Rule: Q[2, 12, 99]

Type

This rule is of Hermite (probabilists') type.

Polynomials

One starts from the polynomial P1 and extends one by one with Pi until the final polynomial defining this rule is reached.
Note: Polynomials might be truncated due to size! The complete polynomials are included in the download.

Node locations in the complex plane

Plot of the node locations in the complex plane.

Magnitude of the Weights

Logarithmic magnitude of the weights
         plotted against the (real part) of the nodes.

Quadrature Rule Data

Nodes

Node (ball center) Error (ball radius)
-14.626599586834575113 + 5.8420080980986002347e-1471j 1.85e-485, 1.85e-485j
13.391972751363416293 - 1.4410574224133290208e-1494j 1.22e-484, 1.22e-484j
19.611042020521576664 - 6.1634578431261306835e-1520j 2.21e-493, 2.21e-493j
-16.979936213335332853 + 1.1025889147959206007e-1517j 2.53e-488, 2.53e-488j
-19.611042020521576664 - 1.0484658205964515709e-1532j 2.33e-493, 2.33e-493j
14.626599586834575113 + 1.6949136011310139169e-1522j 1.81e-485, 1.81e-485j
-15.061266805334031931 - 8.732577124102168312e-1537j 6.97e-486, 6.97e-486j
16.979936213335332853 + 2.5630237702828874078e-1537j 2.49e-488, 2.49e-488j
-5.8272369191325365786 - 3.4462840060765368835e-1561j 4.82e-490, 4.82e-490j
-3.8916542605235862319 + 1.2065241794715752227e-1564j 3.05e-494, 3.05e-494j
2.4101908978024808663 + 1.2813057614403233531e-1569j 5.76e-499, 5.76e-499j
15.977450860244809027 - 1.1377719610898519701e-1554j 6.94e-487, 6.94e-487j
-15.977450860244809027 + 9.3257053016716368988e-1564j 6.42e-487, 6.42e-487j
-10.779391473390169557 + 6.5596740595455835937e-1562j 2.02e-484, 2.02e-484j
18.797271467137639838 - 1.4011496381838849564e-1569j 1.42e-491, 1.42e-491j
14.204537466876811515 - 6.4456850236661174855e-1589j 4.1e-485, 4.1e-485j
15.061266805334031931 + 2.9396495141694841531e-1614j 7.6e-486, 7.6e-486j
-11.135794888377808613 - 2.8513142998139176253e-1625j 2.51e-484, 2.51e-484j
-17.528987894683609968 + 1.4862126492281248506e-1636j 3.21e-489, 3.21e-489j
13.793435536834285683 - 4.0815358108121618573e-1635j 7.91e-485, 7.91e-485j
17.528987894683609968 - 1.3443190875697425909e-1651j 3.32e-489, 3.32e-489j
3.6069468897368460303 - 5.2839518365985807965e-1659j 3.65e-495, 3.65e-495j
15.510634902093655085 + 1.8480295136186899916e-1649j 2.58e-486, 2.58e-486j
-18.126058272519349117 - 1.4376655208398262368e-1659j 2.69e-490, 2.69e-490j
8.7230493018822982651 - 3.913015819085119748e-1652j 8.41e-486, 8.41e-486j
-13.793435536834285683 + 4.668017932510882003e-1653j 7.74e-485, 7.74e-485j
0.87347331941638973596 + 1.50784222687363898e-1674j 3.13e-505, 3.13e-505j
-11.496983046461097868 + 3.4211893301335987823e-1653j 2.93e-484, 2.93e-484j
-12.613821247686598642 - 9.531440034338789641e-1653j 2.59e-484, 2.59e-484j
-1 - 3.1979708541386682684e-1680j 1.55e-504, 1.55e-504j
-3.0130273199142179863 + 6.4790359166311152818e-1673j 7.25e-497, 7.25e-497j
12.235474764490065242 - 7.1517331481557077351e-1659j 2.97e-484, 2.97e-484j
-2.1100064103431242732 + 1.9531310917644084759e-1687j 1.89e-500, 1.89e-500j
