Returned 77 matches (100 formulae, 70 docs)
    Lookup 1.235 ms, Re-ranking 174.230 ms
    Found 6944 tuple postings, 3850 formulae, 2057 documents
[ formulas ] [ documents ] [ documents-by-formula ]

Doc 1
1.0000
3.9834
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000016/Articles/Extension_of_a_topological_group.html
0 G π X ı H 0
0 H i X π G 0
0 H i X π G 0
0 H i X π G 0
0 H i X π G 0
0 H ı X π G 0
0 H ı X π G 0
0 H i X π G 0
0 H ı X π G 0.
0 ı π / 0
0 H i H H × G π G G 0

Doc 2
0.3492
0.3492
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000009/Articles/Regular_category.html
0 R r - s X Y 0

Doc 3
0.3465
0.6272
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000011/Articles/Schanuel's_lemma.html
0 K X P 0 ,
0 K X P 0.

Doc 4
0.2895
0.2895
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000016/Articles/Draft:Exact_couple.html
0 G p + 1 G p K p , * 0

Doc 5
0.2883
2.7423
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000004/Articles/Ext_functor.html
0 B E A 0
0 B E A 0
0 B E A 0
0 B Y A 0
0 B E A 0
0 B E A 0
0 B E A 0.
0 B X n X 1 A 0
P 1 P 0 A 0 ,
0 B I 0 I 1 ,
ξ : 0 B X n X 1 A 0
ξ : 0 B X n X 1 A 0
Doc 6
0.2883
1.6234
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000009/Articles/Exact_category.html
0 A B C 0
0 A B C 0
0 M M M ′′ 0
0 M M M ′′ 0
0 M 𝑓 M M ′′ 0 ,
0 ( 1 2 ) 2 ( - 2 , 1 ) 0 ,
0 / 0 ,

Doc 7
0.2883
1.2782
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000003/Articles/Group_extension.html
0 𝔞 𝔢 𝔤 0
1 K G H 1
1 K G H 1
1 K i G π H 1
1 K i G π H 1
1 A E G 1
1 N G Q 1.

Doc 8
0.2883
1.1183
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000003/Articles/Derived_functor.html
0 A B C 0
0 A B C 0
0 A 𝑓 B 𝑔 C 0
P 2 P 1 P 0 X 0
0 X I 0 I 1 I 2

Doc 9
0.2883
0.5766
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000002/Articles/Exterior_algebra.html
0 U V W 0
0 U V W 0

Doc 10
0.2883
0.5423
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000005/Articles/Grothendieck_group.html
0 A B C 0
0 k l k m k n 0

Doc 11
0.2883
0.4550
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000004/Articles/Derived_category.html
0 X Y Z 0
0 X I 0 I 1 ,

Doc 12
0.2883
0.4411
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000014/Articles/Tilting_theory.html
0 U M V 0
0 A T 1 T n 0

Doc 13
0.2883
0.3804
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000008/Articles/Hilbert_series_and_Hilbert_polynomial.html
0 A B C 0
0 A [ d ] 𝑓 A A / f 0 ,

Doc 14
0.2883
0.2883
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000002/Articles/Homology_(mathematics).html
0 A B C 0

Doc 15
0.2883
0.2883
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000002/Articles/Vector_bundle.html
0 A B C 0

Doc 16
0.2883
0.2883
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000006/Articles/Lie_algebra_cohomology.html
0 M 𝔥 𝔤 0

Doc 17
0.2883
0.2883
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000012/Articles/Stable_module_category.html
0 X E Y 0

Doc 18
0.2883
0.2883
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000002/Articles/Rank_of_an_abelian_group.html
0 A B C 0

Doc 19
0.2883
0.2883
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000016/Articles/K-space_(functional_analysis).html
0 X V 0.

Doc 20
0.2883
0.2883
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000003/Articles/Projective_module.html
0 A B P 0

Doc 21
0.2883
0.2883
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000016/Articles/Sheaf_of_modules.html
0 F G H 0.

Doc 22
0.2883
0.2883
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000004/Articles/Length_of_a_module.html
0 L M N 0

Doc 23
0.2883
0.2883
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000003/Articles/Injective_object.html
0 A B C 0

Doc 24
0.2883
0.2883
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000002/Articles/Group_cohomology.html
0 L M N 0

Doc 25
0.2783
1.0614
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000012/Articles/Dimension_theory_(algebra).html
0 K 𝑓 F M 0
0 P 1 P 0 M 0
0 M 𝑓 M M 1 0
0 M x 1 M M 1 0

Doc 26
0.2759
0.5470
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000013/Articles/Glossary_of_module_theory.html
0 L L P 0
0 I L L 0

Doc 27
0.2714
0.2714
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000016/Articles/Direct_sum_of_topological_groups.html
0 H i G π G / H 0

Doc 28
0.2712
0.2712
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000002/Articles/Complex_geometry.html
0 𝒪 𝒪 * 0

Doc 29
0.2645
0.8402
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000002/Articles/Exact_sequence.html
0 A 𝑓 B 𝑔 C 0
0 A 𝑓 B 𝑔 C 0
0 C k A k C k + 1 0
1 N G G / N 1

Doc 30
0.2645
0.7642
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000001/Articles/Ring_(mathematics).html
0 M M M ′′ 0
0 M M M ′′ 0
0 M 𝔪 M 𝔪 M 𝔪 ′′ 0
Doc 31
0.2645
0.6615
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000003/Articles/Module_homomorphism.html
0 A 𝑓 B 𝑔 C 0
0 A 𝔪 𝑓 B 𝔪 𝑔 C 𝔪 0
0 K M 𝑓 N C 0
Doc 32
0.2645
0.5289
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000001/Articles/Abelian_category.html
0 M M M ′′ 0
0 M M M ′′ 0

