Rule: Q[14, 99]

Type

This rule is of Hermite (physicists') 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.

Warning: This rule has negative weights!

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)
13.842090202327185366 - 3.1591947545446249162e-1117j 1.4e-493, 1.4e-493j
10.012755633762677643 - 9.7324010874391565944e-1125j 2.58e-485, 2.58e-485j
11.614377383248514304 + 3.9310243454733909995e-1151j 8.93e-488, 8.93e-488j
-10.012755633762677643 + 1.7474544618579694255e-1164j 2.51e-485, 2.51e-485j
-11.614377383248514304 + 9.4992133506124201868e-1180j 9.12e-488, 9.12e-488j
10.619704089348928144 + 1.5890049200663184827e-1213j 4.3e-486, 4.3e-486j
-12.367656592908240709 + 1.2090392120698058668e-1262j 1.99e-489, 1.99e-489j
-2.0951832585077168157 - 9.5717196711259662631e-1325j 1.61e-497, 1.61e-497j
9.7214934097341793157 + 6.7461448487720180143e-1327j 4.66e-485, 4.66e-485j
8.885692228571370376 + 1.6700161672441156487e-1389j 1.54e-484, 1.54e-484j
1.8875584838191536265 - 1.2777339341760470254e-1427j 1.13e-498, 1.13e-498j
-9.4370502681164181405 + 4.5929379575413975615e-1412j 7.97e-485, 7.97e-485j
-3.6606511362256702828 + 1.7354443495507455659e-1433j 5.49e-491, 5.49e-491j
12.367656592908240709 + 3.5414563053493547539e-1432j 2.15e-489, 2.15e-489j
-13.842090202327185366 - 1.1411586312497811721e-1453j 1.49e-493, 1.49e-493j
8.0943230723222076136 - 3.0362363211319896277e-1456j 1.83e-484, 1.83e-484j
4.3044485704736318126 + 1.3179142323483622975e-1481j 1.89e-489, 1.89e-489j
-9.7214934097341793157 + 2.1312993109835714226e-1475j 4.75e-485, 4.75e-485j
-10.619704089348928144 - 2.1006442078248526342e-1480j 4.62e-486, 4.62e-486j
9.1586617163275117536 - 6.7489124837840451086e-1483j 1.15e-484, 1.15e-484j
5.8944851889589975893 - 1.4643707346967442407e-1506j 2.54e-486, 2.54e-486j
10.311771282361820662 - 2.9608853754682886136e-1505j 1.16e-485, 1.16e-485j
8.6176063224117958508 + 5.63586574322890754e-1523j 1.75e-484, 1.75e-484j
11.26871433779381976 + 8.3452745454728403831e-1536j 4.01e-487, 4.01e-487j
6.846136967418123739 - 1.2566761182872470389e-1541j 3.76e-485, 3.76e-485j
-11.26871433779381976 + 1.1172130527119025415e-1549j 4.09e-487, 4.09e-487j
-11.978787623347657688 + 1.7385703005023304443e-1550j 1.51e-488, 1.51e-488j
6.6048388815194087144 + 1.3052084577323630548e-1545j 2.19e-485, 2.19e-485j
-2.6838910495866464404 - 8.7833056017628155066e-1562j 1.07e-493, 1.07e-493j
-12.790510397093544632 - 3.6018438072593394587e-1558j 1.7e-490, 1.7e-490j
-10.311771282361820662 - 3.3385256254944931036e-1553j 1.15e-485, 1.15e-485j
-6.846136967418123739 + 3.3383296177652443634e-1552j 3.75e-485, 3.75e-485j
1.4766827311411408706 - 6.4717277179064185155e-1569j 5.46e-501, 5.46e-501j
-6.6048388815194087144 + 6.0504637047427225521e-1553j 2.28e-485, 2.28e-485j
5.2020138590042455326 - 2.1362435086293213818e-1555j 1.61e-487, 1.61e-487j
-5.2020138590042455326 - 9.4139264194312134407e-1555j 1.6e-487, 1.6e-487j