-14.204537466876811515 - 1.5419628379881276067e-1671j 4.05e-485, 4.05e-485j
-6.4548050912602207451 - 8.2230526511763790011e-1676j 6.21e-489, 6.21e-489j
-1.5112696370332255123 - 6.8258317444973756823e-1689j 7.07e-503, 7.07e-503j
-5.2111896351598078518 + 5.9097149133171716742e-1678j 3.2e-491, 3.2e-491j
1.8100151044187559318 - 6.7473280983739893495e-1689j 1.01e-501, 1.01e-501j
-10.427397309588947378 - 2.2766162659377913123e-1671j 1.49e-484, 1.49e-484j
10.779391473390169557 + 2.8874442505962944137e-1669j 1.94e-484, 1.94e-484j
3.8916542605235862319 - 4.6104980079922365605e-1692j 3.24e-494, 3.24e-494j
-9.7353385809009875156 + 1.252842943602788255e-1681j 5.51e-485, 5.51e-485j
-10.079478910732322594 + 7.7171585207543109258e-1681j 9.27e-485, 9.27e-485j
-12.235474764490065242 + 4.8245685892089292854e-1679j 2.99e-484, 2.99e-484j
9.7353385809009875156 - 2.355210324207551216e-1680j 5.6e-485, 5.6e-485j
-15.510634902093655085 + 3.7731651749239382553e-1690j 2.46e-486, 2.46e-486j
-13.391972751363416293 - 2.7643819838326298095e-1688j 1.33e-484, 1.33e-484j
11.496983046461097868 - 2.2615128568383557263e-1702j 3.05e-484, 3.05e-484j
1.2179344376195455601 - 4.0848770209486983517e-1744j 7.08e-504, 7.08e-504j
7.7366330006826615902 + 1.5262749412147162468e-1725j 5.37e-487, 5.37e-487j
16.465446676688631356 - 4.172664244549338218e-1761j 1.49e-487, 1.49e-487j
12.613821247686598642 + 8.4793181730747794454e-1806j 2.54e-484, 2.54e-484j
8.391608024500673957 - 7.3242093412392650652e-1833j 3.6e-486, 3.6e-486j
-18.797271467137639838 - 2.5358196381325580732e-1852j 1.3e-491, 1.3e-491j
3.3117163491408605153 + 5.1996483750358293139e-1859j 5.25e-496, 5.25e-496j
12.99906778637974334 + 1.0962050022926076039e-1845j 1.73e-484, 1.73e-484j
-2.6788642116343808239 + 1.9481576828006383503e-1868j 3.5e-497, 3.5e-497j
7.4128117858774348846 + 7.3057136779534839077e-1858j 1.87e-487, 1.87e-487j
10.079478910732322594 + 1.4490037917302497775e-1853j 9.43e-485, 9.43e-485j
2.7194004874651299638 - 1.7195341115406020937e-1871j 5.27e-497, 5.27e-497j
-8.391608024500673957 - 1.1674229237500179012e-1860j 3.66e-486, 3.66e-486j
-0.87347331941638973596 - 1.6399565887931341262e-1879j 3.17e-505, 3.17e-505j
9.3947094764029853626 - 8.3458884835277214365e-1858j 3.07e-485, 3.07e-485j
5.51735998467861026 + 1.8667018615748818068e-1872j 1.23e-490, 1.23e-490j
2.1100064103431242732 - 2.5975516627736637235e-1882j 1.85e-500, 1.85e-500j
18.126058272519349117 + 2.123317900986968866e-1866j 2.63e-490, 2.63e-490j
4.6254356317132469284 + 2.6448143944426755519e-1876j 2.53e-492, 2.53e-492j
-4.1474402231433696636 + 1.3952970856261929607e-1877j 2.24e-493, 2.24e-493j
-16.465446676688631356 + 3.8926438970213508196e-1871j 1.55e-487, 1.55e-487j
11.135794888377808613 - 1.4183615545905599323e-1866j 2.53e-484, 2.53e-484j
10.427397309588947378 - 1.1594441236906019935e-1883j 1.45e-484, 1.45e-484j
-4.911307173277277574 + 5.6246629342219591965e-1903j 8.71e-492, 8.71e-492j
9.0573517041303281953 + 1.2412282877767729676e-1894j 1.5e-485, 1.5e-485j
