Idiom Library Cool award

GRADE UP “
1. Progressive index of (without replacement) X„A1; Y„A1
  ((X)““XX,Y)(Y)““XY,X
2. Ascending cardinal numbers (ranking, shareable) X„D1
  ˜.5(““X)+““X
3. Cumulative maxima (—\) of subvectors of Y indicated by X X„B1; Y„D1
  Y[A—\A„“A[“(+\X)[A„“Y]]]
4. Cumulative minima (˜\) of subvectors of Y indicated by X X„B1; Y„D1
  Y[A—\A„“A[“(+\X)[A„”Y]]]
5. Progressive index of (without replacement) X„A1; Y„A1
  ((“XX,Y)X)(“XY,X)Y
6. Test if X and Y are permutations of each other X„D1; Y„D1
  Y[“Y]^.=X[“X]
7. Test if X is a permutation vector X„I1
  X^.=““X
8. Grade up (“) for sorting subvectors of X having lengths Y X„D1; Y„I1; (X) „… +/Y
  A[“(+\(Y)+\ŒIO,X)[A„“Y]]
9. Index of the elements of X in Y X„D1; Y„D1
  (((1,A)/B)˜1+Y)[(Y)‡(+\1,A„(1‡A)1‡A„A[B])[“B„“A„Y,X]]
10. Minima (˜/) of elements of subvectors of Y indicated by X X„B1; Y„D1
  Y[A[X/“(+\X)[A„“Y]]]
11. Grade up (“) for sorting subvectors of Y indicated by X X„B1; Y„D1
  A[“(+\X)[A„“Y]]
12. Occurences of the elements of X X„D1
  |-š(2,X)““X,X
13. Sorting rows of matrix X into ascending order X„D2
  (X)(,X)[A[“(,(X)1†X)[A„“,X]]]
14. Adding a new dimension after dimension G Y-fold G„I0; Y„I0; X„A
  (““(G+1),X)(Y,X)X
15. Sorting rows of matrix X into ascending order X„D2
  (X)(,X)[ŒIO+A[“˜A1†X]] ‘ A„(“,X)-ŒIO
16. Y smallest elements of X in order of occurrence X„D1, Y„I0
  ((““X)Y)/X
17. Merging X, Y, Z ... under control of G (mesh) X„A1; Y„A1; Z„A1; ... ; G„I1
  (Y,X,Z,...)[““G]
18. Merging X and Y under control of G (mesh) X„A1; Y„A1; G„B1
  (X,Y)[““G]
19. Ascending cardinal numbers (ranking, all different) X„D1
  ““X
20. Grade down (”) for sorting subvectors of Y having lengths X X„D1; Y„I1; (X) „… +/Y
  A[“(+\(Y)+\ŒIO,X)[A„”Y]]
21. Maxima (—/) of elements of subvectors of Y indicated by X X„B1; Y„D1
  Y[A[X/“(+\X)[A„”Y]]]
22. Grade down (”) for sorting subvectors of Y indicated by X X„B1; Y„D1
  A[“(+\X)[A„”Y]]
23. Y largest elements of X in order of occurrence X„D1; Y„I0
  ((“”X)Y)/X
24. Merging X and Y under control of G (mesh) X„A1; Y„A1; G„B1
  (Y,X)[“”G]
25. Descending cardinal numbers (ranking, all different) X„D1
  “”X
26. Sorting rows of X according to key Y (alphabetizing) X„A2; Y„A1
  X[“(1+Y)ƒYX;]
27. Diagonal ravel X„A
  (,X)[“+š(X)‚(,X)-ŒIO]
28. Grade up according to key Y Y„A1; X„A1
  “YX
29. Test if X is a permutation vector X„I1
  X[“X]^.=X
30. Sorting a matrix into lexicographic order X„D2
  X[“+šA<.-ax,0;]
31. Sorting words in list X according to word length X„C2
  X[“X+.' ';]
32. Classification of X to classes starting with Y X„D1;Y„D1;Y<.1y
  A ‘ A[(B/C)-Y]„B/+\~B„(Y)
33. Rotate first elements (1) of subvectors of Y indicated by X X„B1; Y„A1
  Y[“X++\X]
34. Doubling quotes (for execution) X„C1
  (X,'''')[(ŒIO+X)˜“(X),(''''=X)/X]
35. Inserting Y *'s into vector X after indices G X„C1; Y„I0; G„I1
  (X,'*')[(ŒIO+X)˜“(X),(Y׽G)G]
36. Median X„D1
  X[(“X)[—.5׽X]]
37. Index of last maximum element of X X„D1
  1†“X
38. Index of (first) minimum element of X X„D1
  1†“X
39. Expansion vector with zero after indices Y X„D1; Y„I1
  (X)‰“(X),Y
40. Catenating G elements H before indices Y in vector X X„A1; Y„I1; G„I0; H„A0
  ((AH),X)[“(AY),X] ‘ A„G׽,Y
41. Catenating G elements H after indices Y in vector X X„A1; Y„I1; G„I0; H„A0
  (X,AH)[“(X),AY] ‘ A„G׽,Y
42. Merging X and Y under control of G (mesh) X„A1; Y„A1; G„B1
  A ‘ A[“G]„A„Y,X
43. Sorting a matrix according to Y:th column X„D2
  X[“X[;Y];]
44. Sorting indices X according to data Y X„I1; Y„D1
  X[“Y[X]]
45. Choosing sorting direction during execution X„D1; Y„I0
  “Xׯ1 1[Y]
46. Sorting Y according to X X„A1; Y„A1
  Y[“X]
47. Sorting X into ascending order X„D1
  X[“X]
48. Inverting a permutation X„I1
  “X
GRADE DOWN ”
49. Reverse vector X on condition Y X„A1; Y„B0
  X[”Y!X]
50. Sorting a matrix into reverse lexicographic order X„D2
  X[”+šA<.-ax,0;]
52. Reversal () of subvectors of X having lengths Y X„D1; Y„I1
  X[”+\(X)+\ŒIO,Y]
53. Reversal () of subvectors of Y indicated by X X„B1; Y„A1
  Y[”+\X]
55. Indices of ones in logical vector X X„B1
  (+/X)†”X
56. Index of first maximum element of X X„D1
  1†”X
57. Moving all blanks to end of text X„C1
  X[”' 'X]
58. Sorting X into descending order X„D1
  X[”X]
59. Moving elements satisfying condition Y to the start of X X„A1; Y„B1
  X[”Y]
MATRIX INVERSION / MATRIX DIVISION Ž
60. Interpolated value of series (X,Y) at G X„D1; Y„D1; G„D0
  GƒYŽX.*-ŒIO-X
61. Predicted values of exponential (curve) fit X„D1; Y„D1
  *A+.(Y)ŽA„X.*0 1
62. Coefficients of exponential (curve) fit of points (X,Y) X„D1; Y„D1
  A ‘ A[1]„*A[1] ‘ A„(Y)ŽX.*0 1
63. Predicted values of best linear fit (least squares) X„D1; Y„D1
  A+.YŽA„X.*0 1
64. G-degree polynomial (curve) fit of points (X,Y) X„D1; Y„D1
  YŽX.*0,G
65. Best linear fit of points (X,Y) (least squares) X„D1; Y„D1
  YŽX.*0 1
DECODE ƒ
66. Binary format of decimal number X X„I0
  •10ƒ((1+—2—/,X)2)‚X
67. Barchart of two integer series (across the page) X„I2; 1X „… 2
  ' *'[ŒIO+2ƒX.‰—/,X]
68. Case structure with an encoded branch destination Y„I1; X„B1
  …Y[1+2ƒX]
69. Representation of current time (24 hour clock)  
  A ‘ A[3 6]„':' ‘ A„•1000ƒ3†3‡ŒTS
70. Representation of current date (descending format)  
  A ‘ A[5 8]„'-' ‘ A„•1000ƒ3†ŒTS
71. Representation of current time (12 hour clock)  
  (1,' ::',3 26 0•100ƒ12 0 0|3†3‡ŒTS),'AP'[1+12ˆŒTS[4]],'M'
73. Removing duplicate rows X„A2
  ((AA)=A„2ƒX^.=X)šX
74. Conversion from hexadecimal to decimal X„C
  16ƒ-ŒIO-'0123456789ABCDEF'X
75. Conversion of alphanumeric string into numeric X„C1
  10ƒ1+'0123456789'X
76. Value of polynomial with coefficients Y at points X X„D1; Y„D1
  (X.+,0)ƒY
77. Changing connectivity list X to a connectivity matrix X„C2
  BA ‘ A[ŒIO+B[1]ƒ-ŒIO-X]„1 ‘ A„(/B„0 0+—/,X)0
78. Present value of cash flows X at interest rate Y % X„D1; Y„D0
  (1+Y100)ƒX
79. Justifying right X„C
  (1-(' '=X)ƒ1)X
80. Number of days in month X of years Y (for all leap years) X„I0; Y„I
