code: def test_dup_mul():
      assert dup_mul([], [], ZZ) == []
      assert dup_mul([], [ZZ(1)], ZZ) == []
      assert dup_mul([ZZ(1)], [], ZZ) == []
      assert dup_mul([ZZ(1)], [ZZ(1)], ZZ) == [ZZ(1)]
      assert dup_mul([ZZ(5)], [ZZ(7)], ZZ) == [ZZ(35)]
  
      assert dup_mul([], [], QQ) == []
      assert dup_mul([], [QQ(1, 2)], QQ) == []
      assert dup_mul([QQ(1, 2)], [], QQ) == []
      assert dup_mul([QQ(1, 2)], [QQ(4, 7)], QQ) == [QQ(2, 7)]
      assert dup_mul([QQ(5, 7)], [QQ(3, 7)], QQ) == [QQ(15, 49)]
  
      f = dup_normal([3, 0, 0, 6, 1, 2], ZZ)
      g = dup_normal([4, 0, 1, 0], ZZ)
      h = dup_normal([12, 0, 3, 24, 4, 14, 1, 2, 0], ZZ)
  
      assert dup_mul(f, g, ZZ) == h
      assert dup_mul(g, f, ZZ) == h
  
      f = dup_normal([2, 0, 0, 1, 7], ZZ)
      h = dup_normal([4, 0, 0, 4, 28, 0, 1, 14, 49], ZZ)
  
      assert dup_mul(f, f, ZZ) == h
  
      K = FF(6)
  
      assert dup_mul([K(2), K(1)], [K(3), K(4)], K) == [K(5), K(4)]
  
      p1 = dup_normal(
          [
              79,
              -1,
              78,
              -94,
              -10,
              11,
              32,
              -19,
              78,
              2,
              -89,
              30,
              73,
              42,
              85,
              77,
              83,
              -30,
              -34,
              -2,
              95,
              -81,
              37,
              -49,
              -46,
              -58,
              -16,
              37,
              35,
              -11,
              -57,
              -15,
              -31,
              67,
              -20,
              27,
              76,
              2,
              70,
              67,
              -65,
              65,
              -26,
              -93,
              -44,
              -12,
              -92,
              57,
              -90,
              -57,
              -11,
              -67,
              -98,
              -69,
              97,
              -41,
              89,
              33,
              89,
              -50,
              81,
              -31,
              60,
              -27,
              43,
              29,
              -77,
              44,
              21,
              -91,
              32,
              -57,
              33,
              3,
              53,
              -51,
              -38,
              -99,
              -84,
              23,
              -50,
              66,
              -100,
              1,
              -75,
              -25,
              27,
              -60,
              98,
              -51,
              -87,
              6,
              8,
              78,
              -28,
              -95,
              -88,
              12,
              -35,
              26,
              -9,
              16,
              -92,
              55,
              -7,
              -86,
              68,
              -39,
              -46,
              84,
              94,
              45,
              60,
              92,
              68,
              -75,
              -74,
              -19,
              8,
              75,
              78,
              91,
              57,
              34,
              14,
              -3,
              -49,
              65,
              78,
              -18,
              6,
              -29,
              -80,
              -98,
              17,
              13,
              58,
              21,
              20,
              9,
              37,
              7,
              -30,
              -53,
              -20,
              34,
              67,
              -42,
              89,
              -22,
              73,
              43,
              -6,
              5,
              51,
              -8,
              -15,
              -52,
              -22,
              -58,
              -72,
              -3,
              43,
              -92,
              82,
              83,
              -2,
              -13,
              -23,
              -60,
              16,
              -94,
              -8,
              -28,
              -95,
              -72,
              63,
              -90,
              76,
              6,
              -43,
              -100,
              -59,
              76,
              3,
              3,
              46,
              -85,
              75,
              62,
              -71,
              -76,
              88,
              97,
              -72,
              -1,
              30,
              -64,
              72,
              -48,
              14,
              -78,
              58,
              63,
              -91,
              24,
              -87,
              -27,
              -80,
              -100,
              -44,
              98,
              70,
              100,
              -29,
              -38,
              11,
              77,
              100,
              52,
              86,
              65,
              -5,
              -42,
              -81,
              -38,
              -42,
              43,
              -2,
              -70,
              -63,
              -52,
          ],
          ZZ,
      )
      p2 = dup_normal(
          [
              65,
              -19,
              -47,
              1,
              90,
              81,
              -15,
              -34,
              25,
              -75,
              9,
              -83,
              50,
              -5,
              -44,
              31,
              1,
              70,
              -7,
              78,
              74,
              80,
              85,
              65,
              21,
              41,
              66,
              19,
              -40,
              63,
