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File: TortureTests/Complexity/complex300.xml
Author: Mackichan Software (S. Swanson)
Description: Around 300 equation tests. Red coloring added in markup.
Sample Rendering: N/A

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M1 2 a b

M2 x 3

M3 f ( x ) + sin cos θ = 1

M4
f ( z ) = n = 0 a n z n ,  | z | < R ( R 0 )

M5
C ( n = 0 a n z n ) z = n = 0 a n C z n z

M6
lim n | C [ f ( z ) k = 0 n a k z k ] z | = 0

M7
n N ( ε ) | f ( z ) k = 0 n a k z k | < ε

M8 10  Bq + 10  Ci

M9 10  amol + 10  Emol 10  fmol + 10  Gmol 10  kmol + 10  Mmol

M10 10  μmol + 10  mmol 10  mol + 10  nmol 10  Pmol + 10  pmol 10  Tmol

M11 10  acre + 10  hectare 10  ft 2 + 10  in 2 10  m 2

M12 10  A + 10  kA 10  μA + 10  mA 10  nA

M13 10  F + 10  μF 10  mF + 10  nF 10  pF

M14 10  C + 1.0  m/s/s 0.1  m / s 2

M15 10  kS + 10  μS 10  mS + 10  S

M16 10  kV + 10  MV 10  μV + 10  mV 10  nV + 10  pV 10  V

M17 10  GΩ + 10  kΩ 10  MΩ + 10  mΩ 10  Ω

M18 10  Btu + 10  cal 10  eV + 10  erg 10  GeV + 10  GJ

M19 10  J + 10  kcal 10  kJ + 10  MeV 10  MJ + 10  μJ 10  mJ + 10  nJ

M20 10  dyn + 10  kN 10  MN + 10  μN 10  mN + 10  N 10  ozf + 10  lbf

M21 10  EHz + 10  GHz 10  Hz + 10  kHz 10  MHz + 10  PHz 10  THz

M22 10  fc + 10  lx 10  phot

M23 10  Å + 10  am 10  cm + 10  dm 10  fm + 10  ft 10  in

M24 10  km + 10  m 10  μm + 10  mi 10  mm + 10  nm 10  pm

M25 10  sb

M26 10  lm

M27 10  cd

M28 10  Mx + 10  μWb 10  mWb + 10  nWb 10  Wb

M29 10  G + 10  μT 10  mT + 10  nT 10  pT + 10  T

M30 10  H + 10  μH 10  mH

M31 10  u + 10  cg 10  dg + 10  g 10  kg + 10  μg 10  mg + 10  lb 10  slug

M32 10  ° + 10  μrad 10  mrad + 10 10  rad + 10 ′′

M33 10  GW + 10  hp 10  kW + 10  MW 10  μW + 10  mW 10  nW + 10  W

M34 10  atm + 10  bar 10  kbar + 10  kPa 10  MPa + 10  μPa 10  mbar + 10  mmHg 10  Pa + 10  torr

M35 10  sr

M36 10  °C + 10  °F 10  K

M37 10  as + 10  d 10  fs + 10  h 10  μs + 10  ms 10  min + 10  ns 10  ps + 10  s 10  y

M38 10  ft 3 + 10  in 3 10  m 3 + 10  gal 10  l

M39 10  ml + 10  pint 10  qt

M40 1 x ( y ) = ( e 1 2 y 2 sin y y + C 1 ) e 1 2 y 2

M41 x y y = sin x

M42 ( 1 2 ) ( 1 2 ) ( 1 2 )

M43
[ 1 2 ] ( 1 2 ) { 1 2 }

M44 1 2 1 2 1 2

M45
1 2 1 2 1 2

M46 1 2 1 2 1 2

M47
1 2 1 2 1 2

M48 1 2 1 2 1 2

M49 ( a b ) = b a

M50 2 5 + 3 7 = 2 7 + 3 5 35 = 29 35

M51
| a | = { a if a 0 a if a < 0

M52
a n = a a a n  factors

M53 ( a b ) n = ( b a ) n

M54
a n = b   means  b n = a .

