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Returned 84 matches (100 formulae, 95 docs)
Lookup 3.797 ms, Re-ranking 178.092 ms
Found 74312 tuple postings, 27024 formulae, 8915 documents
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[ documents ]
[ documents-by-formula ]
Doc 1
1.0000
6.6703
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000002/Articles/Quadratic_function.html
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Doc 2
1.0000
5.5895
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000001/Articles/Quadratic_equation.html
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Doc 3
1.0000
3.5385
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000002/Articles/Monic_polynomial.html
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Doc 4
1.0000
2.0000
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000007/Articles/Sridhara.html
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Doc 5
1.0000
1.8966
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000012/Articles/Algebra.html
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Doc 6
1.0000
1.6812
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000001/Articles/Elementary_algebra.html
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Doc 7
1.0000
1.0000
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000008/Articles/Help:Displaying_a_formula.html
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Doc 8
1.0000
1.0000
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000005/Articles/Algebraic_solution.html
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Doc 9
1.0000
1.0000
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000009/Articles/Periodic_continued_fraction.html
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Doc 10
1.0000
1.0000
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000002/Articles/Loss_of_significance.html
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Doc 11
0.9744
0.9744
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000001/Articles/Gerolamo_Cardano.html
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Doc 12
0.8974
2.1987
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000001/Articles/Quadratic_formula.html
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,
Doc 13
0.8966
3.1964
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000009/Articles/Solving_quadratic_equations_with_continued_fractions.html
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Doc 14
0.8966
1.3671
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000012/Articles/Portal:Algebra::Selected_article::4.html
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Doc 15
0.8966
0.8966
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000003/Articles/Closed-form_expression.html
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Doc 16
0.7949
0.7949
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000014/Articles/Numeric_precision_in_Microsoft_Excel.html
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Doc 17
0.7949
0.7949
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000008/Articles/Line–sphere_intersection.html
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Doc 18
0.7949
0.7949
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000007/Articles/Reduction_of_order.html
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Doc 19
0.7949
0.7949
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000002/Articles/Huzita–Hatori_axioms.html
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Doc 20
0.7632
4.3025
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000001/Articles/Parabola.html
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Doc 21
0.7632
1.4455
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000006/Articles/Rational_trigonometry.html
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Doc 22
0.7632
0.7632
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000001/Articles/Slope.html
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Doc 23
0.7632
0.7632
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000001/Articles/Asymptote.html
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Doc 24
0.7632
0.7632
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000015/Articles/Möbius_plane.html
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Doc 25
0.7619
4.9768
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000001/Articles/Discriminant.html
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Doc 26
0.7619
4.3204
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000002/Articles/Completing_the_square.html
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Doc 27
0.7619
3.9563
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000015/Articles/Euler_substitution.html
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c
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∫
R
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)
d
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Doc 28
0.7619
1.8554
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000012/Articles/Integration_by_reduction_formulae.html
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I
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∫
(
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n
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Doc 29
0.7619
1.5238
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000002/Articles/Factorization.html
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Doc 30
0.7619
1.5238
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000001/Articles/MathML.html
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Doc 31
0.7619
1.3619
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000015/Articles/GEORGE_(programming_language).html
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Doc 32
0.7619
0.7619
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000002/Articles/Bode_plot.html
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Doc 33
0.7619
0.7619
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000001/Articles/Coefficient.html
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Doc 34
0.7619
0.7619
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000001/Articles/Algebraic_number.html
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Doc 35
0.7619
0.7619
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000002/Articles/Irreducible_polynomial.html
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Doc 36
0.7213
0.7213
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000001/Articles/Digital_filter.html
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x
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x
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Doc 37
0.7179
0.7179
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000004/Articles/Periodic_points_of_complex_quadratic_mappings.html
A
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=
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Doc 38
0.7179
0.7179
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000003/Articles/Quadratic_Gauss_sum.html
a
n
2
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b
n
+
q
=
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Doc 39
0.6988
1.3292
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000015/Articles/Distance_between_two_straight_lines.html
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1
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a
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,
Doc 40
0.6988
1.3292
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000004/Articles/Parallel_(geometry).html
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1
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0
a
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Doc 41
0.6857
1.6730
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000007/Articles/Variable_(mathematics).html
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,
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↦
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c
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a
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3
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b
x
2
+
c
x
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d
=
0
,
Doc 42
0.6857
1.2250
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000013/Articles/Constant_(mathematics).html
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c
,
x
↦
a
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b
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+
c
,
Doc 43
0.6857
1.1039
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000003/Articles/Seki_Takakazu.html
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b
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c
.
