Changeset cfb500 in git
 Timestamp:
 May 20, 2011, 1:07:49 PM (12 years ago)
 Branches:
 (u'jengelhdatetime', 'ceac47cbc86fe4a15902392bdbb9bd2ae0ea02c6')(u'spielwiese', '00e2e9c41af3fde1273eb3633f4c0c7c3db2579d')
 Children:
 502f5f6f3100e91a41cf8b3762727582bcdcc2fa
 Parents:
 09ed7738e7d4dd96c01950a6f0736d8581f333d2
 gitauthor:
 Frank Seelisch <seelisch@mathematik.unikl.de>20110520 13:07:49+02:00
 gitcommitter:
 Mohamed Barakat <mohamed.barakat@rwthaachen.de>20111109 12:36:13+01:00
 Location:
 libpolys
 Files:

 3 edited
Legend:
 Unmodified
 Added
 Removed

libpolys/polys/ext_fields/algext.cc
r09ed77 rcfb500 437 437 } 438 438 439 /* IMPORTANT NOTE: Since an algebraic field extension is again a field, 440 the gcd of two elements is not very interesting. (It 441 is actually any unit in the field, i.e., any non 442 zero element.) Note that the below method does not operate 443 in this strong sense but rather computes the gcd of 444 two given elements in the underlying polynomial ring. */ 439 445 number naGcd(number a, number b, const coeffs cf) 440 446 { … … 455 461 p_Delete(&theGcd, naRing); 456 462 p_Delete(&mFactor, naRing); 457 /* printf("naInvers\n");458 p_Write((poly)a, naRing);459 p_Write(aFactor, naRing); */460 463 return (number)(aFactor); 461 464 } 
libpolys/polys/monomials/p_polys.cc
r09ed77 rcfb500 1445 1445 poly p_PolyDiv(poly &p, poly divisor, BOOLEAN needResult, ring r) 1446 1446 { 1447 //printf("p_PolyDiv:\n");1448 1447 assume(divisor != NULL); 1449 1448 if (p == NULL) return NULL; … … 1452 1451 number divisorLC = p_GetCoeff(divisor, r); 1453 1452 int divisorLE = p_GetExp(divisor, 1, r); 1454 //p_Write(p, r); p_Write(divisor, r);1455 1453 while ((p != NULL) && (p_Deg(p, r) >= p_Deg(divisor, r))) 1456 1454 { … … 1462 1460 p_SetExp(t, 1, e, r); 1463 1461 p_Setm(t, r); 1464 //printf("t\n");1465 //p_Write(t, r);1466 1462 if (needResult) result = p_Add_q(result, p_Copy(t, r), r); 1467 1463 p = p_Add_q(p, p_Neg(p_Mult_q(t, p_Copy(divisor, r), r), r), r); 1468 //printf("p\n");1469 //p_Write(p, r);1470 1464 } 1471 1465 return result; … … 1483 1477 number lc = p_GetCoeff(p, r); 1484 1478 if (n_IsOne(lc, r>cf)) return; 1485 1486 if( pNext(p) == NULL ) 1487 { 1488 p_SetCoeff(p, n_Init(1, r>cf), r); // will delete the leading coeff 1st! 1489 return; 1490 } 1491 1492 // TODO: consider unsing 1xn_Inverse + n_Mult instead of multiple n_Div 1493 p_SetCoeff0(p, n_Init(1, r>cf), r); // no coeff destruction! 1494 1479 number lcInverse = n_Invers(lc, r>cf); 1480 number n = n_Init(1, r>cf); 1481 p_SetCoeff(p, n, r); // destroys old leading coefficient! 1495 1482 p = pIter(p); 1496 1497 1483 while (p != NULL) 1498 1484 { 1499 number c = p_GetCoeff(p, r); 1500 number n = n_Div(c, lc, r>cf); 1501 n_Delete(&c, r>cf); 1502 p_SetCoeff(p, n, r); 1485 number n = n_Mult(p_GetCoeff(p, r), lcInverse, r>cf); 1486 p_SetCoeff(p, n, r); // destroys old leading coefficient! 