M55 16 81 4 = 16 4 81 4 = 2 3

M56 { x x 0 , x 1 }

M57
a n x n + a n 1 x n 1 + + a 1 x + a 0

M58 a 3 b 3 = ( a b ) ( a 2 + a b + b 2 )

M59 ( x + y ) 2

M60 H = { ( a b c d ) G a d b c = 1 }

M61 | x | + || y || + { z } [ a c ] + ( b ) = [ a , b ]

M62 x = 1

M63 x = 1

M64 x = 1

M65 x = 1

M66
[ 10 3 , 7 3 ) ( 7 3 , 4 3 ]

M67
A u x + B u y + C u = E

M68 x

M69 1 < i < 10 1 < j < 10 2 i + j

M70 Γ 1 2 3 4 5 6 7 1 5 7 6 2 4 3

M71 y ( x ) = x e x e x + 2 e x = x 1 + 2 e x

M72 x x y y = 0 y ( 0 ) = 1 y ( 0 ) = 0

M73 y ( x ) = 1 3 e ( 1 ) 3 x + 2 3 e 1 2 ( 1 ) 3 x cos 1 2 3 ( 1 ) 3 x

M74 y ( t ) = 2 tan ( 2 t 1 4 π )

M75 ( e 2 π i x 2 π Dirac ( x 2 π ) , x , s ) = ( 2 π Dirac ( s 2 π ) 2 π e 2 i π s )

M76
x = 1 x + 3 = 123

M77 t x y z 0 1.0000 1.0000 1.0000 .1 1.1158 1.0938 .8842 .2 1.2668 1.1695 .7332 .3 1.4582 1.2173 .5418 .4 1.6953 1.2253 .3047 .5 1.9830 1.1791 .0170 .6 2.3256 1.0619 .3256 .7 2.7265 .8542 .7265 .8 3.1873 .5344 1.1873 .9 3.7077 .0777 1.7077 1.0 4.2842 .5424 2.2842

M78 K v ( z ) = BesselK v ( z )

M79
z 2 2 w z 2 + z w z ( z 2 + v 2 ) w = 0

M80
2 u ( x , y ) x 2 2 u ( x , y ) y 2 = 0

M81 y ( t , x ) = F 1 ( x a t ) + F 2 ( x a t )

M82 1 2 3 4 5 6

M83
2 x + 1 = 5

M84
1 = 3 9 = 7

M85
a b c d e f

M86
x + 2 y 3 = 5 4 x y 5 = 98

M87
x = z 1 = 3

M88
A 1 = N 0 ( λ ; Ω ) φ ( λ ; Ω ) , A 2 = φ ( λ ; Ω ) φ ( λ ; Ω ) , A 3 = N ( λ ; ω ) .

M89
sin θ cos γ

M90 x = { x if  x < 0 x if  x 0

M91 L M R M L M R M

M92 M A T H M A T H

M93

M94

M95 ∇× F = 0

M96 ∇· F

M97 ∇·∇ F = 2 F + 7 = A

M98 ∇× ( x y , y z , z x ) = [ y z x ]

M99 ∇× ( y , z , x ) = ( 1 , 1 , 1 ) 0

M100 x + y + α = 102

M101 a + b = c

M102 x + 1

M103 x + f ( x ) 1 = 123

M104 T h e q u i c k b r o w n f o x j u m p s o v e r t h e l a z y d o g . T h e e n d .

