Changeset 8519cfb in git


Ignore:
Timestamp:
Sep 9, 1997, 10:39:02 AM (26 years ago)
Author:
Jens Schmidt <schmidt@…>
Branches:
(u'spielwiese', '8e0ad00ce244dfd0756200662572aef8402f13d5')
Children:
7078880fce41b700d9e350ba47533908fc986463
Parents:
030c6813af8a267ae33e85e00dcb4866be1a7aba
Message:
	* cf_ops.cc (swapvar_between): arguments to operator * swapped

	* cf_ops.cc (swapvar_between, swapvar_rec): functions reordered
	  and declarations removed

	* cf_ops.cc (swapvar_between1, swapvar_rec1, swapvar1): new
	  experimental functions, to be removed in future

	* cf_ops.cc: (replacevar, replacevar_between): new functions
	* canonicalform.h (replacevar): new declaration

	* cf_ops.cc (psr, psq, psqr, cden, common_den): functions moved
	  to cf_algorithm.cc

	* cf_ops.cc (apply): bug fix.  In case f.inCoeffDomain() result is
	  now initialized to f.


git-svn-id: file:///usr/local/Singular/svn/trunk@677 2c84dea3-7e68-4137-9b89-c4e89433aadc
File:
1 edited

Legend:

Unmodified
Added
Removed

  • factory/cf_ops.cc

    r030c681 r8519cfb  
    11/* emacs edit mode for this file is -*- C++ -*- */
    2 /* $Id: cf_ops.cc,v 1.6 1997-09-01 09:06:19 schmidt Exp $ */
     2/* $Id: cf_ops.cc,v 1.7 1997-09-09 08:39:02 schmidt Exp $ */
     3
     4//{{{ docu
     5//
     6// cf_ops.cc - simple structural algorithms.
     7//
     8// A 'structural' algorithm is an algorithm which gives
     9// structural information on polynomials in contrast to a
     10// 'mathematical' algorithm which calculates some mathematical
     11// function.
     12//
     13// Compare these functions with the functions in cf_algorithm.cc,
     14// which are mathematical algorithms.
     15//
     16// Used by: allmost everywhere
     17//
     18// Header file: canonicalform.h
     19//
     20//}}}
    321
    422#include <config.h>
    … …  
    624#include "assert.h"
    725
    8 #include "cf_defs.h"
    926#include "canonicalform.h"
     27#include "variable.h"
    1028#include "cf_iter.h"
    1129
     30//{{{ static Variable sv_x1, sv_x2;
     31//{{{ docu
     32//
     33// sv_x1, sv_x2 - variables to swap by swapvar() and replacevar.
     34//
     35// These variables are initialized by swapvar() such that sv_x1 <
     36// sv_x2.  They are used by swapvar_between() and swapvar_rec()
     37// to swap variables efficiently.
     38// Furthermore, sv_x1 and sv_x2 are used by replacevar() and
     39// replacevar_between().
     40//
     41//}}}
     42static Variable sv_x1, sv_x2;
     43//}}}
     44
     45//{{{ static void swapvar_between ( const CanonicalForm & f, CanonicalForm & result, const CanonicalForm & term, int expx2 )
     46//{{{ docu
     47//
     48// swapvar_between() - replace occurences of sv_x1 in f with sv_x2.
     49//
     50// If Psi denotes the map which maps sv_x1 to sv_x2, this
     51// function returns
     52//
     53//   result + Psi(f) * term * sv_x1^expx2
     54//
     55// Used by: swapvar()
     56//
     57//}}}
     58static void
     59swapvar_between ( const CanonicalForm & f, CanonicalForm & result, const CanonicalForm & term, int expx2 )
     60{
     61    if ( f.inCoeffDomain() || f.mvar() < sv_x1 )
     62        // in this case, we do not have to replace anything
     63        result += term * power( sv_x1, expx2 ) * f;
     64    else  if ( f.mvar() == sv_x1 )
     65        // this is where the real work is done: this iterator
     66        // replaces sv_x1 with sv_x2
     67        for ( CFIterator i = f; i.hasTerms(); i++ )
     68            result += power( sv_x2, i.exp() ) * term * power( sv_x1, expx2 ) * i.coeff();
     69    else
     70        // f's level is larger than sv_x1: descend down
     71        for ( CFIterator i = f; i.hasTerms(); i++ )
     72            swapvar_between( i.coeff(), result, term * power( f.mvar(), i.exp() ), expx2 );
     73}
     74static CanonicalForm
     75swapvar_between1 ( const CanonicalForm & f )
     76{
     77    if ( f.inCoeffDomain() || f.mvar() < sv_x1 )
     78        // in this case, we do not have to replace anything
