Entry Cameron:1992:RMG from tog.bib
Last update: Sat Sep 5 02:07:01 MDT 2009
Top |
Symbols |
Numbers |
Math |
A |
B |
C |
D |
E |
F |
G |
H |
I |
J |
K |
L |
M |
N |
O |
P |
Q |
R |
S |
T |
U |
V |
W |
X |
Y |
Z
BibTeX entry
@Article{Cameron:1992:RMG,
author = "Stephen Cameron and Yap Chee-Keng",
title = "Refinement Methods for Geometric Bounds in
Constructive Solid Geometry",
journal = j-TOG,
volume = "11",
number = "1",
pages = "12--39",
month = jan,
year = "1992",
CODEN = "ATGRDF",
ISSN = "0730-0301",
bibdate = "Fri Jan 5 07:58:42 MST 1996",
URL = "http://www.acm.org/pubs/toc/Abstracts/0730-0301/123764.html",
abstract = "In constructive solid geometry, geometric solids are
represented as trees whose leaves are labeled by
primitive solids and whose internal nodes are labeled
by set-theoretic operations. A {\em bounding function}
in this context is an upper or lower estimate on the
extent of the constituent sets; such bounds are
commonly used to speed up algorithms based on such
trees. We introduce the class of {\em totally
consistent bounding functions}, which have the
desirable properties of allowing surprisingly good
bounds to be built quickly. Both outer and inner bounds
can be refined using a set of rewrite rules, for which
we give some complexity and convergence results. We
have implemented the refinement rules for outer bounds
within a solid modeling system, where they have proved
especially useful for intersection testing in three and
four dimensions. Our implementations have used boxes as
bounds, but different classes (shapes) of bounds are
also explored. The rewrite rules are also applicable to
relatively slow, exact operations, which we explore for
their theoretical insight, and to general Boolean
algebras. Results concerning the relationship between
these bounds and active zones are also noted.",
acknowledgement = ack-nhfb,
keywords = "algorithms; design; performance; theory",
subject = "{\bf I.3.5}: Computing Methodologies, COMPUTER
GRAPHICS, Computational Geometry and Object Modeling,
Hierarchy and geometric transformations. {\bf F.2.2}:
Theory of Computation, ANALYSIS OF ALGORITHMS AND
PROBLEM COMPLEXITY, Nonnumerical Algorithms and
Problems, Computations on discrete structures. {\bf
F.2.2}: Theory of Computation, ANALYSIS OF ALGORITHMS
AND PROBLEM COMPLEXITY, Nonnumerical Algorithms and
Problems, Geometrical problems and computations. {\bf
