Annotation of OpenXM_contrib/pari-2.2/src/test/64/elliptic, Revision 1.1
1.1 ! noro 1: echo = 1 (on)
! 2: ? ellinit([0,0,0,-1,0])
! 3: [0, 0, 0, -1, 0, 0, -2, 0, -1, 48, 0, 64, 1728, [1.0000000000000000000000000
! 4: 000000000000, 0.E-38, -1.0000000000000000000000000000000000000]~, 2.62205755
! 5: 42921198104648395898911194136, 2.6220575542921198104648395898911194136*I, -0
! 6: .59907011736779610371996124614016193910, -1.79721035210338831115988373842048
! 7: 58173*I, 6.8751858180203728274900957798105571979]
! 8: ? ellinit([0,0,0,-17,0],1)
! 9: [0, 0, 0, -17, 0, 0, -34, 0, -289, 816, 0, 314432, 1728]
! 10: ? ellj(I)
! 11: 1728.0000000000000000000000000000000000 + 0.E-54*I
! 12: ? ellsub(ellinit([0,0,0,-17,0]),[-1,4],[-4,2])
! 13: [9, -24]
! 14: ? acurve=ellinit([0,0,1,-1,0])
! 15: [0, 0, 1, -1, 0, 0, -2, 1, -1, 48, -216, 37, 110592/37, [0.83756543528332303
! 16: 544481089907503024040, 0.26959443640544455826293795134926000404, -1.10715987
! 17: 16887675937077488504242902444]~, 2.9934586462319596298320099794525081778, 2.
! 18: 4513893819867900608542248318665252253*I, -0.47131927795681147588259389708033
! 19: 769964, -1.4354565186686843187232088566788165076*I, 7.3381327407895767390707
! 20: 210033323055881]
! 21: ? apoint=[2,2]
! 22: [2, 2]
! 23: ? elladd(acurve,apoint,apoint)
! 24: [21/25, -56/125]
! 25: ? ellak(acurve,1000000007)
! 26: 43800
! 27: ? ellan(acurve,100)
! 28: [1, -2, -3, 2, -2, 6, -1, 0, 6, 4, -5, -6, -2, 2, 6, -4, 0, -12, 0, -4, 3, 1
! 29: 0, 2, 0, -1, 4, -9, -2, 6, -12, -4, 8, 15, 0, 2, 12, -1, 0, 6, 0, -9, -6, 2,
! 30: -10, -12, -4, -9, 12, -6, 2, 0, -4, 1, 18, 10, 0, 0, -12, 8, 12, -8, 8, -6,
! 31: -8, 4, -30, 8, 0, -6, -4, 9, 0, -1, 2, 3, 0, 5, -12, 4, 8, 9, 18, -15, 6, 0
! 32: , -4, -18, 0, 4, 24, 2, 4, 12, 18, 0, -24, 4, 12, -30, -2]
! 33: ? ellap(acurve,10007)
! 34: 66
! 35: ? ellap(acurve,10007,1)
! 36: 66
! 37: ? deu=direuler(p=2,100,1/(1-ellap(acurve,p)*x+if(acurve[12]%p,p,0)*x^2))
! 38: [1, -2, -3, 2, -2, 6, -1, 0, 6, 4, -5, -6, -2, 2, 6, -4, 0, -12, 0, -4, 3, 1
! 39: 0, 2, 0, -1, 4, -9, -2, 6, -12, -4, 8, 15, 0, 2, 12, -1, 0, 6, 0, -9, -6, 2,
! 40: -10, -12, -4, -9, 12, -6, 2, 0, -4, 1, 18, 10, 0, 0, -12, 8, 12, -8, 8, -6,
! 41: -8, 4, -30, 8, 0, -6, -4, 9, 0, -1, 2, 3, 0, 5, -12, 4, 8, 9, 18, -15, 6, 0
! 42: , -4, -18, 0, 4, 24, 2, 4, 12, 18, 0, -24, 4, 12, -30, -2]
! 43: ? ellan(acurve,100)==deu
! 44: 1
! 45: ? ellisoncurve(acurve,apoint)
! 46: 1
! 47: ? acurve=ellchangecurve(acurve,[-1,1,2,3])
! 48: [-4, -1, -7, -12, -12, 12, 4, 1, -1, 48, -216, 37, 110592/37, [-0.1624345647
! 49: 1667696455518910092496975959, -0.73040556359455544173706204865073999595, -2.