  (12731 30)[X]-0—1+2ƒ(X=2),[.1](0400|Y)-(0100|Y)-04|Y
81. Number of days in month X of years Y (for most leap years) X„I0; Y„I
  (12731 30)[X]-0—1+2ƒ(X=2),[.1]04|Y
82. Encoding current date  
  100ƒ100|3†ŒTS
83. Removing trailing blanks X„C1
  (1-(' '=X)ƒ1)‡X
84. Index of first non-blank, counted from the rear X„C1
  (' '=X)ƒ1
85. Indexing scattered elements X„A; Y„I2
  (,X)[ŒIO+(X)ƒY-ŒIO]
86. Conversion of indices Y of array X to indices of raveled X X„A; Y„I2
  ŒIO+(X)ƒY-ŒIO
87. Number of columns in array X as a scalar X„A
  0ƒX
88. Future value of cash flows X at interest rate Y % X„D1; Y„D0
  (1+Y100)ƒX
89. Sum of the elements of vector X X„D1
  1ƒX
90. Last element of numeric vector X as a scalar X„D1
  0ƒX
91. Last row of matrix X as a vector X„A
  0ƒX
92. Integer representation of logical vectors X„B
  2ƒX
93. Value of polynomial with coefficients Y at point X X„D0; Y„D
  XƒY
ENCODE ‚
94. Conversion from decimal to hexadecimal (X=1..255) X„I
  '0123456789ABCDEF'[ŒIO+((——/16,X)16)‚X]
95. All binary representations up to X (truth table) X„I0
  ((—21+X)2)‚0,X
96. Representation of X in base Y X„D0; Y„D0
  ((1+˜YX)Y)‚X
97. Digits of X separately X„I0
  ((1+˜10X)10)‚X
98. Helps locating column positions 1..X X„I0
  1 0•10 10‚1-ŒIO-X
99. Conversion of characters to hexadecimal representation (ŒAV) X„C1
  ,' ','0123456789ABCDEF'[ŒIO+16 16‚-ŒIO-ŒAVX]
100. Polynomial with roots X X„D1
  ((0,X).=+š~A)+.(-X).*A„((X)2)‚1+2*X
101. Index pairs of saddle points X„D2
  ŒIO+(X)‚-ŒIO-(,(X=(X)—šX)^X=(X)˜/X)//X
102. Changing connectivity matrix X to a connectivity list X„C2
  (,X)/1+A‚1+/A„X
103. Matrix of all indices of X X„A
  ŒIO+(X)‚(/X)-ŒIO
104. Separating a date YYMMDD to YY, MM, DD X„D
  (3100)‚X
105. Indices of elements Y in array X X„A; Y„A
  ŒIO+(X)‚(-ŒIO)+(,XY)/,X
106. All pairs of elements of X and Y X„I0; Y„I0
  ŒIO+(X,Y)‚(XY)-ŒIO
107. Matrix for choosing all subsets of X (truth table) X„A1
  ((X)2)‚1+2*X
108. All binary representations with X bits (truth table) X„I0
  (X2)‚1+2*X
109. Incrementing cyclic counter X with upper limit Y X„D; Y„D0
  1+Y‚X
110. Decoding numeric code ABBCCC into a matrix X„I
  10 100 1000‚X
111. Integer and fractional parts of positive numbers X„D
  0 1‚X
LOGARITHM
112. Number of decimals of elements of X X„D1
  ˜10(–('.'A)/A„•X)X
113. Number of sortable columns at a time using ƒ and alphabet X X„C1
  ˜(1+X)2*(A=1+A„2*128)1
114. Playing order in a cup for X ranked players X„I0
  ,(A2)(2*A„—2X)†X
115. Arithmetic precision of the system (in decimals)  
  ˜|10|1-33
116. Number of digitpositions in integers in X X„I
  1+(X<0)+10|x+0=x
117. Number of digit positions in integers in X X„I
  1+˜10(X=0)+X1 10[1+X<0]
118. Number of digits in positive integers in X X„I
  1+˜10X+0=X
BRANCH …
119. Case structure according to key vector G X„A0; Y„I1; G„A1
  …Y[GX]
120. Forming a transitive closure X„B2
  …ŒLC—Ÿ/,(X„XŸXŸ.^X)+X
121. Case structure with integer switch X„I0; Y„I1
  …XY
122. For-loop ending construct X„I0; Y„I0; G„I0
  …Y—G‰X„X+1
123. Conditional branch to line Y X„B0; Y„I0; Y>0
  …Y—X
124. Conditional branch out of program X„B0
  …0˜X
125. Conditional branch depending on sign of X X„I0; Y„I1
  …Y[2+X]
126. Continuing from line Y (if X>0) or exit X„D0; Y„I0
  …YX
127. Case structure using levels with limits G X„D0; G„D1; Y„I1
  …(X‰G)/Y
128. Case structure with logical switch (preferring from start) X„B1; Y„I1
  …X/Y
129. Conditional branch out of program X„B0
  …0׼X
EXECUTE –
132. Test for symmetricity of matrix X X„A2
  ––'1','†‡'[ŒIO+^/(X)=X],'''0~0X=X'''
133. Using a variable named according to X X„A0; Y„A
  –'VAR',(•X),'„Y'
134. Rounding to ŒPP precision X„D1
  –•X
135. Convert character or numeric data into numeric X„A1
  –•X
136. Reshaping only one-element numeric vector X into a scalar X„D1
  –•X
137. Graph of F(X) at points X ('X'F) F„A1; X„D1
  ' *'[ŒIO+((1+˜/A)+1+(—/A)-˜/A).=A„˜.5+–F]
138. Conversion of each row to a number (default zero) X„C2
  (XŸ.' ')\1‡–'0 ',,X,' '
139. Test for symmetricity of matrix X X„A2
  –(7*A^.=A„X)†'0~0X=X'
140. Execution of expression X with default value Y X„D1
  –((X^.=' ')/'Y'),X
141. Changing X if a new input value is given X„A
  X„–,((2†'X'),' ',[.5]A)[ŒIO+~' '^.=A„;]
142. Definite integral of F(X) in range Y with G steps ('X'F) F„A1; G„D0; Y„D1; Y „… 2
  A+.–F,0X„Y[1]+(A„--/YG)0,G
143. Test if numeric and conversion to numeric form X„C1
  1‡–'0 ',(^/X' 0123456789')/X
144. Tests the social security number (Finnish) Y„'01...9ABC...Z'; 10=X
  (1†X)=((~Y'GIOQ')/Y)[1+31|–9†X]
145. Conditional execution X„B0
  –X/'EXPRESSION'
146. Conditional branch out of programs X„L0
  –X/'…'
147. Using default value 100 if X does not exist X„A
  –(3*2ŒNC 'X')†'X100'
148. Conditional execution X„B0; Y„A1
  –X‡' ...'
149. Giving a numeric default value for input X„D0
  1(–,',0'),X
150. Assign values of expressions in X to variables named in Y X„C2; Y„C2
  A„–,',','(','0','',Y,'„',X,')'
151. Evaluation of several expressions; results form a vector X„A
  –,',','(',',',X,')'
152. Sum of numbers in character matrix X X„A2
  –,'+',X
153. Indexing when rank is not known beforehand X„A; Y„I
  –'X[',((1+X)';'),'Y]'
FORMAT •
154. Numeric headers (elements of X) for rows of table Y X„D1; Y„A2
  (37 0•X.+,0),•Y
155. Formatting a numerical vector to run down the page X„D1
  •X.+,0
156. Representation of current date (ascending format)  
  A ‘ A[(' '=A)/A]„'.' ‘ A„•3†ŒTS
157. Representation of current date (American)  
  A ‘ A[(' '=A)/A]„'/' ‘ A„•100|13†ŒTS
158. Formatting with zero values replaced with blanks X„A
  (A)B\(B„,('0'A)Ÿ' '1A)/,A„' ',•X
159. Number of digit positions in scalar X (depends on ŒPP) X„D0
  •X
160. Leading zeroes for X in fields of width Y X„I1; Y„I0; X‰0
  0 1‡(2†Y+1)•X.+,10*Y
161. Row-by-row formatting (width G) of X with Y decimals per row X„D2; Y„I1; G„I0
  ((1,G)׽X)2 1 3(G,X)(,G,[1.1]Y)•X
163. Formatting X with H decimals in fields of width G X„D; G„I1; H„I1
  (,G,[1.1]H)•X
ROLL / DEAL ?
