Changeset 0132b0 in git for Singular/LIB/primitiv.lib

Timestamp:

Apr 23, 1998, 3:23:27 PM (26 years ago)

Author:

Olaf Bachmann <obachman@…>

Branches:

(u'spielwiese', '17f1d200f27c5bd38f5dfc6e8a0879242279d1d8')

Children:

e36ae54f25a40adf73b0e8d8180c361742db9def

Parents:

e35965573370ae0d1c2c96e458eb1e3bde28c946

Message:

* incoporated new versions from Martin


git-svn-id: file:///usr/local/Singular/svn/trunk@1437 2c84dea3-7e68-4137-9b89-c4e89433aadc

File:

• Singular/LIB/primitiv.lib (modified) (11 diffs)

Singular/LIB/primitiv.lib

@@ -1 @@
-// $Id: primitiv.lib,v 1.3 1998-04-03 22:47:11 krueger Exp $
-// This library requires Singular 1.0
-
-version="$Id: primitiv.lib,v 1.3 1998-04-03 22:47:11 krueger Exp $";
+// $Id: primitiv.lib,v 1.4 1998-04-23 13:23:27 obachman Exp $
+// author:  Martin Lamm,  email: lamm@mathematik.uni-kl.de
+// last change:           11.3.98
+///////////////////////////////////////////////////////////////////////////////
+version="$Id: primitiv.lib,v 1.4 1998-04-23 13:23:27 obachman Exp $";
 info="
 LIBRARY:    primitiv.lib    PROCEDURES FOR FINDING A PRIMITIVE ELEMENT
 
- primitivE(ideal i); finds minimal polynomial for a primitive element
-
- splitring(poly f,string R[,list L]);  define ring extension with name R
-                                       and switch to it
- randomLast(int b);       random transformation of the last variable
+ primitive(ideal i);   finds minimal polynomial for a primitive element
+ splitring(f,R[,L]);   define ring extension with name R and switch to it
+ randomLast(b);        random transformation of the last variable
 ";
 
+///////////////////////////////////////////////////////////////////////////////
 LIB "random.lib";
 ///////////////////////////////////////////////////////////////////////////////
@@ -21 +21 @@
          a sum of it with a linear random combination of the other
          variables
-NOTE:   
 EXAMPLE: example randomLast; shows an example
 {
@@ -40 +39 @@
 ///////////////////////////////////////////////////////////////////////////////
 
-proc primitivE(ideal i)
-USAGE:  primitivE(i); i ideal of the following form:
+proc primitive(ideal i)
+USAGE:  primitive(i); i ideal of the following form:
  Let k be the ground field of your basering, a_1,...,a_n algebraic over k,
  m_1(x1), m_2(x_1,x_2),...,m_n(x_1,...,x_n) polynomials in k such that
@@ -48 +47 @@
  Then i has to be generated by m_1,...,m_n.
 
-RETURN: ideal j in k[x_n] such that
+RETURN:  ideal j in k[x_n] such that
  j[1] is minimal polynomial for a primitive element b of k(a_1,...,a_n)=k(b)
          over k
  j[2],...,j[n+1] polynomials in k[x_n] : j[i+1](b)=a_i for i=1,...,n
-NOTE: the number of variables in the basering has to be exactly the number n of
-      given algebraic elements (and minimal polynomials)
-EXAMPLE:    example primitivE;  shows an example
+NOTE:    the number of variables in the basering has to be exactly the number n
+         of given algebraic elements (and minimal polynomials)
+EXAMPLE: example primitive;  shows an example
 {
  def altring=basering;
@@ -111 +110 @@
  ring exring=0,(x,y),dp;
  ideal i=x2+1,y2-x;                  // compute Q(i,i^(1/2))=:L
- ideal j=primitivE(i);               // -> we have L=Q(a):
+ ideal j=primitive(i);               // -> we have L=Q(a):
  "minimal polynomial of a:",j[1];    // => a=(-1)^(1/4)
  "polynomial for i:       ",j[2];    // => i=a^2
  "polynomial for i^(1/2): ",j[3];    // => i^(1/2)=a
  // ==> the 2nd element was already primitive!
- j=primitivE(ideal(x2-2,y2-3));      // compute Q(sqrt(2),sqrt(3))
+ j=primitive(ideal(x2-2,y2-3));      // compute Q(sqrt(2),sqrt(3))
  "minimal polynomial:",j[1];
  "polynomial p s.t. p(a)=sqrt(2):",j[2];
@@ -130 +129 @@
 ACTION: defines a ring with name R, in which f is reducible, and changes to it
         If the old ring has no parameter, the name 'a' is chosen for the
-        parameter of R (if a is no variable; if it is, the proc takes 'b'; if
-        this is also impossible, then 'c'), otherwise the name of the parameter
-        is kept and only the minimal polynomial is changed.
+        parameter of R (if a is no variable; if it is, the proc takes 'b',
+        etc.; if a,b,c,o are variables of the ring, produce an error message),
+        otherwise the name of the parameter is kept and only the
+        minimal polynomial is changed.
         The names of variables and orderings are not affected.
 