              -21,
              -27,
              32,
              69,
              83,
              34,
              -35,
              14,
              81,
              57,
              -75,
              32,
              -67,
              -89,
              -100,
              -61,
              46,
              84,
              -78,
              -29,
              -50,
              -94,
              -24,
              -32,
              -68,
              -16,
              100,
              -7,
              -72,
              -89,
              35,
              82,
              58,
              81,
              -92,
              62,
              5,
              -47,
              -39,
              -58,
              -72,
              -13,
              84,
              44,
              55,
              -25,
              48,
              -54,
              -31,
              -56,
              -11,
              -50,
              -84,
              10,
              67,
              17,
              13,
              -14,
              61,
              76,
              -64,
              -44,
              -40,
              -96,
              11,
              -11,
              -94,
              2,
              6,
              27,
              -6,
              68,
              -54,
              66,
              -74,
              -14,
              -1,
              -24,
              -73,
              96,
              89,
              -11,
              -89,
              56,
              -53,
              72,
              -43,
              96,
              25,
              63,
              -31,
              29,
              68,
              83,
              91,
              -93,
              -19,
              -38,
              -40,
              40,
              -12,
              -19,
              -79,
              44,
              100,
              -66,
              -29,
              -77,
              62,
              39,
              -8,
              11,
              -97,
              14,
              87,
              64,
              21,
              -18,
              13,
              15,
              -59,
              -75,
              -99,
              -88,
              57,
              54,
              56,
              -67,
              6,
              -63,
              -59,
              -14,
              28,
              87,
              -20,
              -39,
              84,
              -91,
              -2,
              49,
              -75,
              11,
              -24,
              -95,
              36,
              66,
              5,
              25,
              -72,
              -40,
              86,
              90,
              37,
              -33,
              57,
              -35,
              29,
              -18,
              4,
              -79,
              64,
              -17,
              -27,
              21,
              29,
              -5,
              -44,
              -87,
              -24,
              52,
              78,
              11,
              -23,
              -53,
              36,
              42,
              21,
              -68,
              94,
              -91,
              -51,
              -21,
              51,
              -76,
              72,
              31,
              24,
              -48,
              -80,
              -9,
              37,
              -47,
              -6,
              -8,
              -63,
              -91,
              79,
              -79,
              -100,
              38,
              -20,
              38,
              100,
              83,
              -90,
              87,
              63,
              -36,
              82,
              -19,
              18,
              -98,
              -38,
              26,
              98,
              -70,
              79,
              92,
              12,
              12,
              70,
              74,
              36,
              48,
              -13,
              31,
              31,
              -47,
              -71,
              -12,
              -64,
              36,
              -42,
              32,
              -86,
              60,
              83,
              70,
              55,
              0,
              1,
              29,
              -35,
              8,
              -82,
              8,
              -73,
              -46,
              -50,
              43,
              48,
              -5,
              -86,
              -72,
              44,
              -90,
              19,
              19,
              5,
              -20,
              97,
              -13,
              -66,
              -5,
              5,
              -69,
              64,
              -30,
              41,
              51,
              36,
              13,
              -99,
              -61,
              94,
              -12,
              74,
              98,
              68,
              24,
              46,
              -97,
              -87,
              -6,
              -27,
              82,
              62,
              -11,
              -77,
              86,
              66,
              -47,
              -49,
              -50,
              13,
              18,
              89,
              -89,
              46,
              -80,
              13,
              98,
              -35,
              -36,
              -25,
              12,
              20,
              26,
              -52,
              79,
              27,
              79,
              100,
              8,
              62,
              -58,
              -28,
              37,
          ],
          ZZ,
      )
      res = dup_normal(