I.1.1}: Computing Methodologies, ALGEBRAIC
MANIPULATION, Expressions and Their Representation,
Simplification of expressions. {\bf J.6}: Computer
Applications, COMPUTER-AIDED ENGINEERING,
Computer-aided design (CAD).",
}
Related entries
- active,
5(4)318,
8(1)51,
26(3)5,
26(3)13,
26(3)67,
27(3)30,
27(3)87,
27(5)132,
28(1)10
- AIDED, COMPUTER-,
4(1)12,
4(4)291,
5(1)1,
6(3)238,
6(4)274,
7(1)1,
7(1)42,
7(2)83,
7(3)198,
8(1)25,
8(1)51,
8(3)204,
8(4)263,
8(4)325,
8(4)335,
8(4)360,
9(2)147,
9(2)160,
9(2)212,
10(1)71,
10(3)297,
10(3)312,
10(4)366,
10(4)378,
11(2)140,
11(2)152,
12(1)56,
12(2)113,
12(3)209,
12(4)305,
12(4)327,
13(1)3,
13(3)277,
13(4)400,
14(2)103,
14(3)266,
16(1)34,
16(1)74,
16(2)155,
16(2)179,
16(3)319,
17(4)259,
18(1)35
- aided, Computer-,
4(1)12,
4(4)291,
5(1)1,
6(3)238,
6(4)274,
7(1)1,
7(1)42,
7(2)83,
7(3)198,
8(1)25,
8(1)51,
8(4)263,
8(4)325,
8(4)335,
8(4)360,
9(2)147,
9(2)160,
9(2)212,
10(1)71,
10(3)297,
10(3)312,
10(4)378,
11(2)140,
11(2)152,
12(1)56,
12(2)113,
12(3)209,
12(4)305,
13(1)3,
13(3)277,
13(4)400,
14(2)103,
14(3)266,
16(1)34,
16(2)155,
16(2)179,
17(4)259,
18(4)329,
19(1)27,
19(1)56
- algebra,
4(3)223,
5(2)110,
7(2)83,
8(1)51,
8(4)298,
9(2)212,
9(4)424,
10(4)342,
13(3)277,
21(1)52,
22(3)908,
23(3)787,
28(3)36
- ALGEBRAIC,
8(1)51,
8(3)174,
8(4)325,
16(2)179,
16(3)217,
17(1)1,
17(4)259
- ALGORITHMS,
2(4)237,
4(1)12,
4(4)276,
5(1)1,
6(1)19,
6(1)29,
7(1)1,
8(1)51,
8(4)325,
8(4)360,
9(1)66,
9(2)170,
11(1)1,
11(1)61,
12(3)233,
12(4)305,
12(4)327,
13(1)43,
13(1)73,
13(3)277,
14(2)134,
15(4)301,
15(4)354,
16(2)155,
16(3)319,
17(1)1,
17(4)259,
18(1)35
- allowing,
10(2)111,
12(4)305,
17(1)50,
18(2)96,
18(2)128,
18(2)195,
18(3)213,
26(2)9,
26(3)9,
26(3)22,
26(3)36,
26(3)46,
26(3)54,
26(3)55,
26(3)62,
26(3)72,
26(3)81,
26(3)89,
26(3)100,
26(3)107,
27(3)23,
27(3)37,
27(3)46,
27(3)50,
27(3)51,
27(3)60,
27(3)66,
27(3)78,
27(3)92,
27(3)102,
27(5)118,
27(5)137,
28(1)6,
28(2)18,
28(3)23,
28(3)41,
28(3)44,
28(3)63,
28(3)64
- applicable,
11(2)103,
13(3)277,
17(4)259,
19(2)79,
26(3)13,
26(4)16,
27(3)29,
27(3)64,
27(3)86,
27(3)98,
27(4)107,
28(3)47
- boolean,
5(1)1,
8(1)51,
9(2)212,
10(1)40,
11(2)152,
22(3)651,
24(3)1024,
27(3)79
- bound,
11(1)1,
12(2)160,
13(3)240,
15(4)354,
16(1)3,
16(3)260,
17(3)158,
18(3)213,
18(3)257,
19(1)56,
26(3)57,
27(3)23,
27(4)106,
27(5)128,
27(5)149,
28(2)19,
28(3)74,
28(3)97
- bounding,
3(1)52,