Doc 33
0.2645
0.5289
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000012/Articles/Delta-functor.html
0 M M M ′′ 0
0 M M M ′′ 0

Doc 34
0.2645
0.4216
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000016/Articles/Draft:Divisor_(algebraic_geometry).html
0 E n E 0 0
0 E n E 0 F 0

Doc 35
0.2645
0.2645
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000002/Articles/Subcategory.html
0 M M M ′′ 0

Doc 36
0.2645
0.2645
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000016/Articles/Localizing_subcategory.html
0 A A A ′′ 0

Doc 37
0.2645
0.2645
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000004/Articles/Sheaf_cohomology.html
0 𝒜 ϕ ψ 𝒞 0

Doc 38
0.2645
0.2645
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000012/Articles/Support_of_a_module.html
0 M M M ′′ 0

Doc 39
0.2645
0.2645
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000002/Articles/Chern_class.html
0 E E E ′′ 0

Doc 40
0.2645
0.2645
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000016/Articles/Q-construction.html
0 M M M ′′ 0

Doc 41
0.2645
0.2645
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000016/Articles/Semi-simplicity.html
0 M M M ′′ 0

Doc 42
0.2560
0.2560
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000001/Articles/Trace_(linear_algebra).html
0 𝑠𝑙 n 𝑔𝑙 n tr k 0

Doc 43
0.2540
0.2540
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000015/Articles/Gabriel–Popescu_theorem.html
0 M 1 M 2 M 3 0

Doc 44
0.2540
0.2540
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000001/Articles/Inverse_limit.html
0 A i B i C i 0

Doc 45
0.2462
0.2462
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000003/Articles/Algebraic_K-theory.html
0 V V V ′′ 0 ,

Doc 46
0.2443
0.7345
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000002/Articles/Homological_algebra.html
0 A 𝑓 B 𝑔 C 0
P 1 P 0 A 0 ,
0 B I 0 I 1 ,
P 2 P 1 P 0 A 0

Doc 47
0.2443
0.3520
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000006/Articles/Tensor_product_of_modules.html
0 N 𝑓 N 𝑔 N ′′ 0
0 I R R / I 0

Doc 48
0.2443
0.2443
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000015/Articles/Exact_C*-algebra.html
0 A 𝑓 B 𝑔 C 0

Doc 49
0.2177
0.2177
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000003/Articles/Koszul_complex.html
0 R d 2 R 2 d 1 R 0 ,

Doc 50
0.2148
0.2148
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000006/Articles/Grothendieck_spectral_sequence.html
0 Z n K n 𝑑 B n + 1 0

Doc 51
0.1982
0.1982
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000002/Articles/Sheaf_(mathematics).html
0 K F Q 0.

Doc 52
0.1982
0.1982
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000001/Articles/Fundamental_group.html
1 Γ G H 1.

Doc 53
0.1975
0.6755
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000004/Articles/Spectral_sequence.html
0 E 2 1 , 0 H 1 E 0 , 1 0
0 E p - 1 , 1 H p E p , 0 0
0 E 0 , n 2 H n E 1 , n - 1 2 0
0 E 0 , q H q E n , q - n 0.

Doc 54
0.1833
0.1833
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000008/Articles/Metacyclic_group.html
1 K G H 1 ,

Doc 55
0.1774
0.2804
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000015/Articles/Complexification_(Lie_group).html
{ 1 } G o G Γ { 1 }
{ 1 } ( G o ) 𝐂 G 𝐂 Γ { 1 }

Doc 56
0.1571
0.1571
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000013/Articles/Castelnuovo–Mumford_regularity.html
F j F 0 M 0

Doc 57
0.1517
0.1517
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000004/Articles/Tor_functor.html
P 2 P 1 P 0 A 0

Doc 58
0.1497
0.1497
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000015/Articles/Proper_base_change_theorem.html
0 K 0 K 1 K n 0

Doc 59
0.1474
0.1474
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000009/Articles/Homotopy_category_of_chain_complexes.html
X i d X 0

Doc 60
0.1429
0.2690
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000005/Articles/Triangulated_category.html
X id X 0
X Y Z X Y

Doc 61
0.1366
0.1366
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000014/Articles/Hilbert–Burch_theorem.html
0 R m R n R R / I 0

Doc 62
0.1359
0.1359
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000006/Articles/Klein_geometry.html
H G G / H .

Doc 63
0.1346
0.1346
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000005/Articles/T-structure.html
X 0 X X 1

Doc 64
0.1261
0.1261
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000005/Articles/Crossed_module.html
1 A H G 1

Doc 65
0.1261
0.1261
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000012/Articles/Small_cancellation_theory.html
1 K G Q 1

Doc 66
0.1261
0.1261
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000016/Articles/P-group_generation_algorithm.html
1 Z H G 1

Doc 67
0.1186
0.1186
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000004/Articles/Complete_group.html
1 N G G 1

Doc 68
0.1094
0.1094
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000004/Articles/Compact_group.html
1 A G ~ 0 G 0 1

Doc 69
0.1045
0.1045
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000014/Articles/Bockstein_spectral_sequence.html
0 𝑝 / p 0

Doc 70
0.0946
0.1892
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000009/Articles/Mapping_cone_(homological_algebra).html
A = 0 A 0 0 ,
B = 0 B 0 0 ,