          [
              5135,
              -1566,
              1376,
              -7466,
              4579,
              11710,
              8001,
              -7183,
              -3737,
              -7439,
              345,
              -10084,
              24522,
              -1201,
              1070,
              -10245,
              9582,
              9264,
              1903,
              23312,
              18953,
              10037,
              -15268,
              -5450,
              6442,
              -6243,
              -3777,
              5110,
              10936,
              -16649,
              -6022,
              16255,
              31300,
              24818,
              31922,
              32760,
              7854,
              27080,
              15766,
              29596,
              7139,
              31945,
              -19810,
              465,
              -38026,
              -3971,
              9641,
              465,
              -19375,
              5524,
              -30112,
              -11960,
              -12813,
              13535,
              30670,
              5925,
              -43725,
              -14089,
              11503,
              -22782,
              6371,
              43881,
              37465,
              -33529,
              -33590,
              -39798,
              -37854,
              -18466,
              -7908,
              -35825,
              -26020,
              -36923,
              -11332,
              -5699,
              25166,
              -3147,
              19885,
              12962,
              -20659,
              -1642,
              27723,
              -56331,
              -24580,
              -11010,
              -20206,
              20087,
              -23772,
              -16038,
              38580,
              20901,
              -50731,
              32037,
              -4299,
              26508,
              18038,
              -28357,
              31846,
              -7405,
              -20172,
              -15894,
              2096,
              25110,
              -45786,
              45918,
              -55333,
              -31928,
              -49428,
              -29824,
              -58796,
              -24609,
              -15408,
              69,
              -35415,
              -18439,
              10123,
              -20360,
              -65949,
              33356,
              -20333,
              26476,
              -32073,
              33621,
              930,
              28803,
              -42791,
              44716,
              38164,
              12302,
              -1739,
              11421,
              73385,
              -7613,
              14297,
              38155,
              -414,
              77587,
              24338,
              -21415,
              29367,
              42639,
              13901,
              -288,
              51027,
              -11827,
              91260,
              43407,
              88521,
              -15186,
              70572,
              -12049,
              5090,
              -12208,
              -56374,
              15520,
              -623,
              -7742,
              50825,
              11199,
              -14894,
              40892,
              59591,
              -31356,
              -28696,
              -57842,
              -87751,
              -33744,
              -28436,
              -28945,
              -40287,
              37957,
              -35638,
              33401,
              -61534,
              14870,
              40292,
              70366,
              -10803,
              102290,
              -71719,
              -85251,
              7902,
              -22409,
              75009,
              99927,
              35298,
              -1175,
              -762,
              -34744,
              -10587,
              -47574,
              -62629,
              -19581,
              -43659,
              -54369,
              -32250,
              -39545,
              15225,
              -24454,
              11241,
              -67308,
              -30148,
              39929,
              37639,
              14383,
              -73475,
              -77636,
              -81048,
              -35992,
              41601,
              -90143,
              76937,
              -8112,
              56588,
              9124,
              -40094,
              -32340,
              13253,
              10898,
              -51639,
              36390,
              12086,
              -1885,
              100714,
              -28561,
              -23784,
              -18735,
              18916,
              16286,
              10742,
              -87360,
              -13697,
              10689,
              -19477,
              -29770,
              5060,
              20189,
              -8297,
              112407,
              47071,
              47743,
              45519,
              -4109,
              17468,
              -68831,
              78325,
              -6481,
              -21641,
              -19459,
              30919,
              96115,
              8607,
              53341,
              32105,
              -16211,
              23538,
              57259,
              -76272,
              -40583,
              62093,
              38511,
              -34255,
              -40665,
              -40604,
              -37606,
              -15274,
              33156,
              -13885,
              103636,
              118678,
              -14101,
              -92682,
              -100791,
              2634,
              63791,
              98266,
              19286,
              -34590,