7(3)151,
10(2)152,
18(3)257,
26(1)6,
27(3)86,
28(3)47,
28(3)74
- box,
10(2)152,
15(4)332,
18(3)257,
26(3)57,
27(3)86,
28(2)13,
28(3)47
- built,
5(2)79,
15(3)179,
26(1)6,
26(3)5,
27(1)5,
27(3)71,
27(3)74,
27(5)108,
27(5)126,
28(3)97
- CAD,
4(1)12,
4(4)291,
5(1)1,
6(3)238,
6(4)274,
7(1)1,
7(1)42,
7(2)83,
7(3)198,
8(1)25,
8(1)51,
8(4)263,
8(4)325,
8(4)335,
8(4)360,
9(2)147,
9(2)160,
9(2)212,
10(1)71,
10(3)297,
10(3)312,
10(4)378,
11(2)140,
11(2)152,
12(1)56,
12(2)113,
12(3)209,
13(1)3,
13(3)277,
13(4)400,
14(1)21,
14(2)103,
14(3)266,
15(3)211,
16(1)34,
16(2)155,
16(2)179,
17(4)259,
18(2)195,
18(4)329,
19(1)27,
19(1)56,
26(3)31,
28(3)47
- class,
2(2)91,
4(4)291,
5(3)244,
11(1)1,
13(2)177,
13(4)376,
14(3)266,
16(1)34,
17(1)1,
17(4)209,
21(1)20,
26(3)3,
26(3)28,
26(3)60,
27(1)5,
27(3)22,
27(3)101,
27(5)112,
27(5)135,
27(5)157,
28(3)21
- commonly,
26(3)14,
26(3)35,
26(3)51,
26(3)62,
27(3)21,
27(3)25,
27(3)42,
27(5)138,
28(2)14,
28(3)40,
28(3)86
- COMPLEXITY,
2(4)237,
4(1)12,
4(4)276,
5(1)1,
6(1)19,
6(1)29,
7(1)1,
8(1)51,
8(4)325,
8(4)360,
9(1)66,
9(2)170,
11(1)1,
11(1)61,
12(3)233,
12(4)305,
12(4)327,
13(1)43,
13(1)73,
13(3)277,
14(2)134,
15(4)301,
15(4)354,
16(2)155,
16(3)319,
17(1)1,
17(4)259,
18(1)35
- complexity,
3(2)86,
3(4)244,
6(1)19,
7(2)103,
7(3)151,
9(3)245,
11(1)1,
14(3)203,
15(3)179,
15(3)249,
16(1)74,
17(3)177,
18(3)257,
19(2)79,
19(4)302,
26(3)14,
26(3)59,
26(3)79,
26(3)84,
26(3)90,
26(4)18,
27(2)13,
27(3)19,
27(3)32,
27(3)37,
27(3)60,
27(3)85,
27(4)106,
28(1)5,
28(2)14,
28(2)15,
28(3)21,
28(3)26,
28(3)37,
28(3)62,
28(3)63,
28(3)74,
28(4)104
- COMPUTER-AIDED,
4(1)12,
4(4)291,
5(1)1,
6(3)238,
6(4)274,
7(1)1,
7(1)42,
7(2)83,
7(3)198,
8(1)25,
8(1)51,
8(3)204,
8(4)263,
8(4)325,
8(4)335,
8(4)360,
9(2)147,
9(2)160,
9(2)212,
10(1)71,
10(3)297,
10(3)312,
10(4)366,
10(4)378,
11(2)140,
11(2)152,
12(1)56,
12(2)113,
12(3)209,
12(4)305,
12(4)327,
13(1)3,
13(3)277,
13(4)400,
14(2)103,
14(3)266,
16(1)34,
16(1)74,
16(2)155,
16(2)179,
16(3)319,
17(4)259,
18(1)35
- computer-aided,
4(1)12,
4(4)291,
5(1)1,
6(1)1,
6(3)238,
6(4)274,
7(1)1,
7(1)42,
7(2)83,
7(3)198,
8(1)25,
8(1)51,
8(2)100,
8(3)164,
8(3)204,
8(4)263,
8(4)325,
8(4)335,
8(4)360,
9(1)41,
9(2)147,
9(2)160,
9(2)170,
9(2)212,
9(3)301,
10(1)71,
10(3)297,
10(3)312,
10(4)378,
11(2)140,
11(2)152,
12(1)56,
12(2)113,
12(3)209,
12(4)305,
13(1)3,
13(3)277,
13(4)400,
14(2)103,
14(3)266,
16(1)34,
16(2)155,
