Changeset f49f53 in git
 Timestamp:
 Apr 8, 2009, 1:00:08 PM (14 years ago)
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 (u'jengelhdatetime', 'ceac47cbc86fe4a15902392bdbb9bd2ae0ea02c6')(u'spielwiese', 'a800fe4b3e9d37a38c5a10cc0ae9dfa0c15a4ee6')
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 cc2d2ed599098ef3687b1ec2d563e75a80d312cd
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 2ec47ebaee7fc5079158c6e6581c99b776479b2e
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Singular/LIB/zeroset.lib
r2ec47e rf49f53 1 1 // Last change 12.02.2001 (Eric Westenberger) 2 2 /////////////////////////////////////////////////////////////////////////////// 3 version="$Id: zeroset.lib,v 1.2 1 20090406 14:12:09seelisch Exp $";3 version="$Id: zeroset.lib,v 1.22 20090408 11:00:08 seelisch Exp $"; 4 4 category="Symbolicnumerical solving"; 5 5 info=" … … 82 82 without multiplicities. 83 83 RETURN: ring, a polynomial ring over an extension field of the ground field, 84 containing a list ' roots' and polynomials 'newA' and 'f':84 containing a list 'theRoots' and polynomials 'newA' and 'f': 85 85 @format 86  ' roots' is the list of roots of the polynomial f (no multiplicities)86  'theRoots' is the list of roots of the polynomial f (no multiplicities) 87 87  if the ground field is Q(a') and the extension field is Q(a), then 88 88 'newA' is the representation of a' in Q(a). … … 93 93 @end format 94 94 ASSUME: ground field to be Q or a simple extension of Q given by a minpoly 95 EXAMPLE: example 95 EXAMPLE: example roots; shows an example 96 96 " 97 97 { … … 115 115 // the coefficients of f. 116 116 117 list roots = result[1];117 list theRoots = result[1]; 118 118 poly newA = result[2]; 119 119 map F = basering, maxideal(1); … … 125 125 def RON = NewBaseRing(); 126 126 setring(RON); 127 list roots = imap(ROR, roots);127 list theRoots = imap(ROR, theRoots); 128 128 poly newA = imap(ROR, newA); 129 129 poly f = imap(ROR, fn); 130 130 kill ROR; 131 export( roots);131 export(theRoots); 132 132 export(newA); 133 133 export(f); dbprint(dbPrt," 134 // 'roots' created a new ring which contains the list ' roots' and134 // 'roots' created a new ring which contains the list 'theRoots' and 135 135 // the polynomials 'f' and 'newA' 136 136 // To access the roots, newA and the new representation of f, type 137 def R = roots(f); setring R; roots; newA; f;137 def R = roots(f); setring R; theRoots; newA; f; 138 138 "); 139 139 return(RON); … … 149 149 newA; 150 150 f; 151 roots;151 theRoots; 152 152 map F; 153 F[1] = roots[1];153 F[1] = theRoots[1]; 154 154 F(f); 155 155 } … … 170 170 ASSUME: basering = Q[x,a] ideal mpoly must be defined, it might be 0! 171 171 NOTE: might change the ideal mpoly!! 172 EXAMPLE: example roots; shows an example172 EXAMPLE: example rootsMain; shows an example 173 173 " 174 174 { … … 353 353 // store the zeroset, minimal polynomial and the new representative of 'a' 354 354 355 list zeroset = result[1];355 list theZeroset = result[1]; 356 356 poly newA = result[2]; 357 357 poly minPoly = result[3][1]; … … 369 369 setring RZBN; 370 370 371 list zeroset = imap(ZSR, zeroset);371 list theZeroset = imap(ZSR, theZeroset); 372 372 poly newA = imap(ZSR, newA); 373 373 ideal id = imap(ZSR, id); … … 375 375 376 376 export(id); 377 export( zeroset);377 export(theZeroset); 378 378 export(newA); 379 379 dbprint(dbPrt," 380 // 'zeroSet' created a new ring which contains the list ' zeroset', the ideal380 // 'zeroSet' created a new ring which contains the list 'theZeroset', the ideal 381 381 // 'id' and the polynomial 'newA'. 'id' is the ideal of the input transformed 382 382 // w.r.t. 'newA'. 383 383 // To access the zeroset, 'newA' and the new representation of the ideal, type 384 def R = zeroSet(I); setring R; zeroset; newA; id;384 def R = zeroSet(I); setring R; theZeroset; newA; id; 385 385 "); 386 386 setring RZSB; … … 397 397 newA; 398 398 id; 399 zeroset;400 map F1 = basering, zeroset[1];401 map F2 = basering, zeroset[2];399 theZeroset; 400 map F1 = basering, theZeroset[1]; 401 map F2 = basering, theZeroset[2]; 402 402 F1(id); 403 403 F2(id); … … 481 481 NOTE: This procedure is outdated, and should no longer be used. Use div and mod 482 482 instead. 483 EXAMPLE: example 483 EXAMPLE: example Quotient; shows an example 484 484 " 485 485 { … … 620 620 RETURN: poly 621 621 ASSUME: f, g are polynomials in var(i), last variable is the algebraic number 622 EXAMPLE: example 622 EXAMPLE: example MEGCD; shows an example 623 623 " 624 624 // might be extended to return s1, s2 s.t. f*s1 + g*s2 = gc … … 661 661 ASSUME: f must be squarefree, basering = Q(a)[x] and minpoly != 0. 662 662 NOTE: the norm is an element of Q[x] 663 EXAMPLE: example 663 EXAMPLE: example sqfrNorm; shows an example 664 664 " 665 665 { … … 696 696 'minpoly', this represents the ring Q(a)[x] together with 'minpoly'. 697 697 NOTE: the norm is an element of Q[x] 698 EXAMPLE: example 698 EXAMPLE: example SqfrNorm; shows an example 699 699 " 700 700 { … … 748 748 be defined, representing the minimal polynomial (it might be 0!). 749 749 NOTE: outdated, use factorize instead 750 EXAMPLE: example 750 EXAMPLE: example Factor; shows an example 751 751 " 752 752 { … … 814 814 NOTE: opt = 0 no primary decomposition 815 815 opt > 0 use a primary decomposition 816 EXAMPLE: example zeroSet ; shows an example816 EXAMPLE: example zeroSetMain; shows an example 817 817 " 818 818 { … … 897 897 ideal mpoly must be defined, it might be 0! 898 898 NOTE: might change 'mpoly' !! 899 EXAMPLE: example 899 EXAMPLE: example IdealSolve; shows an example 900 900 " 901 901 {
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