AXIOM SESSIONscale=2.5]
N := PositiveInteger (1) PositiveInteger Type: Domain Time: 0 sec D := DoubleFloat (2) DoubleFloat Type: Domain Time: 0 sec F := Float (3) Float Type: Domain Time: 0 sec Q := Fraction Integer (4) Fraction Integer Type: Domain Time: 0 sec HilbertMatrixD(n:N): Matrix D == _ matrix([[1.0/(i + j) for i in 1..n] for j in 1..n]) Type: Void Time: 0.01 (IN) = 0.01 sec HilbertMatrixF(n:N): Matrix F == _ matrix([[1.0/(i + j) for i in 1..n] for j in 1..n]) Type: Void Time: 0.01 (IN) = 0.01 sec HilbertMatrixQ(n:N): Matrix Q == _ matrix([[1/(i + j) for i in 1..n] for j in 1..n]) Type: Void Time: 0 sec HilbertMatrixD(3) + 0.5 0.333333333333333 0.25 + | | (8) |0.333333333333333 0.25 0.2 | | | + 0.25 0.2 0.166666666666667+ Type: Matrix DoubleFloat Time: 0.04 (IN) + 0.03 (OT) + 0.01 (GC) = 0.08 sec HilbertMatrixQ(3) +1 1 1+ |- - -| |2 3 4| | | |1 1 1| (9) |- - -| |3 4 5| | | |1 1 1| |- - -| +4 5 6+ Type: Matrix Fraction Integer Time: 0.02 (OT) = 0.02 sec HilbertMatrixF(3) (10) + 0.5 0.3333333333 3333333333 0.25 + | | |0.3333333333 3333333333 0.25 0.2 | | | + 0.25 0.2 0.1666666666 6666666667+ Type: Matrix Float Time: 0.01 (IN) + 0.01 (OT) + 0.01 (GC) = 0.03 sec [determinant(HilbertMatrixD(5*n)) for n in 1..6] (11) [1.4878155287776663e-14, 1.1708847390332544e-58, - 7.329551900980472e-127, 1.8972182407450097e-202, - 1.7767073603611213e-280, 0.0] Type: List DoubleFloat Time: 0.43 (IN) + 0.14 (EV) + 0.06 (OT) = 0.63 sec [determinant(HilbertMatrixF(5*n)) for n in 1..6] (12) [0.1487815528 7758289063 E -13, 0.1171371536 8024357091 E -57, 0.8781685580 3800165504 E -132, 0.4005398450 3281293592 E -224, - 0.8672044362 0589913695 E -319, 0.1929750883 9978983829 E -417] Type: List Float Time: 0.48 (EV) + 0.10 (GC) = 0.58 sec [determinant(HilbertMatrixQ(5*n)) for n in 1..6] (13) 1 1 [--------------, ----------------------------------------------------------, 67212633600000 8537000898240926708833515201784986712482596782080000000000 1 / 146538740183666877481333971725269067959384123502368457086504025547136338_ 7281567173259185477862791557143607640064000000000000000000000 , 1 / 327723880133278729476665890222832025204546816520485699917379710978406689_ 52779223214483748651170263631423109857464822124939490164270836312516034_ 15239472195372333133701896827240771248538377176401848565760000000000000_ 00000000000000000000000 , 1 / 943443458848441228956693696279760730359903469457936499731851074111615233_ 14255514417225236246776078681522617448130111877369572484796897612065933_ 52237684747328030203084672090167556606865123046915733557035025165367211_ 81161075206120441411355364487536402146184314196057700767052024312362680_ 20442693962925170374671475057413324800000000000000000000000000000000000_ 000000000000000 , 1 / 347678097173631327706181116037484788665140455596751194236374423476934278_ 72336185915903600949727565688512425687551728790953230983654612947880686_ 