1503 1487 p = pIter(p); 1504 1488 } 1505 n_Delete(&lc , r>cf);1489 n_Delete(&lcInverse, r>cf); 1506 1490 p = pp; 1507 1491 } … … 1552 1536 qFactor = NULL; 1553 1537 pFactor = p_ISet(1, r); 1554 number n = p_GetCoeff(pFactor, r);1555 //printf("p_ExtGcdHelper0:\n");1556 //p_Write(p, r);1557 1538 p_SetCoeff(pFactor, n_Invers(p_GetCoeff(p, r), r>cf), r); 1558 n_Delete(&n, r>cf);1559 1539 p_Monic(p, r); 1560 1540 return p; … … 1562 1542 else 1563 1543 { 1564 //printf("p_ExtGcdHelper1:\n");1565 //p_Write(p, r); p_Write(q, r);1566 1544 poly pDivQ = p_PolyDiv(p, q, TRUE, r); 1567 1545 poly ppFactor = NULL; poly qqFactor = NULL; 1568 //printf("p_ExtGcdHelper2:\n");1569 //p_Write(p, r); p_Write(ppFactor, r);1570 //p_Write(q, r); p_Write(qqFactor, r);1571 1546 poly theGcd = p_ExtGcdHelper(q, qqFactor, p, ppFactor, r); 1572 //printf("p_ExtGcdHelper3:\n");1573 //p_Write(q, r); p_Write(qqFactor, r);1574 //p_Write(p, r); p_Write(ppFactor, r);1575 //p_Write(theGcd, r);1576 1547 pFactor = ppFactor; 1577 1548 qFactor = p_Add_q(qqFactor, 1578 1549 p_Neg(p_Mult_q(pDivQ, p_Copy(ppFactor, r), r), r), 1579 1550 r); 1580 //printf("p_ExtGcdHelper4:\n");1581 //p_Write(pFactor, r); p_Write(qFactor, r);1582 1551 return theGcd; 1583 1552 } … … 1594 1563 poly p_ExtGcd(poly p, poly &pFactor, poly q, poly &qFactor, ring r) 1595 1564 { 1596 //printf("p_ExtGcd1:\n");1597 //p_Write(p, r); p_Write(q, r);1598 1565 assume((p != NULL)  (q != NULL)); 1599 1566 poly a = p; poly b = q; BOOLEAN aCorrespondsToP = TRUE; 
libpolys/tests/polys_test.h
r09ed77 rcfb500 209 209 { 210 210 private: 211 /* replaces n by n + c * var^exp (inplace); 212 expects exp >= 0 */ 213 void plusTerm(number &n, int c, int exp, const coeffs cf) 214 { 215 number x = n_Par(1, cf); 216 number pow = n_Init(1, cf); 217 number temp; 218 for (int i = 1; i <= exp; i++) 219 { 220 temp = n_Mult(pow, x, cf); 221 n_Delete(&pow, cf); 222 pow = temp; 223 } 224 n_Delete(&x, cf); 225 number m = n_Init(c, cf); 226 number t = n_Mult(m, pow, cf); 227 n_Delete(&m, cf); n_Delete(&pow, cf); 228 temp = n_Add(n, t, cf); 229 n_Delete(&n, cf); n_Delete(&t, cf); 230 n = temp; 231 } 211 232 void checkInverse(number n, const coeffs cf) 212 233 { … … 216 237 number n2 = n_Mult(n, n1, cf); 217 238 clog << "(check: n * n^(1) = "; n_Write(n2, cf); 239 TS_ASSERT( n_IsOne(n2, cf) ); 218 240 n_Delete(&n1, cf); n_Delete(&n2, cf); 219 241 } … … 603 625 604 626 clog << endl 605 << "Now let's compute some inverses in Q[a]/<a2+1>..." 627 << "Now let's compute some inverses in Q[a]/<a^2+1>..." 