M105 ( f x 1 ( c 1 , c 2 , , c n ) , f x 2 ( c 1 , c 2 , , c n ) , , f x n 1 ( c 1 , c 2 , , c n ) )

M106 ( c u v + v 2 w ) = ( u v , c v , c u + 2 v w , v 2 )

M107
D u f ( a , b , c ) = f ( a , b , c ) u = f x ( a , b , c ) u 1 + f y ( a , b , c ) u 2 + f z ( a , b , c ) u 3

M108 θ { π + 2 X 3 π ( arccos 1 7 14 ) | X 3 } , θ { 2 X 4 π π + ( arccos 1 7 14 ) | X 4 }

M109 P = A ( A T A ) 1 A T

M110 det ( x y 1 a b 1 a d 1 ) = x b x d + a d a b = 0

M111
A ( θ ) A ( θ ) = [ cos θ sin θ sin θ cos θ ] [ cos θ sin θ sin θ cos θ ]

M112 J ( A ) = [ J n 1 ( λ 1 ) 0 0 0 J n 2 ( λ 2 ) 0 0 0 J n k ( λ k ) ]

M113 det ( 4 + X 1 0 0 4 + X 0 0 0 4 + X ) = ( X 4 ) 3

M114 { ( 1 2 1 6 33 1 ) } 5 2 1 2 33

M115
A = max x 0 A x x

M116 ( a 1 1 a 1 2 a 2 1 a 2 2 ) + ( b 1 1 b 1 2 b 2 1 b 2 2 ) = ( a 1 1 + b 1 1 a 1 2 + b 1 2 a 2 1 + b 2 1 a 2 2 + b 2 2 )

M117 f ( [ 1 2 4 3 ] ) = [ 1 2 4 3 ] 2 5 [ 1 2 4 3 ] 2 = [ 2 2 4 0 ]

M118 x = lim x = 1 1 2 a

M119
a b f ( x ) x = lim P 0 i = 1 n f ( x i ) Δ x i

M120 a b f ( x ) x = lim n b a n i = 1 n f ( a + i b a n )

M121 0 2 x 5 x 3 + 1 x = 1 3 2 3 u ( u 2 ) ( u 2 1 ) 2 3 ( u 2 ( u 2 1 ) 2 3 ( u 2 1 ) 2 3 ) u

M122
f ( g ( x ) ) g ( x ) x = f ( u ) u

M123 x = 2 n = 1 100 n ( n 1 )

M124 lim x 0 sin ( 1 x ) = 1 .. 1

M125 h ( i , j ) = ( 2 j ) g ( i ) + ( j 1 ) f ( g ( i ) )

M126 : [ 0 , 1 ] [ 0 , 1 ]

M127 0 x = x

M128 x y = h 1 ( h ( x ) h ( y ) )

M129 x y = f 1 ( max { f ( x ) + f ( y ) 1 , 0 } )

M130 x y = η ( η ( x ) η ( y ) )

M131 x 0 y = { x y if x y = 1 0 if x y < 1

M132 lim a 1 + log a [ 1 + ( a x 1 ) ( a y 1 ) a 1 ] = lim a 1 log a [ 1 + ( a x 1 ) ( a y 1 ) a 1 ] = x y

M133 g ( x ) = exp ( 1 ( 1 x ) a ( 2 a 1 ) ( 1 x ) a )

M134
Aut ( I ) = { f : [ 0 , 1 ] [ 0 , 1 ] | f  is one-to-one and onto, and x y  implies  f ( x ) f ( y ) }

M135
x 2 + y 2 = r 2 ,    tan θ = y x

M136 2 1 t 2

M137 [ ( 2 + sin t ) 10 cos t , ( 2 + cos t ) 10 sin t , 3 sin 3 t ]

M138 { t = 0 , s = 0 } , { t = π , s = π }

M139
1 2 3 4 5 6 7 8 9 10 2 4 6 8 10 1 3 5 7 9 3 6 9 1 4 7 10 2 5 8 4 8 1 5 9 2 6 10 3 7 5 10 4 9 3 8 2 7 1 6 6 1 7 2 8 3 9 4 10 5 7 3 10 6 2 9 5 1 8 4 8 5 2 10 7 4 1 9 6 3 9 7 5 3 1 10 8 6 4 2 10 9 8 7 6 5 4 3 2 1

M140
testing  x 2  end.