     79        return f;
     80    else  if ( f.mvar() == sv_x1 ) {
     81        // this is where the real work is done: this iterator
     82        // replaces sv_x1 with sv_x2
     83        CanonicalForm result;
     84        for ( CFIterator i = f; i.hasTerms(); i++ )
     85            result += power( sv_x2, i.exp() ) * i.coeff();
     86        return result;
     87    }
     88    else {
     89        // f's level is larger than sv_x1: descend down
     90        CanonicalForm result;
     91        for ( CFIterator i = f; i.hasTerms(); i++ )
     92            result += swapvar_between1( i.coeff() ) * power( f.mvar(), i.exp() );
     93        return result;
     94    }
     95}
     96//}}}
     97
     98//{{{ static void swapvar_rec ( const CanonicalForm & f, CanonicalForm & result, const CanonicalForm & term )
     99//{{{ docu
     100//
     101// swapvar_between() - swap occurences of sv_x1 and sv_x2 in f.
     102//
     103// If Psi denotes the map which swaps sv_x1 and sv_x2, this
     104// function returns
     105//
     106//   result + Psi(f) * term
     107//
     108// Used by: swapvar()
     109//
     110//}}}
     111static void
     112swapvar_rec ( const CanonicalForm & f, CanonicalForm & result, const CanonicalForm & term )
     113{
     114    if ( f.inCoeffDomain() || f.mvar() < sv_x1 )
     115        // in this case, we do not have to swap anything
     116        result += term * f;
     117    else  if ( f.mvar() == sv_x2 )
     118        // this is where the real work is done: this iterator
     119        // replaces sv_x1 with sv_x2 in the coefficients of f and
     120        // remembers the exponents of sv_x2 in the last argument
     121        // of the call to swapvar_between()
     122        for ( CFIterator i = f; i.hasTerms(); i++ )
     123            swapvar_between( i.coeff(), result, term, i.exp() );
     124    else  if ( f.mvar() < sv_x2 )
     125        // sv_x2 does not occur in f, but sv_x1 does.  Replace it.
     126        swapvar_between( f, result, term, 0 );
     127    else
     128        // f's level is larger than sv_x2: descend down
     129        for ( CFIterator i = f; i.hasTerms(); i++ )
     130            swapvar_rec( i.coeff(), result, term * power( f.mvar(), i.exp() ) );
     131}
     132static CanonicalForm
     133swapvar_rec1 ( const CanonicalForm & f )
     134{
     135    if ( f.inCoeffDomain() || f.mvar() < sv_x1 )
     136        return f;
     137    else  if ( f.mvar() == sv_x2 ) {
     138        CanonicalForm result;
     139        for ( CFIterator i = f; i.hasTerms(); i++ )
     140            result += swapvar_between1( i.coeff() ) * power( sv_x1, i.exp() );
     141        return result;
     142    }
     143    else  if ( f.mvar() < sv_x2 )
     144        return swapvar_between1( f );
     145    else {
     146        CanonicalForm result;
     147        for ( CFIterator i = f; i.hasTerms(); i++ )
     148            result += swapvar_rec1( i.coeff() ) * power( f.mvar(), i.exp() );
     149        return result;
     150    }
     151}
     152//}}}
     153
     154//{{{ CanonicalForm swapvar ( const CanonicalForm & f, const Variable & x1, const Variable & x2 )
     155//{{{ docu
     156//
     157// swapvar() - swap variables x1 and x2 in f.
     158//
     159// Returns the image of f under the map which maps x1 to x2 and
     160// x2 to x1.  This is done quite efficiently because it is used
     161// really often.  x1 and x2 should be polynomial variables.
     162//
     163//}}}
    12164CanonicalForm
    13 psr( const CanonicalForm &f, const CanonicalForm &g, const Variable & x )
    14 {
    15     int m = f.degree( x );
    16     int n = g.degree( x );
    17     if ( m < n )
    18         return f;
    19     else
    20         return ( power( LC(g,x), m-n+1 ) * f ) % g;
    21 }
    22 
    23 CanonicalForm
    24 psq( const CanonicalForm &f, const CanonicalForm &g, const Variable & x )
    25 {
