Changeset b60ef7 in git
 Timestamp:
 Oct 10, 1997, 12:40:17 PM (27 years ago)
 Branches:
 (u'fiekerDuVal', '117eb8c30fc9e991c4decca4832b1d19036c4c65')(u'spielwiese', 'c7af8613769b29c741d6c338945669719f1fc4f8')
 Children:
 24725be4e952e9877b5415819b58210ed69fae34
 Parents:
 bbe7bc4d7a630981554453c6e36683b9d34502a9
 File:

 1 edited
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 Unmodified
 Added
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factory/canonicalform.cc
rbbe7bc rb60ef7 1 1 /* emacs edit mode for this file is * C++ * */ 2 /* $Id: canonicalform.cc,v 1. 19 19970924 10:52:23schmidt Exp $ */2 /* $Id: canonicalform.cc,v 1.20 19971010 10:40:17 schmidt Exp $ */ 3 3 4 4 #include <config.h> … … 23 23 #endif /* NOSTREAMIO */ 24 24 25 //{{{ initialization 26 int initializeGMP(); 27 int initializeCharacteristic(); 28 #ifdef SINGULAR 29 int mmInit(void); 30 #endif 31 32 int 33 initCanonicalForm( void ) 34 { 35 static bool initialized = false; 36 if ( ! initialized ) { 37 #if (defined (USE_MEMUTIL) && ! defined (USE_OLD_MEMMAN))  defined (SINGULAR) 38 (void)mmInit(); 39 #endif 40 41 (void)initializeCharacteristic(); 42 (void)initializeGMP(); 43 initPT(); 44 initialized = true; 45 } 46 return 1; 47 } 48 //}}} 49 50 //{{{ constructors, destructors, selectors 25 51 CanonicalForm::CanonicalForm() : value( CFFactory::basic( (int)0 ) ) 26 52 { … … 66 92 } 67 93 94 CanonicalForm 95 CanonicalForm::deepCopy() const 96 { 97 if ( is_imm( value ) ) 98 return *this; 99 else 100 return CanonicalForm( value>deepCopyObject() ); 101 } 102 //}}} 103 104 //{{{ predicates 68 105 bool 69 106 CanonicalForm::isOne() const … … 184 221 } 185 222 223 bool 224 CanonicalForm::isFFinGF() const 225 { 226 return is_imm( value ) == GFMARK && gf_isff( imm2int( value ) ); 227 } 228 229 bool 230 CanonicalForm::isUnivariate() const 231 { 232 if ( is_imm( value ) ) 233 return false; 234 else 235 return value>isUnivariate(); 236 } 237 //}}} 238 239 //{{{ conversion functions 186 240 int 187 241 CanonicalForm::intval() const … … 192 246 return value>intval(); 193 247 } 194 195 CanonicalForm196 CanonicalForm::lc() const197 {198 if ( is_imm( value ) )199 return *this;200 else201 return value>lc();202 }203 204 CanonicalForm205 CanonicalForm::LC() const206 {207 if ( inBaseDomain() )208 return *this;209 else210 return value>LC();211 }212 213 CanonicalForm214 CanonicalForm::LC( const Variable & v ) const215 {216 if ( inBaseDomain() )217 return *this;218 else if ( v == mvar() )219 return value>LC();220 else {221 CanonicalForm f = swapvar( *this, v, mvar() );222 if ( f.mvar() == mvar() )223 return swapvar( f.value>LC(), v, mvar() );224 else225 return *this;226 }227 }228 229 //{{{ int CanonicalForm::degree() const230 //{{{ docu231 //232 // degree()  return degree in main variable.233 //234 // Returns 1 for the zero polynomial.235 //236 //}}}237 int238 CanonicalForm::degree() const239 {240 if ( isZero() )241 return 1;242 else if ( is_imm( value ) )243 return 0;244 else245 return value>degree();246 }247 //}}}248 249 //{{{ int CanonicalForm::degree( const Variable & v ) const250 //{{{ docu251 //252 // degree()  return degree in variable v.253 //254 // Returns 1 for the zero polynomial.255 //256 // Note: If v is less than the main variable of CO we have to swap257 // variables which may be quite expensive. Calculating the degree in258 // respect to an algebraic variable may fail.259 //260 //}}}261 int262 CanonicalForm::degree( const Variable & v ) const263 {264 if ( isZero() )265 return 1;266 else if ( is_imm( value ) )267 return 0;268 else if ( inBaseDomain() )269 return 0;270 271 Variable x = mvar();272 if ( v == x )273 return value>degree();274 else if ( v > x )275 // relatively to v, f is in a coefficient ring276 return 0;277 else {278 // v < mvar(), make v main variable279 CanonicalForm f = swapvar( *this, v, x );280 if ( f.mvar() == x )281 return f.value>degree();282 else283 // in this case, we lost our main variable because284 // v did not occur in CO285 return 0;286 }287 }288 //}}}289 290 int291 CanonicalForm::taildegree() const292 {293 if ( isZero() )294 return 1;295 else if ( is_imm( value ) )296 return 0;297 else298 return value>taildegree();299 }300 301 CanonicalForm302 CanonicalForm::tailcoeff() const303 {304 if ( inCoeffDomain() )305 return *this;306 else307 return value>tailcoeff();308 }309 310 int311 CanonicalForm::level() const312 {313 if ( is_imm( value ) )314 return LEVELBASE;315 else316 return value>level();317 }318 319 Variable320 CanonicalForm::mvar() const321 {322 if ( is_imm( value )  value>inBaseDomain() )323 return Variable();324 else325 return value>variable();326 }327 328 CanonicalForm329 CanonicalForm::num() const330 {331 if ( is_imm( value ) )332 return *this;333 else334 return CanonicalForm( value>num() );335 }336 337 CanonicalForm338 CanonicalForm::den() const339 {340 if ( is_imm( value ) )341 return 1;342 else343 return CanonicalForm( value>den() );344 }345 346 CanonicalForm347 CanonicalForm::deepCopy() const348 {349 if ( is_imm( value ) )350 return *this;351 else352 return CanonicalForm( value>deepCopyObject() );353 }354 355 CanonicalForm356 CanonicalForm::gcd( const CanonicalForm & ) const357 {358 // return ::gcd( *this, f );359 return 1;360 }361 362 //{{{ CanonicalForm CanonicalForm::deriv () const363 //{{{ docu364 //365 // deriv()  return the formal derivation of CO.366 //367 // Derives CO with respect to its main variable. Returns zero if368 // f is in a coefficient domain.369 //370 //}}}371 CanonicalForm372 CanonicalForm::deriv () const373 {374 if ( inCoeffDomain() )375 return 0;376 else {377 CanonicalForm res = 0;378 Variable x = mvar();379 for ( CFIterator i = *this; i.hasTerms(); i++ )380 if ( i.exp() > 0 )381 res += power( x, i.exp()1 ) * i.coeff() * i.exp();382 return res;383 }384 }385 //}}}386 387 //{{{ CanonicalForm CanonicalForm::deriv ( const Variable & x ) const388 //{{{ docu389 //390 // deriv()  return the formal derivation of CO with respect to x.391 //392 // x should be a polynomial variable. Returns zero if f is in a393 // coefficient domain.394 //395 // Timing Note (for the developer): I tried the same without396 // 'Variable y = mvar()', replacing each occurence of y directly397 // with 'mvar()'. It turned out that this version is slower in all398 // cases.399 //400 //}}}401 CanonicalForm402 CanonicalForm::deriv ( const Variable & x ) const403 {404 ASSERT( x.level() > 0, "cannot derive with respect to algebraic variables" );405 if ( inCoeffDomain() )406 return 0;407 408 Variable y = mvar();409 if ( x > y )410 return 0;411 else if ( x == y )412 return deriv();413 else {414 CanonicalForm result;415 CFIterator i;416 for ( i = *this; i.hasTerms(); i++ )417 result += i.coeff().deriv( x ) * power( y, i.exp() );418 return result;419 }420 }421 //}}}422 423 CanonicalForm424 CanonicalForm::genCoeff( int type, int i )425 {426 return CanonicalForm( CFFactory::basic( type, i ) );427 }428 429 CanonicalForm430 CanonicalForm::genZero() const431 {432 int what = is_imm( value );433 if ( what == FFMARK )434 return CanonicalForm( CFFactory::basic( FiniteFieldDomain, 0 ) );435 else if ( what == GFMARK )436 return CanonicalForm( CFFactory::basic( GaloisFieldDomain, 0 ) );437 else if ( what )438 return CanonicalForm( CFFactory::basic( IntegerDomain, 0 ) );439 else440 return CanonicalForm( value>genZero() );441 }442 443 CanonicalForm444 CanonicalForm::genOne() const445 {446 int what = is_imm( value );447 if ( what == FFMARK )448 return CanonicalForm( CFFactory::basic( FiniteFieldDomain, 1 ) );449 else if ( what == GFMARK )450 return CanonicalForm( CFFactory::basic( GaloisFieldDomain, 1 ) );451 else if ( what )452 return CanonicalForm( CFFactory::basic( IntegerDomain, 1 ) );453 else454 return CanonicalForm( value>genOne() );455 }456 457 bool458 CanonicalForm::isUnivariate() const459 {460 if ( is_imm( value ) )461 return false;462 else463 return value>isUnivariate();464 }465 466 #ifndef NOSTREAMIO467 void468 CanonicalForm::print( ostream & os, char * str ) const469 {470 if ( is_imm( value ) )471 imm_print( os, value, str );472 else473 value>print( os, str );474 }475 #endif /* NOSTREAMIO */476 477 bool478 operator == ( const CanonicalForm & lhs, const CanonicalForm & rhs )479 {480 int what = is_imm( lhs.value );481 if ( what )482 if ( what == is_imm( rhs.value ) )483 return lhs.value == rhs.value;484 else485 return false;486 else if ( is_imm( rhs.value ) )487 return false;488 else if ( lhs.level() == rhs.level() )489 if ( lhs.value>levelcoeff() >= rhs.value>levelcoeff() )490 return lhs.value>comparesame( rhs.value ) == 0;491 else492 return rhs.value>comparesame( lhs.value ) == 0;493 else494 return false;495 }496 497 bool498 operator != ( const CanonicalForm & lhs, const CanonicalForm & rhs )499 {500 int what = is_imm( lhs.value );501 if ( what )502 if ( what == is_imm( rhs.value ) )503 return lhs.value != rhs.value;504 else505 return true;506 else if ( is_imm( rhs.value ) )507 return true;508 else if ( lhs.level() == rhs.level() )509 if ( lhs.value>levelcoeff() >= rhs.value>levelcoeff() )510 return lhs.value>comparesame( rhs.value ) != 0;511 else512 return rhs.value>comparesame( lhs.value ) != 0;513 else514 return true;515 }516 517 bool518 operator > ( const CanonicalForm & lhs, const CanonicalForm & rhs )519 {520 int what = is_imm( lhs.value );521 if ( what ) {522 ASSERT ( ! is_imm( rhs.value )  (what==is_imm( rhs.value )), "illegal base coefficients" );523 if ( what == INTMARK ) {524 if ( what == is_imm( rhs.value ) )525 return imm_cmp( lhs.value, rhs.value ) > 0;526 else527 return rhs.value>comparecoeff( lhs.value ) < 0;528 }529 else if ( what == FFMARK ) {530 if ( what == is_imm( rhs.value ) )531 return imm_cmp_p( lhs.value, rhs.value ) > 0;532 else533 return rhs.value>comparecoeff( lhs.value ) < 0;534 }535 else {536 if ( what == is_imm( rhs.value ) )537 return imm_cmp_gf( lhs.value, rhs.value ) > 0;538 else539 return rhs.value>comparecoeff( lhs.value ) < 0;540 }541 }542 else if ( is_imm( rhs.value ) )543 return lhs.value>comparecoeff( rhs.value ) > 0;544 else if ( lhs.level() == rhs.level() )545 if ( lhs.value>levelcoeff() == rhs.value>levelcoeff() )546 return lhs.value>comparesame( rhs.value ) > 0;547 else if ( lhs.value>levelcoeff() > rhs.value>levelcoeff() )548 return lhs.value>comparecoeff( lhs.value ) > 0;549 else550 return rhs.value>comparecoeff( lhs.value ) < 0;551 else552 return lhs.value>level() > rhs.value>level();553 }554 555 bool556 operator < ( const CanonicalForm & lhs, const CanonicalForm & rhs )557 {558 int what = is_imm( lhs.value );559 if ( what ) {560 ASSERT ( ! is_imm( rhs.value )  (what==is_imm( rhs.value )), "illegal base coefficients" );561 if ( what == INTMARK ) {562 if ( what == is_imm( rhs.value ) )563 return imm_cmp( lhs.value, rhs.value ) < 0;564 else565 return rhs.value>comparecoeff( lhs.value ) > 0;566 }567 else if ( what == FFMARK ) {568 if ( what == is_imm( rhs.value ) )569 return imm_cmp( lhs.value, rhs.value ) < 0;570 else571 return rhs.value>comparecoeff( lhs.value ) > 0;572 }573 else {574 if ( what == is_imm( rhs.value ) )575 return imm_cmp( lhs.value, rhs.value ) < 0;576 else577 return rhs.value>comparecoeff( lhs.value ) > 0;578 }579 }580 else if ( is_imm( rhs.value ) )581 return lhs.value>comparecoeff( rhs.value ) < 0;582 else if ( lhs.level() == rhs.level() )583 if ( lhs.value>levelcoeff() == rhs.value>levelcoeff() )584 return lhs.value>comparesame( rhs.value ) < 0;585 else if ( lhs.value>levelcoeff() > rhs.value>levelcoeff() )586 return lhs.value>comparecoeff( lhs.value ) < 0;587 else588 return rhs.value>comparecoeff( lhs.value ) > 0;589 else590 return lhs.value>level() < rhs.value>level();591 }592 593 CanonicalForm&594 CanonicalForm::operator = ( const CanonicalForm & cf )595 {596 if ( this != &cf ) {597 if ( (! is_imm( value )) && value>deleteObject() )598 delete value;599 value = (is_imm( cf.value )) ? cf.value : cf.value>copyObject();600 }601 return *this;602 }603 604 CanonicalForm&605 CanonicalForm::operator = ( const int cf )606 {607 if ( (! is_imm( value )) && value>deleteObject() )608 delete value;609 value = CFFactory::basic( cf );610 return *this;611 }612 613 CanonicalForm&614 CanonicalForm::operator += ( const CanonicalForm & cf )615 {616 int what = is_imm( value );617 if ( what ) {618 ASSERT ( ! is_imm( cf.value )  (what==is_imm( cf.value )), "illegal base coefficients" );619 if ( (what = is_imm( cf.value )) == FFMARK )620 value = imm_add_p( value, cf.value );621 else if ( what == GFMARK )622 value = imm_add_gf( value, cf.value );623 else if ( what )624 value = imm_add( value, cf.value );625 else {626 InternalCF * dummy = cf.value>copyObject();627 value = dummy>addcoeff( value );628 }629 }630 else if ( is_imm( cf.value ) )631 value = value>addcoeff( cf.value );632 else if ( value>level() == cf.value>level() ) {633 if ( value>levelcoeff() == cf.value>levelcoeff() )634 value = value>addsame( cf.value );635 else if ( value>levelcoeff() > cf.value>levelcoeff() )636 value = value>addcoeff( cf.value );637 else {638 InternalCF * dummy = cf.value>copyObject();639 dummy = dummy>addcoeff( value );640 if ( value>deleteObject() ) delete value;641 value = dummy;642 }643 }644 else if ( level() > cf.level() )645 value = value>addcoeff( cf.value );646 else {647 InternalCF * dummy = cf.value>copyObject();648 dummy = dummy>addcoeff( value );649 if ( value>deleteObject() ) delete value;650 value = dummy;651 }652 return *this;653 }654 655 CanonicalForm&656 CanonicalForm::operator = ( const CanonicalForm & cf )657 {658 int what = is_imm( value );659 if ( what ) {660 ASSERT ( ! is_imm( cf.value )  (what==is_imm( cf.value )), "illegal base coefficients" );661 if ( (what = is_imm( cf.value )) == FFMARK )662 value = imm_sub_p( value, cf.value );663 else if ( what == GFMARK )664 value = imm_sub_gf( value, cf.value );665 else if ( what )666 value = imm_sub( value, cf.value );667 else {668 InternalCF * dummy = cf.value>copyObject();669 value = dummy>subcoeff( value, true );670 }671 }672 else if ( is_imm( cf.value ) )673 value = value>subcoeff( cf.value, false );674 else if ( value>level() == cf.value>level() ) {675 if ( value>levelcoeff() == cf.value>levelcoeff() )676 value = value>subsame( cf.value );677 else if ( value>levelcoeff() > cf.value>levelcoeff() )678 value = value>subcoeff( cf.value, false );679 else {680 InternalCF * dummy = cf.value>copyObject();681 dummy = dummy>subcoeff( value, true );682 if ( value>deleteObject() ) delete value;683 value = dummy;684 }685 }686 else if ( level() > cf.level() )687 value = value>subcoeff( cf.value, false );688 else {689 InternalCF * dummy = cf.value>copyObject();690 dummy = dummy>subcoeff( value, true );691 if ( value>deleteObject() ) delete value;692 value = dummy;693 }694 return *this;695 }696 697 CanonicalForm&698 CanonicalForm::operator *= ( const CanonicalForm & cf )699 {700 int what = is_imm( value );701 if ( what ) {702 ASSERT ( ! is_imm( cf.value )  (what==is_imm( cf.value )), "illegal base coefficients" );703 if ( (what = is_imm( cf.value )) == FFMARK )704 value = imm_mul_p( value, cf.value );705 else if ( what == GFMARK )706 value = imm_mul_gf( value, cf.value );707 else if ( what )708 value = imm_mul( value, cf.value );709 else {710 InternalCF * dummy = cf.value>copyObject();711 value = dummy>mulcoeff( value );712 }713 }714 else if ( is_imm( cf.value ) )715 value = value>mulcoeff( cf.value );716 else if ( value>level() == cf.value>level() ) {717 if ( value>levelcoeff() == cf.value>levelcoeff() )718 value = value>mulsame( cf.value );719 else if ( value>levelcoeff() > cf.value>levelcoeff() )720 value = value>mulcoeff( cf.value );721 else {722 InternalCF * dummy = cf.value>copyObject();723 dummy = dummy>mulcoeff( value );724 if ( value>deleteObject() ) delete value;725 value = dummy;726 }727 }728 else if ( level() > cf.level() )729 value = value>mulcoeff( cf.value );730 else {731 InternalCF * dummy = cf.value>copyObject();732 dummy = dummy>mulcoeff( value );733 if ( value>deleteObject() ) delete value;734 value = dummy;735 }736 return *this;737 }738 739 CanonicalForm&740 CanonicalForm::operator /= ( const CanonicalForm & cf )741 {742 int what = is_imm( value );743 if ( what ) {744 ASSERT ( ! is_imm( cf.value )  (what==is_imm( cf.value )), "illegal base coefficients" );745 if ( (what = is_imm( cf.value )) == FFMARK )746 value = imm_div_p( value, cf.value );747 else if ( what == GFMARK )748 value = imm_div_gf( value, cf.value );749 else if ( what )750 value = imm_divrat( value, cf.value );751 else {752 InternalCF * dummy = cf.value>copyObject();753 value = dummy>dividecoeff( value, true );754 }755 }756 else if ( is_imm( cf.value ) )757 value = value>dividecoeff( cf.value, false );758 else if ( value>level() == cf.value>level() ) {759 if ( value>levelcoeff() == cf.value>levelcoeff() )760 value = value>dividesame( cf.value );761 else if ( value>levelcoeff() > cf.value>levelcoeff() )762 value = value>dividecoeff( cf.value, false );763 else {764 InternalCF * dummy = cf.value>copyObject();765 dummy = dummy>dividecoeff( value, true );766 if ( value>deleteObject() ) delete value;767 value = dummy;768 }769 }770 else if ( level() > cf.level() )771 value = value>dividecoeff( cf.value, false );772 else {773 InternalCF * dummy = cf.value>copyObject();774 dummy = dummy>dividecoeff( value, true );775 if ( value>deleteObject() ) delete value;776 value = dummy;777 }778 return *this;779 }780 781 CanonicalForm&782 CanonicalForm::div ( const CanonicalForm & cf )783 {784 int what = is_imm( value );785 if ( what ) {786 ASSERT ( ! is_imm( cf.value )  (what==is_imm( cf.value )), "illegal base coefficients" );787 if ( (what = is_imm( cf.value )) == FFMARK )788 value = imm_div_p( value, cf.value );789 else if ( what == GFMARK )790 value = imm_div_gf( value, cf.value );791 else if ( what )792 value = imm_div( value, cf.value );793 else {794 InternalCF * dummy = cf.value>copyObject();795 value = dummy>divcoeff( value, true );796 }797 }798 else if ( is_imm( cf.value ) )799 value = value>divcoeff( cf.value, false );800 else if ( value>level() == cf.value>level() ) {801 if ( value>levelcoeff() == cf.value>levelcoeff() )802 value = value>divsame( cf.value );803 else if ( value>levelcoeff() > cf.value>levelcoeff() )804 value = value>divcoeff( cf.value, false );805 else {806 InternalCF * dummy = cf.value>copyObject();807 dummy = dummy>divcoeff( value, true );808 if ( value>deleteObject() ) delete value;809 value = dummy;810 }811 }812 else if ( level() > cf.level() )813 value = value>divcoeff( cf.value, false );814 else {815 InternalCF * dummy = cf.value>copyObject();816 dummy = dummy>divcoeff( value, true );817 if ( value>deleteObject() ) delete value;818 value = dummy;819 }820 return *this;821 }822 823 CanonicalForm&824 CanonicalForm::operator %= ( const CanonicalForm& cf )825 {826 int what = is_imm( value );827 if ( what ) {828 ASSERT ( ! is_imm( cf.value )  (what==is_imm( cf.value )), "illegal base coefficients" );829 if ( (what = is_imm( cf.value )) == FFMARK )830 value = imm_mod_p( value, cf.value );831 else if ( what == GFMARK )832 value = imm_mod_gf( value, cf.value );833 else if ( what )834 value = imm_mod( value, cf.value );835 else {836 InternalCF * dummy = cf.value>copyObject();837 value = dummy>modulocoeff( value, true );838 }839 }840 else if ( is_imm( cf.value ) )841 value = value>modulocoeff( cf.value, false );842 else if ( value>level() == cf.value>level() ) {843 if ( value>levelcoeff() == cf.value>levelcoeff() )844 value = value>modulosame( cf.value );845 else if ( value>levelcoeff() > cf.value>levelcoeff() )846 value = value>modulocoeff( cf.value, false );847 else {848 InternalCF * dummy = cf.value>copyObject();849 dummy = dummy>modulocoeff( value, true );850 if ( value>deleteObject() ) delete value;851 value = dummy;852 }853 }854 else if ( level() > cf.level() )855 value = value>modulocoeff( cf.value, false );856 else {857 InternalCF * dummy = cf.value>copyObject();858 dummy = dummy>modulocoeff( value, true );859 if ( value>deleteObject() ) delete value;860 value = dummy;861 }862 return *this;863 }864 865 CanonicalForm&866 CanonicalForm::mod( const CanonicalForm & cf )867 {868 int what = is_imm( value );869 if ( what ) {870 ASSERT ( ! is_imm( cf.value )  (what==is_imm( cf.value )), "illegal base coefficients" );871 if ( (what = is_imm( cf.value )) == FFMARK )872 value = imm_mod_p( value, cf.value );873 else if ( what == GFMARK )874 value = imm_mod_gf( value, cf.value );875 else if ( what )876 value = imm_mod( value, cf.value );877 else {878 InternalCF * dummy = cf.value>copyObject();879 value = dummy>modcoeff( value, true );880 }881 }882 else if ( is_imm( cf.value ) )883 value = value>modcoeff( cf.value, false );884 else if ( value>level() == cf.value>level() ) {885 if ( value>levelcoeff() == cf.value>levelcoeff() )886 value = value>modsame( cf.value );887 else if ( value>levelcoeff() > cf.value>levelcoeff() )888 value = value>modcoeff( cf.value, false );889 else {890 InternalCF * dummy = cf.value>copyObject();891 dummy = dummy>modcoeff( value, true );892 if ( value>deleteObject() ) delete value;893 value = dummy;894 }895 }896 else if ( level() > cf.level() )897 value = value>modcoeff( cf.value, false );898 else {899 InternalCF * dummy = cf.value>copyObject();900 dummy = dummy>modcoeff( value, true );901 if ( value>deleteObject() ) delete value;902 value = dummy;903 }904 return *this;905 }906 907 CanonicalForm908 operator  ( const CanonicalForm & cf )909 {910 CanonicalForm result( cf );911 int what = is_imm( result.value );912 if ( what == FFMARK )913 result.value = imm_neg_p( result.value );914 else if ( what == GFMARK )915 result.value = imm_neg_gf( result.value );916 else if ( what )917 result.value = imm_neg( result.value );918 else919 result.value = result.value>neg();920 return result;921 }922 923 CanonicalForm924 operator + ( const CanonicalForm &c1, const CanonicalForm &c2 )925 {926 CanonicalForm result( c1 );927 result += c2;928 return result;929 }930 931 CanonicalForm932 operator  ( const CanonicalForm &c1, const CanonicalForm &c2 )933 {934 CanonicalForm result( c1 );935 result = c2;936 return result;937 }938 939 CanonicalForm940 operator * ( const CanonicalForm &c1, const CanonicalForm &c2 )941 {942 CanonicalForm result( c1 );943 result *= c2;944 return result;945 }946 947 CanonicalForm948 operator / ( const CanonicalForm &c1, const CanonicalForm &c2 )949 {950 CanonicalForm result( c1 );951 result /= c2;952 return result;953 }954 955 CanonicalForm956 div ( const CanonicalForm &c1, const CanonicalForm &c2 )957 {958 CanonicalForm result( c1 );959 result.div( c2 );960 return result;961 }962 963 CanonicalForm964 mod ( const CanonicalForm &c1, const CanonicalForm &c2 )965 {966 CanonicalForm result( c1 );967 result.mod( c2 );968 return result;969 }970 971 CanonicalForm972 operator % ( const CanonicalForm &c1, const CanonicalForm &c2 )973 {974 CanonicalForm result( c1 );975 result %= c2;976 return result;977 }978 979 void980 divrem ( const CanonicalForm & f, const CanonicalForm & g, CanonicalForm & q, CanonicalForm & r )981 {982 InternalCF * qq = 0, * rr = 0;983 int what = is_imm( f.value );984 if ( what )985 if ( is_imm( g.value ) ) {986 if ( what == FFMARK )987 imm_divrem_p( f.value, g.value, qq, rr );988 else if ( what == GFMARK )989 imm_divrem_gf( f.value, g.value, qq, rr );990 else991 imm_divrem( f.value, g.value, qq, rr );992 }993 else994 g.value>divremcoeff( f.value, qq, rr, true );995 else if ( (what=is_imm( g.value )) )996 f.value>divremcoeff( g.value, qq, rr, false );997 else if ( f.value>level() == g.value>level() )998 if ( f.value>levelcoeff() == g.value>levelcoeff() )999 f.value>divremsame( g.value, qq, rr );1000 else if ( f.value>levelcoeff() > g.value>levelcoeff() )1001 f.value>divremcoeff( g.value, qq, rr, false );1002 else1003 g.value>divremcoeff( f.value, qq, rr, true );1004 else if ( f.value>level() > g.value>level() )1005 f.value>divremcoeff( g.value, qq, rr, false );1006 else1007 g.value>divremcoeff( f.value, qq, rr, true );1008 ASSERT( qq != 0 && rr != 0, "error in divrem" );1009 q = CanonicalForm( qq );1010 r = CanonicalForm( rr );1011 }1012 1013 bool1014 divremt ( const CanonicalForm & f, const CanonicalForm & g, CanonicalForm & q, CanonicalForm & r )1015 {1016 InternalCF * qq = 0, * rr = 0;1017 int what = is_imm( f.value );1018 bool result = true;1019 if ( what )1020 if ( is_imm( g.value ) ) {1021 if ( what == FFMARK )1022 imm_divrem_p( f.value, g.value, qq, rr );1023 else if ( what == GFMARK )1024 imm_divrem_gf( f.value, g.value, qq, rr );1025 else1026 imm_divrem( f.value, g.value, qq, rr );1027 }1028 else1029 result = g.value>divremcoefft( f.value, qq, rr, true );1030 else if ( (what=is_imm( g.value )) )1031 result = f.value>divremcoefft( g.value, qq, rr, false );1032 else if ( f.value>level() == g.value>level() )1033 if ( f.value>levelcoeff() == g.value>levelcoeff() )1034 result = f.value>divremsamet( g.value, qq, rr );1035 else if ( f.value>levelcoeff() > g.value>levelcoeff() )1036 result = f.value>divremcoefft( g.value, qq, rr, false );1037 else1038 result = g.value>divremcoefft( f.value, qq, rr, true );1039 else if ( f.value>level() > g.value>level() )1040 result = f.value>divremcoefft( g.value, qq, rr, false );1041 else1042 result = g.value>divremcoefft( f.value, qq, rr, true );1043 if ( result ) {1044 ASSERT( qq != 0 && rr != 0, "error in divrem" );1045 q = CanonicalForm( qq );1046 r = CanonicalForm( rr );1047 }1048 else {1049 q = 0; r = 0;1050 }1051 return result;1052 }1053 1054 #ifndef NOSTREAMIO1055 ostream&1056 operator << ( ostream & os, const CanonicalForm & cf )1057 {1058 cf.print( os, "" );1059 return os;1060 }1061 #endif /* NOSTREAMIO */1062 1063 #ifndef NOSTREAMIO1064 istream&1065 operator >> ( istream & is, CanonicalForm & cf )1066 {1067 #ifndef SINGULAR1068 cf = readCF( is );1069 return is;1070 #else /* SINGULAR */1071 return 0;1072 #endif /* SINGULAR */1073 }1074 #endif /* NOSTREAMIO */1075 1076 CanonicalForm1077 CanonicalForm::operator () ( const CanonicalForm & f ) const1078 {1079 if ( inBaseDomain() )1080 return *this;1081 else {1082 CanonicalForm result = 0;1083 for ( CFIterator i = *this; i.hasTerms(); i++ )1084 if ( i.exp() == 0 )1085 result += i.coeff();1086 else1087 result += power( f, i.exp() ) * i.coeff();1088 return result;1089 }1090 }1091 1092 CanonicalForm1093 CanonicalForm::operator () ( const CanonicalForm & f, const Variable & v ) const1094 {1095 if ( inBaseDomain()  v > mvar() )1096 return *this;1097 else if ( v == mvar() ) {1098 CanonicalForm result = 0;1099 for ( CFIterator i = *this; i.hasTerms(); i++ )1100 if ( i.exp() == 0 )1101 result += i.coeff();1102 else1103 result += power( f, i.exp() ) * i.coeff();1104 return result;1105 }1106 else {1107 CanonicalForm G = swapvar( *this, v, Variable::highest() );1108 if ( G.mvar() != Variable::highest() )1109 return *this;1110 CanonicalForm result = 0;1111 for ( CFIterator i = G; i.hasTerms(); ++i )1112 if ( i.exp() == 0 )1113 result += i.coeff();1114 else1115 result += power( f, i.exp() ) * i.coeff();1116 return result;1117 }1118 }1119 1120 CanonicalForm1121 CanonicalForm::operator[] ( int i ) const1122 {1123 return value>coeff( i );1124 }1125 1126 //{{{ int CanonicalForm::sign () const1127 //{{{ docu1128 //1129 // sign()  return sign of CO.1130 //1131 // If CO is an integer or a rational number, the sign is defined1132 // as usual. If CO is an element of a prime power domain or in a1133 // finite field and SW_SYMMETRIC_FF is on the sign of CO is the1134 // sign of the symmetric representation of CO. If CO is in GF(q)1135 // or in a finite field and SW_SYMMETRIC_FF is off, the sign of1136 // CO is zero iff CO is zero, otherwise the sign is one.1137 //1138 // If CO is a polynomial or in an extension of one of the base1139 // domains, the sign of CO is the sign of its leading1140 // coefficient.1141 //1142 // See also: InternalCF::sign(), InternalInteger::sign(),1143 // InternalPrimePower::sign(), InternalRational::sign(),1144 // InternalPoly::sign(), imm_sign(), gf_sign()1145 //1146 //}}}1147 int1148 CanonicalForm::sign () const1149 {1150 if ( is_imm( value ) )1151 return imm_sign( value );1152 else1153 return value>sign();1154 }1155 //}}}1156 1157 CanonicalForm1158 power ( const CanonicalForm & f, int n )1159 {1160 ASSERT( n >= 0, "illegal exponent" );1161 if ( f == 0 )1162 return 0;1163 else if ( f == 1 )1164 return f;1165 else if ( f == 1 ) {1166 if ( n % 2 == 0 )1167 return 1;1168 else1169 return 1;1170 }1171 else if ( n == 0 )1172 return 1;1173 else {1174 CanonicalForm result = f;1175 for ( int i = 1; i < n; i++ )1176 result *= f;1177 return result;1178 }1179 }1180 1181 CanonicalForm1182 power ( const Variable & v, int n )1183 {1184 ASSERT( n >= 0, "illegal exponent" );1185 if ( n == 0 )1186 return 1;1187 else if ( n == 1 )1188 return v;1189 else if ( v.level() < 0 ) {1190 CanonicalForm result( v, n1 );1191 return result * v;1192 }1193 else1194 return CanonicalForm( v, n );1195 }1196 1197 1198 int initializeGMP();1199 int initializeCharacteristic();1200 #ifdef SINGULAR1201 int mmInit(void);1202 #endif1203 1204 int1205 initCanonicalForm( void )1206 {1207 static bool initialized = false;1208 if ( ! initialized ) {1209 #if (defined (USE_MEMUTIL) && ! defined (USE_OLD_MEMMAN))  defined (SINGULAR)1210 (void)mmInit();1211 #endif1212 1213 (void)initializeCharacteristic();1214 (void)initializeGMP();1215 initPT();1216 initialized = true;1217 }1218 return 1;1219 }1220 1221 248 1222 249 CanonicalForm … … 1274 301 } 1275 302 } 1276 1277 void 1278 On( int sw ) 1279 { 1280 cf_glob_switches.On( sw ); 1281 } 1282 1283 void 1284 Off( int sw ) 1285 { 1286 cf_glob_switches.Off( sw ); 1287 } 1288 1289 bool 1290 isOn( int sw ) 1291 { 1292 return cf_glob_switches.isOn( sw ); 1293 } 1294 1295 bool 1296 CanonicalForm::isFFinGF() const 1297 { 1298 return is_imm( value ) == GFMARK && gf_isff( imm2int( value ) ); 1299 } 303 //}}} 304 305 //{{{ CanonicalForm CanonicalForm::lc (), Lc (), LC (), LC ( v ) const 306 //{{{ docu 307 // 308 // lc(), Lc(), LC()  leading coefficient functions. 309 // 310 // All methods return CO if CO is in a base domain. 311 // 312 // lc() returns the leading coefficient of CO with respect to 313 // lexicographic ordering. Elements in an algebraic extension 314 // are considered polynomials so lc() always returns a leading 315 // coefficient in a base domain. This method is useful to get 316 // the base domain over which CO is defined. 317 // 318 // Lc() returns the leading coefficient of CO with respect to 319 // lexicographic ordering. In contrast to lc() elements in an 320 // algebraic extension are considered coefficients so Lc() always 321 // returns a leading coefficient in a coefficient domain. 322 // 323 // LC() returns the leading coefficient of CO where CO is 324 // considered a univariate polynomial in its main variable. An 325 // element of an algebraic extension is considered an univariate 326 // polynomial, too. 327 // 328 // LC( v ) returns the leading coefficient of CO where CO is 329 // considered an univariate polynomial in the polynomial variable 330 // v. 331 // Note: If v is less than the main variable of CO we have to 332 // swap variables which may be quite expensive. 333 // 334 // Examples: 335 // Let x < y be polynomial variables, a an algebraic variable. 