! 50: 1071598716887675937077488504242902444]~, -2.99345864623195962983200997945250
! 51: 81778, -2.4513893819867900608542248318665252253*I, 0.47131927795681147588259
! 52: 389708033769964, 1.4354565186686843187232088566788165076*I, 7.33813274078957
! 53: 67390707210033323055881]
! 54: ? apoint=ellchangepoint(apoint,[-1,1,2,3])
! 55: [1, 3]
! 56: ? ellisoncurve(acurve,apoint)
! 57: 1
! 58: ? ellglobalred(acurve)
! 59: [37, [1, -1, 2, 2], 1]
! 60: ? ellheight(acurve,apoint)
! 61: 0.40889126591975072188708879805553617287
! 62: ? ellheight(acurve,apoint,1)
! 63: 0.40889126591975072188708879805553617296
! 64: ? ellordinate(acurve,1)
! 65: [8, 3]
! 66: ? ellztopoint(acurve,ellpointtoz(acurve,apoint))
! 67: [0.99999999999999999999999999999999999990 + 0.E-38*I, 2.99999999999999999999
! 68: 99999999999999998 + 0.E-38*I]
! 69: ? ellpow(acurve,apoint,10)
! 70: [-28919032218753260057646013785951999/292736325329248127651484680640160000,
! 71: 478051489392386968218136375373985436596569736643531551/158385319626308443937
! 72: 475969221994173751192384064000000]
! 73: ? ellwp(acurve)
! 74: x^-2 + 1/5*x^2 - 1/28*x^4 + 1/75*x^6 - 3/1540*x^8 + 1943/3822000*x^10 - 1/11
! 75: 550*x^12 + 193/10510500*x^14 - 1269/392392000*x^16 + 21859/34684650000*x^18
! 76: - 1087/9669660000*x^20 + 22179331/1060517858400000*x^22 - 463/124093970000*x
! 77: ^24 + 47495017/70175140035000000*x^26 - 34997918161/291117454720092000000*x^
! 78: 28 + O(x^30)
! 79: ? ellpointtoz(acurve,apoint)
! 80: 0.72491221490962306778878739838332384646 + 0.E-77*I
! 81: ? q*Ser(ellan(acurve,100),q)
! 82: q - 2*q^2 - 3*q^3 + 2*q^4 - 2*q^5 + 6*q^6 - q^7 + 6*q^9 + 4*q^10 - 5*q^11 -
! 83: 6*q^12 - 2*q^13 + 2*q^14 + 6*q^15 - 4*q^16 - 12*q^18 - 4*q^20 + 3*q^21 + 10*
! 84: q^22 + 2*q^23 - q^25 + 4*q^26 - 9*q^27 - 2*q^28 + 6*q^29 - 12*q^30 - 4*q^31
! 85: + 8*q^32 + 15*q^33 + 2*q^35 + 12*q^36 - q^37 + 6*q^39 - 9*q^41 - 6*q^42 + 2*
! 86: q^43 - 10*q^44 - 12*q^45 - 4*q^46 - 9*q^47 + 12*q^48 - 6*q^49 + 2*q^50 - 4*q
! 87: ^52 + q^53 + 18*q^54 + 10*q^55 - 12*q^58 + 8*q^59 + 12*q^60 - 8*q^61 + 8*q^6
! 88: 2 - 6*q^63 - 8*q^64 + 4*q^65 - 30*q^66 + 8*q^67 - 6*q^69 - 4*q^70 + 9*q^71 -
! 89: q^73 + 2*q^74 + 3*q^75 + 5*q^77 - 12*q^78 + 4*q^79 + 8*q^80 + 9*q^81 + 18*q
! 90: ^82 - 15*q^83 + 6*q^84 - 4*q^86 - 18*q^87 + 4*q^89 + 24*q^90 + 2*q^91 + 4*q^
! 91: 92 + 12*q^93 + 18*q^94 - 24*q^96 + 4*q^97 + 12*q^98 - 30*q^99 - 2*q^100 + O(
! 92: q^101)
! 93: ? bcurve=ellinit([0,0,0,-3,0])
! 94: [0, 0, 0, -3, 0, 0, -6, 0, -9, 144, 0, 1728, 1728, [1.7320508075688772935274
! 95: 463415058723669, 0.E-38, -1.7320508075688772935274463415058723669]~, 1.99233
! 96: 28995834907073368080310227454215, 1.9923328995834907073368080310227454215*I,
! 97: -0.78842061340415606811560792095228873037, -2.36526184021246820434682376285
! 98: 68661911*I, 3.9693903827627596663162680332564652027]
! 99: ? elllocalred(bcurve,2)
! 100: [6, 2, [1, 1, 1, 0], 1]
! 101: ? elltaniyama(bcurve)
! 102: [x^-2 - x^2 + 3*x^6 - 2*x^10 + 7*x^14 + O(x^15), -x^-3 + 3*x - 3*x^5 + 8*x^9
! 103: - 9*x^13 + O(x^14)]