@@ -138 +138 @@
         will be REPLACED by the new ring (with the same name as the old ring).
 
-RETURNs: list L mapped into the new ring R, if L is given; else nothing
-ASSUME : the active ring must be bivariate and allow an algebraic extension
+RETURN: list L mapped into the new ring R, if L is given; else nothing
+ASSUME: the active ring must allow an algebraic extension
          (e.g. it cannot be a transcendent ring extension of Q or Z/p)
 EXAMPLE: example splitring;  shows an example
@@ -162 +162 @@
  string varnames=varstr(altring);
  string algname;
+ int i;
+ int anzvar=size(maxideal(1));
  //--------------- Fall 1: Bisheriger Ring hatte kein Minimalpolynom ----------
  if (minp=="0") {
   if (find(varnames,"a")==0)        { algname="a";}
   else { if (find(varnames,"b")==0) { algname="b";}
-         else                       { algname="c";}
- //----------- nur ZWEI Variablen erlaubt ==> c ist kein Variablenname --------
+         else { if (find(varnames,"c")==0)
+                                    { algname="c";}
+         else { if (find(varnames,"o")==0)
+                                    { algname="o";}
+         else {
+           "** Sorry -- could not find a free name for the primitive element.";
+           "** Try e.g. a ring without 'a' or 'b' as variable.";
+           return();
+         }}
+       }
   }
  //-- erzeuge einen String, der das Minimalpolynom des neuen Rings enthaelt: --
   execute("ring splt1="+charakt+","+algname+",dp;");
-  map nach_splt1=altring,var(1),var(1);
+  ideal abbnach=var(1);
+  for (i=1; i<anzvar; i++) { abbnach=abbnach,var(1); }
+  map nach_splt1=altring,abbnach;
   execute("poly mipol="+string(nach_splt1(f))+";");
   string Rminp=string(mipol);
@@ -198 +210 @@
   execute("ring splt3="+charakt+",("+algname+","+varnames+"),dp;");
   poly f=imap(altring,f);
- //-------------- Vorbereitung des Aufrufes von primitivE: --------------------
+ //-------------- Vorbereitung des Aufrufes von primitive: --------------------
   execute("ring splt1="+charakt+",(x,y),dp;");
-  map nach_splt1_3=splt3,x,y,y;
+  ideal abbnach=x;
+  for (i=1; i<=anzvar; i++) { abbnach=abbnach,y; }
+  map nach_splt1_3=splt3,abbnach;
   map nach_splt1_2=splt2,x;
   ideal maxid=nach_splt1_2(mipol),nach_splt1_3(f);
-  ideal primit=primitivE(maxid);
+  ideal primit=primitive(maxid);
   "new minimal polynomial:",primit[1];
  //-- erzeuge einen String, der das Minimalpolynom des neuen Rings enthaelt: --
@@ -210 +224 @@
   minp=string(nach_splt2(primit)[1]);
  //--------------------- definiere den neuen Ring: ----------------------------
-  execute("ring "+@R+" = ("+charakt+","+algname+"),("+varnames+"),("+ordstr(altring)+");");
+  execute("ring "+@R+" = ("+charakt+","+algname+"),("+varnames+"),("
+          +ordstr(altring)+");");
   execute("minpoly="+minp+";");
   execute("export "+@R+";");
@@ -225 +240 @@
     map nach_splt3_1=splt1,0,var(1);  // x->0, y->a
  //----- rechne das primitive Element von altring in das von neuring um: ------
-    map convert=splt3,nach_splt3_1(primit)[2],var(2),var(3); 
+    ideal convid=maxideal(1);
+    convid[1]=nach_splt3_1(primit)[2];
+    map convert=splt3,convid; 
     zwi=convert(zwi);
     setring neuring;