336 // 337 // (3*a*x*y^2+y+x).lc() = 3 338 // (3*a*x*y^2+y+x).Lc() = 3*a 339 // (3*a*x*y^2+y+x).LC() = 3*a*x 340 // (3*a*x*y^2+y+x).LC( x ) = 3*a*y^2+1 341 // 342 // (3*a^2+4*a).lc() = 3 343 // (3*a^2+4*a).Lc() = 3*a^2+4*a 344 // (3*a^2+4*a).LC() = 3 345 // (3*a^2+4*a).LC( x ) = 3*a^2+4*a 346 // 347 // See also: InternalCF::lc(), InternalCF::Lc(), InternalCF::LC(), 348 // InternalPoly::lc(), InternalPoly::Lc(), InternalPoly::LC(), 349 // ::lc(), ::Lc(), ::LC(), ::LC( v ) 350 // 351 //}}} 352 CanonicalForm 353 CanonicalForm::lc () const 354 { 355 if ( is_imm( value ) ) 356 return *this; 357 else 358 return value>lc(); 359 } 360 361 CanonicalForm 362 CanonicalForm::Lc () const 363 { 364 if ( is_imm( value )  value>inCoeffDomain() ) 365 return *this; 366 else 367 return value>Lc(); 368 } 369 370 CanonicalForm 371 CanonicalForm::LC () const 372 { 373 if ( is_imm( value ) ) 374 return *this; 375 else 376 return value>LC(); 377 } 378 379 CanonicalForm 380 CanonicalForm::LC ( const Variable & v ) const 381 { 382 if ( is_imm( value )  value>inCoeffDomain() ) 383 return *this; 384 385 Variable x = value>variable(); 386 if ( v > x ) 387 return *this; 388 else if ( v == x ) 389 return value>LC(); 390 else { 391 CanonicalForm f = swapvar( *this, v, x ); 392 if ( f.mvar() == x ) 393 return swapvar( f.value>LC(), v, x ); 394 else 395 // v did not occur in f 396 return *this; 397 } 398 } 399 //}}} 400 401 //{{{ int CanonicalForm::degree (), degree ( v ) const 402 //{{{ docu 403 // 404 // degree()  degree methods. 405 // 406 // Both methods returns 1 for the zero polynomial and 0 if 407 // CO is in a base domain. 408 // 409 // degree() returns the degree of CO in its main variable. 410 // Elements in an algebraic extension are considered polynomials. 411 // degree( v ) returns the degree of CO with respect to v. 412 // Elements in an algebraic extension are considered polynomials, 413 // and v may be algebraic. 414 // 415 // See also: InternalCf::degree(), InternalPoly::degree(), 416 // ::degree(), ::degree( v ) 417 // 418 //}}} 419 int 420 CanonicalForm::degree() const 421 { 422 if ( isZero() ) 423 return 1; 424 else if ( is_imm( value ) ) 425 return 0; 426 else 427 return value>degree(); 428 } 429 430 int 431 CanonicalForm::degree( const Variable & v ) const 432 { 433 if ( isZero() ) 434 return 1; 435 else if ( is_imm( value )  value>inBaseDomain() ) 436 return 0; 437 438 Variable x = value>variable(); 439 if ( v == x ) 440 return value>degree(); 441 else if ( v > x ) 442 // relatively to v, f is in a coefficient ring 443 return 0; 444 else { 445 int coeffdeg, result = 0; 446 // search for maximum of coefficient degree 447 for ( CFIterator i = *this; i.hasTerms(); i++ ) { 448 coeffdeg = i.coeff().degree( v ); 449 if ( coeffdeg > result ) 450 result = coeffdeg; 451 } 452 return result; 453 } 454 } 455 //}}} 456 457 //{{{ CanonicalForm CanonicalForm::tailcoeff (), int CanonicalForm::taildegree () const 458 //{{{ docu 459 // 460 // tailcoeff(), taildegree()  return last coefficient and 461 // degree, resp. 462 // 463 // tailcoeff() returns the coefficient of the term with the least 464 // degree in CO. Elements in an algebraic extension are 465 // considered coefficients. 466 // 467 // taildegree() returns 1 for the zero polynomial, 0 if CO is in 468 // a base domain, the least degree of all terms occuring in CO 469 // otherwise. In contrast to tailcoeff(), elements in an 470 // algebraic extension are considered polynomials, not 471 // coefficients, and such may have a taildegree larger than 472 // zero. 473 // 474 // See also: InternalCF::tailcoeff(), InternalCF::tailcoeff(), 475 // InternalPoly::tailcoeff(), InternalPoly::taildegree, 476 // ::tailcoeff(), ::taildegree() 477 // 478 //}}} 479 CanonicalForm 480 CanonicalForm::tailcoeff () const 481 { 482 if ( is_imm( value )  value>inCoeffDomain() ) 483 return *this; 484 else 485 return value>tailcoeff(); 486 } 487 488 int 489 CanonicalForm::taildegree () const 490 { 491 if ( isZero() ) 492 return 1; 493 else if ( is_imm( value ) ) 494 return 0; 495 else 496 return value>taildegree(); 497 } 498 //}}} 499 500 //{{{ int CanonicalForm::level (), Variable CanonicalForm::mvar () const 501 //{{{ docu 502 // 503 // level(), mvar()  return level and main variable of CO. 504 // 505 // level() returns the level of CO. For a list of the levels, 506 // see cf_defs.h. 507 // 508 // mvar() returns the main variable of CO or Variable() if CO is 509 // in a base domain. 510 // 511 // See also: InternalCF::level(), InternalCF::variable(), 512 // InternalPoly::level(), InternalPoly::variable(), ::level(), 513 // ::mvar() 514 // 515 //}}} 516 int 517 CanonicalForm::level () const 518 { 519 if ( is_imm( value ) ) 520 return LEVELBASE; 521 else 522 return value>level(); 523 } 524 525 Variable 526 CanonicalForm::mvar () const 527 { 528 if ( is_imm( value )  value>inBaseDomain() ) 529 return Variable(); 530 else 531 return value>variable(); 532 } 533 //}}} 534 535 //{{{ CanonicalForm CanonicalForm::num (), den () const 536 //{{{ docu 537 // 538 // num(), den()  return numinator and denominator of CO. 539 // 540 // num() returns the numinator of CO if CO is a rational number, 541 // CO itself otherwise. 542 // 543 // den() returns the denominator of CO if CO is a rational 544 // number, 1 (from the current domain!) otherwise. 545 // 546 // See also: InternalCF::num(), InternalCF::den(), 547 // InternalRational::num(), InternalRational::den(), ::num(), 548 // ::den() 549 // 550 //}}} 551 CanonicalForm 552 CanonicalForm::num () const 553 { 554 if ( is_imm( value ) ) 555 return *this; 556 else 557 return CanonicalForm( value>num() ); 558 } 559 560 CanonicalForm 561 CanonicalForm::den () const 562 { 563 if ( is_imm( value ) ) 564 return 1; 565 else 566 return CanonicalForm( value>den() ); 567 } 568 //}}} 569 570 //{{{ assignment operators 571 CanonicalForm& 572 CanonicalForm::operator = ( const CanonicalForm & cf ) 573 { 574 if ( this != &cf ) { 575 if ( (! is_imm( value )) && value>deleteObject() ) 576 delete value; 577 value = (is_imm( cf.value )) ? cf.value : cf.value>copyObject(); 578 } 579 return *this; 580 } 581 582 CanonicalForm& 583 CanonicalForm::operator = ( const int cf ) 584 { 585 if ( (! is_imm( value )) && value>deleteObject() ) 586 delete value; 587 value = CFFactory::basic( cf ); 588 return *this; 589 } 590 591 CanonicalForm& 592 CanonicalForm::operator += ( const CanonicalForm & cf ) 593 { 594 int what = is_imm( value ); 595 if ( what ) { 596 ASSERT ( ! is_imm( cf.value )  (what==is_imm( cf.value )), "illegal base coefficients" ); 597 if ( (what = is_imm( cf.value )) == FFMARK ) 598 value = imm_add_p( value, cf.value ); 599 else if ( what == GFMARK ) 600 value = imm_add_gf( value, cf.value ); 601 else if ( what ) 602 value = imm_add( value, cf.value ); 603 else { 604 InternalCF * dummy = cf.value>copyObject(); 605 value = dummy>addcoeff( value ); 606 } 607 } 608 else if ( is_imm( cf.value ) ) 609 value = value>addcoeff( cf.value ); 610 else if ( value>level() == cf.value>level() ) { 611 if ( value>levelcoeff() == cf.value>levelcoeff() ) 612 value = value>addsame( cf.value ); 613 else if ( value>levelcoeff() > cf.value>levelcoeff() ) 614 value = value>addcoeff( cf.value ); 615 else { 616 InternalCF * dummy = cf.value>copyObject(); 617 dummy = dummy>addcoeff( value ); 618 if ( value>deleteObject() ) delete value; 619 value = dummy; 620 } 621 } 622 else if ( level() > cf.level() ) 623 value = value>addcoeff( cf.value ); 624 else { 625 InternalCF * dummy = cf.value>copyObject(); 626 dummy = dummy>addcoeff( value ); 627 if ( value>deleteObject() ) delete value; 628 value = dummy; 629 } 630 return *this; 631 } 632 633 CanonicalForm& 634 CanonicalForm::operator = ( const CanonicalForm & cf ) 635 { 636 int what = is_imm( value ); 637 if ( what ) { 638 ASSERT ( ! is_imm( cf.value )  (what==is_imm( cf.value )), "illegal base coefficients" ); 639 if ( (what = is_imm( cf.value )) == FFMARK ) 640 value = imm_sub_p( value, cf.value ); 641 else if ( what == GFMARK ) 642 value = imm_sub_gf( value, cf.value ); 643 else if ( what ) 644 value = imm_sub( value, cf.value ); 645 else { 646 InternalCF * dummy = cf.value>copyObject(); 647 value = dummy>subcoeff( value, true ); 648 } 649 } 650 else if ( is_imm( cf.value ) ) 651 value = value>subcoeff( cf.value, false ); 652 else if ( value>level() == cf.value>level() ) { 653 if ( value>levelcoeff() == cf.value>levelcoeff() ) 654 value = value>subsame( cf.value ); 655 else if ( value>levelcoeff() > cf.value>levelcoeff() ) 656 value = value>subcoeff( cf.value, false ); 657 else { 658 InternalCF * dummy = cf.value>copyObject(); 659 dummy = dummy>subcoeff( value, true ); 660 if ( value>deleteObject() ) delete value; 661 value = dummy; 662 } 663 } 664 else if ( level() > cf.level() ) 665 value = value>subcoeff( cf.value, false ); 666 else { 667 InternalCF * dummy = cf.value>copyObject(); 668 dummy = dummy>subcoeff( value, true ); 669 if ( value>deleteObject() ) delete value; 670 value = dummy; 671 } 672 return *this; 673 } 674 675 CanonicalForm& 676 CanonicalForm::operator *= ( const CanonicalForm & cf ) 677 { 678 int what = is_imm( value ); 679 if ( what ) { 680 ASSERT ( ! is_imm( cf.value )  (what==is_imm( cf.value )), "illegal base coefficients" ); 681 if ( (what = is_imm( cf.value )) == FFMARK ) 682 value = imm_mul_p( value, cf.value ); 683 else if ( what == GFMARK ) 684 value = imm_mul_gf( value, cf.value ); 685 else if ( what ) 686 value = imm_mul( value, cf.value ); 687 else { 688 InternalCF * dummy = cf.value>copyObject(); 689 value = dummy>mulcoeff( value ); 690 } 691 } 692 else if ( is_imm( cf.value ) ) 693 value = value>mulcoeff( cf.value ); 694 else if ( value>level() == cf.value>level() ) { 695 if ( value>levelcoeff() == cf.value>levelcoeff() ) 696 value = value>mulsame( cf.value ); 697 else if ( value>levelcoeff() > cf.value>levelcoeff() ) 698 value = value>mulcoeff( cf.value ); 699 else { 700 InternalCF * dummy = cf.value>copyObject(); 701 dummy = dummy>mulcoeff( value ); 702 if ( value>deleteObject() ) delete value; 703 value = dummy; 704 } 705 } 706 else if ( level() > cf.level() ) 707 value = value>mulcoeff( cf.value ); 708 else { 709 InternalCF * dummy = cf.value>copyObject(); 710 dummy = dummy>mulcoeff( value ); 711 if ( value>deleteObject() ) delete value; 712 value = dummy; 713 } 714 return *this; 715 } 716 717 CanonicalForm& 718 CanonicalForm::operator /= ( const CanonicalForm & cf ) 719 { 720 int what = is_imm( value ); 721 if ( what ) { 722 ASSERT ( ! is_imm( cf.value )  (what==is_imm( cf.value )), "illegal base coefficients" ); 723 if ( (what = is_imm( cf.value )) == FFMARK ) 724 value = imm_div_p( value, cf.value ); 725 else if ( what == GFMARK ) 726 value = imm_div_gf( value, cf.value ); 727 else if ( what ) 728 value = imm_divrat( value, cf.value ); 729 else { 730 InternalCF * dummy = cf.value>copyObject(); 731 value = dummy>dividecoeff( value, true ); 732 } 733 } 734 else if ( is_imm( cf.value ) ) 735 value = value>dividecoeff( cf.value, false ); 736 else if ( value>level() == cf.value>level() ) { 737 if ( value>levelcoeff() == cf.value>levelcoeff() ) 738 value = value>dividesame( cf.value ); 739 else if ( value>levelcoeff() > cf.value>levelcoeff() ) 740 value = value>dividecoeff( cf.value, false ); 741 else { 742 InternalCF * dummy = cf.value>copyObject(); 743 dummy = dummy>dividecoeff( value, true ); 744 if ( value>deleteObject() ) delete value; 745 value = dummy; 746 } 747 } 748 else if ( level() > cf.level() ) 749 value = value>dividecoeff( cf.value, false ); 750 else { 751 InternalCF * dummy = cf.value>copyObject(); 752 dummy = dummy>dividecoeff( value, true ); 753 if ( value>deleteObject() ) delete value; 754 value = dummy; 755 } 756 return *this; 757 } 758 759 CanonicalForm& 760 CanonicalForm::div ( const CanonicalForm & cf ) 761 { 762 int what = is_imm( value ); 763 if ( what ) { 764 ASSERT ( ! is_imm( cf.value )  (what==is_imm( cf.value )), "illegal base coefficients" ); 765 if ( (what = is_imm( cf.value )) == FFMARK ) 766 value = imm_div_p( value, cf.value ); 767 else if ( what == GFMARK ) 768 value = imm_div_gf( value, cf.value ); 769 else if ( what ) 770 value = imm_div( value, cf.value ); 771 else { 772 InternalCF * dummy = cf.value>copyObject(); 773 value = dummy>divcoeff( value, true ); 774 } 775 } 776 else if ( is_imm( cf.value ) ) 777 value = value>divcoeff( cf.value, false ); 778 else if ( value>level() == cf.value>level() ) { 779 if ( value>levelcoeff() == cf.value>levelcoeff() ) 780 value = value>divsame( cf.value ); 781 else if ( value>levelcoeff() > cf.value>levelcoeff() ) 782 value = value>divcoeff( cf.value, false ); 783 else { 784 InternalCF * dummy = cf.value>copyObject(); 785 dummy = dummy>divcoeff( value, true ); 786 if ( value>deleteObject() ) delete value; 787 value = dummy; 788 } 789 } 790 else if ( level() > cf.level() ) 791 value = value>divcoeff( cf.value, false ); 792 else { 793 InternalCF * dummy = cf.value>copyObject(); 794 dummy = dummy>divcoeff( value, true ); 795 if ( value>deleteObject() ) delete value; 796 value = dummy; 797 } 798 return *this; 799 } 800 801 CanonicalForm& 802 CanonicalForm::operator %= ( const CanonicalForm& cf ) 803 { 804 int what = is_imm( value ); 805 if ( what ) { 806 ASSERT ( ! is_imm( cf.value )  (what==is_imm( cf.value )), "illegal base coefficients" ); 807 if ( (what = is_imm( cf.value )) == FFMARK ) 808 value = imm_mod_p( value, cf.value ); 809 else if ( what == GFMARK ) 810 value = imm_mod_gf( value, cf.value ); 811 else if ( what ) 812 value = imm_mod( value, cf.value ); 813 else { 814 InternalCF * dummy = cf.value>copyObject(); 815 value = dummy>modulocoeff( value, true ); 816 } 817 } 818 else if ( is_imm( cf.value ) ) 819 value = value>modulocoeff( cf.value, false ); 820 else if ( value>level() == cf.value>level() ) { 821 if ( value>levelcoeff() == cf.value>levelcoeff() ) 822 value = value>modulosame( cf.value ); 823 else if ( value>levelcoeff() > cf.value>levelcoeff() ) 824 value = value>modulocoeff( cf.value, false ); 825 else { 826 InternalCF * dummy = cf.value>copyObject(); 827 dummy = dummy>modulocoeff( value, true ); 828 if ( value>deleteObject() ) delete value; 829 value = dummy; 830 } 831 } 832 else if ( level() > cf.level() ) 833 value = value>modulocoeff( cf.value, false ); 834 else { 835 InternalCF * dummy = cf.value>copyObject(); 836 dummy = dummy>modulocoeff( value, true ); 837 if ( value>deleteObject() ) delete value; 838 value = dummy; 839 } 840 return *this; 841 } 842 843 CanonicalForm& 844 CanonicalForm::mod( const CanonicalForm & cf ) 845 { 846 int what = is_imm( value ); 847 if ( what ) { 848 ASSERT ( ! is_imm( cf.value )  (what==is_imm( cf.value )), "illegal base coefficients" ); 849 if ( (what = is_imm( cf.value )) == FFMARK ) 850 value = imm_mod_p( value, cf.value ); 851 else if ( what == GFMARK ) 852 value = imm_mod_gf( value, cf.value ); 853 else if ( what ) 854 value = imm_mod( value, cf.value ); 855 else { 856 InternalCF * dummy = cf.value>copyObject(); 857 value = dummy>modcoeff( value, true ); 858 } 859 } 860 else if ( is_imm( cf.value ) ) 861 value = value>modcoeff( cf.value, false ); 862 else if ( value>level() == cf.value>level() ) { 863 if ( value>levelcoeff() == cf.value>levelcoeff() ) 864 value = value>modsame( cf.value ); 865 else if ( value>levelcoeff() > cf.value>levelcoeff() ) 866 value = value>modcoeff( cf.value, false ); 867 else { 868 InternalCF * dummy = cf.value>copyObject(); 869 dummy = dummy>modcoeff( value, true ); 870 if ( value>deleteObject() ) delete value; 871 value = dummy; 872 } 873 } 874 else if ( level() > cf.level() ) 875 value = value>modcoeff( cf.value, false ); 876 else { 877 InternalCF * dummy = cf.value>copyObject(); 878 dummy = dummy>modcoeff( value, true ); 