164. Y-shaped array of random numbers within ( X[1],X[2] ] X„I1; Y„I1
  X[1]+?Y--/X
165. Removing punctuation characters X„A1
  (~X' .,:;?''')/X
166. Choosing Y objects out of X with replacement (roll) Y„I; X„I
  ?YX
167. Choosing Y objects out of X without replacement (deal) X„I0; Y„I0
  Y?X
GEOMETRICAL FUNCTIONS
168. Arctan YX X„D; Y„D
  ((X0)ׯ3YX+X=0)+((X=0).5Y)+(X<0)1-2y<0
169. Conversion from degrees to radians X„D
  Xױ180
170. Conversion from radians to degrees X„D
  X1801
171. Rotation matrix for angle X (in radians) counter-clockwise X„D0
  2 21 1 1 12 1 1 2X
FACTORIAL / BINOMIAL !
172. Number of permutations of X objects taken Y at a time X„D; Y„D
  (!Y)Y!X
173. Value of Taylor series with coefficients Y at point X X„D0; Y„D1
  +/Y(X*A)!A„1+Y
174. Poisson distribution of states X with average number Y X„I; Y„D0
  (*-Y)(Y*X)!X
175. Gamma function X„D0
  !X-1
176. Binomial distribution of X trials with probability Y X„I0; Y„D0
  (A!X)(Y*A)(1-Y)*X-A„-ŒIO-X+1
177. Beta function X„D0; Y„D0
  Y(X-1)!Y+X-1
178. Selecting elements satisfying condition X, others to 1 X„B; Y„D
  X!Y
179. Number of combinations of X objects taken Y at a time X„D; Y„D
  Y!X
INDEX OF
180. Removing elements Y from beginning and end of vector X X„A1; Y„A
  ((A1)-ŒIO)‡(ŒIO-(A„~XY)1)‡X
181. Alphabetical comparison with alphabets G X„A; Y„A
  (GX)
183. Sum over elements of X determined by elements of Y X„D1; Y„D1
  X+.Y.=((Y)=YY)/Y
184. First occurrence of string X in string Y X„A1; Y„A1
  (^š(1+X)X.=Y)1
185. Removing duplicate rows X„A2
  ((AA)=A„ŒIO++š^™XŸ.X)šX
186. First occurrence of string X in matrix Y X„A2; Y„A1; 1†Y„…X
  (Y^.=X)1
187. Indices of ones in logical vector X X„B1
  (+\X)+/X
188. Executing costly monadic function F on repetitive arguments X„A1
  (F B/X)[+\B„(XX)=X]
189. Index of (first) maximum element of X X„D1
  X—/X
190. Index of first occurrence of elements of Y X„C1; Y„C1
  ˜/XY
191. Index of (first) minimum element of X X„D1
  X˜/X
192. Test if each element of X occurs only once X„A1
  ^/(XX)=X
193. Test if all elements of vector X are equal X„A1
  ^/ŒIO=XX
194. Interpretation of roman numbers X„A
  +/Aׯ1*A<1a0,1000 500 100 50 10 5 1['MDCLXVI'X]
195. Removing elements Y from end of vector X X„A1; Y„A
  (ŒIO-(~XY)1)‡X
196. Removing trailing blanks X„C1
  (1-(' 'X)1)‡X
198. Index of last occurrence of Y in X (ŒIO-1 if not found) X„A1; Y„A
  (1 1[2ŒIO]+X)-(X)Y
199. Index of last occurrence of Y in X (0 if not found) X„A1; Y„A
  (1+X)-(X)Y
200. Index of last occurrence of Y in X, counted from the rear X„A1; Y„A
  (X)Y
201. Index of first occurrence of G in X (circularly) after Y X„A1; Y„I0; G„A
  ŒIO+(X)|Y+(YX)G
202. Alphabetizing X; equal alphabets in same column of Y Y„C2; X„C
  (1†Y)|(,Y)X
203. Changing index of an unfound element to zero Y„A1; X„A
  (1+Y)|YX
204. Replacing elements of G in set X with corresponding Y X„A1, Y„A1, G„A
  (G)A ‘ A[B/B]„Y[(B„BˆY)/B„XA„,G]
205. Removing duplicate elements (nub) X„A1
  ((XX)=X)/X
206. First word in X X„C1
  (1+X' ')†X
207. Removing elements Y from beginning of vector X X„A1; Y„A
  (((~XY)1)-ŒIO)‡X
208. Removing leading zeroes X„A1
  (1+(X='0')0)‡X
209. Index of first one after index Y in X G„I0; X„B1
  Y+(Y‡X)1
210. Changing index of an unfound element to zero (not effective) X„A; Y„A1
  (XY)YX
211. Indicator of first occurrence of each unique element of X X„A1
  (XX)=X
212. Inverting a permutation X„I1
  XX
213. Index of first differing element in vectors X and Y X„A1; Y„A1
  (YX)1
214. Which elements of X are not in set Y (difference of sets) X„A; Y„A1
  (ŒIO+Y)=YX
215. Changing numeric code X into corresponding name in Y X„D; Y„D1; G„C2
  G[YX;]
216. Index of key Y in key vector X X„A1; Y„A
  XY
217. Conversion from characters to numeric codes X„A
  ŒAVX
218. Index of first satisfied condition in X X„B1
  X1
OUTER PRODUCT .! .— .|
219. Pascal's triangle of order X (binomial coefficients) X„I0
  A.!A„0,X
220. Maximum table X„I0
  (X).—X
221. Number of decimals (up to Y) of elements of X X„D; Y„I0
  0+.(—(10*Y)10*ŒIO-Y+1).|—X10*Y
222. Greatest common divisor of elements of X X„I1
  —/(^/0=A.|X)/A„˜/X
223. Divisibility table X„I1
  0=(—/X).|X
224. All primes up to X X„I0
  (2=+š0=(X).|X)/X
OUTER PRODUCT .* . .- .+
225. Compound interest for principals Y at rates G % in times X X„D; Y„D; G„D
  Y.(1+G100).*X
226. Product of two polynomials with coefficients X and Y X„D1; Y„D1
  +š(ŒIO-X)X.Y,01‡X
228. Shur product X„D2; Y„D2
  1 2 1 2X.Y
229. Direct matrix product X„D2; Y„D2
  1 3 2 4X.Y
230. Multiplication table X„I0
  (X).׼X
231. Replicating a dimension of rank three array X Y-fold Y„I0; X„A3
  X[;,(Y1).׼(X)[2];]
232. Array and its negative ('plus minus') X„D
  X.1 1
233. Move set of points X into first quadrant X„D2
  1 2 1X.-˜/X
234. Test relations of elements of X to range Y; result in 2..2 X„D; Y„D; 2=1†Y
  +/X.-Y
235. Occurrences of string X in string Y X„A1; Y„A1
  (Y[A.+1+X]^.=X)/A„(A=1†X)/A„(1-X)‡Y
236. Sum of common parts of matrices (matrix sum) X„D2; Y„D2
  1 2 1 2X.+Y
237. Adding X to each column of Y X„D1; Y„D2
  1 1 2X.+Y
238. Adding X to each column of Y X„D1; Y„D2
  1 2 1Y.+X
240. Adding X to each row of Y X„D1; Y„D2
  2 1 2X.+Y
241. Adding X to each row of Y X„D1; Y„D2
  1 2 2Y.+X
242. Hilbert matrix of order X X„0
  1+(X).+X
243. Moving index of width Y for vector X X„A1; Y„I0
  (0,(X)-Y).+Y
244. Indices of subvectors of length Y starting at X+1 X„I1; Y„I0
  X.+Y
245. Reshaping numeric vector X into a one-column matrix X„D1
  X.+,0
246. Annuity coefficient: X periods at interest rate Y % X„I; Y„D
  ((A)Y100)A„1-(1+Y100).*-X
OUTER PRODUCT .<. . .>
247. Matrix with X[i] trailing zeroes on row i X„I1
  X.
248. Matrix with X[i] leading zeroes on row i X„I1
  X.