! 104: ? ccurve=ellinit([0,0,-1,-1,0])
! 105: [0, 0, -1, -1, 0, 0, -2, 1, -1, 48, -216, 37, 110592/37, [0.8375654352833230
! 106: 3544481089907503024040, 0.26959443640544455826293795134926000404, -1.1071598
! 107: 716887675937077488504242902444]~, 2.9934586462319596298320099794525081778, 2
! 108: .4513893819867900608542248318665252253*I, -0.4713192779568114758825938970803
! 109: 3769964, -1.4354565186686843187232088566788165076*I, 7.338132740789576739070
! 110: 7210033323055881]
! 111: ? l=elllseries(ccurve,2)
! 112: 0.38157540826071121129371040958008663666
! 113: ? elllseries(ccurve,2,1.2)-l
! 114: 1.322431144675073446 E-38
! 115: ? tcurve=ellinit([1,0,1,-19,26]);
! 116: ? ellorder(tcurve,[1,2])
! 117: 6
! 118: ? elltors(tcurve)
! 119: [12, [6, 2], [[-2, 8], [3, -2]]]
! 120: ? mcurve=ellinit([0,0,0,-17,0])
! 121: [0, 0, 0, -17, 0, 0, -34, 0, -289, 816, 0, 314432, 1728, [4.1231056256176605
! 122: 498214098559740770251, 0.E-38, -4.1231056256176605498214098559740770251]~, 1
! 123: .2913084409290072207105564235857096009, 1.2913084409290072207105564235857096
! 124: 009*I, -1.2164377440798088266474269946818791934, -3.649313232239426479942280
! 125: 9840456375802*I, 1.6674774896145033307120230298772362381]
! 126: ? mpoints=[[-1,4],[-4,2]]~
! 127: [[-1, 4], [-4, 2]]~
! 128: ? mhbi=ellbil(mcurve,mpoints,[9,24])
! 129: [-0.72448571035980184146215805860545027438, 1.307328627832055544492943428892
! 130: 1943055]~
! 131: ? ma=ellheightmatrix(mcurve,mpoints)
! 132:
! 133: [1.1721830987006970106016415566698834134 0.447697388340895169139483498064433
! 134: 13905]
! 135:
! 136: [0.44769738834089516913948349806443313905 1.75502601617295071363242692695662
! 137: 74446]
! 138:
! 139: ? matsolve(ma,mhbi)
! 140: [-0.99999999999999999999999999999999999996, 0.999999999999999999999999999999
! 141: 99999997]~
! 142: ? cmcurve=ellinit([0,-3/4,0,-2,-1])
! 143: [0, -3/4, 0, -2, -1, -3, -4, -4, -1, 105, 1323, -343, -3375, [2.000000000000
! 144: 0000000000000000000000000, -0.62500000000000000000000000000000000000 + 0.330
! 145: 71891388307382381270196920490755321*I, -0.6250000000000000000000000000000000
! 146: 0000 - 0.33071891388307382381270196920490755321*I]~, 1.933311705616811546733
! 147: 0768390298137310, 0.96665585280840577336653841951490686552 + 2.5575309899160
! 148: 994790492257969408742846*I, -0.85584863309985585256414907906657726119 + 4.98
! 149: 6061280778447916 E-39*I, -0.42792431654992792628207453953328863060 - 2.75716
! 150: 12171661472068745043203629203178*I, 4.9445046002825467364981969681843776438]
! 151: ? ellpow(cmcurve,[x,y],quadgen(-7))
! 152: [((-2 + 3*w)*x^2 + (6 - w))/((-2 - 5*w)*x + (-4 - 2*w)), ((34 - 11*w)*y*x^2
! 153: + (40 - 28*w)*y*x + (22 + 23*w)*y)/((-90 - w)*x^2 + (-136 + 44*w)*x + (-40 +
! 154: 28*w))]
! 155: ? \p96
! 156: realprecision = 96 significant digits
! 157: ? precision(cmcurve)
! 158: 38
! 159: ? getheap
! 160: [56, 4347]
! 161: ? print("Total time spent: ",gettime);
! 162: Total time spent: 422
! 163: ? \q
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