-8.885692228571370376 - 6.8562671263034471376e-1551j 1.48e-484, 1.48e-484j
-10.938037072391108695 - 1.3960385907290968498e-1554j 1.41e-486, 1.41e-486j
9.4370502681164181405 + 1.2805313648154490253e-1551j 8.06e-485, 8.06e-485j
-6.3658901062773421703 + 8.8647604361833378783e-1562j 1.15e-485, 1.15e-485j
13.265843323690522794 - 2.2386273484698266512e-1567j 8.25e-492, 8.25e-492j
-5.4309944274647258725 - 5.0654675672824066673e-1563j 4.72e-487, 4.72e-487j
12.790510397093544632 - 3.3703231567801485919e-1566j 1.72e-490, 1.72e-490j
3.870131950073084201 + 1.425641575200782519e-1566j 1.68e-490, 1.68e-490j
5.6617967204614986219 + 1.3426228791582387482e-1561j 1.14e-486, 1.14e-486j
-1.2746731195700282242 - 9.9493277586566334377e-1580j 4.18e-502, 4.18e-502j
-1.6811634726406030805 + 8.026842953947867591e-1576j 7.96e-500, 7.96e-500j
7.8383916789566452895 + 6.3721070429067509441e-1559j 1.56e-484, 1.56e-484j
11.978787623347657688 - 3.3679253359962614557e-1564j 1.52e-488, 1.52e-488j
2.7484707249854025686 - 4.3431907985616789543e-1573j 2.27e-493, 2.27e-493j
3.1119553299045111977 - 3.8466584028658931591e-1571j 1.82e-492, 1.82e-492j
-2.5089155621010687797 - 2.235309125537239806e-1574j 5.32e-495, 5.32e-495j
-4.3044485704736318126 + 6.4421207266012467944e-1568j 1.91e-489, 1.91e-489j
3.6606511362256702828 + 5.5244650866161671974e-1570j 6.04e-491, 6.04e-491j
2.6838910495866464404 - 3.1857328477230969244e-1572j 1.16e-493, 1.16e-493j
-1.4766827311411408706 - 7.3645738551038672042e-1580j 5.62e-501, 5.62e-501j
-7.0899466357911967841 - 5.8369805037035170882e-1562j 6.09e-485, 6.09e-485j
-7.5858550585666561357 + 1.9559425390627600692e-1561j 1.29e-484, 1.29e-484j
-8.6176063224117958508 + 7.1402983749814230045e-1562j 1.95e-484, 1.95e-484j
6.1291472957232186171 - 8.1901412011205635669e-1564j 5.65e-486, 5.65e-486j
-4.5258979843894408853 + 3.1056192391490168241e-1568j 6.19e-489, 6.19e-489j
4.7494225404674750504 - 2.3878426460272473411e-1566j 1.96e-488, 1.96e-488j
-0.68349898402767068481 + 3.8329591267904072806e-1585j 1.13e-505, 1.13e-505j
-1.8875584838191536265 - 1.0024545945847200733e-1576j 1.15e-498, 1.15e-498j
4.9748204085583761838 + 8.9740225512355886984e-1566j 5.74e-488, 5.74e-488j
4.5258979843894408853 + 4.7616959526384175372e-1568j 5.89e-489, 5.89e-489j
10.938037072391108695 - 1.3680040554440205386e-1562j 1.54e-486, 1.54e-486j
-0.29174551067256207845 + 3.2104329253401584585e-1588j 3.04e-508, 3.04e-508j
0.87871378732939941611 - 2.7887268232239835443e-1584j 1.94e-504, 1.94e-504j
2.0951832585077168157 - 1.7564074472184150016e-1578j 1.75e-497, 1.75e-497j
4.0855243968476380337 - 2.007199694584739162e-1569j 5.58e-490, 5.58e-490j
-4.0855243968476380337 + 2.5632590691498038024e-1570j 6.16e-490, 6.16e-490j
-4.9748204085583761838 - 7.9076409134370159106e-1568j 5.82e-488, 5.82e-488j
-3.2834247703582644075 - 3.9522891537040947375e-1572j 6.74e-492, 6.74e-492j
-8.0943230723222076136 - 9.681889652337894234e-1566j 1.82e-484, 1.82e-484j