249. Distribution of X into intervals between Y X„D; Y„D1
  +/((1‡Y).ˆX)^(1‡Y).>X
250. Histogram (distribution barchart; down the page) X„I1
  ' Œ'[ŒIO+(—/A).ˆA„+/(1+(—/X)-˜/X).=X]
251. Barchart of integer values (down the page) X„I1
  ' Œ'[ŒIO+(—/X).ˆX]
252. Test if X is an upper triangular matrix X„D2
  ^/,(0X)ˆA.ˆA„1†X
253. Number of ?s intersecting ?s (X=starts, Y=stops) X„D1; Y„D1
  +/A^A„X.ˆY
254. Contour levels Y at points with altitudes X X„D0; Y„D1
  Y[+šY.ˆX]
255. XX upper triangular matrix X„I0
  (X).ˆX
256. Classification of elements Y into X classes of equal size X„I0; Y„D1
  +/(AX—/A„Y-˜/Y).‰1+X
257. Matrix with X[i] trailing ones on row i X„I1
  X.‰—/X
258. Comparison table X„I1
  X.‰—/X,0
259. Barchart of X with height Y (across the page) X„D1; Y„D0
  ' Œ'[ŒIO+X.‰(—/X)(Y)Y]
260. Barchart of integer values (across the page) X„I1
  ' Œ'[ŒIO+X.‰—/X]
261. Matrix with X[i] leading ones on row i X„I1
  X.‰—/X
263. Test if X is a lower triangular matrix X„D2
  ^/,(0X)ˆA.‰A„1†X
264. Test if X is within range [ Y[1],Y[2] ) X„D; Y„D1
  /X.‰Y
265. Ordinal numbers of words in X that indices Y point to X„C1; Y„I
  ŒIO++/Y.‰(' '=X)/X
266. Which class do elements of X belong to X„D
  +/X.‰0 50 100 1000
267. XX lower triangular matrix X„I0
  (X).‰X
268. Moving all blanks to end of each row X„C
  (X)(,(+/A).>-ŒIO-1†X)\(,A„X' ')/,X
269. Justifying right fields of X (lengths Y) to length G X„A1; Y„I1; G„I0
  (,Y.>(G)-ŒIO)\X
270. Justifying left fields of X (lengths Y) to length G X„A1; Y„I1; G„I0
  (,Y.>(G)-ŒIO)\X
OUTER PRODUCT . .=
271. Indices of elements of Y in corr. rows of X (X[i;]Y[i;]) X„A2; Y„A2
  1++/^\1 2 1 3Y.X
273. Indicating equal elements of X as a logical matrix X„A1
  X.=(1 1<\x.=x)/x
275. Changing connection matrix X (1 … 1) to a node matrix X„I2
  (1 1.=X)+.׼1†Œ„X
276. Sums according to codes G X„A; Y„D; G„A
  (G.=X)+.Y
277. Removing duplicate elements (nub) X„A1
  (1 1<\x.=x)/x
278. Changing node matrix X (starts,ends) to a connection matrix X„I2
  -/(—/,X).=X
279. Test if all elements of vector X are equal X„B1
  Ÿ/^/0 1.=X
280. Test if elements of X belong to corr. row of Y (X[i;]Y[i;]) X„A2; Y„A2; 1†X„…1†Y
  Ÿ/1 2 1 3X.=Y
281. Test if X is a permutation vector X„I1
  ^/1=+/X.=X
282. Occurrences of string X in string Y X„C1; Y„C1
  (^š(1+X)(X.=Y),0)/1+Y
283. Division to Y classes with width H, minimum G X„D; Y„I0; G„D0; H„D0
  +/(Y).=—(X-G)H
285. Repeat matrix X„A1; Y„A1
  (((1~A)^A„(1‡X=1X),0)/Y).=Y
286. XX identity matrix X„I0
  (X).=X
INNER PRODUCT —. ˜. ˜.+ . .* +.*
287. Maxima of elements of subsets of X specified by Y X„A1; Y„B
  A+(X-A„˜/X)—.Y
288. Indices of last non-blanks in rows X„C
  (' 'X)—.׼1†X
289. Maximum of X with weights Y X„D1; Y„D1
  Y—.X
290. Minimum of X with weights Y X„D1; Y„D1
  Y˜.X
292. Extending a distance table to next leg X„D2
  X„X˜.+X
293. A way to combine trigonometric functions (sin X cos Y) X„D0; Y„D0
  1 2.X,Y
294. Sine of a complex number X„D; 2=1†X
  (2 21 6 2 5).X
295. Products over subsets of X specified by Y X„A1; Y„B
  X.*Y
296. Sum of squares of X X„D1
  X+.*2
297. Randomizing random numbers (in ŒLX in a workspace)  
  ŒRL„ŒTS+.*2
INNER PRODUCT Ÿ.^ <.< <. <. .>.>
298. Extending a transitive binary relation X„B2
  X„XŸ.^X
299. Test if X is within range [ Y[1;],Y[2;] ) X„D0; Y„D2; 1†Y „… 2
  X<.
300. Test if X is within range ( Y[1;],Y[2;] ] X„D0; Y„D2; 1†Y „… 2
  X<.y
301. Test if X is within range ( Y[1;],Y[2;] ] X„D; Y„D2; 1†Y „… 2
  X<.y
302. Test if the elements of X are ascending X„D1
  X<.1x
303. Test if X is an integer within range [ G,H ) X„I0; G„I0; H„I0
  ~Xˆ.‰(—X),G,H
304. Test if X is within range ( Y[1;],Y[2;] ] X„D; Y„D2; 1†Y „… 2
  (X,[.1+X]X)>.>Y
INNER PRODUCT Ÿ. ^.= +. +.=
306. Removing trailing blank columns X„C2
  (Ÿ\' 'Ÿ.X)/X
307. Removing leading blank rows X„C2
  (Ÿ\XŸ.' ')šX
308. Removing leading blank columns X„C2
  (Ÿ\' 'Ÿ.X)/X
309. Index of first occurrences of rows of X as rows of Y X„A, Y„A2
  ŒIO++š^™YŸ.X
310. 'XY' for rows of matrices X„A2; Y„A2
  ŒIO++š^™XŸ.Y
311. Removing duplicate blank rows X„C2
  (AŸ1‡11,A„XŸ.' ')šX
312. Removing duplicate blank columns X„C2
  (AŸ1,1‡A„' 'Ÿ.X)/X
313. Removing blank columns X„C2
  (' 'Ÿ.X)/X
314. Removing blank rows X„C2
  (XŸ.' ')šX
315. Test if rows of X contain elements differing from Y X„A; Y„A0
  XŸ.Y
316. Removing trailing blank rows X„C2
  (-2†+/^\X^.=' ')‡X
317. Removing duplicate rows X„A2
  (Ÿš<\x^.=x)x
318. Removing duplicate rows X„A2
  (1 1<\x^.=x)x
319. Test if circular lists are equal (excluding phase) X„A1; Y„A1
  Ÿ/Y^.=(X)(2X)X
320. Test if all elements of vector X are equal X„B1
  X^.=Ÿ/X
321. Test if all elements of vector X are equal X„B1
  X^.=^/X
322. Rows of matrix X starting with string Y X„A2; Y„A1
  ((((1†X),Y)†X)^.=Y)šX
323. Occurrences of string X in string Y X„A1; Y„A1
  ((-A)‡X^.=(A,1+Y)Y)/(Y)+1-A„X
324. Test if vector Y is a row of array X X„A; Y„A1
  1X^.=Y
325. Comparing vector Y with rows of array X X„A; Y„A1
  X^.=Y
326. Word lengths of words in list X X„C
  X+.' '
327. Number of occurrences of scalar X in array Y X„A0; Y„A
  X+.=,Y
328. Counting pairwise matches (equal elements) in two vectors X„A1; Y„A1
  X+.=Y
INNER PRODUCT -. +. +.