-4.6254356317132469284 + 6.4241542929509390121e-1908j 2.61e-492, 2.61e-492j
-7.4128117858774348846 - 2.6181752675406003298e-1902j 1.88e-487, 1.88e-487j
0.59480287177806697504 + 9.6793051232218769485e-1922j 4.75e-507, 4.75e-507j
-7.0912802697852635692 + 1.5659596193270873059e-1902j 6.62e-488, 6.62e-488j
-8.7230493018822982651 - 7.9546962154771830626e-1900j 7.59e-486, 7.59e-486j
-0.59480287177806697504 + 5.489540915543824116e-1922j 4.75e-507, 4.75e-507j
-12.99906778637974334 + 3.290174114152124171e-1898j 1.84e-484, 1.84e-484j
4.1474402231433696636 + 3.1177281295171326684e-1918j 1.99e-493, 1.99e-493j
2.6788642116343808239 - 2.2854011264715491999e-1921j 3.53e-497, 3.53e-497j
-6.7719577730876256554 - 2.7338239982106778584e-1912j 2.04e-488, 2.04e-488j
-11.863381287245301785 - 7.7265699735430592391e-1907j 3.19e-484, 3.19e-484j
-3.6069468897368460303 - 3.3007580186169414147e-1932j 3.94e-495, 3.94e-495j
6.7719577730876256554 + 6.4024777346128868866e-1921j 2.13e-488, 2.13e-488j
1.5112696370332255123 - 3.2657518841769884558e-1943j 7.07e-503, 7.07e-503j
-1.2179344376195455601 - 7.2291448506334704938e-1944j 7.02e-504, 7.02e-504j
5.2111896351598078518 + 2.4578501664020923804e-1931j 3.37e-491, 3.37e-491j
-9.0573517041303281953 + 1.0535878976714175125e-1923j 1.5e-485, 1.5e-485j
-1.8100151044187559318 - 9.892647041843889493e-1959j 1.1e-501, 1.1e-501j
1 + 5.5391261791542038345e-1961j 1.63e-504, 1.63e-504j
5.8272369191325365786 + 4.5928257395149867808e-1941j 5.1e-490, 5.1e-490j
11.863381287245301785 + 5.3031239351044617337e-1940j 2.91e-484, 2.91e-484j
-8.0628539455744387152 + 1.1103232248488425652e-1955j 1.43e-486, 1.43e-486j
-6.1398492581121750839 - 1.3378786197850577338e-1958j 1.75e-489, 1.75e-489j
3.0130273199142179863 + 5.6904495783045768057e-1966j 7.24e-497, 7.24e-497j
6.1398492581121750839 - 7.1026946960688010785e-1959j 1.77e-489, 1.77e-489j
-0.2983537964726121739 - 2.896240728801135708e-1977j 1.55e-508, 1.55e-508j
-2.7194004874651299638 + 2.6063014660390587487e-1966j 5.01e-497, 5.01e-497j
-3.3117163491408605153 - 3.3340625065619237268e-1965j 4.69e-496, 4.69e-496j
-2.6190026620577062328e-2062 - 1.7898866073883584361e-2062j 3.58e-2060, 3.58e-2060j
4.911307173277277574 + 9.0940703912128546168e-1961j 8.59e-492, 8.59e-492j
4.3728152787336414322 + 1.7894678678509634666e-1962j 7.99e-493, 7.99e-493j
-9.3947094764029853626 + 1.5289643596789463856e-1952j 3.01e-485, 3.01e-485j
-5.51735998467861026 - 1.1644099478731501903e-1961j 1.23e-490, 1.23e-490j
-4.3728152787336414322 + 1.7496523342629719763e-1963j 7.78e-493, 7.78e-493j
8.0628539455744387152 + 1.5138331490082292049e-1954j 1.35e-486, 1.35e-486j
0.2983537964726121739 - 6.9526908681337104537e-1982j 1.37e-508, 1.37e-508j
6.4548050912602207451 - 4.2473265258973259798e-1963j 6.14e-489, 6.14e-489j
7.0912802697852635692 + 1.0529796136482706277e-1960j 6.35e-488, 6.35e-488j
-2.4101908978024808663 + 1.9810990490478088353e-1972j 5.65e-499, 5.65e-499j
-7.7366330006826615902 + 4.4009284185628514256e-1958j 5.43e-487, 5.43e-487j