7.3364507260452729996 + 4.3929240846185175716e-1563j 9.69e-485, 9.69e-485j
7.0899466357911967841 - 2.5113677468200184769e-1565j 6.3e-485, 6.3e-485j
-13.265843323690522794 + 3.7671039011655594915e-1573j 8.32e-492, 8.32e-492j
-3.4626569336022705502 + 3.8839806225365649718e-1574j 1.88e-491, 1.88e-491j
-4.7494225404674750504 + 1.3763376884763658762e-1570j 1.93e-488, 1.93e-488j
1.0754352358656331622 + 8.0555740738325088519e-1586j 3e-503, 3e-503j
3.4626569336022705502 + 1.1249275092503487356e-1573j 2e-491, 2e-491j
7.5858550585666561357 - 2.6721833372094872458e-1564j 1.26e-484, 1.26e-484j
-3.1119553299045111977 + 1.7904349268755982351e-1589j 1.76e-492, 1.76e-492j
-5.8944851889589975893 - 1.2157970932057375684e-1582j 2.54e-486, 2.54e-486j
8.3539475749363128959 + 1.4324784558989257003e-1579j 1.99e-484, 1.99e-484j
2.9269973666858036758 + 4.5152892366142534508e-1605j 4.91e-493, 4.91e-493j
3.2834247703582644075 - 1.0974080601665275119e-1604j 6.3e-492, 6.3e-492j
-6.1291472957232186171 + 9.909373612417485862e-1599j 5.63e-486, 5.63e-486j
0.68349898402767068481 + 8.2989056881393877065e-1623j 1.15e-505, 1.15e-505j
-3.870131950073084201 - 4.4623960718301584846e-1604j 1.73e-490, 1.73e-490j
2.3030809132678924574 + 2.0244159453727234008e-1608j 2.67e-496, 2.67e-496j
1.2746731195700282242 + 6.5822041186729409235e-1616j 3.97e-502, 3.97e-502j
-8.3539475749363128959 - 6.9217842297884736879e-1596j 2.02e-484, 2.02e-484j
-0.87871378732939941611 - 1.5372833322404646395e-1616j 1.77e-504, 1.77e-504j
-6.3721973699114690377e-1683 - 6.5330850356882989568e-1683j 1.03e-1680, 1.03e-1680j
6.3658901062773421703 + 8.6844932870248360621e-1597j 1.15e-485, 1.15e-485j
0.48831969227098406376 - 3.1273683407133730193e-1621j 6.1e-507, 6.1e-507j
2.5089155621010687797 - 9.8642004901687185668e-1610j 5.02e-495, 5.02e-495j
-5.6617967204614986219 - 2.8309996271566235819e-1601j 1.2e-486, 1.2e-486j
-2.7484707249854025686 - 1.3309431016896937521e-1609j 2.19e-493, 2.19e-493j
-9.1586617163275117536 - 1.0319942158521931029e-1598j 1.12e-484, 1.12e-484j
0.29174551067256207845 - 1.189894309881640539e-1623j 3.04e-508, 3.04e-508j
1.6811634726406030805 + 7.3247607553605070319e-1615j 8.89e-500, 8.89e-500j
-1.0754352358656331622 - 3.1827862021840581604e-1618j 2.89e-503, 2.89e-503j
-0.08892855796166572972 - 6.3666193986643757125e-1675j 1.42e-509, 1.42e-509j
-2.9269973666858036758 - 2.1507345046361351785e-1608j 4.97e-493, 4.97e-493j
-7.8383916789566452895 + 4.5871828688425623419e-1600j 1.62e-484, 1.62e-484j
0.08892855796166572972 - 3.6217922838961208632e-1626j 1.42e-509, 1.42e-509j
5.4309944274647258725 - 3.2018616917558395867e-1604j 4.8e-487, 4.8e-487j
-2.3030809132678924574 - 2.7682660240144575991e-1613j 2.64e-496, 2.64e-496j
-0.48831969227098406376 + 3.9709773638743722624e-1624j 6.53e-507, 6.53e-507j
-7.3364507260452729996 - 1.7405909430199817321e-1600j 9.24e-485, 9.24e-485j

Weights

Weight (ball center) Error (ball radius)
2.3080737195164811589e-84 - 2.5330756329777391631e-1190j 6.22e-130, 4.1e-370j