329. Sum of alternating reciprocal series YX X„D1; Y„D1
  Y-.X
330. Limits X to fit in • field Y[1 2] X„D; Y„I1
  (X—1‡A)˜1†A„(2 21 1 1 .1)+.10*(-1‡Y),-/Y+Y>99 0
331. Value of polynomial with coefficients Y at point X X„D0; Y„D
  (X*1+Y)+.ײY
332. Arithmetic average (mean value) of X weighted by Y X„D1; Y„D1
  (Y+.X)X
333. Scalar (dot) product of vectors X„D1; Y„D1
  Y+.X
334. Sum of squares of X X„D1
  X+.X
335. Summation over subsets of X specified by Y X„A1; Y„B
  X+.Y
336. Matrix product X„D; Y„D; 1†X „… 1†Y
  X+.Y
337. Sum of reciprocal series YX X„D1; Y„D1
  Y+.X
SCAN —\ ˜\ \ -\
338. Groups of ones in Y pointed to by X (or trailing parts) X„B; Y„B
  Y^A=—\XA„+\Y>1‡0,Y
339. Test if X is in ascending order along direction Y X„D; Y„I0
  ^/[Y]X=—\[Y]X
340. Duplicating element of X belonging to Y,1†X until next found X„A1; Y„B1
  X[1——\Y׼Y]
341. Test if X is in descending order along direction Y X„D; Y„I0
  ^/[Y]X=˜\[Y]X
342. Value of Taylor series with coefficients Y at point X X„D0; Y„D1
  +/Y\1,X1+Y
343. Alternating series (1 1 2 2 3 3 ...) X„I0
  -\X
SCAN Š\ <\ \ \
346. Value of saddle point X„D2
  (<\,(x=(x)x)^x=(x)/x)/,x
348. First one (turn off all ones after first one) X„B
  <\x
350. Not first zero (turn on all zeroes after first zero) X„B
  ˆ\X
351. Running parity (\) over subvectors of Y indicated by X X„B1; Y„B1
  \YX\A1‡0,A„X/\1‡0,Y
352. Vector (X[1]1),(X[2]0),(X[3]1),... X„I1; ^/0
  \(+/X)+\ŒIO,X
353. Not leading zeroes(Ÿ\) in each subvector of Y indicated by X X„B1; Y„B1
  \(YŸX)\A1‡0,A„(YŸX)/Y
354. Leading ones (^\) in each subvector of Y indicated by X X„B1; Y„B1
  ~\(YˆX)\A1‡0,A„~(YˆX)/Y
355. Locations of texts between and including quotes X„C1
  AŸ1‡0,A„\X=''''
356. Locations of texts between quotes X„C1
  A^1‡0,A„\X=''''
357. Joining pairs of ones X„B
  XŸ\X
358. Places between pairs of ones X„B
  (~X)^\X
359. Running parity X„B
  \X
SCAN Ÿ\ ^\
360. Removing leading and trailing blanks X„C1
  ((Ÿ\A)^Ÿ\A„' 'X)/X
361. First group of ones X„B
  X^^\X=Ÿ\X
362. Removing trailing blank columns X„C2
  (Ÿ\Ÿš' 'X)/X
363. Removing trailing blanks X„C1
  (Ÿ\' 'X)/X
364. Removing leading blanks X„C1
  (Ÿ\' 'X)/X
365. Not leading zeroes (turn on all zeroes after first one) X„B
  Ÿ\X
366. Centering character array X with ragged edges X„C
  (A-˜0.5(A„+/^\A)++/^\A„' '=X)X
367. Decommenting a matrix representation of a function (ŒCR) X„C2
  (Ÿ/A)š(X)(,A)\(,A„^\(''X)Ÿ\X='''')/,X
369. Centering character array X with only right edge ragged X„C
  (-˜0.5+/^\' '=X)X
370. Justifying right X„C
  (-+/^\' '=X)X
371. Removing trailing blanks X„C1
  (-+/^\' '=X)‡X
372. Justifying left X„C
  (+/^\' '=X)X
373. Editing X with Y ’-wise X„C1; Y„C1
  ((~(A†X)†'/'=Y)/A†X),(1‡A‡Y),(A„+/^\Y',')‡X
374. Removing leading blanks X„C1
  (+/^\' '=X)‡X
375. Indices of first blanks in rows of array X X„C
  ŒIO++/^\' 'X
377. Leading ones (turn off all ones after first zero) X„B
  ^\X
SCAN +\
378. Vector (X[1]1),(Y[1]0),(X[2]1),... Q„I1; Y„I1
  (+/X,Y)+\1+1‡0,((+/X)+\X)\Y
379. Replicate Y[i] X[i] times (for all i) X„I1; Y„A1
  ((X0)/Y)[+\1(+/X)+\X]
380. Vector (Y[1]+X[1]),(Y[2]+X[2]),(Y[3]+X[3]),... X„I1; Y„I1; X„…Y
  ŒIO++\1+((+/X)+\ŒIO,X)\Y-1‡1,X+Y
381. Replicate Y[i] X[i] times (for all i) X„I1; Y„A1; ^/0
  Y[+\(+/X)1‡1++\0,X]
382. Replicate Y[i] X[i] times (for all i) X„I1; Y„A1; ^/0
  Y[ŒIO++\(+/X)ŒIO++\X]
383. Cumulative sums (+\) over subvectors of Y indicated by X X„B1; Y„D1
  +\Y-X\A-1‡0,A„X/+\1‡0,Y
384. Sums over (+/) subvectors of Y, lengths in X X„I1; Y„D1
  A-1‡0,A„(+\Y)[+\X]
386. X first figurate numbers X„I0
  +\+\X
387. Insert vector for X[i] zeroes after i:th subvector X„I1; Y„B1
  ((Y)++/X)+\1+1‡0,(1Y)\X
388. Open a gap of X[i] after Y[G[i]] (for all i) X„I1; Y„A1; G„I1
  (((Y)++/X)+\1+1‡0,((Y)G)\X)\Y
389. Open a gap of X[i] before Y[G[i]] (for all i) X„I1; Y„A1; G„I1
  (((Y)++/X)+\1+((Y)G)\X)\Y
390. Changing lengths X of subvectors to starting indicators X„I1
  A ‘ A[+\1‡ŒIO,X]„1 ‘ A„(+/X)0
391. Changing lengths X of subvectors to ending indicators X„I1
  (+/X)(+\X)-~ŒIO
392. Changing lengths X of subvectors to starting indicators X„I1
  (+/X)+\ŒIO,X
393. Insert vector for X[i] elements before i:th element X„I1
  (+/A)+\A„1+X
394. Sums over (+/) subvectors of Y indicated by X X„B1; Y„D1
  A-1‡0,A„(1X)/+\Y
395. Fifo stock Y decremented with X units Y„D1; X„D0
  G-1‡0,G„0—(+\Y)-X
396. Locations of texts between and including quotes X„C1
  AŸ1‡0,A„2|+\X=''''
397. Locations of texts between quotes X„C1
  A^1‡0,A„2|+\X=''''
398. X:th subvector of Y (subvectors separated by Y[1]) Y„A1; X„I0
  1‡(X=+\Y=1†Y)/Y
399. Locating field number Y starting with first element of X Y„I0; X„C1
  (Y=+\X=1†X)/X
400. Sum elements of X marked by succeeding identicals in Y X„D1; Y„D1
  A-1‡0,A„(Y1‡Y,0)/+\X
401. Groups of ones in Y pointed to by X X„B1; Y„B1
  Y^A(X^Y)/A„+\Y>1‡0,Y
402. ith starting indicators X X„B1; Y„B1
  (+\X)Y/Y
403. G:th subvector of Y (subvectors indicated by X) X„B1; Y„A1; G„I0
  (G=+\X)/Y
404. Running sum of Y consecutive elements of X X„D1; Y„I0
  ((Y-1)‡A)-0,(-Y)‡A„+\X
405. Depth of parentheses X„C1
  +\('('=X)-1‡0,')'=X
406. Starting positions of subvectors having lengths X X„I1
  +\1‡ŒIO,X
407. Changing lengths X of subvectors of Y to ending indicators X„I1
  (Y)(+\X)-~ŒIO
408. Changing lengths X of subvectors of Y to starting indicators X„I1
  (Y)+\ŒIO,X
409. X first triangular numbers X„I0
  +\X
410. Cumulative sum X„D
  +\X
REDUCTION / / -/ /
411. Complementary angle (arccos sin X) X„D0
  /2 1,X
412. Evaluating a two-row determinant X„D2
  -//0 1X
413. Evaluating a two-row determinant X„D2
  -/š0 1X
414. Area of triangle with side lengths in X (Heron's formula) X„D1; 3 „… X
  (/(+/X2)-0,X)*.5
415. Juxtapositioning planes of rank 3 array X X„A3
  (š2 21,X)2 1 3X
416. Number of rows in array X (also of a vector) X„A
  /1‡X
417. (Real) solution of quadratic equation with coefficients X X„D1; 3 „… X
  (-X[2]-1 1((X[2]*2)-/4,X[1 3])*.5)2X[1]
418. Reshaping planes of rank 3 array to rows of a matrix X„A3
  (/2 21,X)X
419. Reshaping planes of rank 3 array to a matrix X„A3
  (/2 2(X),1)X
420. Number of elements (also of a scalar) X„A
  /X
421. Product of elements of X X„D1
  /X
422. Alternating product X„D
  /X
423. Centering text line X into a field of width Y X„C1; Y„I0
  Y†((˜-/.5Y,X)' '),X
424. Alternating sum X„D
  -/X
REDUCTION —/ ˜/
425. Test if all elements of vector X are equal X„D1
  (—/X)=˜/X
426. Size of range of elements of X X„D1
  (—/X)-˜/X