16(2)179,
17(4)259,
18(1)35,
18(4)329,
19(1)27,
19(1)56
- consistent,
14(3)266,
26(2)7,
26(3)17,
26(3)42,
27(1)5,
27(3)82,
27(5)145,
27(5)155,
28(3)73,
28(3)84,
28(3)90
- constructive,
7(3)180,
10(1)40,
12(1)35,
14(3)266,
18(1)35
- context,
17(4)209,
20(4)232,
26(1)3,
26(3)47,
26(3)56,
26(3)96,
26(3)107,
26(4)16,
27(3)14,
27(3)32,
27(3)48,
27(3)67,
27(3)90,
27(5)154,
28(3)24,
28(3)61,
28(4)105
- convergence,
20(2)95,
26(3)2,
26(3)14,
27(3)21,
27(3)73,
27(3)93,
28(3)24,
28(3)70,
28(4)101
- desirable,
10(1)92,
15(3)211,
26(1)4,
26(3)55,
27(2)12,
27(3)67,
28(2)13,
28(3)97
- dimension,
9(3)245,
11(4)406,
14(1)3,
14(3)266,
15(2)121,
15(3)223,
18(1)35,
18(3)257,
24(2)209,
26(3)7,
26(3)24,
26(3)71,
26(3)74,
26(4)19,
27(3)20,
27(3)33,
27(3)46,
27(3)64,
27(4)107,
28(3)30,
28(3)47,
28(3)53,
28(4)103
- discrete,
6(1)19,
7(2)83,
8(2)121,
9(1)41,
9(3)301,
9(4)424,
13(1)3,
14(3)203,
15(4)301,
17(4)238,
21(2)88,
22(3)445,
25(2)412,
25(3)605,
25(3)1144,
26(1)4,
26(1)5,
26(3)56,
26(3)65,
26(3)97,
27(3)37,
27(3)63,
27(3)76,
27(3)77,
27(5)144,
27(5)162,
27(5)164,
28(1)7,
28(2)16,
28(3)37,
28(3)56,
28(3)72,
28(3)79,
28(4)104
- ENGINEERING,
4(1)12,
4(4)291,
5(1)1,
5(2)110,
5(3)179,
5(3)244,
5(4)283,
5(4)318,
5(4)345,
6(3)238,
6(4)274,
7(1)1,
7(1)42,
7(2)83,
7(3)180,
7(3)198,
8(1)25,
8(1)51,
8(3)204,
8(4)263,
8(4)325,
8(4)335,
8(4)360,
9(1)28,
9(1)133,
9(2)147,
9(2)160,
9(2)212,
10(1)1,
10(1)71,
10(2)111,
10(2)201,
10(3)213,
10(3)297,
10(3)312,
10(4)366,
10(4)378,
11(2)140,
11(2)152,
12(1)56,
12(2)113,
12(3)209,
12(4)277,
12(4)305,
12(4)327,
13(1)3,
13(1)43,
13(3)209,
13(3)277,
13(4)400,
14(2)103,
14(3)266,
15(3)211,
15(4)265,
16(1)34,
16(1)74,
16(2)155,
16(2)179,
16(3)319,
17(4)259,
18(1)35
- especially,
15(3)211,
19(3)185,
20(4)232,
26(3)64,
27(1)6,
27(5)162,
28(3)26
- estimate,
11(2)140,
13(3)240,
14(1)77,
18(2)171,
19(2)122,
26(2)9,
26(3)1,
26(3)9,
26(3)23,
26(3)68,
26(3)74,
26(3)77,
27(3)59,
27(3)70,
27(3)72,
27(5)130,
27(5)133,
27(5)134,
27(5)139,
28(1)1,
28(3)28,
28(3)98,
28(4)104
- exact,
3(3)223,
11(4)373,
12(4)348,
13(2)156,
13(3)240,
14(3)233,
15(3)223,
16(4)359,
17(3)143,
18(2)128,
24(3)553,
26(3)78,
27(1)2,
27(5)164,
28(3)74,
28(4)104
- explore,
13(2)156,
19(4)279,
26(3)31,
26(3)64,
26(3)76,
26(4)17,
27(3)38,
27(3)56,
27(3)60,
27(3)101,
27(5)122,
27(5)127,
28(3)23,
28(3)68
- explored,
16(2)155,
20(3)151,
26(2)11
- expression,
4(3)223,
5(4)318,
8(1)51,
