# Idiom Library

1. Progressive index of (without replacement) X„A1; Y„A1
((½X)½““X¼X,Y)¼(½Y)½““X¼Y,X
2. Ascending cardinal numbers (ranking, shareable) X„D1
˜.5×(““X)+²““²X
3. Cumulative maxima (—\) of subvectors of Y indicated by X X„B1; Y„D1
Y[A¼—\A„“A[“(+\X)[A„“Y]]]
4. Cumulative minima (˜\) of subvectors of Y indicated by X X„B1; Y„D1
Y[A¼—\A„“A[“(+\X)[A„”Y]]]
5. Progressive index of (without replacement) X„A1; Y„A1
((“X¼X,Y)¼¼½X)¼(“X¼Y,X)¼¼½Y
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; (½X) „… +/Y
A[“(+\(¼½Y)¹+\ŒIO,X)[A„“Y]]
9. Index of the elements of X in Y X„D1; Y„D1
(((1,A)/B)˜1+½Y)[(½Y)‡(+\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(2,½X)½““X,X
13. Sorting rows of matrix X into ascending order X„D2
(½X)½(,X)[A[“(,³(²½X)½¼1†½X)[A„“,X]]]
14. Adding a new dimension after dimension G Y-fold G„I0; Y„I0; X„A
(““(G+1),¼½½X)³(Y,½X)½X
15. Sorting rows of matrix X into ascending order X„D2
(½X)½(,X)[ŒIO+A[“˜A÷¯1†½X]] ‘ A„(“,X)-ŒIO
16. Y smallest elements of X in order of occurrence X„D1, Y„I0
((““X)¹¼Y)/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; (½X) „… +/Y
A[“(+\(¼½Y)¹+\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)¹¼Y)/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+½Y)ƒY¼³X;]
27. Diagonal ravel X„A
(,X)[“+š(½X)‚(¼½,X)-ŒIO]
28. Grade up according to key Y Y„A1; X„A1
“Y¼X
29. Test if X is a permutation vector X„I1
X[“X]^.=¼½X
30. Sorting a matrix into lexicographic order X„D2
X[“+šA<.-³a„x,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<.‰1²y
A ‘ A[(B/C)-½Y]„B/+\~B„(½Y)
33. Rotate first elements (1²) of subvectors of Y indicated by X X„B1; Y„A1
Y[“X++\X]
34. Doubling quotes (for execution) X„C1
(X,'''')[(ŒIO+½X)˜“(¼½X),(''''=X)/¼½X]
35. Inserting Y *'s into vector X after indices G X„C1; Y„I0; G„I1
(X,'*')[(ŒIO+½X)˜“(¼½X),(Y×½G)½G]
36. Median X„D1
X[(“X)[—.5×½X]]
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
(½X)‰“(¼½X),Y
40. Catenating G elements H before indices Y in vector X X„A1; Y„I1; G„I0; H„A0
((A½H),X)[“(A½Y),¼½X] ‘ A„G×½,Y
41. Catenating G elements H after indices Y in vector X X„A1; Y„I1; G„I0; H„A0
(X,A½H)[“(¼½X),A½Y] ‘ A„G×½,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
“X×¯1 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
49. Reverse vector X on condition Y X„A1; Y„B0
X[”Y!¼½X]
50. Sorting a matrix into reverse lexicographic order X„D2
X[”+šA<.-³a„x,0;]
52. Reversal (²) of subvectors of X having lengths Y X„D1; Y„I1
X[²”+\(¼½X)¹+\ŒIO,Y]
53. Reversal (²) of subvectors of Y indicated by X X„B1; Y„A1
Y[²”+\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°.*²-ŒIO-¼½X
61. Predicted values of exponential (curve) fit X„D1; Y„D1
*A+.×(µY)ŽA„X°.*0 1
62. Coefficients of exponential (curve) fit of points (X,Y) X„D1; Y„D1