    26     return ( power( LC(g,x), degree(f,x)-degree(g,x)+1 ) * f ) / g;
    27 }
    28 
    29 void
    30 psqr( const CanonicalForm &f, const CanonicalForm &g, CanonicalForm &q, CanonicalForm &r, const Variable& x )
    31 {
    32     divrem( power( LC(g,x), degree(f,x)-degree(g,x)+1 ) * f, g, q, r );
    33 }
    34 
    35 static void swapvar_rec ( const CanonicalForm &f, CanonicalForm &result, const CanonicalForm &term );
    36 
    37 static void swapvar_between ( const CanonicalForm &f, CanonicalForm &result, const CanonicalForm &term, int expx2 );
    38 
    39 static Variable sv_x1, sv_x2;
    40 
    41 CanonicalForm
    42 swapvar ( const CanonicalForm &f, const Variable &x1, const Variable &x2 )
     165swapvar ( const CanonicalForm & f, const Variable & x1, const Variable & x2 )
    43166{
    44167    ASSERT( x1.level() > 0 && x2.level() > 0, "cannot swap algebraic Variables" );
    … …  
    54177        }
    55178        if ( f.mvar() < sv_x2 )
     179            // we only have to replace sv_x1 by sv_x2
    56180            swapvar_between( f, result, 1, 0 );
    57181        else
     182            // we really have to swap variables
    58183            swapvar_rec( f, result, 1 );
    59184        return result;
    60185    }
    61186}
    62 
    63 void
    64 swapvar_rec ( const CanonicalForm &f, CanonicalForm &result, const CanonicalForm &term )
    65 {
    66     if ( f.inCoeffDomain() || f.mvar() < sv_x1 )
    67         result += term * f;
    68     else  if ( f.mvar() == sv_x2 )
    69         for ( CFIterator i = f; i.hasTerms(); i++ )
    70             swapvar_between( i.coeff(), result, term, i.exp() );
    71     else  if ( f.mvar() < sv_x2 )
    72         swapvar_between( f, result, term, 0 );
    73     else
    74         for ( CFIterator i = f; i.hasTerms(); i++ )
    75             swapvar_rec( i.coeff(), result, term*power( f.mvar(), i.exp() ) );
    76 }
    77 
    78 void
    79 swapvar_between ( const CanonicalForm &f, CanonicalForm &result, const CanonicalForm &term, int expx2 )
    80 {
    81     if ( f.inCoeffDomain() || f.mvar() < sv_x1 )
    82         result += term * power( sv_x1, expx2 ) * f;
    83     else  if ( f.mvar() == sv_x1 )
    84         for ( CFIterator i = f; i.hasTerms(); i++ )
    85             result += power( sv_x2, i.exp() ) * term * i.coeff() * power( sv_x1, expx2 );
    86     else
    87         for ( CFIterator i = f; i.hasTerms(); i++ )
    88             swapvar_between( i.coeff(), result, term*power( f.mvar(), i.exp() ), expx2 );
    89 }
    90 
     187CanonicalForm
     188swapvar1 ( const CanonicalForm & f, const Variable & x1, const Variable & x2 )
     189{
     190    ASSERT( x1.level() > 0 && x2.level() > 0, "cannot swap algebraic variables" );
     191    if ( f.inCoeffDomain() || x1 == x2 || ( x1 > f.mvar() && x2 > f.mvar() ) )
     192        return f;
     193    else {
     194        CanonicalForm result = 0;
     195        if ( x1 > x2 ) {
     196            sv_x1 = x2; sv_x2 = x1;
     197        }
     198        else {
     199            sv_x1 = x1; sv_x2 = x2;
     200        }
     201        if ( f.mvar() < sv_x2 )
     202            // we only have to replace sv_x1 by sv_x2
     203            return swapvar_between1( f );
     204        else
     205            // we really have to swap variables
     206            return swapvar_rec1( f );
     207    }
     208}
     209//}}}
     210
     211//{{{ static CanonicalForm replacevar_between ( const CanonicalForm & f )
     212//{{{ docu
     213//
     214// replacevar_between() - replace occurences of sv_x1 in f with sv_x2.
     215//
     216// This is allmost the same as swapvar_between() except that
     217// sv_x1 may be an algebraic variable, so we have to test on
     218// 'f.inBaseDomain()' instead of 'f.inCoeffDomain()' in the
     219// beginning.
     220//
     221// Used by: replacevar()
     222//
     223//}}}
     224static CanonicalForm
     225replacevar_between ( const CanonicalForm & f )
     226{
     227    if ( f.inBaseDomain() )