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Doc 44
0.6857
0.6857
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000002/Articles/Constant_term.html
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,
Doc 45
0.6824
0.6824
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000012/Articles/Tangent_lines_to_circles.html
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Doc 46
0.6824
0.6824
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000001/Articles/Linear_equation.html
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x
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y
+
c
=
0
,
Doc 47
0.6812
2.2044
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000009/Articles/History_of_algebra.html
x
2
+
p
x
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0
x
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a
x
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b
x
=
c
x
+
a
x
+
b
x
=
c
Doc 48
0.6667
2.0926
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000002/Articles/Quintic_function.html
x
5
+
a
x
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x
5
+
a
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0
,
x
5
+
a
x
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b
x
5
+
a
x
2
+
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Doc 49
0.6667
0.6667
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000008/Articles/Erland_Samuel_Bring.html
x
5
+
p
x
+
q
=
0
Doc 50
0.6500
0.6500
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000002/Articles/Abel–Ruffini_theorem.html
a
x
2
+
b
x
+
c
=
0
,
a
≠
0
Doc 51
0.6301
0.6301
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000014/Articles/Jigu_Suanjing.html
x
4
+
p
x
2
+
q
=
0
Doc 52
0.6000
3.0000
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000015/Articles/Laguerre_plane.html
y
=
a
x
2
+
b
x
+
c
y
=
a
x
2
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b
x
+
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y
=
a
x
2
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b
x
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c
y
=
a
x
2
+
b
x
+
c
z
=
a
x
2
+
b
x
+
c
Doc 53
0.6000
1.2000
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000012/Articles/Benz_plane.html
y
=
a
x
2
+
b
x
+
c
y
=
a
x
2
+
b
x
+
c
Doc 54
0.5974
0.5974
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000006/Articles/Nested_radical.html
x
3
+
p
x
+
q
=
0
,
Doc 55
0.5714
1.4286
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000001/Articles/Diophantus.html
a
x
2
+
b
x
=
c
a
x
2
=
b
x
+
c
a
x
2
+
c
=
b
x
Doc 56
0.5714
0.5714
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000005/Articles/Lenstra–Lenstra–Lovász_lattice_basis_reduction_algorithm.html
a
r
2
+
b
r
+
c
Doc 57
0.5714
0.5714
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000002/Articles/Brahmagupta.html
a
x
2
+
b
x
=
c
Doc 58
0.5714
0.5714
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000005/Articles/Indian_mathematics.html
a
x
2
+
b
x
=
c
Doc 59
0.5600
2.9683
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000002/Articles/Cubic_function.html
x
3
+
b
x
2
+
c
x
+
d
=
0
x
3
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b
x
2
+
c
x
+
d
=
0
a
x
3
+
b
x
2
+
c
x
+
d
=
0
a
x
3
+
b
x
2
+
c
x
+
d
=
0
a
x
3
+
b
x
2
+
c
x
+
d
=
0.
a
x
3
+
b
x
2
+
c
x
+
d
=
0
(
1
)
Doc 60
0.5472
0.5472
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000001/Articles/Linear_algebra.html
λ
:
a
x
+
b
y
+
c
=
0
,
Doc 61
0.5393
0.5393
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000015/Articles/Parent_function.html
y
=
a
x
2
+
b
x
+
c
,
Doc 62
0.5393
0.5393
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000003/Articles/Curve_fitting.html
y
=
a
x
2
+
b
x
+
c
.
Doc 63
0.5366
0.5366
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000004/Articles/Cyclonic_separation.html
x
′′
+
c
1
x
′
+
c
2
=
0
Doc 64
0.5306
0.5306
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000003/Articles/Field_trace.html
a
x
2
+
b
x
+
c
=
0
,
with
a
≠
0
,
Doc 65
0.5217
1.0217
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000011/Articles/Permutation_polynomial.html
g
(
x
)
=
a
x
2
+
b
x
+
c
a
x
2
+
b
x
Doc 66
0.5217
0.5217
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000004/Articles/Vieta's_formulas.html
P
(
x
)
=
a
x
2
+
b
x
+
c
Doc 67
0.5217
0.5217
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000004/Articles/Polynomial_remainder_theorem.html
f
(
x
)
=
a
x
2
+
b
x
+
c
Doc 68
0.5217
0.5217
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000001/Articles/Prime_number.html
f
(
n
)
=
a
x
2
+
b
x
+
c
Doc 69
0.5217
0.5217
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000001/Articles/Parameter.html
f
(
x
)
=
a
x
2
+
b
x
+
c
Doc 70
0.5000
1.7898
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000007/Articles/Bring_radical.html
x
5
+
d
1
x
+
d
0
=
0
x
5
+
d
1
x
+
d
0
=
0
a
x
N
+
b
x
2
+
c
=
0
,
N
≡
1
(
mod
2
)
x
5
+
c
2
x
2
+
c
1
x
+
c
0
=
0
Doc 71
0.4956
0.9469
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000009/Articles/Casus_irreducibilis.html
a
x
3
+
b
x
2
+
c
x
+
d
=
0
a
x
3
+
b
x
2
+
c
x
+
d
=
0.
