Changeset 257093d in git for Singular/LIB/nfmodstd.lib
 Timestamp:
 Jun 11, 2015, 8:15:51 AM (8 years ago)
 Branches:
 (u'spielwiese', 'e7cc1ebecb61be8b9ca6c18016352af89940b21a')
 Children:
 7036d0b9fb90dfbbb225e698220889d8bfd08fb3
 Parents:
 8aa9770fc6e41a905d10dd6cac4556354095e462
 File:

 1 edited
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Singular/LIB/nfmodstd.lib
r8aa977 r257093d 524 524 I; 525 525 } 526 527 ////////////////////////////////////////////////////////////////////////////// 528 529 /* 530 Benchmark Problems from 531 532 Boku, Decker, Fieker, Steenpass: Groebner Bases over Algebraic Number 533 Fields. 534 535 // 1 536 ring R = (0,a), (x,y,z), dp; 537 minpoly = (a^2+1); 538 poly f1 = (a+8)*x^2*y^2+5*x*y^3+(a+3)*x^3*z 539 +x^2*y*z; 540 poly f2 = x^5+2*y^3*z^2+13*y^2*z^3+5*y*z^4; 541 poly f3 = 8*x^3+(a+12)*y^3+x*z^2+3; 542 poly f4 = (a+7)*x^2*y^4+y^3*z^3+18*y^3*z^2; 543 ideal I1 = f1,f2,f3,f4; 544 545 // 2 546 ring R = (0,a), (x,y,z), dp; 547 minpoly = (a^5+a^2+2); 548 poly f1 = 2*x*y^4*z^2+(a1)*x^2*y^3*z 549 +(2*a)*x*y*z^2+7*y^3+(7*a+1); 550 poly f2 = 2*x^2*y^4*z+(a)*x^2*y*z^2x*y^2*z^2 551 +(2*a+3)*x^2*y*z12*x+(12*a)*y; 552 poly f3 = (2*a)*y^5*z+x^2*y^2*zx*y^3*z 553 +(a)*x*y^3+y^4+2*y^2*z; 554 poly f4 = (3*a)*x*y^4*z^3+(a+1)*x^2*y^2*z 555 x*y^3*z+4*y^3*z^2+(3*a)*x*y*z^3 556 +4*z^2x+(a)*y; 557 ideal I2 = f1,f2,f3,f4; 558 559 // 3a 560 ring R = (0,a), (v,w,x,y,z), dp; 561 minpoly = (a^77*a+3); 562 poly f1 = (a)*v+(a1)*w+x+(a+2)*y+z; 563 poly f2 = v*w+(a1)*w*x+(a+2)*v*y+x*y+(a)*y*z; 564 poly f3 = (a)*v*w*x+(a+5)*w*x*y+(a)*v*w*z 565 +(a+2)*v*y*z+(a)*x*y*z; 566 poly f4 = (a11)*v*w*x*y+(a+5)*v*w*x*z 567 +(a)*v*w*y*z+(a)*v*x*y*z 568 +(a)*w*x*y*z; 569 poly f5 = (a+3)*v*w*x*y*z+(a+23); 570 ideal I3a = f1,f2,f3,f4,f5; 571 572 // 3b 573 ring R = (0,a), (u,v,w,x,y,z), dp; 574 minpoly = (a^77*a+3); 575 poly f1 = (a)*u+(a+2)*v+w+x+y+z; 576 poly f2 = u*v+v*w+w*x+x*y+(a+3)*u*z+y*z; 577 poly f3 = u*v*w+v*w*x+(a+1)*w*x*y+u*v*z+u*y*z 578 +x*y*z; 579 poly f4 = (a1)*u*v*w*x+v*w*x*y+u*v*w*z 580 +u*v*y*z+u*x*y*z+w*x*y*z; 581 poly f5 = u*v*w*x*y+(a+1)*u*v*w*x*z+u*v*w*y*z 582 +u*v*x*y*z+u*w*x*y*z+v*w*x*y*z; 583 poly f6 = u*v*w*x*y*z+(a+2); 584 ideal I3b = f1,f2,f3,f4,f5,f6; 585 586 // 4 587 ring R = (0,a), (w,x,y,z), dp; 588 minpoly = (a^6+a^5+a^4+a^3+a^2+a+1); 589 poly f1 = (a+5)*w^3*x^2*y+(a3)*w^2*x^3*y 590 +(a+7)*w*x^2*y^2; 591 poly f2 = (a)*w^5+(a+3)*w*x^2*y^2 592 +(a^2+11)*x^2*y^2*z; 593 poly f3 = (a+7)*w^3+12*x^3+4*w*x*y+(a)*z^3; 594 poly f4 = 3*w^3+(a4)*x^3+x*y^2; 595 ideal I4 = f1,f2,f3,f4; 596 597 // 5 598 ring R = (0,a), (w,x,y,z), dp; 599 minpoly = (a^125*a^11+24*a^10115*a^9+551*a^8 600 2640*a^7+12649*a^62640*a^5+551*a^4 601 115*a^3+24*a^25*a+1); 602 poly f1 = (2*a+3)*w*x^4*y^2+(a+1)*w^2*x^3*y*z 603 +2*w*x*y^2*z^3+(7*a1)*x^3*z^4; 604 poly f2 = 2*w^2*x^4*y+w^2*x*y^2*z^2 605 +(a)*w*x^2*y^2*z^2 606 +(a+11)*w^2*x*y*z^312*w*z^6 607 +12*x*z^6; 608 poly f3 = 2*x^5*y+w^2*x^2*y*zw*x^3*y*z 609 w*x^3*z^2+(a)*x^4*z^2+2*x^2*y*z^3; 610 poly f4 = 3*w*x^4*y^3+w^2*x^2*y*z^3 611 w*x^3*y*z^3+(a+4)*x^3*y^2*z^3 612 +3*w*x*y^3*z^3+(4*a)*y^2*z^6w*z^7 613 +x*z^7; 614 ideal I5 = f1,f2,f3,f4; 615 616 // 6 617 ring R = (0,a), (u,v,w,x,y,z), dp; 618 minpoly = (a^2+5*a+1); 619 poly f1 = u+v+w+x+y+z+(a); 620 poly f2 = u*v+v*w+w*x+x*y+y*z+(a)*u+(a)*z; 621 poly f3 = u*v*w+v*w*x+w*x*y+x*y*z+(a)*u*v 622 +(a)*u*z+(a)*y*z; 623 poly f4 = u*v*w*x+v*w*x*y+w*x*y*z+(a)*u*v*w 624 +(a)*u*v*z+(a)*u*y*z+(a)*x*y*z; 625 poly f5 = u*v*w*x*y+v*w*x*y*z+(a)*u*v*w*x 626 +(a)*u*v*w*z+(a)*u*v*y*z+(a)*u*x*y*z 627 +(a)*w*x*y*z; 628 poly f6 = u*v*w*x*y*z+(a)*u*v*w*x*y 629 +(a)*u*v*w*x*z+(a)*u*v*w*y*z 630 +(a)*u*v*x*y*z+(a)*u*w*x*y*z 631 +(a)*v*w*x*y*z; 632 poly f7 = (a)*u*v*w*x*y*z1; 633 ideal I6 = f1,f2,f3,f4,f5,f6,f7; 634 635 // 7 636 ring R = (0,a), (w,x,y,z), dp; 637 minpoly = (a^816*a^7+19*a^6a^55*a^4+13*a^3 638 9*a^2+13*a+17); 639 poly f1 = (a^21)*x^2*y+2*w*x*z2*w 640 +(a^2+1)*y; 641 poly f2 = (a^3a3)*w^3*y+4*w*x^2*y+4*w^2*x*z 642 +2*x^3*z+(a)*w^210*x^2+4*w*y10*x*z 643 +(2*a^2+a); 644 poly f3 = (a^2+a+11)*x*y*z+w*z^2w2*y; 645 poly f4 = w*y^3+4*x*y^2*z+4*w*y*z^2+2*x*z^3 646 +(2*a^3+a^2)*w*y+4*y^210*x*z10*z^2 647 +(3*a^2+5); 648 ideal I7 = f1,f2,f3,f4; 649 650 // 8 651 ring R = (0,a), (t,u,v,w,x,y,z), dp; 652 minpoly = (a^7+10*a^5+5*a^3+10*a+1); 653 poly f1 = v*x+w*yx*zwy; 654 poly f2 = v*wu*x+x*yw*z+v+x+z; 655 poly f3 = t*ww^2+x^2t; 656 poly f4 = (a)*v^2u*y+y^2v*zz^2+u; 657 poly f5 = t*v+v*w+(a^2a5)*x*yt*z+w*z+v+x+z 658 +(a+1); 659 poly f6 = t*u+u*w+(a11)*v*xt*y+w*yx*ztu 660 +w+y; 661 poly f7 = w^2*y^3w*x*y^3+x^2*y^3+w^2*y^2*z 662 w*x*y^2*z+x^2*y^2*z+w^2*y*z^2 663 w*x*y*z^2+x^2*y*z^2+w^2*z^3w*x*z^3 664 +x^2*z^3; 665 poly f8 = t^2*u^3+t^2*u^2*v+t^2*u*v^2+t^2*v^3 666 t*u^3*xt*u^2*v*xt*u*v^2*xt*v^3*x 667 +u^3*x^2+u^2*v*x^2+u*v^2*x^2 668 +v^3*x^2; 669 ideal I8 = f1,f2,f3,f4,f5,f6,f7,f8; 670 */
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