13(3)256,
14(3)266,
18(3)278,
19(1)27,
19(4)246,
26(3)33,
26(3)52,
26(3)108,
27(3)78,
27(5)121,
28(3)34,
28(3)57
- extent,
5(2)79,
26(3)75,
26(3)104,
26(4)18,
27(3)33,
27(3)85
- F.2.2,
2(4)237,
4(1)12,
4(4)276,
5(1)1,
6(1)19,
6(1)29,
7(1)1,
8(1)51,
9(1)66,
9(2)170,
11(1)1,
12(4)305,
13(1)43,
13(1)73,
13(3)277,
15(4)301,
15(4)354,
17(4)259,
18(1)35,
18(3)257
- four,
10(1)71,
11(3)228,
13(4)337,
16(4)420,
17(1)1,
19(2)79,
26(3)68,
27(3)46,
27(4)104,
27(5)138,
28(3)55,
28(3)95
- general,
1(1)1,
1(3)191,
4(1)1,
4(2)74,
9(1)1,
9(2)160,
9(4)424,
10(1)1,
10(2)182,
11(2)183,
12(1)35,
12(2)136,
12(3)251,
13(1)3,
13(3)308,
13(4)400,
15(1)1,
15(1)37,
15(1)72,
15(3)223,
15(4)301,
16(2)179,
16(3)296,
16(3)319,
17(1)32,
17(2)71,
17(2)84,
17(2)116,
17(3)158,
17(4)238,
17(4)259,
18(1)35,
18(1)56,
18(2)96,
18(2)128,
18(2)171,
18(2)195,
18(3)257,
18(4)329,
18(4)361,
19(1)27,
19(4)246,
19(4)279,
22(2)131,
26(3)24,
26(3)58,
26(3)76,
26(3)96,
27(2)13,
27(3)19,
27(3)22,
27(3)46,
27(3)62,
27(4)106,
27(5)126,
27(5)127,
27(5)135,
27(5)143,
27(5)145,
27(5)148,
28(1)10,
28(2)16,
28(3)65,
28(3)74,
28(3)80,
28(3)81
- geometrical,
2(4)237,
3(4)244,
4(1)12,
4(4)276,
5(1)1,
7(1)1,
8(1)51,
9(1)66,
9(2)170,
11(1)1,
12(4)305,
13(1)43,
13(3)277,
14(3)266,
15(4)354,
17(4)259,
18(1)35,
18(3)257,
18(3)278
- give,
13(2)156,
13(4)337,
15(3)179,
16(4)359,
17(3)177,
18(4)316,
19(4)302,
20(2)95,
26(3)9,
26(3)17,
26(3)32,
26(3)85,
26(3)100,
27(2)10,
27(3)24,
27(3)32,
27(5)149,
28(1)11,
28(3)96
- good,
7(3)151,
10(1)92,
11(3)259,
14(3)203,
15(4)301,
15(4)354,
16(3)319,
20(1)39,
21(1)52,
26(3)6,
26(3)22,
26(3)45,
26(3)51,
26(3)57,
26(3)78,
26(3)97,
26(3)101,
27(5)120,
28(1)1,
28(1)2,
28(2)13,
28(3)24,
28(3)29,
28(3)40,
28(3)48,
28(3)60
- hierarchy,
5(2)79,
9(1)28,
13(2)177,
13(3)256,
13(3)308,
14(3)266,
14(4)363,
15(3)179,
16(1)3,
17(3)177,
18(2)128,
18(4)293,
19(3)204,
21(4)833,
26(1)6,
27(3)101,
28(3)56,
28(3)74
- I.1.1,
8(1)51,
19(1)27
- implementation,
5(3)244,
9(1)66,
9(1)105,
10(1)71,
11(3)276,
12(2)160,
13(1)3,
13(1)43,
13(3)300,
13(4)313,
14(1)21,
14(1)77,
15(1)37,
17(2)84,
17(3)177,
18(2)128,
18(4)361,
20(3)169,
22(3)908,
26(2)12,
26(3)26,
26(3)55,
26(3)59,
26(3)72,
26(3)82,
26(3)90,
26(3)91,
26(3)99,
27(1)9,
27(3)20,
27(3)24,
27(3)51,
27(3)54,
27(3)57,
27(3)92,
27(4)104,
27(4)105,
27(5)116,
27(5)143,
28(1)4,
28(1)9,
28(2)12,
28(2)13,
28(3)21,
28(3)41,
28(3)66,
28(3)67,
28(3)74
