadc

File:

• Singular/LIB/ainvar.lib (modified) (7 diffs)

Singular/LIB/ainvar.lib

@@ -1 @@
-// $Id: ainvar.lib,v 1.7 2002-04-12 16:19:41 Singular Exp $
+// $Id: ainvar.lib,v 1.8 2006-07-18 12:17:36 Singular Exp $
 /////////////////////////////////////////////////////////////////////////////
-version="$Id: ainvar.lib,v 1.7 2002-04-12 16:19:41 Singular Exp $";
+version="$Id: ainvar.lib,v 1.8 2006-07-18 12:17:36 Singular Exp $";
 category="Invariant theory";
 info="
@@ -62 +62 @@
 proc derivate (matrix m, id)
 "USAGE:  derivate(m,id);  m matrix, id poly/vector/ideal
-ASSUME:  m is a nx1 matrix, where n = number of variables of the basering
+ASSUME:  m is an nx1 matrix, where n = number of variables of the basering
 RETURN:  poly/vector/ideal (same type as input), result of applying the
          vector field by the matrix m componentwise to id;
@@ -274 +274 @@
 proc completeReduction(poly p, ideal dom, list #)
 "USAGE:   completeReduction(p,I[,q,n]); p poly, I ideal, [q monomial, n int]
-RETURN:  a polynomial, the SAGBI reduction of the polynomial p with I
+RETURN:  a polynomial, the SAGBI reduction of the polynomial p with respect to I
          via the procedure 'reduction' as long as possible
          if n=1, a different algorithm is chosen which is sometimes faster
@@ -338 +338 @@
 @end format
          with respect to p,q,h. It is defined as follows: set inv = p if p is
-         invariant, and else as
+         invariant, and else set
          inv = m(q)^N * sum_i=1..N-1{ (-1)^i*(1/i!)*m^i(p)*(q/m(q))^i }
-         where m^N(p) = 0,  m^(N-1)(p) != 0;
-         the result is inv divided by h as much as possible
+         where m^N(p) = 0,  m^(N-1)(p) != 0; the result is inv divided by h
+         as often as possible
 EXAMPLE: example localInvar; shows an example
 "
@@ -405 +405 @@
 @end format
          i.e. we compute elements in the (invariant) subring generated by id
-         which are divisible by q and divide them by q as much as possible
-         the second ideal contains all invariants given before
-         if n=1, a different algorithm is chosen which is sometimes faster
+         which are divisible by q and divide them by q as often as possible.
+         The second ideal contains all invariants given before.
+         If n=1, a different algorithm is chosen which is sometimes faster
          (default: n=0)
 EXAMPLE: example furtherInvar; shows an example
@@ -508 +508 @@
          If b<=0, the computation continues until all generators
          of the ring of invariants are computed (should be used only if the
-         ring of invariants is known to be finitely generated otherwise the
+         ring of invariants is known to be finitely generated, otherwise the
          algorithm might not stop).
          If r=1 a different reduction is used which is sometimes faster
@@ -514 +514 @@
 DISPLAY: if pa is given (any string as 5th or 6th argument), the computation
          pauses whenever new invariants are found and displays them
-THEORY:  The algorithm to compute the ring of invariants works in char 0
-         or big enough characteristic. (K,+) acts as the exponential of the
-         vector field defined by the matrix m. For background see G.-M. Greuel,
-         G. Pfister, Geometric quotients of unipotent group actions, Proc.
+THEORY:  The algorithm for computing the ring of invariants works in char 0
+         or suffiently large characteristic.
+         (K,+) acts as the exponential of the vector field defined by the
+         matrix m.
+         For background see G.-M. Greuel, G. Pfister,
+         Geometric quotients of unipotent group actions, Proc.
          London Math. Soc. (3) 67, 75-105 (1993).
 EXAMPLE: example invariantRing; shows an example