628 << endl; 629 630 number u; 631 u = NULL; plusTerm(u, 1, 1, cf); plusTerm(u, 1, 0, cf); // a + 1 632 checkInverse(u, cf); n_Delete(&u, cf); 633 u = NULL; plusTerm(u, 1, 1, cf); plusTerm(u, 1, 0, cf); // a  1 634 checkInverse(u, cf); n_Delete(&u, cf); 635 u = NULL; plusTerm(u, 1, 1, cf); plusTerm(u, 5, 0, cf); // a + 5 636 checkInverse(u, cf); n_Delete(&u, cf); 637 u = NULL; plusTerm(u, 1, 1, cf); plusTerm(u, 5, 0, cf); // a  5 638 checkInverse(u, cf); n_Delete(&u, cf); 639 u = NULL; plusTerm(u, 17, 1, cf); plusTerm(u, 5, 0, cf); // 17a + 5 640 checkInverse(u, cf); n_Delete(&u, cf); 641 642 rDelete(s); // kills 'cf' and 'r' as well 643 } 644 void test_Q_Ext_b() 645 { 646 clog << "Start by creating Q[b]..." << endl; 647 648 char* n[] = {"b"}; 649 ring r = rDefault( 0, 1, n); // Q[b] 650 TS_ASSERT_DIFFERS( r, NULLp ); 651 652 PrintRing(r); 653 654 TS_ASSERT( rField_is_Domain(r) ); 655 TS_ASSERT( rField_is_Q(r) ); 656 657 TS_ASSERT( !rField_is_Zp(r) ); 658 TS_ASSERT( !rField_is_Zp(r, 11) ); 659 660 TS_ASSERT_EQUALS( rVar(r), 1); 661 662 poly minPoly = p_ISet(1, r); // minPoly = 1 663 p_SetExp(minPoly, 1, 7, r); p_Setm(minPoly, r); // minPoly = b^7 664 minPoly = p_Add_q(minPoly, p_ISet(17, r), r); // minPoly = b^7 + 17 665 ideal minIdeal = idInit(1); // minIdeal = < 0 > 666 minIdeal>m[0] = minPoly; // minIdeal = < b^7 + 17 > 667 668 n_coeffType type = nRegister(n_Ext, naInitChar); 669 TS_ASSERT(type == n_Ext); 670 671 ExtInfo extParam; 672 extParam.r = r; 673 extParam.i = minIdeal; 674 675 clog << "Next create the extension field Q[b]/<b^7+17>..." << endl; 676 677 const coeffs cf = nInitChar(type, &extParam); // Q[b]/<b^7+17> 678 679 if( cf == NULL ) 680 TS_FAIL("Could not get needed coeff. domain"); 681 682 TS_ASSERT_DIFFERS( cf>cfCoeffWrite, NULLp ); 683 684 if( cf>cfCoeffWrite != NULL ) 685 { 686 clog << "Coeffdomain: " << endl; 687 n_CoeffWrite(cf); PrintLn(); 688 } 689 690 // some tests for the coefficient field represented by cf: 691 TestArithCf(cf); 692 TestSumCf(cf, 10); 693 TestSumCf(cf, 100); 694 TestSumCf(cf, 101); 695 TestSumCf(cf, 1001); 696 TestSumCf(cf, 9000); 697 698 clog << "Finally create the polynomial ring (Q[b]/<b^7+17>)[u, v, w]..." 699 << endl; 700 701 char* m[] = {"u", "v", "w"}; 702 ring s = rDefault(cf, 3, m); // (Q[b]/<b^7+17>)[u, v, w] 703 TS_ASSERT_DIFFERS(s, NULLp); 704 705 PrintRing(s); 706 707 TS_ASSERT( rField_is_Domain(s) ); 708 TS_ASSERT( !rField_is_Q(s) ); 709 TS_ASSERT( !rField_is_Zp(s) ); 710 TS_ASSERT( !rField_is_Zp(s, 11) ); 711 TS_ASSERT( !rField_is_Zp(s, 13) ); 712 TS_ASSERT( !rField_is_GF(s) ); 713 TS_ASSERT( rField_is_Extension(s) ); 714 TS_ASSERT( !rField_is_GF(s, 25) ); 715 TS_ASSERT_EQUALS(rVar(s), 3); 716 717 Test(s); 718 719 clog << endl 720 << "Now let's compute some inverses in Q[b]/<b^7+17>..." 