- implemented,
3(1)52,
10(1)71,
12(2)113,
12(4)327,
13(3)209,
15(3)223,
17(3)158,
18(4)293,
19(2)79,
26(3)15,
26(3)39,
26(3)90,
27(1)9,
27(3)19,
27(3)29,
27(3)36,
27(3)91,
27(5)122,
28(3)41,
28(3)47
- insight,
12(2)113,
13(4)337,
21(1)52,
26(3)4,
26(3)18,
26(3)62,
26(4)13,
26(4)20,
27(3)26,
27(4)106,
28(3)24,
28(3)48
- internal,
13(2)103,
18(2)195,
23(3)322,
26(3)24,
26(3)57,
26(3)72,
28(3)58
- intersection,
2(3)161,
3(3)223,
4(4)291,
6(4)274,
8(1)25,
8(3)174,
8(3)235,
9(2)147,
10(1)92,
10(4)378,
11(2)140,
13(1)73,
13(3)277,
13(3)308,
13(4)337,
13(4)400,
14(1)21,
15(3)223,
16(1)74,
16(3)296,
18(3)257,
25(3)1154,
27(1)3,
27(3)79,
27(3)87,
28(3)47,
28(3)84
- J.6,
4(1)12,
4(4)291,
5(1)1,
6(3)238,
6(4)274,
7(1)1,
7(1)42,
7(2)83,
7(3)198,
8(1)25,
8(1)51,
8(3)204,
8(4)263,
8(4)325,
8(4)335,
8(4)360,
9(2)147,
9(2)160,
9(2)212,
10(1)71,
10(3)297,
10(3)312,
10(4)366,
10(4)378,
11(2)140,
11(2)152,
12(1)56,
12(2)113,
12(3)209,
12(4)305,
12(4)327,
13(1)3,
13(3)277,
13(4)400,
14(2)103,
14(3)266,
16(1)34,
16(1)74,
16(2)155,
16(2)179,
16(3)319,
17(4)259,
18(1)35,
18(4)329,
19(1)27,
19(1)56
- leave,
24(3)712,
26(3)88,
26(4)19,
27(3)59,
27(5)108,
27(5)109
- lower,
13(4)400,
27(3)32,
27(5)137,
28(3)42,
28(3)93
- MANIPULATION,
8(1)51,
8(3)174,
8(4)325,
16(2)179,
16(3)217,
17(1)1,
17(4)259
- node,
7(3)151,
14(4)363,
19(3)185,
20(1)1,
23(3)385,
26(3)13,
26(3)65,
26(3)80,
27(5)126
- Nonnumerical,
2(4)237,
4(1)12,
4(4)276,
5(1)1,
6(1)19,
6(1)29,
7(1)1,
8(1)51,
9(1)66,
9(2)170,
11(1)1,
12(4)305,
13(1)43,
13(1)73,
13(3)277,
15(4)301,
15(4)354,
17(4)259,
18(1)35,
18(3)257
- noted,
17(1)1
- operation,
3(4)244,
5(1)1,
9(2)170,
11(1)40,
11(2)152,
11(3)276,
13(1)73,
13(2)156,
14(1)21,
15(3)211,
15(3)223,
16(3)319,
17(4)209,
18(3)213,
19(1)27,
19(2)79,
21(1)20,
22(3)651,
26(1)2,
26(3)45,
26(3)53,
26(3)55,
26(3)64,
26(3)66,
26(3)86,
26(3)91,
26(3)101,
26(3)104,
27(3)17,
27(3)21,
27(3)46,
27(3)59,
27(3)80,
27(3)92,
27(3)93,
27(3)97,
27(3)103,
27(5)116,
27(5)118,
27(5)134,
27(5)148,
27(5)159,
27(5)160,
28(1)8,
28(3)23,
28(3)58,
28(3)66,
28(3)67,
28(3)72,
28(3)86,
28(4)104
- outer,
27(5)140
- primitive,
2(2)135,
4(2)74,
7(3)151,
9(3)245,
10(1)40,
13(2)103,
13(2)177,
13(3)277,
15(3)223,
17(2)116,
20(3)169,
26(3)44,
26(3)46,
26(3)90,
27(3)92,
27(5)126,
27(5)135,
27(5)143,
27(5)144,
28(2)19
- PROBLEM,
2(4)237,
4(1)12,
4(4)276,
5(1)1,
6(1)19,
6(1)29,
7(1)1,
8(1)51,
8(4)325,
8(4)360,