              -21067,
              -71130,
              25380,
              -40839,
              -27614,
              -26060,
              52358,
              -15537,
              27138,
              -6749,
              36269,
              -33306,
              13207,
              -91084,
              -5540,
              -57116,
              69548,
              44169,
              -57742,
              -41234,
              -103327,
              -62904,
              -8566,
              41149,
              -12866,
              71188,
              23980,
              1838,
              58230,
              73950,
              5594,
              43113,
              -8159,
              -15925,
              6911,
              85598,
              -75016,
              -16214,
              -62726,
              -39016,
              8618,
              -63882,
              -4299,
              23182,
              49959,
              49342,
              -3238,
              -24913,
              -37138,
              78361,
              32451,
              6337,
              -11438,
              -36241,
              -37737,
              8169,
              -3077,
              -24829,
              57953,
              53016,
              -31511,
              -91168,
              12599,
              -41849,
              41576,
              55275,
              -62539,
              47814,
              -62319,
              12300,
              -32076,
              -55137,
              -84881,
              -27546,
              4312,
              -3433,
              -54382,
              113288,
              -30157,
              74469,
              18219,
              79880,
              -2124,
              98911,
              17655,
              -33499,
              -32861,
              47242,
              -37393,
              99765,
              14831,
              -44483,
              10800,
              -31617,
              -52710,
              37406,
              22105,
              29704,
              -20050,
              13778,
              43683,
              36628,
              8494,
              60964,
              -22644,
              31550,
              -17693,
              33805,
              -124879,
              -12302,
              19343,
              20400,
              -30937,
              -21574,
              -34037,
              -33380,
              56539,
              -24993,
              -75513,
              -1527,
              53563,
              65407,
              -101,
              53577,
              37991,
              18717,
              -23795,
              -8090,
              -47987,
              -94717,
              41967,
              5170,
              -14815,
              -94311,
              17896,
              -17734,
              -57718,
              -774,
              -38410,
              24830,
              29682,
              76480,
              58802,
              -46416,
              -20348,
              -61353,
              -68225,
              -68306,
              23822,
              -31598,
              42972,
              36327,
              28968,
              -65638,
              -21638,
              24354,
              -8356,
              26777,
              52982,
              -11783,
              -44051,
              -26467,
              -44721,
              -28435,
              -53265,
              -25574,
              -2669,
              44155,
              22946,
              -18454,
              -30718,
              -11252,
              58420,
              8711,
              67447,
              4425,
              41749,
              67543,
              43162,
              11793,
              -41907,
              20477,
              -13080,
              6559,
              -6104,
              -13244,
              42853,
              42935,
              29793,
              36730,
              -28087,
              28657,
              17946,
              7503,
              7204,
              21491,
              -27450,
              -24241,
              -98156,
              -18082,
              -42613,
              -24928,
              10775,
              -14842,
              -44127,
              55910,
              14777,
              31151,
              -2194,
              39206,
              -2100,
              -4211,
              11827,
              -8918,
              -19471,
              72567,
              36447,
              -65590,
              -34861,
              -17147,
              -45303,
              9025,
              -7333,
              -35473,
              11101,
              11638,
              3441,
              6626,
              -41800,
              9416,
              13679,
              33508,
              40502,
              -60542,
              16358,
              8392,
              -43242,
              -35864,
              -34127,
              -48721,
              35878,
              30598,
              28630,
              20279,
              -19983,
              -14638,
              -24455,
              -1851,
              -11344,
              45150,
              42051,
              26034,
              -28889,
              -32382,
              -3527,
              -14532,
              22564,
              -22346,
              477,
              11706,
              28338,
              -25972,
              -9185,
              -22867,
              -12522,
              32120,
              -4424,
              11339,
              -33913,
              -7184,
              5101,
              -23552,
              -17115,
              -31401,
              -6104,
              21906,