606 721 << endl; 607 722 608 number a = n_Par(1, cf); 609 number n1 = n_Init(1, cf); 610 number n5 = n_Init(5, cf); 611 number n17 = n_Init(17, cf); 612 number u; number v; 613 614 u = n_Add(a, n1, cf); checkInverse(u, cf); n_Delete(&u, cf); // a + 1 615 u = n_Sub(a, n1, cf); checkInverse(u, cf); n_Delete(&u, cf); // a  1 616 u = n_Add(a, n5, cf); checkInverse(u, cf); n_Delete(&u, cf); // a + 5 617 u = n_Sub(a, n5, cf); checkInverse(u, cf); n_Delete(&u, cf); // a  5 618 v = n_Mult(a, n17, cf); 619 u = n_Add(v, n5, cf); n_Delete(&v, cf); // 17a + 5 620 checkInverse(u, cf); n_Delete(&u, cf); 621 622 n_Delete(&a, cf); n_Delete(&n1, cf); n_Delete(&n5, cf); 623 n_Delete(&n17, cf); 723 number u; 724 u = NULL; plusTerm(u, 1, 2, cf); plusTerm(u, 33, 0, cf); // b^2 + 33 725 checkInverse(u, cf); n_Delete(&u, cf); 726 u = NULL; plusTerm(u, 1, 5, cf); plusTerm(u, 137, 0, cf); // b^5  137 727 checkInverse(u, cf); n_Delete(&u, cf); 728 729 clog << endl 730 << "Now let's check a gcd computation in Q[b]..." 731 << endl; 732 733 number v; 734 v = NULL; plusTerm(v, 1, 2, cf); plusTerm(v, 7, 1, cf); 735 plusTerm(v, 1, 0, cf); // b^2 + 7b + 1 736 number w = n_Mult(v, v, cf); // (b^2 + 7b + 1)^2 737 number y = n_Mult(v, w, cf); // (b^2 + 7b + 1)^3 738 n_Delete(&v, cf); 739 v = NULL; plusTerm(v, 2, 2, cf); plusTerm(v, 61, 1, cf); // 2b^2  61b 740 number z = n_Mult(w, v, cf); // (b^2 + 7b + 1)^2 * (2b^2  61b) 741 n_Delete(&v, cf); 742 743 clog << "z = "; n_Write(z, cf); 744 clog << "y = "; n_Write(y, cf); 745 number theGcd = n_Gcd(z, y, cf); // should yield w = (b^2 + 7b + 1)^2 746 clog << "gcd(z, y) = "; n_Write(theGcd, cf); 747 748 v = n_Sub(theGcd, w, cf); 749 TS_ASSERT( v == NULL ); 750 n_Delete(&v, cf); 751 752 clog << endl 753 << "Now let's check an ext_gcd computation in Q[b]..." 754 << endl; 755 756 poly zFactor; poly yFactor; 757 poly ppp = p_ExtGcd((poly)z, zFactor, (poly)y, yFactor, cf>algring); 758 v = n_Sub(theGcd, (number)ppp, cf); 759 TS_ASSERT( v == NULL ); 760 clog << "z = "; n_Write(z, cf); 761 clog << "zFactor = "; p_Write(zFactor, cf>algring); 762 clog << "y = "; n_Write(y, cf); 763 clog << "yFactor = "; p_Write(yFactor, cf>algring); 764 number v1 = n_Mult(z, (number)zFactor, cf); 765 number v2 = n_Mult(y, (number)yFactor, cf); 766 number v3 = n_Add(v1, v2, cf); 767 clog << "z * zFactor + y * yFactor = "; n_Write(v3, cf); 768 clog << "gcd(z, y) = "; p_Write(ppp, cf>algring); 769 number v4 = n_Sub(v3, w, cf); 770 TS_ASSERT( v4 == NULL ); 771 772 p_Delete(&ppp, cf>algring); p_Delete(&zFactor, cf>algring); 773 p_Delete(&yFactor, cf>algring); 774 n_Delete(&z, cf); n_Delete(&y, cf); n_Delete(&w, cf); 775 n_Delete(&theGcd, cf); n_Delete(&v, cf); n_Delete(&v1, cf); 776 n_Delete(&v2, cf); n_Delete(&v3, cf); n_Delete(&v4, cf); 624 777 625 778 rDelete(s); // kills 'cf' and 'r' as well
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