Changeset 999d8e2 in git for Singular

Timestamp:

Oct 13, 2016, 3:56:34 PM (8 years ago)

Author:

Hans Schoenemann <hannes@…>

Branches:

(u'spielwiese', '17f1d200f27c5bd38f5dfc6e8a0879242279d1d8')

Children:

488bf28ce21dbdca62e23e85309e403e926731b0

Parents:

0750b0232fb64224c4524f35243e993f0bbfc3fa

Message:

doc: grobcov.lib: index tries

File:

• Singular/LIB/grobcov.lib (modified) (20 diffs)

Singular/LIB/grobcov.lib

@@ -733 +733 @@
           locusdg, envelop, WLemma, and killed before the output. The user does not need to call it.
           The basering R, must be of the form Q[a][x], (a=parameters, x=variables), and should be defined previously.
-KEYWORDS: ring; rings;
+KEYWORDS: ring
 EXAMPLE:  setglobalrings; shows an example"
 {
@@ -837 +837 @@
           m*f=r+sum(q.F),
           and no lpp of a divisor divides a pp of r.
-KEYWORDS: division; reduce;
+KEYWORDS: division; reduce
 EXAMPLE:  pdivi; shows an example"
 {
@@ -1065 +1065 @@
 RETURN: a reduced polynomial g of f, whose coefficients are reduced modulo E and having no factor in N.
 NOTE: Should be called from ring Q[a][x]. Ideals E and N must be given by polynomials in Q[a].
-KEYWORDS: division; pdivi; reduce;
+KEYWORDS: division; pdivi; reduce
 EXAMPLE: pnormalf; shows an example"
 {
@@ -1372 +1372 @@
 RETURN: The canonical C-representation [P,Q] of the locally closed set, formed by a pair of radical ideals with P
            included in Q, representing the set V(P) - V(Q) = V(N) - V(M)
- KEYWORDS: locally closed set; canoncial form;
+ KEYWORDS: locally closed set; canoncial form
  EXAMPLE:  Crep; shows an example"
 {
@@ -1461 +1461 @@
            Output: [Comp_1, .. , Comp_s ] where
            Comp_i=[p_i,[p_i1,..,p_is_i]]
- KEYWORDS: locally closed set; canoncial form;
+ KEYWORDS: locally closed set; canoncial form
  EXAMPLE:  Prep; shows an example"
 {
@@ -1550 +1550 @@
  RETURN:The canonical C-representation [P,Q] of the locally closed set. A pair of radical ideals with P included in Q,
           representing the set V(P) - V(Q)
- KEYWORDS: locally closed set; canoncial form;
+ KEYWORDS: locally closed set; canoncial form
  EXAMPLE:  PtoCrep; shows an example"
 {
@@ -1665 +1665 @@
           expensive (\"can\",0-1,\"out\",0).
 