Weights

Weight (ball center) Error (ball radius)
5.977138124863732536e-48 + 2.7183511418732130475e-1517j 1.39e-106, 2.92e-345j
1.8007990987902722621e-40 - 1.2574090779994269274e-1515j 7.36e-103, 1.54e-341j
1.152572390921136427e-84 - 5.9317520831049539876e-1539j 1.63e-121, 3.41e-360j
5.2211033761108997522e-64 + 4.9590073891841617753e-1527j 1.56e-114, 3.27e-353j
1.152572390921136427e-84 + 4.074461780368285433e-1538j 7.3e-122, 1.53e-360j
5.977138124863732536e-48 + 1.1936639518161826911e-1519j 4.88e-108, 1.02e-346j
9.7252177995998663251e-51 + 2.647890221202899332e-1519j 6.73e-109, 1.41e-347j
5.2211033761108997522e-64 - 3.6923419237840831865e-1528j 1.14e-115, 2.39e-354j
5.2546660540474275415e-09 - 1.0511494960078113488e-1496j 1.58e-68, 3.31e-307j
5.6327580430773746082e-05 + 3.026967822418269169e-1493j 1.45e-50, 3.05e-289j
0.0065511193994139872287 + 1.0935169930605673729e-1491j 2.55e-30, 5.36e-269j
7.0148567320418322051e-57 - 2.125988910400605775e-1524j 7.84e-113, 1.65e-351j
7.0148567320418322051e-57 + 4.8165089040170389575e-1523j 1.09e-112, 2.3e-351j
8.2908755097844773048e-27 + 2.8065518115771547519e-1507j 6.58e-97, 1.38e-335j
5.4247187912902739973e-78 + 1.7657572800230571256e-1535j 2.67e-121, 5.61e-360j
2.5515245120269167678e-45 - 3.0624834881059832504e-1518j 5.17e-108, 1.08e-346j
9.7252177995998663251e-51 - 3.8768399929399650834e-1521j 1.38e-110, 2.9e-349j
1.6909543591594501963e-28 - 3.5187981953843873449e-1508j 6.48e-101, 1.36e-339j
4.3157555321024234765e-68 - 2.9357443794241012517e-1529j 4.13e-120, 8.66e-359j
7.8584890146934420856e-43 + 6.6776330658171557471e-1517j 1.52e-107, 3.2e-346j
4.3157555321024234765e-68 + 2.6498256847496227398e-1530j 3.63e-119, 7.62e-358j
0.00017415074878258403594 - 3.4886796142149905657e-1493j 3.42e-60, 7.19e-299j
1.0474309195328699659e-53 + 1.0234056905667165945e-1522j 2.79e-112, 5.85e-351j
1.1331635445894332387e-72 + 9.9042430991237665152e-1532j 9.89e-124, 2.08e-362j
3.9816996386826311319e-18 + 4.5571010964888094279e-1503j 1.07e-95, 2.24e-334j
7.8584890146934420856e-43 + 2.2778055086921983429e-1515j 2.64e-112, 5.54e-351j
0.064465161965901055518 + 1.2705767959304667538e-1490j 2.89e-39, 6.06e-278j
2.8775159521723216479e-30 + 4.0984504360442891223e-1509j 8.01e-106, 1.68e-344j
4.291813962361794855e-36 - 4.0885291003040698106e-1512j 8.98e-110, 1.89e-348j
0.024315621777564023614 - 1.5458133297626610238e-1490j 1.62e-39, 3.39e-278j
0.0012752832013586843945 - 4.2207387476251301032e-1492j 1.76e-60, 3.7e-299j
4.6414393827101190727e-34 + 3.9345992079159536262e-1512j 5.49e-110, 1.15e-348j
0.012930783488577142642 - 1.3442287778824460201e-1491j 1.53e-48, 3.21e-287j
2.5515245120269167678e-45 - 2.0919878140011122565e-1516j 2.25e-113, 4.73e-352j
1.1307198771544756299e-10 - 6.9035540192031445844e-1498j 1.98e-88, 4.15e-327j
0.037877302437174253753 - 2.8173655835317730811e-1491j 1.27e-39, 2.67e-278j
1.5359841820187303362e-07 - 1.5702210388119457432e-1495j 5.72e-81, 1.2e-319j
0.023229387168099414623 + 1.3436443593193814422e-1491j 5.57e-48, 1.17e-286j