879 if ( value>deleteObject() ) delete value; 880 value = dummy; 881 } 882 return *this; 883 } 884 //}}} 885 886 //{{{ evaluation operators 887 CanonicalForm 888 CanonicalForm::operator () ( const CanonicalForm & f ) const 889 { 890 if ( inBaseDomain() ) 891 return *this; 892 else { 893 CanonicalForm result = 0; 894 for ( CFIterator i = *this; i.hasTerms(); i++ ) 895 if ( i.exp() == 0 ) 896 result += i.coeff(); 897 else 898 result += power( f, i.exp() ) * i.coeff(); 899 return result; 900 } 901 } 902 903 CanonicalForm 904 CanonicalForm::operator () ( const CanonicalForm & f, const Variable & v ) const 905 { 906 if ( inBaseDomain()  v > mvar() ) 907 return *this; 908 else if ( v == mvar() ) { 909 CanonicalForm result = 0; 910 for ( CFIterator i = *this; i.hasTerms(); i++ ) 911 if ( i.exp() == 0 ) 912 result += i.coeff(); 913 else 914 result += power( f, i.exp() ) * i.coeff(); 915 return result; 916 } 917 else { 918 CanonicalForm G = swapvar( *this, v, Variable::highest() ); 919 if ( G.mvar() != Variable::highest() ) 920 return *this; 921 CanonicalForm result = 0; 922 for ( CFIterator i = G; i.hasTerms(); ++i ) 923 if ( i.exp() == 0 ) 924 result += i.coeff(); 925 else 926 result += power( f, i.exp() ) * i.coeff(); 927 return result; 928 } 929 } 930 //}}} 931 932 //{{{ CanonicalForm CanonicalForm::operator[] ( int i ) const 933 CanonicalForm 934 CanonicalForm::operator[] ( int i ) const 935 { 936 return value>coeff( i ); 937 } 938 //}}} 939 940 //{{{ CanonicalForm CanonicalForm::deriv (), deriv ( x ) 941 //{{{ docu 942 // 943 // deriv()  return the formal derivation of CO. 944 // 945 // deriv() derives CO with respect to its main variable. Returns 946 // zero if f is in a coefficient domain. 947 // 948 // deriv( x ) derives CO with respect to x. x should be a 949 // polynomial variable. Returns zero if f is in a coefficient 950 // domain. 951 // 952 // See also: ::deriv() 953 // 954 //}}} 955 CanonicalForm 956 CanonicalForm::deriv () const 957 { 958 if ( is_imm( value )  value>inCoeffDomain() ) 959 return 0; 960 else { 961 CanonicalForm result = 0; 962 Variable x = value>variable(); 963 for ( CFIterator i = *this; i.hasTerms(); i++ ) 964 if ( i.exp() > 0 ) 965 result += power( x, i.exp()1 ) * i.coeff() * i.exp(); 966 return result; 967 } 968 } 969 970 CanonicalForm 971 CanonicalForm::deriv ( const Variable & x ) const 972 { 973 ASSERT( x.level() > 0, "cannot derive with respect to algebraic variables" ); 974 if ( is_imm( value )  value>inCoeffDomain() ) 975 return 0; 976 977 Variable y = value>variable(); 978 if ( x > y ) 979 return 0; 980 else if ( x == y ) 981 return deriv(); 982 else { 983 CanonicalForm result = 0; 984 for ( CFIterator i = *this; i.hasTerms(); i++ ) 985 result += i.coeff().deriv( x ) * power( y, i.exp() ); 986 return result; 987 } 988 } 989 //}}} 990 991 //{{{ int CanonicalForm::sign () const 992 //{{{ docu 993 // 994 // sign()  return sign of CO. 995 // 996 // If CO is an integer or a rational number, the sign is defined 997 // as usual. If CO is an element of a prime power domain or in a 998 // finite field and SW_SYMMETRIC_FF is on the sign of CO is the 999 // sign of the symmetric representation of CO. If CO is in GF(q) 1000 // or in a finite field and SW_SYMMETRIC_FF is off, the sign of 1001 // CO is zero iff CO is zero, otherwise the sign is one. 1002 // 1003 // If CO is a polynomial or in an extension of one of the base 1004 // domains, the sign of CO is the sign of its leading 1005 // coefficient. 1006 // 1007 // See also: InternalCF::sign(), InternalInteger::sign(), 1008 // InternalPrimePower::sign(), InternalRational::sign(), 1009 // InternalPoly::sign(), imm_sign(), gf_sign() 1010 // 1011 //}}} 1012 int 1013 CanonicalForm::sign () const 1014 { 1015 if ( is_imm( value ) ) 1016 return imm_sign( value ); 1017 else 1018 return value>sign(); 1019 } 1020 //}}} 1300 1021 1301 1022 //{{{ CanonicalForm CanonicalForm::sqrt () const … … 1369 1090 //}}} 1370 1091 1371 bool 1372 divides ( const CanonicalForm & f, const CanonicalForm & g ) 1373 { 1374 if ( g.level() > 0 && g.level() == f.level() ) 1375 if ( divides( f.tailcoeff(), g.tailcoeff() ) && divides( f.LC(), g.LC() ) ) { 1376 CanonicalForm q, r; 1377 bool ok = divremt( g, f, q, r ); 1378 return ok && r == 0; 1379 } 1092 //{{{ CanonicalForm CanonicalForm::gcd( const CanonicalForm & ) const 1093 CanonicalForm 1094 CanonicalForm::gcd( const CanonicalForm & ) const 1095 { 1096 // return ::gcd( *this, f ); 1097 return 1; 1098 } 1099 //}}} 1100 1101 //{{{ comparison operators 1102 bool 1103 operator == ( const CanonicalForm & lhs, const CanonicalForm & rhs ) 1104 { 1105 int what = is_imm( lhs.value ); 1106 if ( what ) 1107 if ( what == is_imm( rhs.value ) ) 1108 return lhs.value == rhs.value; 1380 1109 else 1381 1110 return false; 1382 else { 1383 CanonicalForm q, r; 1384 bool ok = divremt( g, f, q, r ); 1385 return ok && r == 0; 1386 } 1387 } 1111 else if ( is_imm( rhs.value ) ) 1112 return false; 1113 else if ( lhs.level() == rhs.level() ) 1114 if ( lhs.value>levelcoeff() >= rhs.value>levelcoeff() ) 1115 return lhs.value>comparesame( rhs.value ) == 0; 1116 else 1117 return rhs.value>comparesame( lhs.value ) == 0; 1118 else 1119 return false; 1120 } 1121 1122 bool 1123 operator != ( const CanonicalForm & lhs, const CanonicalForm & rhs ) 1124 { 1125 int what = is_imm( lhs.value ); 1126 if ( what ) 1127 if ( what == is_imm( rhs.value ) ) 1128 return lhs.value != rhs.value; 1129 else 1130 return true; 1131 else if ( is_imm( rhs.value ) ) 1132 return true; 1133 else if ( lhs.level() == rhs.level() ) 1134 if ( lhs.value>levelcoeff() >= rhs.value>levelcoeff() ) 1135 return lhs.value>comparesame( rhs.value ) != 0; 1136 else 1137 return rhs.value>comparesame( lhs.value ) != 0; 1138 else 1139 return true; 1140 } 1141 1142 bool 1143 operator > ( const CanonicalForm & lhs, const CanonicalForm & rhs ) 1144 { 1145 int what = is_imm( lhs.value ); 1146 if ( what ) { 1147 ASSERT ( ! is_imm( rhs.value )  (what==is_imm( rhs.value )), "illegal base coefficients" ); 1148 if ( what == INTMARK ) { 1149 if ( what == is_imm( rhs.value ) ) 1150 return imm_cmp( lhs.value, rhs.value ) > 0; 1151 else 1152 return rhs.value>comparecoeff( lhs.value ) < 0; 1153 } 1154 else if ( what == FFMARK ) { 1155 if ( what == is_imm( rhs.value ) ) 1156 return imm_cmp_p( lhs.value, rhs.value ) > 0; 1157 else 1158 return rhs.value>comparecoeff( lhs.value ) < 0; 1159 } 1160 else { 1161 if ( what == is_imm( rhs.value ) ) 1162 return imm_cmp_gf( lhs.value, rhs.value ) > 0; 1163 else 1164 return rhs.value>comparecoeff( lhs.value ) < 0; 1165 } 1166 } 1167 else if ( is_imm( rhs.value ) ) 1168 return lhs.value>comparecoeff( rhs.value ) > 0; 1169 else if ( lhs.level() == rhs.level() ) 1170 if ( lhs.value>levelcoeff() == rhs.value>levelcoeff() ) 1171 return lhs.value>comparesame( rhs.value ) > 0; 1172 else if ( lhs.value>levelcoeff() > rhs.value>levelcoeff() ) 1173 return lhs.value>comparecoeff( lhs.value ) > 0; 1174 else 1175 return rhs.value>comparecoeff( lhs.value ) < 0; 1176 else 1177 return lhs.value>level() > rhs.value>level(); 1178 } 1179 1180 bool 1181 operator < ( const CanonicalForm & lhs, const CanonicalForm & rhs ) 1182 { 1183 int what = is_imm( lhs.value ); 1184 if ( what ) { 1185 ASSERT ( ! is_imm( rhs.value )  (what==is_imm( rhs.value )), "illegal base coefficients" ); 1186 if ( what == INTMARK ) { 1187 if ( what == is_imm( rhs.value ) ) 1188 return imm_cmp( lhs.value, rhs.value ) < 0; 1189 else 1190 return rhs.value>comparecoeff( lhs.value ) > 0; 1191 } 1192 else if ( what == FFMARK ) { 1193 if ( what == is_imm( rhs.value ) ) 1194 return imm_cmp( lhs.value, rhs.value ) < 0; 1195 else 1196 return rhs.value>comparecoeff( lhs.value ) > 0; 1197 } 1198 else { 1199 if ( what == is_imm( rhs.value ) ) 1200 return imm_cmp( lhs.value, rhs.value ) < 0; 1201 else 1202 return