     228        return f;
     229
     230    Variable x = f.mvar();
     231
     232    if ( x < sv_x1 )
     233        // in this case, we do not have to replace anything
     234        return f;
     235    else  if ( x == sv_x1 ) {
     236        // this is where the real work is done: this iterator
     237        // replaces sv_x1 with sv_x2
     238        CanonicalForm result;
     239        for ( CFIterator i = f; i.hasTerms(); i++ )
     240            result += power( sv_x2, i.exp() ) * i.coeff();
     241        return result;
     242    }
     243    else {
     244        // f's level is larger than sv_x1: descend down
     245        CanonicalForm result;
     246        for ( CFIterator i = f; i.hasTerms(); i++ )
     247            result += replacevar_between( i.coeff() ) * power( x, i.exp() );
     248        return result;
     249    }
     250}
     251//}}}
     252
     253//{{{ CanonicalForm replacevar ( const CanonicalForm & f, const Variable & x1, const Variable & x2 )
     254//{{{ docu
     255//
     256// replacevar() - replace all occurences of x1 in f by x2.
     257//
     258// In contrast to swapvar(), x1 may be an algebraic variable, but
     259// x2 must be a polynomial variable.
     260//
     261//}}}
     262CanonicalForm
     263replacevar ( const CanonicalForm & f, const Variable & x1, const Variable & x2 )
     264{
     265    ASSERT( x2.level() > 0, "cannot replace with algebraic variable" );
     266    if ( f.inBaseDomain() || x1 == x2 || ( x1 > f.mvar() ) )
     267        return f;
     268    else {
     269        sv_x1 = x1;
     270        sv_x2 = x2;
     271        return replacevar_between( f );
     272    }
     273}
     274//}}}
     275
     276//{{{ static void fillVarsRec ( const CanonicalForm & f, int * vars )
     277//{{{ docu
     278//
     279// fillVarsRec - fill array describing occurences of variables in f.
     280//
     281// Only polynomial variables are looked up.  The information is
     282// stored in the arrary vars.  vars should be large enough to
     283// hold all information, i.e. larger than the level of f.
     284//
     285// Used by getVars() and getNumVars().
     286//
     287//}}}
     288static void
     289fillVarsRec ( const CanonicalForm & f, int * vars )
     290{
     291    int n;
     292    if ( (n = f.level()) > 0 ) {
     293        vars[n] = 1;
     294        CFIterator i;
     295        for ( i = f; i.hasTerms(); ++i )
     296            fillVarsRec( i.coeff(), vars );
     297    }
     298}
     299//}}}
     300
     301//{{{ int getNumVars ( const CanonicalForm & f )
     302//{{{ docu
     303//
     304// getNumVars() - get number of polynomial variables in f.
     305//
     306//}}}
     307int
     308getNumVars ( const CanonicalForm & f )
     309{
     310    int n;
     311    if ( f.inCoeffDomain() )
     312        return 0;
     313    else  if ( (n = f.level()) == 1 )
     314        return 1;
     315    else {
     316        int * vars = new int[ n+1 ];
     317        int i;
     318        for ( i = 0; i < n; i++ ) vars[i] = 0;
     319
     320        // look for variables
     321        for ( CFIterator I = f; I.hasTerms(); ++I )
     322            fillVarsRec( I.coeff(), vars );
     323
     324        // count them
     325        int m = 0;
     326        for ( i = 1; i < n; i++ )
     327            if ( vars[i] != 0 ) m++;
     328
     329        delete [] vars;
     330        // do not forget to count our own variable
     331        return m+1;
     332    }
     333}
     334//}}}
     335
     336//{{{ CanonicalForm getVars ( const CanonicalForm & f )
     337//{{{ docu
     338//
     339// getVars() - get polynomial variables of f.
     340//
     341// Return the product of all of them, 1 if there are not any.
     342//
     343//}}}
     344CanonicalForm
     345getVars ( const CanonicalForm & f )
     346{
     347    int n;
     348    if ( f.inCoeffDomain() )
     349        return 1;