4.796062656710809024e-45 + 5.0179586273916651242e-1168j 1.3e-114, 8.57e-355j
5.2138868744280780896e-60 + 3.2387045834234692135e-1177j 1.12e-121, 7.4e-362j
4.796062656710809024e-45 + 2.3308870766055243168e-1170j 4.35e-117, 2.87e-357j
5.2138868744280780896e-60 - 2.3984592395818673668e-1178j 2.2e-124, 1.45e-364j
1.852902853488893757e-50 - 9.8013580869190795344e-1172j 3.45e-118, 2.27e-358j
8.4794568412296386686e-68 - 1.8728078733426272757e-1182j 9.58e-128, 6.32e-368j
0.0014552985971929251904 - 9.6361180340693140121e-1145j 3.49e-47, 2.3e-287j
1.4666517364608438459e-42 - 3.4864979876550739728e-1167j 2.5e-114, 1.65e-354j
7.8262841867376479416e-36 + 4.0681867411947352872e-1164j 2.16e-111, 1.42e-351j
0.0033139241969109383145 + 2.0029088750948166463e-1144j 3.53e-45, 2.33e-285j
3.3360535569346458444e-40 + 9.8167780246206928255e-1168j 2.04e-116, 1.34e-356j
1.7521659600776676067e-07 + 1.6418681297817647192e-1147j 6.24e-76, 4.11e-316j
8.4794568412296386686e-68 + 1.7798715509971386256e-1181j 3.7e-127, 2.44e-367j
2.3080737195164811589e-84 + 4.0662572950054214567e-1191j 2.31e-135, 1.53e-375j
5.1103065010152186148e-30 - 3.9093248075148892879e-1161j 5.32e-109, 3.51e-349j
1.1160841473917305735e-09 - 4.4144237380715904e-1149j 2.21e-84, 1.46e-324j
1.4666517364608438459e-42 - 5.1458008648968226499e-1169j 9.62e-118, 6.34e-358j
1.852902853488893757e-50 + 2.883281602573907818e-1173j 4.26e-122, 2.81e-362j
5.7887419814309013978e-38 - 3.6811984063887171038e-1165j 1.45e-113, 9.58e-354j
1.0726673806520303573e-16 + 1.0335932986370423525e-1153j 2.79e-99, 1.84e-339j
1.1312620464964211865e-47 + 6.1027347216297692284e-1170j 1.55e-118, 1.02e-358j
8.3928979070668208851e-34 - 4.2851068458161871557e-1163j 6.98e-112, 4.61e-352j
1.3535722780922790341e-56 - 2.6227260433602308525e-1175j 1.01e-123, 6.64e-364j
6.0391665213931325686e-22 + 9.4484404897970135933e-1157j 8.81e-106, 5.81e-346j
1.3535722780922790341e-56 + 1.547842140079194123e-1176j 4.53e-129, 2.99e-369j
1.0197315989009166488e-63 + 2.6350757754556791964e-1180j 3.92e-132, 2.58e-372j
1.5353097905767742644e-20 - 5.8922684662678010665e-1156j 2e-106, 1.32e-346j
4.0617677249898780538e-05 + 1.5524700959226089232e-1144j 1.21e-78, 7.98e-319j
2.2397998941499924278e-72 + 7.406953975068677555e-1185j 2.57e-136, 1.7e-376j
1.1312620464964211865e-47 - 8.9783796127703314021e-1172j 1.24e-125, 8.18e-366j
6.0391665213931325686e-22 + 1.7747077895746724924e-1157j 4.21e-115, 2.78e-355j
0.012959731877032056973 + 4.3695201039918861393e-1144j 5.09e-62, 3.35e-302j
1.5353097905767742644e-20 - 1.2083794917786585236e-1156j 5.53e-114, 3.65e-354j
2.2756206617118080247e-13 - 1.1983667943831059076e-1151j 2.48e-104, 1.64e-344j
2.2756206617118080247e-13 - 3.7891032144610120804e-1152j 5.75e-107, 3.79e-347j
7.8262841867376479416e-36 + 2.4261804116963104828e-1165j 1.37e-123, 9.05e-364j
2.0085012299433975188e-53 - 7.529205598004271246e-1175j 3.69e-129, 2.43e-369j