9(1)66,
9(2)170,
11(1)1,
11(1)61,
12(3)233,
12(4)305,
12(4)327,
13(1)43,
13(1)73,
13(3)277,
14(2)134,
15(4)301,
15(4)354,
16(2)155,
16(3)319,
17(1)1,
17(4)259,
18(1)35
- property,
6(2)81,
9(2)198,
9(4)424,
10(1)92,
11(2)127,
11(4)373,
15(3)179,
16(3)319,
17(1)50,
17(2)84,
17(3)158,
17(4)259,
18(1)56,
18(4)361,
19(3)204,
20(2)95,
20(3)169,
20(4)203,
21(1)1,
21(1)20,
23(3)488,
25(3)1003,
26(1)2,
26(1)4,
26(1)5,
26(2)7,
26(2)10,
26(3)3,
26(3)23,
26(3)59,
26(3)60,
26(3)78,
26(3)90,
26(4)15,
26(4)16,
27(1)2,
27(1)4,
27(1)7,
27(1)9,
27(2)13,
27(3)20,
27(3)35,
27(3)42,
27(3)48,
27(3)60,
27(3)65,
27(3)76,
27(3)78,
27(3)87,
27(3)88,
27(3)89,
27(5)131,
27(5)132,
27(5)162,
27(5)164,
28(1)5,
28(1)6,
28(2)13,
28(3)24,
28(3)25,
28(3)28,
28(3)30,
28(3)33,
28(3)34,
28(3)51,
28(3)52,
28(3)54,
28(3)73,
28(3)91,
28(4)105
- proved,
16(2)179,
27(5)128,
28(2)13
- quickly,
20(3)169,
26(2)9,
26(3)11,
26(3)14,
26(3)44,
26(3)86,
26(3)92,
26(3)94,
27(3)40,
27(3)50,
27(5)119,
27(5)122,
27(5)124,
27(5)137,
28(2)13,
28(3)24,
28(3)27,
28(3)53,
28(3)69,
28(3)88,
28(3)92,
28(3)94
- refined,
5(4)318,
19(3)164,
20(1)1,
26(3)34,
26(3)90,
27(3)40,
27(3)44,
27(3)50,
27(3)72,
28(3)94
- refinement,
9(1)41,
15(1)37,
16(4)420,
18(2)128,
19(2)122,
19(4)302,
22(2)131,
23(3)276,
26(3)25,
26(4)20,
27(5)108,
27(5)117,
27(5)141,
28(3)41,
28(3)75
- relationship,
9(1)1,
11(1)40,
13(4)400,
14(1)58,
16(2)155,
18(1)35,
26(3)27,
27(3)27,
27(3)61,
27(5)121,
28(3)89
- relatively,
11(2)152,
11(4)336,
13(2)177,
15(3)223,
17(2)116,
26(3)45,
26(3)74,
26(3)100,
27(4)105,
27(5)132,
27(5)152,
28(3)26,
28(3)29,
28(3)98
- represented,
10(1)1,
12(4)305,
13(1)3,
13(2)156,
13(3)256,
19(2)79,
19(4)302,
26(3)80,
26(3)83,
26(4)19,
27(1)3,
27(3)36,
27(3)41,
27(5)128,
28(1)6,
28(3)30,
28(3)34,
28(3)83
- rule,
10(1)1,
16(4)420,
17(2)116,
26(3)85,
26(3)88,
27(3)38,
27(3)62,
27(3)102,
27(5)165,
28(3)46,
28(3)80
- set-theoretic,
17(2)71
- simplification,
8(1)51,
19(3)204,
21(2)88,
21(2)207,
22(3)543,
22(3)689,
23(3)276,
24(2)209,
24(3)445,
26(2)7,
26(3)79,
26(4)15,
27(3)32,
27(3)45,
27(3)100,
27(5)137,
27(5)148
- slow,
18(3)213,
19(4)302,
26(3)73,
26(3)82,
28(3)53
- speed,
7(3)151,
11(3)276,
13(1)3,
15(4)265,
17(3)143,
18(2)96,
19(2)122,
20(1)39,
26(3)9,
26(3)14,
26(3)36,
26(3)46,
26(3)58,
26(3)89,
26(3)105,
27(1)1,
27(3)20,
27(3)52,
27(3)71,
27(3)78,
27(5)126,
27(5)127,
28(3)39,
28(3)52,
28(3)64,
28(3)67
- surprisingly,