M141 x

M142 x

M143 x

M144 x

M145 f x ( x 1 ) = 5

M146 x x = x y x y = x y z x y z = x y z t x y z t

M147 mod a

M148 5 mod 3 = 2

M149 f ( 0 ) mod 3 = 1

M150 5 x + 4 8 ( mod 13 )

M151 a = ( 5 3 ) / 5 mod 7 = 6

M152 ( 2 x 2 + x + 2 ) + ( 2 x + 1 ) mod 3 = 2 x 2

M153 + 0 1 000 000 111 1 1 0

M154 4. 974 9

M155 x F ( x )

M156 [ 86.333 , 146.33 , 129.33 ]

M157 BinomialDist ( x ; n , p ) = k = 0 x ( n k ) p k q n k

M158 Pr ( X 54 ) = BinomialDist ( 54 ; 100 , .55 ) = .45846

M159
k = max { | f y ( x , y ) | : ( x , y ) D } .

M160
m = lim x a f ( x ) f ( a ) x a

M161
| A | = | a 1 1 a 1 2 a 1 n a 2 1 a 2 2 a 2 n a n 1 a n 2 a n n | = a 1 1 A 1 1 + a 1 2 A 1 2 + + a 1 n A 1 n

M162
x = 1 ( hl text  x  end. )

M163
x = 1 ( hl to URI  x  end )

M164
x = 1 ( sex )

M165
x = 1 ( jbm )

M166

M167 f ( x ) g [ y ] h { z } + a b c

M168 123 456 A | A B A / 1 2 A / ( 3 4 A ) 5 6 A 7 8 A 9 20 10 A 11 12 A 13 14 A 15 16 A 17 18 A

M169 x x x x x x

M170
( a 1 , a 2 , , a n ) ( b 1 , b 2 , , b n ) = a 1 b 1 * + a 2 b 2 * + + a n b n *

M171
n 5 + n 5 2 + n 5 3 + n 5 4 +

M172 x 1 + + x n

M173 x + + x k  times

M174 x 1 x 2 x n n

M175 n ! = 1 × 2 × 3 × 4 × × n

M176 P : a = x 0 < x 1 < x 2 < < x n = b

M177
f ( x ) = 30 13 cos x + 10 3 ( 100 + 9 cos 2 x 60 cos x sin ( x + 29 90 π ) )

M178
cos ( A x ) sin ( B x ) x = cos ( B A ) x 2 ( B A ) + cos ( B + A ) x 2 ( B + A ) + C  .

M179 235.3 + 813 = 1048. 3

M180 max 2 x 2 ( x 3 6 x + 3 ) = 8.0

M181 x decade = 2 century

M182
5 ( x 7 3 x 6 ) x 5    n sin x x n    3 x 3 f ( x )    2 t 2 ( 4 t 5 3 t )

M183 f ( x ) = 30 13 cos x + 10 3 ( 100 + 9 cos 2 x 60 cos x sin ( x + 29 90 π ) )

M184
R 3 ( | u 1 | 2 + | u 0 | 2 2 + | u 0 | 6 6 ) x <

M185
( ∇× F ) k = z + 1

M186 M M M M M

M187
x x 2    x ( x 2 )    x x ( x 2 )    x 2 ( x 2 )    x y ( x 2 y 3 )    x s y t ( x 2 y 3 )

M188
5 24 ! x 6

M189
x + a y 1 12.34 2 sin θ 1

M190 0 1 1 0

M191 ( 0 i i 0 )

M192 [ 1 0 0 1 ]

M193 | a b c d |

M194 1 0 1 0 11

M195 1 2 3 4 5

M196
testing  sin θ

M197 a ^ + b ˇ + c ˜ + d ´ + e ` + f ˘ + g ¯ + h + i ˚ + j ˙ + k ¨ + l + m + n

M198 f ( g ( x ) ) = sin 3 x 2 + sin x 2 sin ( sin x 2 )

M199 ( x 2 + 12 x 2 + 12 ) + 1234

M200
x = 1 not here x 2 merged y 1 jbm lowlife The end.