3.3360535569346458444e-40 + 3.316530269704174738e-1166j 6.2e-123, 4.09e-363j
3.3735586855319304803e-19 + 7.7353561340197185068e-1156j 7.29e-114, 4.81e-354j
1.0789181906906783111e-77 + 8.7565434731267690068e-1187j 1.88e-142, 1.24e-382j
2.009609714406361814e-14 + 7.5856467890104013714e-1153j 1.9e-110, 1.25e-350j
2.2397998941499924278e-72 - 6.080549089395605259e-1184j 3.83e-140, 2.52e-380j
3.7585238106132193642e-08 - 8.0988185577909774217e-1148j 6.18e-102, 4.08e-342j
1.5656452450421410884e-15 - 5.2510182018626356131e-1153j 2.08e-111, 1.37e-351j
0.022294728375722759631 - 5.1639692670845455222e-1144j 5.26e-72, 3.47e-312j
0.0068686945535902158675 - 2.070962514629311174e-1144j 1.25e-79, 8.24e-320j
2.9741264154062869747e-28 + 3.3640092513111994324e-1160j 2.19e-120, 1.44e-360j
1.0197315989009166488e-63 - 2.9475300100838808375e-1179j 2.25e-136, 1.49e-376j
3.6922411038802001862e-05 - 2.2327936347256794869e-1144j 6.85e-95, 4.52e-335j
6.2104821882771174831e-06 - 1.4463550078232383672e-1145j 2.63e-98, 1.73e-338j
0.00021095733276972897172 - 8.2493884683565239659e-1145j 6.93e-94, 4.57e-334j
1.1160841473917305735e-09 - 1.7600423829231190626e-1149j 1.07e-109, 7.08e-350j
1.7521659600776676067e-07 + 3.534250862822608308e-1147j 1.62e-102, 1.07e-342j
4.0617677249898780538e-05 + 2.6895249691114831181e-1144j 1.18e-94, 7.76e-335j
0.012959731877032056973 + 3.2463329340010046537e-1144j 8.12e-82, 5.36e-322j
2.0416538871579113065e-23 - 2.4406290857856353886e-1158j 9.01e-124, 5.94e-364j
1.4434945531667003338e-26 - 3.7256690005856078061e-1160j 1e-126, 6.62e-367j
8.3928979070668208851e-34 - 3.208935971879671904e-1164j 2.44e-130, 1.61e-370j
6.4395127961903042318e-18 - 1.9426131739984915868e-1154j 2.44e-118, 1.61e-358j
1.5953037369130979187e-10 + 3.9041331402425118846e-1150j 1.03e-113, 6.78e-354j
2.0240423566831817682e-11 - 2.3952161271282091911e-1150j 6e-113, 3.96e-353j
0.068936426716172478926 + 2.0239805302592568894e-1143j 2.99e-87, 1.97e-327j
0.0033139241969109383145 + 1.3675294049156843298e-1144j 1.3e-94, 8.58e-335j
2.2794442399062216858e-12 + 5.4321697564349678488e-1151j 5e-114, 3.29e-354j
1.5953037369130979187e-10 + 1.0344871879723678241e-1149j 4.41e-112, 2.91e-352j
2.0085012299433975188e-53 + 1.7048091438886542763e-1173j 8.9e-139, 5.87e-379j
0.10251822527315767718 + 6.0156723135597775277e-1143j 1.03e-90, 6.78e-331j
0.051023826899651377352 - 1.540928542249041247e-1143j 1.18e-91, 7.78e-332j
0.0014552985971929251904 - 1.4736022960747952617e-1144j 6.88e-100, 4.54e-340j
6.912786736274363016e-09 + 1.8811770956236726638e-1148j 3.01e-110, 1.98e-350j
6.912786736274363016e-09 + 7.9088879062945136088e-1149j 6.78e-116, 4.47e-356j
2.2794442399062216858e-12 + 1.8259736789993952639e-1151j 2.43e-120, 1.6e-360j
2.0044062011428099557e-06 + 2.6266286688718675756e-1146j 3.11e-112, 2.05e-352j
5.1103065010152186148e-30 - 4.1419028026265660557e-1162j 5.95e-134, 3.93e-374j
5.8949453932489999057e-25 + 2.0288450672014597303e-1158j 6.41e-128, 4.23e-368j
