Changeset 5bc4ee3 in git
 Timestamp:
 Apr 27, 2005, 9:32:14 PM (18 years ago)
 Branches:
 (u'jengelhdatetime', 'ceac47cbc86fe4a15902392bdbb9bd2ae0ea02c6')(u'spielwiese', 'a800fe4b3e9d37a38c5a10cc0ae9dfa0c15a4ee6')
 Children:
 8647dd78e27cd22cb1d534128af44420765ce382
 Parents:
 06d5e10cda81b8b254f3c4e329dd70a92415fcd6
 Location:
 Singular/LIB
 Files:

 2 edited
Legend:
 Unmodified
 Added
 Removed

Singular/LIB/gkdim.lib
r06d5e10 r5bc4ee3 1 1 /////////////////////////////////////////////////////////////////////////////// 2 version="$Id: gkdim.lib,v 1. 6 20050223 18:10:45levandov Exp $";2 version="$Id: gkdim.lib,v 1.7 20050427 19:32:14 levandov Exp $"; 3 3 category="Noncommutative"; 4 4 info=" … … 47 47 proc GKdim(list L) 48 48 "USAGE: GKdim(L); L is a left ideal/module/matrix 49 RETURN: int, the GelfandKirillov dimension of the factormodule, whose presentation is given by L 49 PURPOSE: compute the GelfandKirillov dimension of the factormodule, whose presentation is given by L 50 RETURN: int 50 51 NOTE: if the factormodule is zero, 1 is returned 51 52 EXAMPLE: example GKdim; shows examples 
Singular/LIB/involut.lib
r06d5e10 r5bc4ee3 1 version="$Id: involut.lib,v 1. 2 20050223 18:10:45levandov Exp $";1 version="$Id: involut.lib,v 1.3 20050427 19:32:14 levandov Exp $"; 2 2 category="Noncommutative"; 3 3 info=" … … 17 17 find_invo_diag(); describes a variety of homothetic (diagonal) involutions on a basering; 18 18 find_auto(); describes a variety of linear automorphisms of a basering; 19 ncdetection(ring r); computes an ideal, presenting an involution map on some classicalnoncommutative algebras;20 involution(m, map theta); applies the involution , presented by theta, to the object m =19 ncdetection(ring r); computes an ideal, presenting an involution map on some particular noncommutative algebras; 20 involution(m, map theta); applies the involution to an object. 21 21 "; 22 22 … … 27 27 proc ncdetection(def r) 28 28 "USAGE: ncdetection(r), r a ring 29 RETURN: ideal, presenting an involution map on a noncommutative algebra r 30 NOTE: returns optimized involutions for some classical noncomm algebras, 31 arising in the Control Theory, namely algebras with 32 differential, shift or advance operators 29 PURPOSE: compute optimized involutions for some particular noncommutative algebras 30 RETURN: ideal (presenting an involution map) 31 NOTE: the procedure is aimed at noncommutative algebras with differential, shift or advance operators arising in the Control Theory 33 32 EXAMPLE: example ncdetection; shows an example 34 " 35 { 33 "{ 36 34 // in this procedure an involution map is generated from the NCRelations 37 35 // that will be used in the function involution … … 272 270 RETURN: object of the same type as m 273 271 EXAMPLE: example involution; shows an example 274 " 275 { 272 "{ 276 273 // applies the involution map theta to m, 277 274 // where m= vector, polynomial, module, matrix, ideal … … 411 408 RETURN: a ring together with a list of pairs L, where 412 409 @* L[i][1] = Groebner Basis of an ith associated prime, 413 @* L[i][2] = multiplication matrix, reduced wrt L[i][1] 414 NOTE: for convenience, the full ideal of relations 'idJ' 415 and the matrix with indeterminates 'matD' are exported in the output ring. 416 " 417 { 410 @* L[i][2] = matrix, defining a linear map, with entries, reduced with respect to L[i][1] 411 NOTE: for convenience, the full ideal of relations @code{idJ} 412 and the initial matrix with indeterminates @code{matD} are exported in the output ring. 413 "{ 418 414 def @B = basering; //save the name of basering 419 415 int NVars = nvars(@B); //number of variables in basering … … 503 499 matrix IM = @@D; // involution map 504 500 list L = list(); // the answer 505 list TL; 501 list TL; 502 ideal tmp = 0; 506 503 for (i=1; i<=sL; i++) // compute GBs of components 507 504 { 508 505 TL = list(); 509 506 TL[1] = std(mL[i]); 510 TL[2] = NF( ideal(IM), TL[1] ); 507 tmp = NF( ideal(IM), TL[1] ); 508 TL[2] = matrix(tmp, NVars,NVars); 511 509 