3.422203482315907211e-25 - 2.0851257714972403474e-1506j 7.72e-104, 1.62e-342j
8.2908755097844773048e-27 + 4.2499380853541909455e-1508j 8.29e-110, 1.74e-348j
5.6327580430773746082e-05 + 1.7547191190922374555e-1493j 1.27e-75, 2.67e-314j
3.5879520923767196466e-22 - 9.4104838254827513253e-1505j 4.8e-103, 1.01e-341j
1.1986595205801535673e-23 + 1.4471743803004370431e-1505j 1.48e-103, 3.11e-342j
4.6414393827101190727e-34 + 4.4201580560763173315e-1511j 2.12e-110, 4.45e-349j
3.5879520923767196466e-22 - 1.8893871360166462765e-1505j 6e-110, 1.26e-348j
1.0474309195328699659e-53 - 3.4888444773129641763e-1521j 1.73e-120, 3.62e-359j
1.8007990987902722621e-40 - 2.8535591644732870447e-1514j 5.31e-114, 1.11e-352j
2.8775159521723216479e-30 + 4.909961414785830495e-1510j 3.86e-115, 8.11e-354j
0.054108929681399088604 + 5.61146720407382953e-1491j 2.67e-50, 5.61e-289j
1.304186683098907885e-14 - 6.5824742682885868839e-1501j 2.76e-105, 5.79e-344j
2.6856289078390043406e-60 + 3.3278128971338377193e-1526j 1.46e-127, 3.07e-366j
4.291813962361794855e-36 - 3.0209896029357172897e-1513j 1.05e-117, 2.21e-356j
6.7329672313234469307e-17 - 2.5193762717372228653e-1502j 4.38e-108, 9.19e-347j
5.4247187912902739973e-78 - 1.4150823976067557317e-1534j 1.05e-136, 2.21e-375j
0.00049318913150143758233 + 8.4121263893300986019e-1493j 1.46e-83, 3.06e-322j
3.1489842530170298407e-38 + 2.0719428704926237133e-1514j 1.46e-118, 3.07e-357j
0.00064116180192205658516 - 6.3076378010158805646e-1491j 2.35e-79, 4.93e-318j
1.5047441242262853947e-13 + 3.1336670652415930065e-1500j 3.88e-106, 8.14e-345j
1.1986595205801535673e-23 + 2.6635050751731561225e-1506j 3.64e-113, 7.65e-352j
0.0024256042514334116113 + 3.9420028995795982479e-1491j 3.51e-82, 7.36e-321j
6.7329672313234469307e-17 - 9.3009790781836439701e-1502j 7.33e-112, 1.54e-350j
0.064465161965901055518 + 1.4319677276990538474e-1490j 6.42e-62, 1.35e-300j
9.2366476221170600273e-21 + 1.252401622372117177e-1504j 1.3e-111, 2.73e-350j
3.0171567626770179889e-08 + 1.8295625663524379405e-1496j 7.01e-102, 1.47e-340j
0.012930783488577142642 - 1.0052913208164248032e-1491j 1.77e-78, 3.71e-317j
1.1331635445894332387e-72 - 1.0582191432279028661e-1532j 4.33e-137, 9.09e-376j
2.4651902085645104207e-06 - 1.2878810667497539105e-1494j 9.96e-98, 2.09e-336j
1.720162335736315155e-05 - 1.7177775541243634296e-1493j 3.58e-97, 7.51e-336j
2.6856289078390043406e-60 - 5.6268143841283975371e-1525j 6.41e-133, 1.35e-371j
1.6909543591594501963e-28 - 4.7679718922042266525e-1509j 2.56e-116, 5.38e-355j
3.422203482315907211e-25 - 3.4947976261882049633e-1507j 1.55e-114, 3.26e-353j
6.8054288890002637769e-07 + 6.2317700216310724484e-1495j 5.09e-103, 1.07e-341j
2.0567287472604459071e-19 - 7.7865743467726053246e-1504j 5.96e-112, 1.25e-350j
2.4651902085645104207e-06 - 2.4791446041308709451e-1494j 6.5e-102, 1.36e-340j
1.5047441242262853947e-13 + 9.5739131038502485121e-1500j 4.33e-114, 9.09e-353j
0.098200377400454711697 - 5.5240631560778229913e-1491j 3.33e-79, 6.99e-318j