     350    else  if ( (n = f.level()) == 1 )
     351        return Variable( 1 );
     352    else {
     353        int * vars = new int[ n+1 ];
     354        int i;
     355        for ( i = 0; i <= n; i++ ) vars[i] = 0;
     356
     357        // look for variables
     358        for ( CFIterator I = f; I.hasTerms(); ++I )
     359            fillVarsRec( I.coeff(), vars );
     360
     361        // multiply them all
     362        CanonicalForm result = 1;
     363        for ( i = n; i > 0; i-- )
     364            if ( vars[i] != 0 ) result *= Variable( i );
     365
     366        delete [] vars;
     367        // do not forget our own variable
     368        return f.mvar() * result;
     369    }
     370}
     371//}}}
     372
     373//{{{ CanonicalForm apply ( const CanonicalForm & f, void (*mf)( CanonicalForm &, int & ) )
     374//{{{ docu
     375//
     376// apply() - apply mf to terms of f.
     377//
     378// Calls mf( f[i], i ) for each term f[i]*x^i of f and builds a
     379// new term from the result.  If f is in a coefficient domain,
     380// mf( f, i ) should result in an i == 0, since otherwise it is
     381// not clear which variable to use for the resulting term.
     382//
     383// An example:
     384//
     385// void
     386// diff( CanonicalForm & f, int & i )
     387// {
     388//     f = f * i;
     389//     if ( i > 0 ) i--;
     390// }
     391//
     392// Then apply( f, diff ) is differentation of f with respect to the
     393// main variable of f.
     394//
     395//}}}
    91396CanonicalForm
    92397apply ( const CanonicalForm & f, void (*mf)( CanonicalForm &, int & ) )
    … …  
    94399    if ( f.inCoeffDomain() ) {
    95400        int exp = 0;
    96         CanonicalForm result;
     401        CanonicalForm result = f;
    97402        mf( result, exp );
    98403        ASSERT( exp == 0, "illegal result, do not know what variable to use" );
    … …  
    114419    }
    115420}
     421//}}}
     422
     423//{{{ CanonicalForm mapdomain ( const CanonicalForm & f, CanonicalForm (*mf)( const CanonicalForm & ) )
     424//{{{ docu
     425//
     426// mapdomain() - map all coefficients of f through mf.
     427//
     428// Recursively descends down through f to the coefficients which
     429// are in a coefficient domain mapping each such coefficient
     430// through mf and returns the result.
     431//
     432//}}}
     433CanonicalForm
     434mapdomain ( const CanonicalForm & f, CanonicalForm (*mf)( const CanonicalForm & ) )
     435{
     436    if ( f.inCoeffDomain() )
     437        return mf( f );
     438    else {
     439        CanonicalForm result = 0;
     440        CFIterator i;
     441        Variable x = f.mvar();
     442        for ( i = f; i.hasTerms(); i++ )
     443            result += power( x, i.exp() ) * mapdomain( i.coeff(), mf );
     444        return result;
     445    }
     446}
     447//}}}
    116448
    117449//{{{ static void degreesRec ( const CanonicalForm & f, int * degs )
    … …  
    119451//
    120452// degreesRec() - recursively get degrees of f.
     453//
     454// Used by degrees().
    121455//
    122456//}}}
    … …  
    166500        degreesRec( f, degs );
    167501        return degs;
    168     }
    169 }
    170 //}}}
    171 
    172 //{{{ CanonicalForm mapdomain ( const CanonicalForm & f, CanonicalForm (*mf)( const CanonicalForm & ) )
    173 //{{{ docu
    174 //
    175 // mapdomain() - map all coefficients of f through mf.
    176 //
    177 // Recursively descends down through f to the coefficients which
    178 // are in a coefficient domain mapping each such coefficient
    179 // through mf and returns the result.
    180 //
    181 //}}}
    182 CanonicalForm
    183 mapdomain ( const CanonicalForm & f, CanonicalForm (*mf)( const CanonicalForm & ) )
    184 {
    185     if ( f.inCoeffDomain() )
    186         return mf( f );
    187     else {
    188         CanonicalForm result = 0;
    189         CFIterator i;
    190         Variable x = f.mvar();