              25708,
              8406,
              6317,
              -7525,
              5014,
              20750,
              20179,
              22724,
              11692,
              13297,
              2493,
              -253,
              -16841,
              -17339,
              -6753,
              -4808,
              2976,
              -10881,
              -10228,
              -13816,
              -12686,
              1385,
              2316,
              2190,
              -875,
              -1924,
          ],
          ZZ,
      )
  
      assert dup_mul(p1, p2, ZZ) == res
  
      p1 = dup_normal(
          [
              83,
              -61,
              -86,
              -24,
              12,
              43,
              -88,
              -9,
              42,
              55,
              -66,
              74,
              95,
              -25,
              -12,
              68,
              -99,
              4,
              45,
              6,
              -15,
              -19,
              78,
              65,
              -55,
              47,
              -13,
              17,
              86,
              81,
              -58,
              -27,
              50,
              -40,
              -24,
              39,
              -41,
              -92,
              75,
              90,
              -1,
              40,
              -15,
              -27,
              -35,
              68,
              70,
              -64,
              -40,
              78,
              -88,
              -58,
              -39,
              69,
              46,
              12,
              28,
              -94,
              -37,
              -50,
              -80,
              -96,
              -61,
              25,
              1,
              71,
              4,
              12,
              48,
              4,
              34,
              -47,
              -75,
              5,
              48,
              82,
              88,
              23,
              98,
              35,
              17,
              -10,
              48,
              -61,
              -95,
              47,
              65,
              -19,
              -66,
              -57,
              -6,
              -51,
              -42,
              -89,
              66,
              -13,
              18,
              37,
              90,
              -23,
              72,
              96,
              -53,
              0,
              40,
              -73,
              -52,
              -68,
              32,
              -25,
              -53,
              79,
              -52,
              18,
              44,
              73,
              -81,
              31,
              -90,
              70,
              3,
              36,
              48,
              76,
              -24,
              -44,
              23,
              98,
              -4,
              73,
              69,
              88,
              -70,
              14,
              -68,
              94,
              -78,
              -15,
              -64,
              -97,
              -70,
              -35,
              65,
              88,
              49,
              -53,
              -7,
              12,
              -45,
              -7,
              59,
              -94,
              99,
              -2,
              67,
              -60,
              -71,
              29,
              -62,
              -77,
              1,
              51,
              17,
              80,
              -20,
              -47,
              -19,
              24,
              -9,
              39,
              -23,
              21,
              -84,
              10,
              84,
              56,
              -17,
              -21,
              -66,
              85,
              70,
              46,
              -51,
              -22,
              -95,
              78,
              -60,
              -96,
              -97,
              -45,
              72,
              35,
              30,
              -61,
              -92,
              -93,
              -60,
              -61,
              4,
              -4,
              -81,
              -73,
              46,
              53,
              -11,
              26,
              94,
              45,
              14,
              -78,
              55,
              84,
              -68,
              98,
              60,
              23,
              100,
              -63,
              68,
              96,
              -16,
              3,
              56,
              21,
              -58,
              62,
              -67,
              66,
              85,
              41,
              -79,
              -22,
              97,
              -67,
              82,
              82,
              -96,
              -20,
              -7,
              48,
              -67,
              48,
              -9,
              -39,
              78,
          ],
          ZZ,
      )
      p2 = dup_normal(
          [
              52,
              88,
              76,
              66,
              9,
              -64,
              46,
              -20,
              -28,
              69,
              60,
              96,
              -36,
              -92,
              -30,
              -11,
              -35,
              35,
              55,
              63,
              -92,
              -7,
              25,
              -58,
              74,
              55,
              -6,
              4,
              47,
              -92,
              -65,
              67,
              -45,
              74,
              -76,
              59,
              -6,