1.5385201021744668613e-12 - 4.1223060334429815988e-1499j 4.67e-113, 9.8e-352j
3.9816996386826311319e-18 + 1.8024189753176726837e-1502j 7.98e-118, 1.68e-356j
0.098200377400454711697 - 5.9923893007393720173e-1491j 4.81e-82, 1.01e-320j
3.1489842530170298407e-38 + 3.5169085200385072416e-1513j 4.65e-127, 9.76e-366j
1.720162335736315155e-05 - 9.58816798261708087e-1494j 3.53e-104, 7.41e-343j
0.00064116180192205658516 - 4.3548088723178170176e-1491j 1.15e-95, 2.42e-334j
1.3976994816955684958e-11 + 1.7128939083987753938e-1498j 6.31e-113, 1.33e-351j
4.0444678875990994771e-32 - 4.4242989094518418415e-1510j 2.79e-124, 5.85e-363j
0.00017415074878258403594 - 5.7725051447773539934e-1493j 3.39e-103, 7.11e-342j
1.3976994816955684958e-11 + 6.2874183007402391975e-1499j 2.26e-115, 4.74e-354j
0.037877302437174253753 - 2.2896876102195705053e-1491j 3.11e-93, 6.52e-332j
0.054108929681399088604 + 6.6308675809732829186e-1491j 4.72e-92, 9.9e-331j
1.5359841820187303362e-07 - 7.4525818526026030077e-1496j 9.24e-111, 1.94e-349j
2.0567287472604459071e-19 - 3.3113420597628773347e-1503j 7.55e-120, 1.59e-358j
0.023229387168099414623 + 1.7231552326993894352e-1491j 9.84e-98, 2.07e-336j
0.024315621777564023614 - 1.3479694775320055187e-1490j 8.63e-93, 1.81e-331j
5.2546660540474275415e-09 - 4.5221079334659567962e-1497j 3.12e-113, 6.55e-352j
4.0444678875990994771e-32 - 4.6150670200794691047e-1511j 7.82e-126, 1.64e-364j
9.9865322762021011802e-16 + 4.5640392105229992594e-1501j 3.85e-118, 8.08e-357j
8.1589158642126323778e-10 + 2.7157437997829049857e-1497j 1.8e-113, 3.78e-352j
0.0012752832013586843945 - 2.7788487094691042656e-1492j 2.09e-104, 4.39e-343j
8.1589158642126323778e-10 + 1.1098594544315546606e-1497j 8.34e-115, 1.75e-353j
0.11367557067125949528 + 4.2091724218995513445e-1491j 1.58e-98, 3.32e-337j
0.0024256042514334116113 + 5.7425748925806046625e-1491j 6.67e-105, 1.4e-343j
0.00049318913150143758233 + 1.3336362178485640911e-1492j 3.23e-107, 6.78e-346j
0.11910602226117142873 - 3.7697522231887965e-1491j 3.92e-100, 8.23e-339j
6.8054288890002637769e-07 + 3.0987694207749176735e-1495j 1.74e-111, 3.66e-350j
6.4808383917788296621e-06 + 4.3366948567238561975e-1494j 8.29e-110, 1.74e-348j
9.2366476221170600273e-21 + 5.7501831665610122901e-1504j 5.73e-122, 1.2e-360j
3.0171567626770179889e-08 + 4.0458519020001082263e-1496j 1.11e-113, 2.33e-352j
6.4808383917788296621e-06 + 8.0355371492627465231e-1494j 5.98e-111, 1.26e-349j
9.9865322762021011802e-16 + 1.32031352944753081e-1501j 1.85e-120, 3.88e-359j
0.11367557067125949528 + 4.040887464509181812e-1491j 8.94e-107, 1.88e-345j
1.1307198771544756299e-10 - 2.6760277882547078371e-1498j 1.53e-117, 3.21e-356j
1.5385201021744668613e-12 - 1.4302911927714494455e-1499j 6.82e-119, 1.43e-357j
0.0065511193994139872287 + 1.5249997258923772795e-1491j 4.86e-111, 9.61e-350j
1.304186683098907885e-14 - 2.1365183883322731671e-1500j 9.76e-121, 2.13e-359j

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All rules of Hermite (probabilists') type can be downloaded here packed into a single file.