Doc 72
0.4928
0.4928
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000016/Articles/Draft:Leaving_Certificate_Mathematics_Ordinary_Level.html
x
2
+
2
x
+
5
=
0
Doc 73
0.4928
0.4928
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000011/Articles/Extraneous_and_missing_solutions.html
x
2
+
4
x
+
4
=
0
Doc 74
0.4706
0.8471
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000009/Articles/Distance_from_a_point_to_a_plane.html
a
x
+
b
y
+
c
z
a
x
+
b
y
+
c
z
=
d
Doc 75
0.4706
0.4706
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000009/Articles/Portal:Mathematics::Selected_article::31.html
f
(
x
)
=
a
x
2
+
b
x
+
c
.
Doc 76
0.4660
0.4660
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000001/Articles/Normal_distribution.html
f
(
x
)
=
e
a
x
2
+
b
x
+
c
Doc 77
0.4632
0.4632
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000007/Articles/Tridiagonal_matrix_algorithm.html
a
1
x
n
+
b
1
x
1
+
c
1
x
2
Doc 78
0.4571
0.4571
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000003/Articles/Nagell–Lutz_theorem.html
y
2
=
x
3
+
a
x
2
+
b
x
+
c
Doc 79
0.4533
0.8819
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000007/Articles/Babylonian_mathematics.html
a
x
3
+
b
x
2
=
c
.
x
2
+
b
x
=
c
Doc 80
0.4400
0.4400
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000012/Articles/Like_terms.html
a
x
+
b
x
Doc 81
0.4337
0.4337
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000004/Articles/List_of_important_publications_in_mathematics.html
a
x
2
+
b
y
2
+
c
x
y
Doc 82
0.4337
0.4337
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000002/Articles/Joseph-Louis_Lagrange.html
a
x
2
+
b
y
2
+
c
x
y
Doc 83
0.3916
1.7683
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000002/Articles/Quartic_function.html
x
4
+
a
x
3
+
b
x
2
+
c
x
+
d
=
0
x
4
+
a
x
3
+
b
x
2
+
c
x
+
d
=
0
,
a
x
4
+
b
x
3
+
c
x
2
+
d
x
+
e
=
0
a
x
4
+
b
x
3
+
c
x
2
+
d
x
+
e
=
0
a
x
4
+
b
x
3
+
c
x
2
+
d
x
+
e
=
0
,
Doc 84
0.3765
1.1294
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000003/Articles/Incidence_(geometry).html
a
x
+
b
y
+
c
z
=
0
a
x
+
b
y
+
c
z
=
0
a
x
+
b
y
+
c
z
=
0
Doc 85
0.3765
0.3765
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000016/Articles/Intersection_(Euclidean_geometry).html
a
x
+
b
y
+
c
z
=
d
Doc 86
0.3765
0.3765
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000004/Articles/Transformation_matrix.html
a
x
+
b
y
+
c
z
=
0
Doc 87
0.3765
0.3765
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000003/Articles/Duality_(projective_geometry).html
a
x
+
b
y
+
c
z
=
0
Doc 88
0.3710
0.6769
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000003/Articles/Catastrophe_theory.html
V
=
x
5
+
a
x
3
+
b
x
2
+
c
x
V
=
x
4
+
a
x
2
+
b
x
Doc 89
0.3600
0.3600
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000001/Articles/Quadratic_reciprocity.html
a
x
2
+
b
y
2
+
c
z
2
=
0
Doc 90
0.3600
0.3600
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000001/Articles/Number_theory.html
a
x
2
+
b
y
2
+
c
z
2
=
0
Doc 91
0.3396
0.3396
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000002/Articles/Normal_(geometry).html
a
x
+
b
y
+
c
z
+
d
=
0
Doc 92
0.3396
0.3396
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000001/Articles/Equation.html
a
x
+
b
y
+
c
z
+
d
=
0
Doc 93
0.3396
0.3396
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000002/Articles/Plane_(geometry).html
a
x
+
b
y
+
c
z
+
d
=
0
Doc 94
0.3357
0.3357
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000006/Articles/Hilbert's_thirteenth_problem.html
x
7
+
a
x
3
+
b
x
2
+
c
x
+
1
=
0
Doc 95
0.3259
0.3259
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000014/Articles/Poincaré_disk_model.html
x
2
+
y
2
+
a
x
+
b
y
+
1
=
0
,