2.0416538871579113065e-23 - 1.4281245416123467033e-1157j 7.52e-127, 4.96e-367j
1.0789181906906783111e-77 - 1.2236906453091768731e-1187j 4.97e-157, 3.28e-397j
6.6290591313883295235e-07 - 7.248617335126618089e-1147j 2.76e-115, 1.82e-355j
2.0240423566831817682e-11 - 8.5399459068553813818e-1151j 6.18e-121, 4.08e-361j
0.03511781225267985482 + 1.018531726025483752e-1143j 2.16e-101, 1.42e-341j
6.6290591313883295235e-07 - 1.4912463705513960147e-1146j 5.38e-114, 3.55e-354j
1.4434945531667003338e-26 - 2.7016598446467625054e-1159j 2.97e-129, 1.96e-369j
6.2104821882771174831e-06 - 7.6047442912178313747e-1146j 7.25e-115, 4.78e-355j
1.0726673806520303573e-16 + 2.6758988445395217913e-1154j 9.8e-128, 6.47e-368j
7.2493069107682582595e-32 + 4.2361862065688697112e-1162j 2.63e-132, 1.74e-372j
2.0512916202167642763e-05 + 4.3745519113552122405e-1145j 1.25e-113, 8.26e-354j
2.0044062011428099557e-06 + 5.1898367526918629919e-1146j 1.07e-114, 7.08e-355j
6.4395127961903042318e-18 - 4.6737666265865736208e-1155j 4.29e-129, 2.83e-369j
0.068936426716172478926 + 2.3205504903452095608e-1143j 5.47e-109, 3.61e-349j
3.7585238106132193642e-08 - 3.5834039844115287461e-1148j 3.63e-120, 2.4e-360j
0.00058199158147819340128 + 1.2297770797299552366e-1144j 6.6e-114, 4.35e-354j
0.022294728375722759631 - 6.6705636038479875167e-1144j 1.39e-110, 9.2e-351j
7.2493069107682582595e-32 + 3.8259559912990139212e-1163j 1.46e-138, 9.66e-379j
0.051023826899651377352 - 1.2922871325344662797e-1143j 5.27e-112, 3.48e-352j
-0.030397061381664338906 + 3.7744666209034653374e-1142j 9.36e-112, 6.17e-352j
3.3735586855319304803e-19 + 3.4740699057036073646e-1155j 1.14e-127, 7.55e-368j
0.08696150154200311109 - 3.5985930989657255601e-1143j 8.38e-112, 5.52e-352j
0.00021095733276972897172 - 1.3765769123695701975e-1144j 8.9e-115, 5.87e-355j
1.5656452450421410884e-15 - 1.4575832172451516593e-1153j 7.19e-128, 4.74e-368j
3.6922411038802001862e-05 - 1.2710102187041575605e-1144j 1.27e-118, 8.39e-359j
5.7887419814309013978e-38 - 1.6399878581586602919e-1166j 8.23e-142, 5.42e-382j
0.10251822527315767718 + 6.3767552399085216416e-1143j 9.3e-115, 6.1e-355j
0.0068686945535902158675 - 2.9067275077942250314e-1144j 1.61e-116, 1.06e-356j
0.03511781225267985482 + 8.2095848438627578531e-1144j 1.96e-116, 1.29e-356j
0.12284825968067284762 - 2.2748332109052140095e-1142j 1.43e-115, 9.36e-356j
2.0512916202167642763e-05 + 2.3954875622120716967e-1145j 6.41e-120, 4.21e-360j
2.9741264154062869747e-28 + 4.0975408087628431334e-1161j 3.17e-137, 2.09e-377j
0.12284825968067284762 - 2.3156032959749341096e-1142j 1.92e-116, 1.18e-356j
2.009609714406361814e-14 + 2.556895215337081666e-1152j 2.55e-128, 1.6e-368j
0.00058199158147819340128 + 7.6983656183149486471e-1145j 1.36e-120, 7.99e-361j
0.08696150154200311109 - 3.2639104459737210377e-1143j 1.16e-118, 4.75e-359j
5.8949453932489999057e-25 + 3.1297155026901562657e-1159j 2.27e-135, 1.51e-375j

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