427. Conversion of set of positive integers X to a mask X„I1
  (—/X)X
428. Negative infinity; the smallest representable value  
  —/0
429. Vectors as column matrices in catenation beneath each other X„A1/2; Y„A1/2
  X,[1+.5—/(X),Y]Y
430. Vectors as row matrices in catenation upon each other X„A1/2; Y„A1/2
  X,[.5—/(X),Y]Y
431. Quick membership () for positive integers X„I1; Y„I1
  A[X] ‘ A[Y]„1 ‘ A„(—/X,Y)0
432. Positive maximum, at least zero (also for empty X) X„D1
  —/X,0
433. Maximum of elements of X X„D1
  —/X
434. Positive infinity; the largest representable value  
  ˜/0
435. Minimum of elements of X X„D1
  ˜/X
REDUCTION Ÿ/ Š/ /
436. Test if all elements of vector X are equal X„B1
  Š/0 1X
437. Test if all elements of vector X are equal X„B1
  (^/X)Ÿ~Ÿ/X
438. Test if all elements of vector X are equal X„B1
  (^/X)=Ÿ/X
439. Test if all elements of vector X are equal X„B1
  ^/XŸ/X
440. Removing duplicate rows from ordered matrix X X„A2
  (11‡(Ÿ/X1X),1)šX
441. Vector having as many ones as X has rows X„A2
  Ÿ/0/X
442. Test if X and Y have elements in common X„A; Y„A1
  Ÿ/YX
443. None, neither X„B
  ~Ÿ/X
444. Any, anyone X„B
  Ÿ/X
445. Test if all elements of vector X are equal X„B1
  /0 1X
446. Parity X„B
  /X
REDUCTION ^/
447. Number of areas intersecting areas in X X„D3 (n 2 dim)
  +/A^A„^/X[;A1;]ˆ2 1 3X[;(A„1†X)2;]
448. Test if all elements of vector X are equal X„B1
  ^/X/1X
449. Comparison of successive rows X„A2
  ^/X=1X
450. Test if all elements of vector X are equal X„A1
  ^/X=1X
451. Test if X is a valid APL name X„C1
  ^/((1†X)10‡A),XA„'0..9A..Z‘a..x'
452. Test if all elements of vector X are equal X„A1
  ^/X=1†X
453. Identity of two sets X„A1; Y„A1
  ^/(XY),YX
454. Test if X is a permutation vector X„I1
  ^/(X)X
455. Test if all elements of vector X are equal X„B1
  ~^/X~X
456. Test if X is boolean X„A
  ^/,X0 1
457. Test if Y is a subset of X (Y › X) X„A; Y„A1
  ^/YX
458. Test if arrays of equal shape are identical X„A; Y„A; X „… Y
  ^/,X=Y
459. Test if all elements of vector X are equal X„A1
  ^/X=X[1]
460. Blank rows X„C2
  ^/' '=X
461. All, both X„B
  ^/X
REDUCTION +/
462. Standard deviation of X X„D1
  ((+/(X-(+/X)X)*2)X)*.5
463. Y:th moment of X X„D1
  (+/(X-(+/X)X)*Y)X
464. Variance (dispersion) of X X„D1
  (+/(X-(+/X)X)*2)X
465. Arithmetic average (mean value), also for an empty array X„D
  (+/,X)1—,X
466. Test if all elements of vector X are equal X„B1
  0=(X)|+/X
467. Average (mean value) of columns of matrix X X„D2
  (+šX)1†(X),1
468. Average (mean value) of rows of matrix X X„D2
  (+/X)1†1,X
469. Number of occurrences of scalar X in array Y X„A0; Y„A
  +/X=,Y
470. Average (mean value) of elements of X along direction Y X„D; Y„I0
  (+/[Y]X)(X)[Y]
471. Arithmetic average (mean value) X„D1
  (+/X)X
472. Resistance of parallel resistors X„D1
  +/X
473. Sum of elements of X X„D1
  +/X
474. Row sum of a matrix X„D2
  +/X
475. Column sum of a matrix X„D2
  +šX
476. Reshaping one-element vector X into a scalar X„A1
  +/X
477. Number of elements satisfying condition X X„B1
  +/X
REVERSE
478. Scan from end with function X„A
  \X
479. The index of positive integers in Y X„I; Y„I1
  A[X] ‘ A[Y]„Y ‘ A„9999ŒIO+Y
480. 'Transpose' of matrix X with column fields of width Y X„A2; G„I0
  ((A)1,Y)2 1 3(1Y,A„(X)1,Y)X
482. Adding X to each column of Y X„D1; Y„D; (X)=1†Y
  Y+(Y)X
483. Matrix with shape of Y and X as its columns X„A1; Y„A2
  (Y)X
484. Derivate of polynomial X X„D1
  1‡Xײ1+X
485. Reverse vector X on condition Y X„A1; Y„B0
  ,[ŒIO+Y](1,X)X
486. Reshaping vector X into a one-column matrix X„A1
  (1,X)X
487. Avoiding parentheses with help of reversal  
  (1, ...)
ROTATE
488. Vector (cross) product of vectors X„D; Y„D
  ((1X)ׯ1Y)-(1X)1Y
489. A magic square, side X X„I0; 1=2|X
  A(A„(X)-—X2)(X,X)XX
490. Removing duplicates from an ordered vector X„A1
  (11‡(X1X),1)/X
491. An expression giving itself  
  12211'''12211'''
492. Transpose matrix X on condition Y X„A2; Y„B0
  (Y1 2)X
493. Any element true (Ÿ/) on each subvector of Y indicated by X X„B1; Y„B1
  (X/Y)‰A/1A„(YŸX)/X
494. All elements true (^/) on each subvector of Y indicated by X X„B1; Y„B1
  (X/Y)^A/1A„(YˆX)/X
495. Removing leading, multiple and trailing Y's X„A1; Y„A0
  (1†A)‡(AŠ1A„Y=X)/X
496. Changing starting indicators X of subvectors to lengths X„B1
  A-1‡0,A„(1X)/X
498. (Cyclic) compression of successive blanks X„C1
  (AŸ1A„X' ')/X
499. Aligning columns of matrix X to diagonals X„A2
  (1-1†X)X
500. Aligning diagonals of matrix X to columns X„A2
  (1+1†X)X
501. Diagonal matrix with elements of X X„D1
  0 1‡(-X)((2X)0),X
502. Test if elements differ from previous ones (non-empty X) X„A1
  1,1‡X1X
503. Test if elements differ from next ones (non-empty X) X„A1
  (1‡X1X),1
504. Replacing first element of X with Y X„A1; Y„A0
  11‡X,Y
505. Replacing last element of X with Y X„A1; Y„A0
  11‡Y,X
506. Ending points for X in indices pointed by Y X„A1; Y„I1
  1(X)Y
507. Leftmost neighboring elements cyclically X„A
  1X
508. Rightmost neighboring elements cyclically X„A
  1X
TRANSPOSE
509. Applying to columns action defined on rows X„A1; Y„I0
  ... X
510. Retrieving scattered elements Y from matrix X X„A2; Y„I2
  1 1X[Y[1;];Y[2;]]
511. Successive transposes of G (X after Y: XYG) X„I1; Y„I1
  X[Y]G
512. Major diagonal of array X X„A
  (1*X)X
513. Reshaping a 40012 character matrix to fit into one page X„C2
  40 1202 1 310 40 12X
514. Transpose of planes of a rank three array X„A3
  1 3 2X
515. Major diagonal of matrix X X„A2
  1 1X
516. Selecting specific elements from a 'large' outer product X„A; Y„A; G„I1
  GX.Y
517. Test for antisymmetricity of square matrix X X„D2
  ~0X=-X
518. Test for symmetricity of square matrix X X„A2
  ~0X=X
519. Matrix with X columns Y X„I0; Y„D1
  (X,Y)Y
MAXIMUM — MINIMUM ˜
520. Limiting X between Y[1] and Y[2], inclusive X„D; Y„D1
  Y[1]—Y[2]˜X
521. Inserting vector Y to the end of matrix X X„A2; Y„A1
  (A†X),[1](1‡A„(X)—0,Y)†Y
522. Widening matrix X to be compatible with Y X„A2; Y„A2
  ((0 1׽Y)—X)†X
523. Lengthening matrix X to be compatible with Y X„A2; Y„A2
  ((1 0׽Y)—X)†X
524. Reshaping non-empty lower-rank array X into a matrix X„A; 2‰X
  (1—2†X)X
525. Take of at most X elements from Y X„I; Y„A
  (X˜Y)†Y
526. Limiting indices and giving a default value G X„A1; Y„I; G„A0
  (X,G)[(1+X)˜Y]
CEILING — FLOOR ˜
527. Reshaping X into a matrix of width Y X„D, Y„I0
  ((—(,X)Y),Y)X
528. Rounding to nearest even integer X„D
  ˜X+1ˆ2|X
529. Rounding, to nearest even integer for .5 = 1||X X„D