-KEYWORDS: CGS; disjoint; reduced; Comprehensive Groebner System;
+KEYWORDS: CGS; disjoint; reduced; Comprehensive Groebner System
 EXAMPLE:  cgsdr; shows an example"
 {
@@ -2409 +2409 @@
 NOTE: The basering R, must be of the form Q[a][x], (a=parameters, x=variables), and should be defined previously.
           The ideal must be defined on R.
-KEYWORDS: Groebner cover; parametric ideal; canonical; discussion of parametric ideal;
+KEYWORDS: Groebner cover; parametric ideal; canonical; discussion of parametric ideal
 EXAMPLE:  grobcov; shows an example"
 {
@@ -2591 +2591 @@
           The ideals must be defined on R.
 KEYWORDS: Groebner cover; parametric ideal; locally closed set; parametric ideal; generic representation;
-           full representation;
+           full representation
 EXAMPLE:  extendpoly; shows an example"
 {
@@ -2727 +2727 @@
 NOTE: The basering R, must be of the form Q[a][x], (a=parameters, x=variables), and should be defined previously.
           The ideal must be defined on R.
-KEYWORDS: Groebner cover; parametric ideal; canonical, discussion of parametric ideal; full representation;
+KEYWORDS: Groebner cover; parametric ideal; canonical, discussion of parametric ideal; full representation
 EXAMPLE:  extendGC; shows an example"
 {
@@ -4119 +4119 @@
          J.M. Brunat, A. Montes. \"Computing the canonical representation of constructible sets.\"
          Math.  Comput. Sci. (2016) 19: 165-178.
-KEYWORDS: constructible set; locally closed set; canonical form;
+KEYWORDS: constructible set; locally closed set; canonical form
 EXAMPLE:  ConsLevels; shows an example"
 {
@@ -4180 +4180 @@
 RETURN: The levels of the constructible set:
           Lc=[ [1,[a1,a2]],[3,[a3,a4]],..,[2l-1,[a_{2l-1},a_{2l}]] ] the list of  Levels of S
-KEYWORDS: constructible sets; canonical form;
+KEYWORDS: constructible sets; canonical form
 EXAMPLE:  ConsLevelsToLevels shows an example"
 {
@@ -4712 +4712 @@
           If all levels of a locus are 1, then all subsets are locally closed.
 NOTE: The input must be the grobcov of the locus system in generic representation (\"ext\",0), which is the default.
-KEYWORDS: geometrical locus; locus; dynamic geometry;
+KEYWORDS: geometrical locus; locus; dynamic geometry
 EXAMPLE: locus; shows an example"
 {
@@ -4820 +4820 @@
            The \"Relevant\" components are the \"Normal\" and \"Accumulation\" components of the locus. (See help for
            locus).
-KEYWORDS: geometrical locus; locus; dynamic geometry;
+KEYWORDS: geometrical locus; locus; dynamic geometry
 EXAMPLE: locusdg; shows an example"
 {
@@ -4862 +4862 @@
            - locusdg(locus(grobcov(F)))  -> locusto( locusdg(locus(grobcov(F))) )
            - envelop(F,C)                       -> locusto( envelop(F,C) )
-KEYWORDS: geometrical locus; locus; envelop; string;
+KEYWORDS: geometrical locus; locus; envelop; string
 EXAMPLE:  locusto; shows an example"
 {
@@ -4983 +4983 @@
           This routine uses the generalized definition of envelop introduced in the book
            A. Montes. \"Discussing Parametric Polynomial Systems: The Groebner Cover\" not yet published.
-KEYWORDS: geometrical locus; locus; envelop;
+KEYWORDS: geometrical locus; locus; envelop
 EXAMPLE:  envelop; shows an example"
 {
@@ -5200 +5200 @@
           A. Montes. \"Discussing Parametric Polynomial Systems: The Groebner Cover\".
 NOTE: grobcov is called internally. The basering R, must be of the form Q[a][x] (a=parameters, x=variables).
-KEYWORDS: geometrical locus; locus; envelop; associated tangent;
+KEYWORDS: geometrical locus; locus; envelop; associated tangent
 EXAMPLE:  AssocTanToEnv; shows an example"
 {
@@ -5354 +5354 @@
 NOTE: grobcov is called internally.
           The basering R, must be of the form Q[a][x] (a=parameters, x=variables).
-KEYWORDS: geometrical locus; locus; envelop; associated tangent;
+KEYWORDS: geometrical locus; locus; envelop; associated tangent
 EXAMPLE:  FamElemsAtEnvCompPoints; shows an example"
 {
@@ -5405 +5405 @@
           poly x: can be a variable or a parameter of the ring.
 RETURN: the factorized discriminant of f wrt x for discussing its sign
-KEYWORDS: second degree; solve;
+KEYWORDS: second degree; solve
 EXAMPLE:  discrim; shows an example"
 {
@@ -5566 +5566 @@
 
 NOTE: The basering R, must be of the form Q[a][x] (a=parameters, x=variables).
-KEYWORDS: Wibmer's Lemma;
+KEYWORDS: Wibmer's Lemma
 EXAMPLE:  WLemma; shows an example"
 {