L[i] = TL; 512 510 } … … 521 519 { "EXAMPLE:"; echo = 2; 522 520 def a = CreateWeyl(1); 523 setring a; 521 setring a; // this algebra is a first Weyl algebra 524 522 def X = find_invo(); 525 setring X; 523 setring X; // ring with new variables, corresponding to unknown coefficients 526 524 L; 525 print(L[1][2]); // L[i][2] is a matrix in new variables, defining the linear involution 526 L[1][1]; // where new variables obey these relations 527 527 } 528 528 /////////////////////////////////////////////////////////////////////////// … … 532 532 RETURN: a ring together with a list of pairs L, where 533 533 @* L[i][1] = Groebner Basis of an ith associated prime, 534 @* L[i][2] = multiplication matrix, reduced wrt L[i][1] 535 NOTE: for convenience, the full ideal of relations 'idJ' 536 and the matrix with indeterminates 'matD' are exported in the output ring. 537 " 538 { 534 @* L[i][2] = matrix, defining a linear map, with entries, reduced with respect to L[i][1] 535 NOTE: for convenience, the full ideal of relations @code{idJ} 536 and the initial matrix with indeterminates @code{matD} are exported in the output ring. 537 "{ 539 538 def @B = basering; //save the name of basering 540 539 int NVars = nvars(@B); //number of variables in basering … … 626 625 list L = list(); // the answer 627 626 list TL; 628 for (i=1; i<=sL; i++)// compute GBs of components 627 ideal tmp = 0; 628 for (i=1; i<=sL; i++) // compute GBs of components 629 629 { 630 630 TL = list(); 631 631 TL[1] = std(mL[i]); 632 TL[2] = NF( ideal(IM), TL[1] ); 632 tmp = NF( ideal(IM), TL[1] ); 633 TL[2] = matrix(tmp, NVars,NVars); 633 634 L[i] = TL; 634 } 635 } 635 636 export(L); 636 637 ideal idJ = J; // debugcomfortable exports … … 643 644 { "EXAMPLE:"; echo = 2; 644 645 def a = CreateWeyl(1); 645 setring a; 646 setring a; // this algebra is a first Weyl algebra 646 647 def X = find_invo_diag(); 647 setring X; 648 L; 648 setring X; // ring with new variables, corresponding to unknown coefficients 649 print(L[1][2]); // a first matrix, defining the linear involution: we see it is constant 650 print(L[2][2]); // and a second possible matrix; it is constant too 651 L; // let us take a look on the whole list 649 652 } 650 653 ///////////////////////////////////////////////////////////////////// … … 653 656 PURPOSE: describes a variety of linear automorphisms of a basering 654 657 RETURN: a ring together with a list of pairs L, where 655 @* L[i][1] = Groebner Basis of an ith associated prime, 656 @* L[i][2] = multiplication matrix, reduced wrt L[i][1] 657 NOTE: for convenience, the full ideal of relations 'idJ' 658 and the matrix with indeterminates 'matD' are exported in the output ring. 659 " 660 { 658 @* L[i][1] = Groebner Basis of an ith associated prime, 659 @* L[i][2] = matrix, defining a linear map, with entries, reduced with respect to L[i][1] 660 NOTE: for convenience, the full ideal of relations @code{idJ} 661 and the initial matrix with indeterminates @code{matD} are exported in the output ring. 662 "{ 661 663 def @B = basering; //save the name of basering 662 664 int NVars = nvars(@B); //number of variables in basering … … 747 749 list L = list(); // the answer 748 750 list TL; 751 ideal tmp = 0; 749 752 for (i=1; i<=sL; i++)// compute GBs of components 750 753 { 751 754 TL = list(); 752 755 TL[1] = std(mL[i]); 753 TL[2] = NF( ideal(IM), TL[1] ); 756 tmp = NF( ideal(IM), TL[1] ); 757 TL[2] = matrix(tmp,NVars, NVars); 754 758 L[i] = TL; 755 759 } … … 764 768 { "EXAMPLE:"; echo = 2; 765 769 def a = CreateWeyl(1); 766 setring a; 770 setring a; // this algebra is a first Weyl algebra 767 771 def X = find_auto(); 768 setring X; 769 L; 770 } 772 setring X; // ring with new variables, corresponding to unknown coefficients 773 print(L[1][2]); // a first matrix, defining the linear automorphism : we see it is constant 774 print(L[2][2]); // and a second possible matrix; it is constant too 775 L; // let us take a look on the whole list 776 }
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