  ˜X+.5.52|X
530. Rounding, to nearest even integer for .5 = 1||X X„D
  ˜X+.5.52|X
531. Arithmetic progression from X to Y with step G X„D0; Y„D0; G„D0
  X+(GY-X)(1+|˜(Y-X)G)-ŒIO
532. Centering text line X into a field of width Y X„C1; Y„I0
  (-˜.5Y+X)†X
533. Test if integer X„D
  X=˜X
534. Rounding currencies to nearest 5 subunits X„D
  .05˜.5+X.05
535. First part of numeric code ABBB X„I
  ˜X1000
536. Rounding to X decimals X„I; Y„D
  (10*-X)˜0.5+Y10*X
537. Rounding to nearest hundredth X„D
  0.01˜0.5+100X
538. Rounding to nearest integer X„D
  ˜0.5+X
539. Demote floating point representations to integers X„I
  ˜X
RESIDUE |
540. Test if X is a leap year X„I
  (0=400|X)Ÿ(0100|X)^0=4|X
541. Framing X„C2
  '_',[1]('|',X,'|'),[1]''
542. Magnitude of fractional part X„D
  1||X
543. Fractional part with sign X„D
  (X)|X
544. Increasing the dimension of X to multiple of Y X„A1; Y„I0
  X,(Y|-X)†0/X
545. Removing every Y:th element of X X„A1; Y„I0
  (0Y|X)/X
546. Taking every Y:th element of X X„A1; Y„I0
  (0=Y|X)/X
547. Divisors of X X„I0
  (0=A|X)/A„X
548. Removing every second element of X X„A1
  (2|X)/X
549. Elements of X divisible by Y X„D1; Y„D0/1
  (0=Y|X)/X
550. Ravel of a matrix to Y[1] columns with a gap of Y[2] X„A2; Y„I1
  (AY[1]*1 1)(A„(X)+(Y[1]|-1†X),Y[2])†X
551. Test if even X„I
  ~2|X
552. Last part of numeric code ABBB X„I
  1000|X
553. Fractional part X„D
  1|X
MAGNITUDE |, SIGNUM
554. Increasing absolute value without change of sign X„D; Y„D
  (X)Y+|X
555. Rounding to zero values of X close to zero X„D; Y„D
  XYˆ|X
556. Square of elements of X without change of sign X„D
  X|X
557. Choosing according to signum X„D; Y„A1
  Y[2+X]
EXPAND \ ™
558. Not first zero (ˆ\) in each subvector of Y indicated by X X„B1; Y„B1
  ~(B^X)Ÿ(BŸX)\A>1‡0,A„(BŸX)/B„~Y
559. First one (<\) in each subvector of Y indicated by X X„B1; Y„B1
  (Y^X)Ÿ(YŸX)\A>1‡0,A„(YŸX)/Y
560. Replacing elements of X in set Y with blanks/zeroes X„A0; Y„A1
  A\(A„~XY)/X
561. Replacing elements of X not in set Y with blanks/zeroes X„A1; Y„A
  A\(A„XY)/X
562. Merging X and Y under control of G (mesh) X„A1; Y„A1; G„B1
  A ‘ A[(~G)/G]„Y ‘ A„G\X
563. Replacing elements of X not satisfying Y with blanks/zeroes X„A; Y„B1
  Y\Y/X
564. Adding an empty row into X after rows Y X„A2; Y„I1
  (~((Y)+1X)Y+Y)™X
565. Test if numeric X„A1
  00\0X
566. Adding an empty row into X after row Y X„A2; Y„I0
  ((Y+1)1+1X)™X
567. Underlining words X„C1
  X,[ŒIO-.1](' 'X)\''
568. Using boolean matrix Y in expanding X X„A1; Y„B2
  (Y)(,Y)\X
569. Spacing out text X„C1
  ((2׽X)1 0)\X
COMPRESS / š
570. Lengths of groups of ones in X X„B1
  (A>0)/A„(1‡A)-1+1‡A„(~A)/A„0,X,0
571. Syllabization of a Finnish word X X„A1
  (~A1,X)/A„A/A„(1‡A,0)
572. Choosing a string according to boolean value G X„C1; Y„C1; G„B0
  (G/X),(~G)/Y
573. Removing leading, multiple and trailing blanks X„C1
  (' '=1†X)‡((1‡A,0)ŸA„' 'X)/X
575. Removing columns Y from array X X„A; Y„I1
  (~(1†X)Y)/X
576. Removing trailing blanks X„C1
  (1†(' 'X)/X)X
577. Lengths of subvectors of X having equal elements X„A1
  (1‡A)-1‡A„(A,1)/1+A„1,(1‡X)1‡X
578. Field lengths of vector X; G „… ending indices X„A1; G„I1
  G-1‡0,G„(~ŒIO)+(((1‡X)1‡X),1)/X
580. Removing multiple and trailing blanks X„C1
  ((1‡A,0)ŸA„' 'X)/X
581. Removing leading and multiple blanks X„C1
  (AŸ1‡0,A„' 'X)/X
582. Removing multiple blanks X„C1
  (AŸ1‡1,A„' 'X)/X
583. Removing duplicate Y's from vector X X„A1; Y„A0
  (AŸ1‡1,A„XY)/X
584. Indices of all occurrences of elements of Y in X X„A1; Y„A
  (XY)/X
585. Union of sets, ž X„A1; Y„A1
  Y,(~XY)/X
586. Elements of X not in Y (difference of sets) X„A1; Y„A
  (~XY)/X
587. Rows of non-empty matrix X starting with a character in Y X„A2; Y„A1
  (X[;1]Y)šX
588. Intersection of sets,  X„A1; Y„A
  (XY)/X
589. Reduction with function in dimension Y, rank unchanged Y„I0; X„A
  ((X)*YX) /[Y]X
590. Replacing all values X in G with Y X„A0; Y„A0; G„A
  (G)A ‘ A[(A=X)/A„,G]„Y
591. Indices of all occurrences of Y in X X„A1; Y„A0
  (Y=X)/X
592. Replacing elements of G satisfying X with Y Y„A0; X„B1; G„A1
  G[X/G]„Y
593. Removing duplicates from positive integers X„I1
  A/9999 ‘ A[X]„1 ‘ A„99990
594. Indices of ones in logical vector X X„B1
  X/X
595. Conditional in text X„B0
  ((~X)/'IN'),'CORRECT'
596. Removing blanks X„A1
  (' 'X)/X
597. Removing elements Y from vector X X„A1; Y„A0
  (XY)/X
598. Vector to expand a new element after each one in X X„B1
  (,X,[1.5]1)/,X,[1.5]~X
599. Reduction with FUNCTION without respect to shape X„D
  /,X
600. Reshaping scalar X into a one-element vector X„A
  1/X
601. Empty matrix X„A2
  0šX
602. Selecting elements of X satisfying condition Y X„A; Y„B1
  Y/X
TAKE †
603. Inserting vector X into matrix Y after row G X„A1; Y„A2; G„I0
  Y[G;],[1]((1‡Y)†X),[1](2†G)‡Y
604. Filling X with last element of X to length Y X„A1; Y„I0
  Y†X,Y1†X
605. Input of row Y of text matrix X X„C2; Y„I0
  X[Y;]„(1†X)†
606. First ones in groups of ones X„B
  X>((-X)†1)‡0,X
607. Inserting X into Y after index G X„A1; Y„A1; G„I0
  (G†Y),X,G‡Y
608. Pairwise differences of successive columns (inverse of +\) X„D
  X-((-X)†1)‡0,X
609. Leftmost neighboring elements X„D
  ((-X)†1)‡0,X
610. Rightmost neighboring elements X„D
  ((-X)†1)‡X,0
611. Shifting vector X right with Y without rotate X„A1; Y„I0
  (-X)†(-Y)‡X
612. Shifting vector X left with Y without rotate X„A1; Y„I0
  (X)†Y‡X
613. Drop of Y first rows from matrix X X„A2; Y„I0
  (2†Y)‡X
614. Test if numeric X„A
  01†0X
615. Reshaping non-empty lower-rank array X into a matrix X„A; 2‰X
  (2†1 1,X)X
616. Giving a character default value for input X„C0
  1†,X
617. Adding scalar Y to last element of X X„D; Y„D0
  X+(-X)†Y
618. Number of rows in matrix X X„A2
  1†X
619. Number of columns in matrix X X„A2
  1†X
620. Ending points for X fields of width Y X„I0; Y„I0
  (XY)(-Y)†1
621. Starting points for X fields of width Y X„I0; Y„I0
  (XY)Y†1
622. Zero or space depending on the type of X (fill element) X„A
  1†0X
623. Forming first row of a matrix to be expanded X„A1
  1 8080†X
624. Vector of length Y with X ones on the left, the rest zeroes X„I0; Y„I0
  Y†X1
625. Justifying text X to right edge of field of width Y Y„I0; X„C1
  (-Y)†X
DROP ‡
627. Starting points of groups of equal elements (non-empty X) X„A1
  1,(1‡X)1‡X
628. Ending points of groups of equal elements (non-empty X) X„A1
  ((1‡X)1‡X),1
629. Pairwise ratios of successive elements of vector X X„D1
  (1‡X)1‡X