              69,
              39,
              24,
              -71,
              -7,
              39,
              -45,
              60,
              -68,
              98,
              97,
              -79,
              17,
              4,
              94,
              -64,
              68,
              -100,
              -96,
              -2,
              3,
              22,
              96,
              54,
              -77,
              -86,
              67,
              6,
              57,
              37,
              40,
              89,
              -78,
              64,
              -94,
              -45,
              -92,
              57,
              87,
              -26,
              36,
              19,
              97,
              25,
              77,
              -87,
              24,
              43,
              -5,
              35,
              57,
              83,
              71,
              35,
              63,
              61,
              96,
              -22,
              8,
              -1,
              96,
              43,
              45,
              94,
              -93,
              36,
              71,
              -41,
              -99,
              85,
              -48,
              59,
              52,
              -17,
              5,
              87,
              -16,
              -68,
              -54,
              76,
              -18,
              100,
              91,
              -42,
              -70,
              -66,
              -88,
              -12,
              1,
              95,
              -82,
              52,
              43,
              -29,
              3,
              12,
              72,
              -99,
              -43,
              -32,
              -93,
              -51,
              16,
              -20,
              -12,
              -11,
              5,
              33,
              -38,
              93,
              -5,
              -74,
              25,
              74,
              -58,
              93,
              59,
              -63,
              -86,
              63,
              -20,
              -4,
              -74,
              -73,
              -95,
              29,
              -28,
              93,
              -91,
              -2,
              -38,
              -62,
              77,
              -58,
              -85,
              -28,
              95,
              38,
              19,
              -69,
              86,
              94,
              25,
              -2,
              -4,
              47,
              34,
              -59,
              35,
              -48,
              29,
              -63,
              -53,
              34,
              29,
              66,
              73,
              6,
              92,
              -84,
              89,
              15,
              81,
              93,
              97,
              51,
              -72,
              -78,
              25,
              60,
              90,
              -45,
              39,
              67,
              -84,
              -62,
              57,
              26,
              -32,
              -56,
              -14,
              -83,
              76,
              5,
              -2,
              99,
              -100,
              28,
              46,
              94,
              -7,
              53,
              -25,
              16,
              -23,
              -36,
              89,
              -78,
              -63,
              31,
              1,
              84,
              -99,
              -52,
              76,
              48,
              90,
              -76,
              44,
              -19,
              54,
              -36,
              -9,
              -73,
              -100,
              -69,
              31,
              42,
              25,
              -39,
              76,
              -26,
              -8,
              -14,
              51,
              3,
              37,
              45,
              2,
              -54,
              13,
              -34,
              -92,
              17,
              -25,
              -65,
              53,
              -63,
              30,
              4,
              -70,
              -67,
              90,
              52,
              51,
              18,
              -3,
              31,
              -45,
              -9,
              59,
              63,
              -87,
              22,
              -32,
              29,
              -38,
              21,
              36,
              -82,
              27,
              -11,
          ],
          ZZ,
      )
      res = dup_normal(
          [
              4316,
              4132,
              -3532,
              -7974,
              -11303,
              -10069,
              5484,
              -3330,
              -5874,
              7734,
              4673,
              11327,
              -9884,
              -8031,
              17343,
              21035,
              -10570,
              -9285,
              15893,
              3780,
              -14083,
              8819,
              17592,
              10159,
              7174,
              -11587,
              8598,
              -16479,
              3602,
              25596,
              9781,
              12163,
              150,
              18749,
              -21782,
              -12307,
              27578,
              -2757,
              -12573,
              12565,
              6345,
              -18956,
              19503,
              -15617,
              1443,
              -16778,
              36851,
              23588,
              -28474,