rhs.value>comparecoeff( lhs.value ) > 0; 1203 } 1204 } 1205 else if ( is_imm( rhs.value ) ) 1206 return lhs.value>comparecoeff( rhs.value ) < 0; 1207 else if ( lhs.level() == rhs.level() ) 1208 if ( lhs.value>levelcoeff() == rhs.value>levelcoeff() ) 1209 return lhs.value>comparesame( rhs.value ) < 0; 1210 else if ( lhs.value>levelcoeff() > rhs.value>levelcoeff() ) 1211 return lhs.value>comparecoeff( lhs.value ) < 0; 1212 else 1213 return rhs.value>comparecoeff( lhs.value ) > 0; 1214 else 1215 return lhs.value>level() < rhs.value>level(); 1216 } 1217 //}}} 1218 1219 //{{{ arithmetic operators 1220 CanonicalForm 1221 operator  ( const CanonicalForm & cf ) 1222 { 1223 CanonicalForm result( cf ); 1224 int what = is_imm( result.value ); 1225 if ( what == FFMARK ) 1226 result.value = imm_neg_p( result.value ); 1227 else if ( what == GFMARK ) 1228 result.value = imm_neg_gf( result.value ); 1229 else if ( what ) 1230 result.value = imm_neg( result.value ); 1231 else 1232 result.value = result.value>neg(); 1233 return result; 1234 } 1235 1236 CanonicalForm 1237 operator + ( const CanonicalForm &c1, const CanonicalForm &c2 ) 1238 { 1239 CanonicalForm result( c1 ); 1240 result += c2; 1241 return result; 1242 } 1243 1244 CanonicalForm 1245 operator  ( const CanonicalForm &c1, const CanonicalForm &c2 ) 1246 { 1247 CanonicalForm result( c1 ); 1248 result = c2; 1249 return result; 1250 } 1251 1252 CanonicalForm 1253 operator * ( const CanonicalForm &c1, const CanonicalForm &c2 ) 1254 { 1255 CanonicalForm result( c1 ); 1256 result *= c2; 1257 return result; 1258 } 1259 1260 CanonicalForm 1261 operator / ( const CanonicalForm &c1, const CanonicalForm &c2 ) 1262 { 1263 CanonicalForm result( c1 ); 1264 result /= c2; 1265 return result; 1266 } 1267 1268 CanonicalForm 1269 div ( const CanonicalForm &c1, const CanonicalForm &c2 ) 1270 { 1271 CanonicalForm result( c1 ); 1272 result.div( c2 ); 1273 return result; 1274 } 1275 1276 CanonicalForm 1277 mod ( const CanonicalForm &c1, const CanonicalForm &c2 ) 1278 { 1279 CanonicalForm result( c1 ); 1280 result.mod( c2 ); 1281 return result; 1282 } 1283 1284 CanonicalForm 1285 operator % ( const CanonicalForm &c1, const CanonicalForm &c2 ) 1286 { 1287 CanonicalForm result( c1 ); 1288 result %= c2; 1289 return result; 1290 } 1291 1292 void 1293 divrem ( const CanonicalForm & f, const CanonicalForm & g, CanonicalForm & q, CanonicalForm & r ) 1294 { 1295 InternalCF * qq = 0, * rr = 0; 1296 int what = is_imm( f.value ); 1297 if ( what ) 1298 if ( is_imm( g.value ) ) { 1299 if ( what == FFMARK ) 1300 imm_divrem_p( f.value, g.value, qq, rr ); 1301 else if ( what == GFMARK ) 1302 imm_divrem_gf( f.value, g.value, qq, rr ); 1303 else 1304 imm_divrem( f.value, g.value, qq, rr ); 1305 } 1306 else 1307 g.value>divremcoeff( f.value, qq, rr, true ); 1308 else if ( (what=is_imm( g.value )) ) 1309 f.value>divremcoeff( g.value, qq, rr, false ); 1310 else if ( f.value>level() == g.value>level() ) 1311 if ( f.value>levelcoeff() == g.value>levelcoeff() ) 1312 f.value>divremsame( g.value, qq, rr ); 1313 else if ( f.value>levelcoeff() > g.value>levelcoeff() ) 1314 f.value>divremcoeff( g.value, qq, rr, false ); 1315 else 1316 g.value>divremcoeff( f.value, qq, rr, true ); 1317 else if ( f.value>level() > g.value>level() ) 1318 f.value>divremcoeff( g.value, qq, rr, false ); 1319 else 1320 g.value>divremcoeff( f.value, qq, rr, true ); 1321 ASSERT( qq != 0 && rr != 0, "error in divrem" ); 1322 q = CanonicalForm( qq ); 1323 r = CanonicalForm( rr ); 1324 } 1325 1326 bool 1327 divremt ( const CanonicalForm & f, const CanonicalForm & g, CanonicalForm & q, CanonicalForm & r ) 1328 { 1329 InternalCF * qq = 0, * rr = 0; 1330 int what = is_imm( f.value ); 1331 bool result = true; 1332 if ( what ) 1333 if ( is_imm( g.value ) ) { 1334 if ( what == FFMARK ) 1335 imm_divrem_p( f.value, g.value, qq, rr ); 1336 else if ( what == GFMARK ) 1337 imm_divrem_gf( f.value, g.value, qq, rr ); 1338 else 1339 imm_divrem( f.value, g.value, qq, rr ); 1340 } 1341 else 1342 result = g.value>divremcoefft( f.value, qq, rr, true ); 1343 else if ( (what=is_imm( g.value )) ) 1344 result = f.value>divremcoefft( g.value, qq, rr, false ); 1345 else if ( f.value>level() == g.value>level() ) 1346 if ( f.value>levelcoeff() == g.value>levelcoeff() ) 1347 result = f.value>divremsamet( g.value, qq, rr ); 1348 else if ( f.value>levelcoeff() > g.value>levelcoeff() ) 1349 result = f.value>divremcoefft( g.value, qq, rr, false ); 1350 else 1351 result = g.value>divremcoefft( f.value, qq, rr, true ); 1352 else if ( f.value>level() > g.value>level() ) 1353 result = f.value>divremcoefft( g.value, qq, rr, false ); 1354 else 1355 result = g.value>divremcoefft( f.value, qq, rr, true ); 1356 if ( result ) { 1357 ASSERT( qq != 0 && rr != 0, "error in divrem" ); 1358 q = CanonicalForm( qq ); 1359 r = CanonicalForm( rr ); 1360 } 1361 else { 1362 q = 0; r = 0; 1363 } 1364 return result; 1365 } 1366 //}}} 1367 1368 //{{{ input/output 1369 #ifndef NOSTREAMIO 1370 void 1371 CanonicalForm::print( ostream & os, char * str ) const 1372 { 1373 if ( is_imm( value ) ) 1374 imm_print( os, value, str ); 1375 else 1376 value>print( os, str ); 1377 } 1378 1379 ostream& 1380 operator << ( ostream & os, const CanonicalForm & cf ) 1381 { 1382 cf.print( os, "" ); 1383 return os; 1384 } 1385 1386 istream& 1387 operator >> ( istream & is, CanonicalForm & cf ) 1388 { 1389 #ifndef SINGULAR 1390 cf = readCF( is ); 1391 return is; 1392 #else /* SINGULAR */ 1393 return 0; 1394 #endif /* SINGULAR */ 1395 } 1396 #endif /* NOSTREAMIO */ 1397 //}}} 1398 1399 //{{{ genCoeff(), genOne(), genZero() 1400 CanonicalForm 1401 CanonicalForm::genCoeff( int type, int i ) 1402 { 1403 return CanonicalForm( CFFactory::basic( type, i ) ); 1404 } 1405 1406 CanonicalForm 1407 CanonicalForm::genZero() const 1408 { 1409 int what = is_imm( value ); 1410 if ( what == FFMARK ) 1411 return CanonicalForm( CFFactory::basic( FiniteFieldDomain, 0 ) ); 1412 else if ( what == GFMARK ) 1413 return CanonicalForm( CFFactory::basic( GaloisFieldDomain, 0 ) ); 1414 else if ( what ) 1415 return CanonicalForm( CFFactory::basic( IntegerDomain, 0 ) ); 1416 else 1417 return CanonicalForm( value>genZero() ); 1418 } 1419 1420 CanonicalForm 1421 CanonicalForm::genOne() const 1422 { 1423 int what = is_imm( value ); 1424 if ( what == FFMARK ) 1425 return CanonicalForm( CFFactory::basic( FiniteFieldDomain, 1 ) ); 1426 else if ( what == GFMARK ) 1427 return CanonicalForm( CFFactory::basic( GaloisFieldDomain, 1 ) ); 1428 else if ( what ) 1429 return CanonicalForm( CFFactory::basic( IntegerDomain, 1 ) ); 1430 else 1431 return CanonicalForm( value>genOne() ); 1432 } 1433 //}}} 1434 1435 //{{{ exponentiation 1436 CanonicalForm 1437 power ( const CanonicalForm & f, int n ) 1438 { 1439 ASSERT( n >= 0, "illegal exponent" ); 1440 if ( f == 0 ) 1441 return 0; 1442 else if ( f == 1 ) 1443 return f; 1444 else if ( f == 1 ) { 1445 if ( n % 2 == 0 ) 1446 return 1; 1447 else 1448 return 1; 1449 } 1450 else if ( n == 0 ) 1451 return 1; 1452 else { 1453 CanonicalForm result = f; 1454 for ( int i = 1; i < n; i++ ) 1455 result *= f; 1456 return result; 1457 } 1458 } 1459 1460 CanonicalForm 1461 power ( const Variable & v, int n ) 1462 { 1463 ASSERT( n >= 0, "illegal exponent" ); 1464 if ( n == 0 ) 1465 return 1; 1466 else if ( n == 1 ) 1467 return v; 1468 else if ( v.level() < 0 ) { 1469 CanonicalForm result( v, n1 ); 1470 return result * v; 1471 } 1472 else 1473 return CanonicalForm( v, n ); 1474 } 1475 //}}} 1476 1477 //{{{ switches 1478 void 1479 On( int sw ) 1480 { 1481 cf_glob_switches.On( sw ); 1482 } 1483 1484 void 1485 Off( int sw ) 1486 { 1487 cf_glob_switches.Off( sw ); 1488 } 1489 1490 bool 1491 isOn( int sw ) 1492 { 1493 return cf_glob_switches.isOn( sw ); 1494 } 1495 //}}}
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