7(3)151,
14(3)203,
19(4)279,
26(3)20,
26(3)38
- testing,
13(1)3
- theoretic, set-,
17(2)71
- theoretical,
12(2)113,
15(4)354,
16(3)217,
16(3)296,
17(3)177,
18(3)257,
26(1)2,
26(3)28,
26(3)60,
26(3)62,
26(3)69,
26(3)99,
27(1)4,
27(3)32,
27(5)128,
27(5)131,
28(3)24,
28(3)75
- three,
5(3)244,
7(3)151,
9(1)1,
9(3)245,
10(4)378,
11(3)276,
15(2)121,
15(3)223,
17(1)1,
17(2)84,
19(1)1,
20(1)10,
25(3)805,
26(1)6,
26(3)36,
26(3)71,
26(3)85,
27(3)21,
27(3)39,
27(3)46,
27(3)84,
27(5)123,
27(5)134,
27(5)138,
28(1)4,
28(3)26,
28(3)65,
28(3)72,
28(3)87
- transformation,
1(3)215,
1(4)259,
4(4)276,
6(1)79,
6(4)308,
9(1)28,
9(4)424,
13(2)177,
13(3)256,
13(3)277,
13(3)308,
14(3)266,
15(1)72,
16(4)359,
17(4)209,
18(3)278,
18(4)293,
21(3)380,
24(2)289,
24(3)756,
26(3)21,
26(3)35,
26(3)63,
26(3)76,
26(3)80,
26(3)83,
26(4)15,
27(3)17,
27(3)43,
27(3)85,
27(4)105,
27(4)106,
27(5)111,
28(3)72
- tree,
3(1)52,
3(4)266,
7(1)42,
7(2)129,
9(3)278,
10(1)40,
11(1)92,
11(3)228,
14(4)363,
17(2)84,
22(3)453,
22(3)657,
23(3)720,
25(3)735,
26(3)87,
26(3)88,
26(4)19,
27(3)53,
27(5)108,
27(5)109,
27(5)114,
27(5)126,
27(5)128,
28(3)58,
28(3)91
- upper,
18(3)257,
27(5)112,
27(5)126,
28(3)55,
28(3)97,
28(4)99
- useful,
9(3)245,
11(3)201,
11(3)276,
13(1)43,
13(2)177,
13(4)313,
16(1)34,
16(4)359,
17(1)1,
17(4)209,
17(4)259,
19(2)79,
21(1)20,
26(2)7,
26(3)24,
26(3)26,
26(3)62,
26(3)64,
27(1)5,
27(3)26,
27(3)44,
27(3)45,
27(3)56,
27(3)62,
27(4)106,
27(5)111,
27(5)159,
28(1)6,
28(3)34,
28(3)36,
28(3)67
- where,
4(4)291,
9(3)245,
11(1)40,
11(1)61,
11(4)348,
13(4)313,
13(4)337,
14(4)363,
17(1)1,
17(2)71,
17(2)116,
18(1)56,
18(4)316,
19(2)79,
19(3)185,
19(4)302,
20(3)151,
26(1)3,
26(2)8,
26(3)10,
26(3)18,
26(3)43,
26(3)50,
26(3)57,
26(3)60,
26(3)63,
26(3)74,
26(3)78,
26(3)86,
26(3)94,
26(3)101,
26(4)14,
27(1)7,
27(1)8,
27(3)33,
27(3)52,
27(3)58,
27(3)69,
27(3)85,
27(3)86,
27(3)88,
27(4)104,
27(5)114,
27(5)121,
27(5)130,
27(5)134,
27(5)145,
27(5)146,
27(5)147,
27(5)153,
27(5)157,
27(5)159,
27(5)163,
28(1)9,
28(2)18,
28(3)33,
28(3)42,
28(3)55,
28(3)67,
28(3)71,
28(3)77,
28(3)82,
28(3)84,
28(3)94,
28(3)98,
28(4)104
- whose,
11(1)40,
11(3)201,
12(2)160,
13(1)3,
13(3)240,
13(4)337,
19(2)79,
20(1)1,
20(2)67,
26(1)6,
26(3)20,
26(3)44,
26(3)46,
26(3)56,
26(3)57,
26(3)83,
26(3)104,
26(4)18,
27(1)5,
27(3)27,
27(3)53,
27(3)77,
27(3)92,
27(3)95,
27(5)147,
27(5)166,
28(3)34,
28(3)77
- zone,
8(1)51