              5749,
              40695,
              -7521,
              -53669,
              -2497,
              -18530,
              6770,
              57038,
              3926,
              -6927,
              -15399,
              1848,
              -64649,
              -27728,
              3644,
              49608,
              15187,
              -8902,
              -9480,
              -7398,
              -40425,
              4824,
              23767,
              -7594,
              -6905,
              33089,
              18786,
              12192,
              24670,
              31114,
              35334,
              -4501,
              -14676,
              7107,
              -59018,
              -21352,
              20777,
              19661,
              20653,
              33754,
              -885,
              -43758,
              6269,
              51897,
              -28719,
              -97488,
              -9527,
              13746,
              11644,
              17644,
              -21720,
              23782,
              -10481,
              47867,
              20752,
              33810,
              -1875,
              39918,
              -7710,
              -40840,
              19808,
              -47075,
              23066,
              46616,
              25201,
              9287,
              35436,
              -1602,
              9645,
              -11978,
              13273,
              15544,
              33465,
              20063,
              44539,
              11687,
              27314,
              -6538,
              -37467,
              14031,
              32970,
              -27086,
              41323,
              29551,
              65910,
              -39027,
              -37800,
              -22232,
              8212,
              46316,
              -28981,
              -55282,
              50417,
              -44929,
              -44062,
              73879,
              37573,
              -2596,
              -10877,
              -21893,
              -133218,
              -33707,
              -25753,
              -9531,
              17530,
              61126,
              2748,
              -56235,
              43874,
              -10872,
              -90459,
              -30387,
              115267,
              -7264,
              -44452,
              122626,
              14839,
              -599,
              10337,
              57166,
              -67467,
              -54957,
              63669,
              1202,
              18488,
              52594,
              7205,
              -97822,
              612,
              78069,
              -5403,
              -63562,
              47236,
              36873,
              -154827,
              -26188,
              82427,
              -39521,
              5628,
              7416,
              5276,
              -53095,
              47050,
              26121,
              -42207,
              79021,
              -13035,
              2499,
              -66943,
              29040,
              -72355,
              -23480,
              23416,
              -12885,
              -44225,
              -42688,
              -4224,
              19858,
              55299,
              15735,
              11465,
              101876,
              -39169,
              51786,
              14723,
              43280,
              -68697,
              16410,
              92295,
              56767,
              7183,
              111850,
              4550,
              115451,
              -38443,
              -19642,
              -35058,
              10230,
              93829,
              8925,
              63047,
              3146,
              29250,
              8530,
              5255,
              -98117,
              -115517,
              -76817,
              -8724,
              41044,
              1312,
              -35974,
              79333,
              -28567,
              7547,
              -10580,
              -24559,
              -16238,
              10794,
              -3867,
              24848,
              57770,
              -51536,
              -35040,
              71033,
              29853,
              62029,
              -7125,
              -125585,
              -32169,
              -47907,
              156811,
              -65176,
              -58006,
              -15757,
              -57861,
              11963,
              30225,
              -41901,
              -41681,
              31310,
              27982,
              18613,
              61760,
              60746,
              -59096,
              33499,
              30097,
              -17997,
              24032,
              56442,
              -83042,
              23747,
              -20931,
              -21978,
              -158752,
              -9883,
              -73598,
              -7987,
              -7333,
              -125403,
              -116329,
              30585,
              53281,
              51018,
              -29193,
              88575,
              8264,
              -40147,
              -16289,
              113088,
              12810,
              -6508,
              101552,
              -13037,
              34440,
              -41840,
              101643,
              24263,
              80532,
              61748,
              65574,
              6423,
              -20672,
              6591,
              -10834,
              -71716,
              86919,
              -92626,
              39161,
              28490,
              81319,
              46676,
              106720,
              43530,
              26998,
              57456,
              -8862,