64034084877513911919412368602956835751833985175217203858528427028478411_ 07420065708261775033449064671483311289619473162541454992338969245601369_ 24601181973306894033338133775362887249764402725843635016814711320344415_ 32672272163948431375908684874930724465894995883925403831087253290653960_ 68715359788388174845939833221273153240082092406289203200000000000000000_ 00000000000000000000000000000000000000 ] Type: List Fraction Integer Time: 0.31 (EV) + 0.01 (OT) = 0.32 sec h6F := HilbertMatrixF(6) (14) [ [0.5, 0.3333333333 3333333333, 0.25, 0.2, 0.1666666666 6666666667, 0.1428571428 5714285714] , [0.3333333333 3333333333, 0.25, 0.2, 0.1666666666 6666666667, 0.1428571428 5714285714, 0.125] , [0.25, 0.2, 0.1666666666 6666666667, 0.1428571428 5714285714, 0.125, 0.1111111111 1111111111] , [0.2, 0.1666666666 6666666667, 0.1428571428 5714285714, 0.125, 0.1111111111 1111111111, 0.1] , [0.1666666666 6666666667, 0.1428571428 5714285714, 0.125, 0.1111111111 1111111111, 0.1, 0.0909090909 0909090909 1] , [0.1428571428 5714285714, 0.125, 0.1111111111 1111111111, 0.1, 0.0909090909 0909090909 1, 0.0833333333 3333333333 3] ] Type: Matrix Float Time: 0.02 (OT) = 0.02 sec h6F * inverse(h6F) (15) [[1.0,- 0.4 E -14,0.1 E -13,- 0.4 E -13,0.2 E -13,- 0.5 E -14], [0.6 E -16,0.9999999999 99999,0.2 E -14,- 0.2 E -13,0.0,- 0.7 E -14], [0.6 E -16,- 0.2 E -14,1.0,- 0.2 E -13,0.7 E -14,- 0.4 E -14], [0.6 E -16,- 0.2 E -14,0.5 E -14,0.9999999999 9998,0.0,- 0.5 E -14], [0.7 E -16,- 0.1 E -14,0.0,- 0.2 E -13,1.0,- 0.4 E -14], [0.3 E -16,- 0.9 E -15,0.4 E -14,- 0.1 E -13,0.7 E -14,1.0]] Type: Matrix Float Time: 0.01 (EV) + 0.01 (OT) = 0.02 sec h6Q := HilbertMatrixQ(6) +1 1 1 1 1 1 + |- - - - - - | |2 3 4 5 6 7 | | | |1 1 1 1 1 1 | |- - - - - - | |3 4 5 6 7 8 | | | |1 1 1 1 1 1 | |- - - - - - | |4 5 6 7 8 9 | (16) | | |1 1 1 1 1 1| |- - - - - --| |5 6 7 8 9 10| | | |1 1 1 1 1 1| |- - - - -- --| |6 7 8 9 10 11| | | |1 1 1 1 1 1| |- - - -- -- --| +7 8 9 10 11 12+ Type: Matrix Fraction Integer Time: 0 sec h6Q * inverse(h6Q) +1 0 0 0 0 0+ | | |0 1 0 0 0 0| | | |0 0 1 0 0 0| (17) | | |0 0 0 1 0 0| | | |0 0 0 0 1 0| | | +0 0 0 0 0 1+ Type: Matrix Fraction Integer Time: 0.01 (IN) = 0.01 sec [determinant(HilbertMatrixF(5*n)) for n in 1..10]; Type: List Float Time: 3.02 (EV) + 0.29 (GC) = 3.31 sec [determinant(HilbertMatrixQ(5*n)) for n in 1..10]; Type: List Fraction Integer Time: 2.96 (EV) + 0.38 (GC) = 3.34 sec [determinant(HilbertMatrixF(5*n)) for n in 1..15]; Type: List Float Time: 0.01 (IN) + 14.09 (EV) + 1.59 (GC) = 15.69 sec [determinant(HilbertMatrixQ(5*n)) for n in 1..15]; Type: List Fraction Integer Time: 19.41 (EV) + 2.75 (GC) = 22.16 sec [determinant(HilbertMatrixF(5*n)) for n in 1..20]; Type: List Float Time: 42.99 (EV) + 5.07 (GC) = 48.06 sec [determinant(HilbertMatrixQ(5*n)) for n in 1..20]; Type: List Fraction Integer Time: 75.55 (EV) + 11.16 (GC) = 86.71 sec
Marc Moreno Maza