diff --git a/src/sage/libs/eclib/interface.py b/src/sage/libs/eclib/interface.py index e898456720..6b98c12328 100644 --- a/src/sage/libs/eclib/interface.py +++ b/src/sage/libs/eclib/interface.py @@ -758,78 +758,78 @@ class mwrank_MordellWeil(SageObject): sage: EQ = mwrank_MordellWeil(E, verbose=True) sage: EQ.search(1) - P1 = [0:1:0] is torsion point, order 1 - P1 = [-3:0:1] is generator number 1 - saturating up to 20...Checking 2-saturation + P1 = [0:1:0] is torsion point, order 1 + P1 = [-3:0:1] is generator number 1 + saturating up to 20...Checking 2-saturation... Points have successfully been 2-saturated (max q used = 7) - Checking 3-saturation + Checking 3-saturation... Points have successfully been 3-saturated (max q used = 7) - Checking 5-saturation + Checking 5-saturation... Points have successfully been 5-saturated (max q used = 23) - Checking 7-saturation + Checking 7-saturation... Points have successfully been 7-saturated (max q used = 41) - Checking 11-saturation + Checking 11-saturation... Points have successfully been 11-saturated (max q used = 17) - Checking 13-saturation + Checking 13-saturation... Points have successfully been 13-saturated (max q used = 43) - Checking 17-saturation + Checking 17-saturation... Points have successfully been 17-saturated (max q used = 31) - Checking 19-saturation + Checking 19-saturation... Points have successfully been 19-saturated (max q used = 37) done - P2 = [-2:3:1] is generator number 2 - saturating up to 20...Checking 2-saturation + P2 = [-2:3:1] is generator number 2 + saturating up to 20...Checking 2-saturation... possible kernel vector = [1,1] This point may be in 2E(Q): [14:-52:1] ...and it is! Replacing old generator #1 with new generator [1:-1:1] Points have successfully been 2-saturated (max q used = 7) Index gain = 2^1 - Checking 3-saturation + Checking 3-saturation... Points have successfully been 3-saturated (max q used = 13) - Checking 5-saturation + Checking 5-saturation... Points have successfully been 5-saturated (max q used = 67) - Checking 7-saturation + Checking 7-saturation... Points have successfully been 7-saturated (max q used = 53) - Checking 11-saturation + Checking 11-saturation... Points have successfully been 11-saturated (max q used = 73) - Checking 13-saturation + Checking 13-saturation... Points have successfully been 13-saturated (max q used = 103) - Checking 17-saturation + Checking 17-saturation... Points have successfully been 17-saturated (max q used = 113) - Checking 19-saturation + Checking 19-saturation... Points have successfully been 19-saturated (max q used = 47) done (index = 2). Gained index 2, new generators = [ [1:-1:1] [-2:3:1] ] - P3 = [-14:25:8] is generator number 3 - saturating up to 20...Checking 2-saturation + P3 = [-14:25:8] is generator number 3 + saturating up to 20...Checking 2-saturation... Points have successfully been 2-saturated (max q used = 11) - Checking 3-saturation + Checking 3-saturation... Points have successfully been 3-saturated (max q used = 13) - Checking 5-saturation + Checking 5-saturation... Points have successfully been 5-saturated (max q used = 71) - Checking 7-saturation + Checking 7-saturation... Points have successfully been 7-saturated (max q used = 101) - Checking 11-saturation + Checking 11-saturation... Points have successfully been 11-saturated (max q used = 127) - Checking 13-saturation + Checking 13-saturation... Points have successfully been 13-saturated (max q used = 151) - Checking 17-saturation + Checking 17-saturation... Points have successfully been 17-saturated (max q used = 139) - Checking 19-saturation + Checking 19-saturation... Points have successfully been 19-saturated (max q used = 179) done (index = 1). - P4 = [-1:3:1] = -1*P1 + -1*P2 + -1*P3 (mod torsion) - P4 = [0:2:1] = 2*P1 + 0*P2 + 1*P3 (mod torsion) - P4 = [2:13:8] = -3*P1 + 1*P2 + -1*P3 (mod torsion) - P4 = [1:0:1] = -1*P1 + 0*P2 + 0*P3 (mod torsion) - P4 = [2:0:1] = -1*P1 + 1*P2 + 0*P3 (mod torsion) - P4 = [18:7:8] = -2*P1 + -1*P2 + -1*P3 (mod torsion) - P4 = [3:3:1] = 1*P1 + 0*P2 + 1*P3 (mod torsion) - P4 = [4:6:1] = 0*P1 + -1*P2 + -1*P3 (mod torsion) - P4 = [36:69:64] = 1*P1 + -2*P2 + 0*P3 (mod torsion) - P4 = [68:-25:64] = -2*P1 + -1*P2 + -2*P3 (mod torsion) - P4 = [12:35:27] = 1*P1 + -1*P2 + -1*P3 (mod torsion) + P4 = [-1:3:1] = -1*P1 + -1*P2 + -1*P3 (mod torsion) + P4 = [0:2:1] = 2*P1 + 0*P2 + 1*P3 (mod torsion) + P4 = [2:13:8] = -3*P1 + 1*P2 + -1*P3 (mod torsion) + P4 = [1:0:1] = -1*P1 + 0*P2 + 0*P3 (mod torsion) + P4 = [2:0:1] = -1*P1 + 1*P2 + 0*P3 (mod torsion) + P4 = [18:7:8] = -2*P1 + -1*P2 + -1*P3 (mod torsion) + P4 = [3:3:1] = 1*P1 + 0*P2 + 1*P3 (mod torsion) + P4 = [4:6:1] = 0*P1 + -1*P2 + -1*P3 (mod torsion) + P4 = [36:69:64] = 1*P1 + -2*P2 + 0*P3 (mod torsion) + P4 = [68:-25:64] = -2*P1 + -1*P2 + -2*P3 (mod torsion) + P4 = [12:35:27] = 1*P1 + -1*P2 + -1*P3 (mod torsion) sage: EQ Subgroup of Mordell-Weil group: [[1:-1:1], [-2:3:1], [-14:25:8]] @@ -1076,7 +1076,7 @@ class mwrank_MordellWeil(SageObject): sage: EQ.search(1) P1 = [0:1:0] is torsion point, order 1 P1 = [-3:0:1] is generator number 1 - saturating up to 20...Checking 2-saturation + saturating up to 20...Checking 2-saturation... ... P4 = [12:35:27] = 1*P1 + -1*P2 + -1*P3 (mod torsion) sage: EQ