M201
x 2 + y 2 = z 2 1

M202
x 2 + y 2 = z 2 1 x + y 3 = z 3

M203
x 2 + y 2 = z 2 1 x + y 3 = z 3

M204
x 2 + y 2 = 1 x = 1 y 2

M205
( a + b ) 2 = a 2 + 2 a b + b 2 ( a + b ) ( a b ) = a 2 b 2

M206
First line of equation Middle line of equation Other middle line of equation Last line of equation

M207
L 1 = R 1    L 2 = R 2 L 3 = R 3    L 4 = R 4

M208 ( a + b ) 4 = ( a + b ) 2 ( a + b ) 2 = ( a 2 + 2 a b + b 2 ) ( a 2 + 2 a b + b 2 ) = a 4 + 4 a 3 b + 6 a 2 b 2 + 4 a b 3 + b 4

M209
x 2 + y 2 = 1 x = 1 y 2    ( a + b ) 2 = a 2 + 2 a b + b 2 ( a + b ) ( a b ) = a 2 b 2

M210
Vertex V ( 0 , 0 ) Focus F ( 0 , p ) Directrix y = p

M211 x    ( csc 1 x ) = 1 | x | x 2 1

M212 tanh 1 x = 1 2 ln ( 1 + x 1 x )    1 < x < 1

M213 α + A B C + 1 = a b c

M214 y = e P x [ e P x Q x + c ]

M215 x = 1 + y 3 and x = 1 + y

M216 $ 1.00 + 25 ¢ 3 £ + 2.45 ¤ 0.7 ¥ a + 20 + 30 4.56

M217
2 x + y = 3 3 x 4 y = 5 a + b = c + 12345

M218 Unrestricted     Symmetric Antisymmetric    Triangular

M219 a b x

M220 c d y

M221 e f 11

M222 g h Z

M223 k l 3

M224 A B C

M225 A ⫅̸ B C

M226 10 11 12

M227 x y z

M228 lim x

M229 lim _ x

M230 lim x

M231 lim x

M232
x = y + z = k + m

M233
College Algebra  Second Edition James Stewart  McMaster Universitiy Lothar Redlin  Pennsylvania State University Saleem Watson  California State University, Long Beach Copyright 1996, ISBN 0 534-33983-2 Brooks/Cole Publishing Company An International Thomson Publishing Company

M234 { 1 2 1 2 1 2 }

M235 1 2 1 2 | 1 2

M236 1 2 1 2 | 1 2

M237 1 2 1 2 1 2

M238 [ 1 2 1 2 ]

M239 ( 1 2 1 2 )

M240 { 1 2 1 2 }

M241 1 2 1 2

M242 1 2 1 2

M243 1 2 1 2

M244 1 2 1 2

M245 1 2 1 2

M246 1 2 1 2

M247 1 2 1 2

M248 1 2 1 2

M249 1 2 1 2

M250 1 2 1 2

M251 \arrowvert 1 2 1 2 \arrowvert

M252 \Arrowvert 1 2 1 2 \Arrowvert

M253 \bracevert 1 2 1 2 \bracevert

M254 | 1 2 1 2 |

M255 | 1 2 1 2 |

M256 | 1 2 1 2 |

M257 1 2 1 2

M258 1 2 1 2

M259 / 1 2 1 2 /

M260 \ 1 2 1 2 \

M261 1 2 1 2

M262 \lgroup 1 2 1 2 \rgroup

M263 1 2 1 2

M264 1 2 1 2

M265
A n + μ 1 B T n ± i 1 C

M266
1 2 + 1 3 + 1 4 + 1 5 + 1 6 +

M267
1 2 + 1 3 + 1 4 + 1 5 + 1 6 +

M268 ( sin θ M

M269 ( sin θ M

M270 ( sin θ M

M271 ( sin θ M

M272 ( sin θ M

M273 ( sin θ M

M274 ( sin θ M

M275 ( sin θ M

M276 ( sin θ M

M277 sin θ M

M278 sin θ M

M279 sin θ M

M280 sin θ M

M281 sin θ M

M282 sin θ M

M283 sin θ M

M284 sin θ M

M285 sin θ M

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