    191         for ( i = f; i.hasTerms(); i++ )
    192             result += power( x, i.exp() ) * mapdomain( i.coeff(), mf );
    193         return result;
    194502    }
    195503}
    … …  
    274582}
    275583//}}}
    276 
    277 //{{{ static void fillVarsRec ( const CanonicalForm & f, int * vars )
    278 //{{{ docu
    279 //
    280 // fillVarsRec - fill array describing occurences of variables in f.
    281 //
    282 // Only polynomial variables are looked up.  The information is
    283 // stored in the arrary vars.  vars should be large enough to
    284 // hold all information, i.e. larger than the level of f.
    285 //
    286 //}}}
    287 static void
    288 fillVarsRec ( const CanonicalForm & f, int * vars )
    289 {
    290     int n;
    291     if ( (n = f.level()) > 0 ) {
    292         vars[n] = 1;
    293         CFIterator i;
    294         for ( i = f; i.hasTerms(); ++i )
    295             fillVarsRec( i.coeff(), vars );
    296     }
    297 }
    298 //}}}
    299 
    300 //{{{ int getNumVars( const CanonicalForm & f )
    301 //{{{ docu
    302 //
    303 // getNumVars() - get number of polynomial variables in f.
    304 //
    305 //}}}
    306 int
    307 getNumVars( const CanonicalForm & f )
    308 {
    309     int n;
    310     if ( f.inCoeffDomain() )
    311         return 0;
    312     else  if ( (n = f.level()) == 1 )
    313         return 1;
    314     else {
    315         int * vars = new int[ n+1 ];
    316         int i;
    317         for ( i = 0; i < n; i++ ) vars[i] = 0;
    318 
    319         // look for variables
    320         for ( CFIterator I = f; I.hasTerms(); ++I )
    321             fillVarsRec( I.coeff(), vars );
    322 
    323         // count them
    324         int m = 0;
    325         for ( i = 1; i < n; i++ )
    326             if ( vars[i] != 0 ) m++;
    327 
    328         delete [] vars;
    329         // do not forget to count our own variable
    330         return m+1;
    331     }
    332 }
    333 //}}}
    334 
    335 //{{{ CanonicalForm getVars( const CanonicalForm & f )
    336 //{{{ docu
    337 //
    338 // getVars() - get polynomial variables of f.
    339 //
    340 // Return the product of all of them, 1 if there are not any.
    341 //
    342 //}}}
    343 CanonicalForm
    344 getVars( const CanonicalForm & f )
    345 {
    346     int n;
    347     if ( f.inCoeffDomain() )
    348         return 1;
    349     else  if ( (n = f.level()) == 1 )
    350         return Variable( 1 );
    351     else {
    352         int * vars = new int[ n+1 ];
    353         int i;
    354         for ( i = 0; i <= n; i++ ) vars[i] = 0;
    355 
    356         // look for variables
    357         for ( CFIterator I = f; I.hasTerms(); ++I )
    358             fillVarsRec( I.coeff(), vars );
    359 
    360         // multiply them all
    361         CanonicalForm result = 1;
    362         for ( i = n; i > 0; i-- )
    363             if ( vars[i] != 0 ) result *= Variable( i );
    364 
    365         delete [] vars;
    366         // do not forget our own variable
    367         return f.mvar() * result;
    368     }
    369 }
    370 //}}}
    371 
    372 static CanonicalForm
    373 cden ( const CanonicalForm & f )
    374 {
    375     if ( f.inCoeffDomain() )
    376         return f.den();
    377     else {
    378         CFIterator i;
    379         CanonicalForm cd = 1;
    380         for ( i = f; i.hasTerms(); i++ )
    381             cd = lcm( cd, cden( i.coeff() ) );
    382         return cd;
    383     }
    384 }
    385 
    386 CanonicalForm
    387 common_den ( const CanonicalForm & f )
    388 {
    389     if ( getCharacteristic() == 0 && isOn( SW_RATIONAL ) ) {
    390         Off( SW_RATIONAL );
    391         CanonicalForm cd = cden( f );
    392         On( SW_RATIONAL );
    393         return cd;
    394     }
    395     else
    396         return 1;
    397 }
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