              60989,
              13982,
              3119,
              -2224,
              14743,
              55415,
              -49093,
              -29303,
              28999,
              1789,
              55953,
              -84043,
              -7780,
              -65013,
              57129,
              -47251,
              61484,
              61994,
              -78361,
              -82778,
              22487,
              -26894,
              9756,
              -74637,
              -15519,
              -4360,
              30115,
              42433,
              35475,
              15286,
              69768,
              21509,
              -20214,
              78675,
              -21163,
              13596,
              11443,
              -10698,
              -53621,
              -53867,
              -24155,
              64500,
              -42784,
              -33077,
              -16500,
              873,
              -52788,
              14546,
              -38011,
              36974,
              -39849,
              -34029,
              -94311,
              83068,
              -50437,
              -26169,
              -46746,
              59185,
              42259,
              -101379,
              -12943,
              30089,
              -59086,
              36271,
              22723,
              -30253,
              -52472,
              -70826,
              -23289,
              3331,
              -31687,
              14183,
              -857,
              -28627,
              35246,
              -51284,
              5636,
              -6933,
              66539,
              36654,
              50927,
              24783,
              3457,
              33276,
              45281,
              45650,
              -4938,
              -9968,
              -22590,
              47995,
              69229,
              5214,
              -58365,
              -17907,
              -14651,
              18668,
              18009,
              12649,
              -11851,
              -13387,
              20339,
              52472,
              -1087,
              -21458,
              -68647,
              52295,
              15849,
              40608,
              15323,
              25164,
              -29368,
              10352,
              -7055,
              7159,
              21695,
              -5373,
              -54849,
              101103,
              -24963,
              -10511,
              33227,
              7659,
              41042,
              -69588,
              26718,
              -20515,
              6441,
              38135,
              -63,
              24088,
              -35364,
              -12785,
              -18709,
              47843,
              48533,
              -48575,
              17251,
              -19394,
              32878,
              -9010,
              -9050,
              504,
              -12407,
              28076,
              -3429,
              25324,
              -4210,
              -26119,
              752,
              -29203,
              28251,
              -11324,
              -32140,
              -3366,
              -25135,
              18702,
              -31588,
              -7047,
              -24267,
              49987,
              -14975,
              -33169,
              37744,
              -7720,
              -9035,
              16964,
              -2807,
              -421,
              14114,
              -17097,
              -13662,
              40628,
              -12139,
              -9427,
              5369,
              17551,
              -13232,
              -16211,
              9804,
              -7422,
              2677,
              28635,
              -8280,
              -4906,
              2908,
              -22558,
              5604,
              12459,
              8756,
              -3980,
              -4745,
              -18525,
              7913,
              5970,
              -16457,
              20230,
              -6247,
              -13812,
              2505,
              11899,
              1409,
              -15094,
              22540,
              -18863,
              137,
              11123,
              -4516,
              2290,
              -8594,
              12150,
              -10380,
              3005,
              5235,
              -7350,
              2535,
              -858,
          ],
          ZZ,
      )
  
      assert dup_mul(p1, p2, ZZ) == res
  
imports: from sympy.external.gmpy import GROUND_TYPES
  from sympy.polys.densebasic import dup_normal, dmp_normal
  from sympy.polys.densearith import dup_add_term, dmp_add_term, dup_sub_term, dmp_sub_term, dup_mul_term, dmp_mul_term, dup_add_ground, dmp_add_ground, dup_sub_ground, dmp_sub_ground, dup_mul_ground, dmp_mul_ground, dup_quo_ground, dmp_quo_ground, dup_exquo_ground, dmp_exquo_ground, dup_lshift, dup_rshift, dup_abs, dmp_abs, dup_neg, dmp_neg, dup_add, dmp_add, dup_sub, dmp_sub, dup_mul, dmp_mul, dup_sqr, dmp_sqr, dup_pow, dmp_pow, dup_add_mul, dmp_add_mul, dup_sub_mul, dmp_sub_mul, dup_pdiv, dup_prem, dup_pquo, dup_pexquo, dmp_pdiv, dmp_prem, dmp_pquo, dmp_pexquo, dup_rr_div, dmp_rr_div, dup_ff_div, dmp_ff_div, dup_div, dup_rem, dup_quo, dup_exquo, dmp_div, dmp_rem, dmp_quo, dmp_exquo, dup_max_norm, dmp_max_norm, dup_l1_norm, dmp_l1_norm, dup_l2_norm_squared, dmp_l2_norm_squared, dup_expand, dmp_expand
  from sympy.polys.polyerrors import ExactQuotientFailed
  from sympy.polys.specialpolys import f_polys
  from sympy.polys.domains import FF, ZZ, QQ
  from sympy.testing.pytest import raises
label_desc: Use image node_id 29 for calling a global function with example usage: test_dup_mul() without return types