630. Pairwise differences of successive elements of vector X X„D1
  (1‡X)-1‡X
631. Differences of successive elements of X along direction Y X„D; Y„I0
  X-(-Y=X)‡0,[Y]X
632. Ascending series of integers Y..X (for small Y and X) X„I0; Y„I0
  (Y-1)‡X
633. First ones in groups of ones X„B1
  X>1‡0,X
634. Last ones in groups of ones X„B1
  X>1‡X,0
635. List of names in X (one per row) X„C2
  1‡,',',X
636. Selection of X or Y depending on condition G X„A0; Y„A0; G„B0
  ''G‡X,Y
637. Restoring argument of cumulative sum (inverse of +\) X„D1
  X-1‡0,X
638. Drop of Y first rows from matrix X X„A2; Y„I0
  (Y,0)‡X
639. Drop of Y first columns from matrix X X„A2; Y„I0
  (0,Y)‡X
640. Number of rows in matrix X X„A2
  1‡X
641. Number of columns in matrix X X„A2
  1‡X
642. Conditional drop of Y elements from array X X„A; Y„I1; G„B1
  (YG)‡X
643. Conditional drop of last element of X X„A1; Y„B0
  (-Y)‡X
MEMBER OF
644. Expansion vector with zero after indices Y X„A1; Y„I1
  ~((Y)+X)Y+Y
645. Boolean vector of length Y with zeroes in locations X X„I; Y„I0
  (~(Y)X)
646. Starting points for X in indices pointed by Y X„A1; Y„I1
  (X)Y
647. Boolean vector of length Y with ones in locations X X„I; Y„I0
  (Y)X
648. Check for input in range 1..X X„A
  (Y„Œ)X
649. Test if arrays are identical X„A; Y„A
  ~0X=Y
650. Zeroing elements of Y depending on their values Y„D; X„D
  Y~YX
651. Test if single or scalar X„A
  1,X
652. Test if vector X„A
  1X
653. Test if X is an empty array X„A
  0X
INDEX GENERATOR
654. Inverting a permutation X„I1
  A ‘ A[X]„A ‘ A„X
655. All axes of array X X„A
  X
656. All indices of vector X X„A1
  X
657. Arithmetic progression of Y numbers from X with step G X„D0; Y„D0; G„D0
  X+G(Y)-ŒIO
658. Consecutive integers from X to Y (arithmetic progression) X„I0; Y„I0
  (X-ŒIO)+1+Y-X
659. Empty numeric vector  
  0
660. Index origin (ŒIO) as a vector  
  1
LOGICAL FUNCTIONS ~ Ÿ ^ ‹ Š
661. Demote non-boolean representations to booleans X„B
  0ŸX
662. Test if X is within range ( Y[1],Y[2] ) X„D; Y„D1
  (Y[1]
663. Test if X is within range [ Y[1],Y[2] ] X„D; Y„D1; 2=Y
  (Y[1]ˆX)^(XˆY[2])
664. Zeroing all boolean values X„B
  0^X
666. Selection of elements of X and Y depending on condition G X„D; Y„D; G„B
  (XG)+Y~G
667. Changing an index origin dependent result to be as ŒIO=1 X„I
  (~ŒIO)+X
668. Conditional change of elements of Y to one according to X Y„D; X„B
  Y*~X
COMPARISON <>
669. X implies Y X„B; Y„B
  XˆY
670. X but not Y X„B; Y„B
  X>Y
671. Avoiding division by zero error (gets value zero) X„D; Y„D
  (0X)YX+0=X
672. Exclusive or X„B; Y„B
  XY
673. Replacing zeroes with corresponding elements of Y X„D; Y„D
  X+YX=0
674. Kronecker delta of X and Y (element of identity matrix) X„I; Y„I
  Y=X
RAVEL ,
675. Catenating Y elements G after every element of X X„A1; Y„I0; G„A
  ,X,((X),Y)G
676. Catenating Y elements G before every element of X X„A1; Y„I0; G„A0
  ,(((X),Y)G),X
677. Merging vectors X and Y alternately X„A1; Y„A1
  ,Y,[ŒIO+.5]X
678. Inserting Y after each element of X X„A1; Y„A0
  ,X,[1.1]Y
679. Spacing out text X„C1
  ,X,[1.1]' '
680. Reshaping X into a matrix of width Y X„D, Y„I0
  (((,X),1)Y*1 1)X
681. Temporary ravel of X for indexing with G X„A; Y„A; G„I
  X„AX ‘ X[G]„Y ‘ X„,X ‘ A„X
682. Temporary ravel of X for indexing with G X„A; Y„A; G„I
  X„(X)A ‘ A[G]„Y ‘ A„,X
683. First column as a matrix X„A2
  X[;,1]
684. Number of elements (also of a scalar) X„A
  ,X
CATENATE ,
685. Separating variable length lines X„A1; Y„A1
  X,ŒTC[2],Y
686. XX identity matrix X„I0
  (X,X)1,X0
687. Array and its negative ('plus minus') X„D
  X,[.5+X]-X
688. Underlining a string X„C1
  X,[ŒIO-.1]''
689. Forming a two-column matrix X„A1; Y„A1
  X,[1.1]Y
690. Forming a two-row matrix X„A1; Y„A1
  X,[.1]Y
691. Selection of X or Y depending on condition G X„A0; Y„A0; G„B0
  (X,Y)[ŒIO+G]
692. Increasing rank of Y to rank of X X„A; Y„A
  ((((X)-Y)1),Y)Y
693. Identity matrix of shape of matrix X X„D2
  (X)1,0X
694. Reshaping vector X into a two-column matrix X„A1
  ((0.5׽X),2)X
696. Reshaping vector X into a one-row matrix X„A1
  (1,X)X
697. Reshaping vector X into a one-column matrix X„A1
  ((X),1)X
698. Forming a Y-row matrix with all rows alike (X) X„A1; Y„I0
  (Y,X)X
699. Handling array X temporarily as a vector X„A
  (X) ... ,X
700. Joining sentences X„A; Y„A1
  Y,0X
701. Entering from terminal data exceeding input (printing) width X„D
  X„0 2 1 2 5 8 0 4 5,Œ
INDEXING [ ]
702. Value of fixed-degree polynomial Y at points X Y„D1; X„D
  Y[3]+XY[2]+XY[1]
703. Number of columns in array X X„A
  (X)[X]
704. Number of rows in matrix X X„A2
  (X)[1]
705. Number of columns in matrix X X„A2
  (X)[2]
706. Conditional elementwise change of sign Y„D; X„B
  Y1 1[1+X]
707. Selection depending on index origin X„A1
  X[2ŒIO]
708. Indexing with boolean value X (plotting a curve) X„B
  ' *'[ŒIO+X]
709. Indexing independent of index origin X„A1; Y„I
  X[ŒIO+Y]
710. Selection depending on index origin X„A1
  X[1]
711. Zeroing a vector (without change of size) X„D1
  X[]„0
712. First column as a vector X„A2
  X[;1]
SHAPE
713. Rank of array X X„A
  X
715. Duplicating vector X Y times X„A1; Y„I0
  (Y׽X)X
716. Adding X to each row of Y X„D1; Y„D; (X)=1†Y
  Y+(Y)X
717. Array with shape of Y and X as its rows X„A1; Y„A
  (Y)X
718. Number of rows in matrix X X„A2
  1X
RESHAPE
720. Forming an initially empty array to be expanded  
  0 800
721. Output of an empty line X„A
  0X„
722. Reshaping first element of X into a scalar X„A
  ''X
723. Corner element of a (non-empty) array X„A
  1X
ARITHMETIC + -
724. Continued fraction  
  1+2+3+4+5+6+ ...
725. Force 00 into DOMAIN ERROR in division X„D; Y„D
  YX
726. Conditional elementwise change of sign X„D; Y„B; X „… Y
  Xׯ1*Y
727. Zero array of shape and size of X X„D
  0X
728. Selecting elements satisfying condition Y, zeroing others X„D; Y„B
  YX
729. Number and its negative ('plus minus') X„D0
  1 1X
730. Changing an index origin dependent result to be as ŒIO=0 X„I
  -ŒIO-X
731. Changing an index origin dependent argument to act as ŒIO=1 X„I
  (ŒIO-1)+X
732. Output of assigned numeric value X„D
  +X„
733. Changing an index origin dependent argument to act as ŒIO=0 X„I
  ŒIO+X
734. Selecting elements satisfying condition Y, others to one X„D; Y„B
  X*Y
MISCELLANEOUS
736. Setting a constant with hyphens  
  ŒLX„
737. Output of assigned value X„A
  Œ„X„
738. Syntax error to stop execution  
  *
888. Meaning of life  
  –•œ›|˜-*+—!Ž~“”,?0


Last updated 12.7.2002 by Olli Paavola