A ‘ A[1]„*A[1] ‘ A„(µY)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
²YŽX°.*0,¼G
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+—2µ—/,X)½2)‚X
67. Barchart of two integer series (across the page) X„I2; 1½½X „… 2
' *±µ'[ŒIO+2ƒX°.‰¼—/,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)
(1²,' ::',3 2½6 0•100ƒ12 0 0|3†3‡ŒTS),'AP'[1+12ˆŒTS[4]],'M'
73. Removing duplicate rows X„A2
((A¼A)=¼½A„2ƒX^.=³X)šX
74. Conversion from hexadecimal to decimal X„C
16ƒ-ŒIO-'0123456789ABCDEF'¼³X
75. Conversion of alphanumeric string into numeric X„C1
10ƒ¯1+'0123456789'¼X
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
B½A ‘ A[ŒIO+B[1]ƒ-ŒIO-X]„1 ‘ A„(×/B„0 0+—/,X)½0
78. Present value of cash flows X at interest rate Y % X„D1; Y„D0
(÷1+Y÷100)ƒ²X
79. Justifying right X„C
(1-(' '=X)ƒ1)²X
80. Number of days in month X of years Y (for all leap years) X„I0; Y„I
(12½7½31 30)[X]-0—¯1+2ƒ(X=2),[.1](0¬400|Y)-(0¬100|Y)-0¬4|Y
81. Number of days in month X of years Y (for most leap years) X„I0; Y„I
(12½7½31 30)[X]-0—¯1+2ƒ(X=2),[.1]0¬4|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+(½X)ƒY-ŒIO]
86. Conversion of indices Y of array X to indices of raveled X X„A; Y„I2
ŒIO+(½X)ƒY-ŒIO
87. Number of columns in array X as a scalar X„A
0ƒ½X
88. Future value of cash flows X at interest rate Y % X„D1; Y„D0
(1+Y÷100)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
³'0123456789ABCDEF'[ŒIO+((——/16µ,X)½16)‚X]
95. All binary representations up to X (truth table) X„I0
((—2µ1+X)½2)‚0,¼X
96. Representation of X in base Y X„D0; Y„D0
((1+˜YµX)½Y)‚X
97. Digits of X separately X„I0
((1+˜10µX)½10)‚X
98. Helps locating column positions 1..X X„I0
1 0•10 10‚1-ŒIO-¼X
99. Conversion of characters to hexadecimal representation (ŒAV) X„C1
,' ',³'0123456789ABCDEF'[ŒIO+16 16‚-ŒIO-ŒAV¼X]
100. Polynomial with roots X X„D1
²((0,¼½X)°.=+š~A)+.×(-X)×.*A„((½X)½2)‚¯1+¼2*½X
101. Index pairs of saddle points X„D2
ŒIO+(½X)‚-ŒIO-(,(X=(½X)½—šX)^X=³(²½X)½˜/X)/¼×/½X
102. Changing connectivity matrix X to a connectivity list X„C2
(,X)/1+A‚¯1+¼×/A„½X
103. Matrix of all indices of X X„A
ŒIO+(½X)‚(¼×/½X)-ŒIO
104. Separating a date YYMMDD to YY, MM, DD X„D
³(3½100)‚X
105. Indices of elements Y in array X X„A; Y„A
ŒIO+(½X)‚(-ŒIO)+(,X¹Y)/¼½,X
106. All pairs of elements of ¼X and ¼Y X„I0; Y„I0
ŒIO+(X,Y)‚(¼X×Y)-ŒIO
107. Matrix for choosing all subsets of X (truth table) X„A1
((½X)½2)‚¯1+¼2*½X
108. All binary representations with X bits (truth table) X„I0
(X½2)‚¯1+¼2*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 µ
112. Number of decimals of elements of X X„D1
˜10µ(–('.'¬A)/A„•X)÷X
113. Number of sortable columns at a time using ƒ and alphabet X X„C1
˜(1+½X)µ2*(A=¯1+A„2*¼128)¼1
114. Playing order in a cup for X ranked players X„I0
,³(A½2)½(2*A„—2µX)†¼X
115. Arithmetic precision of the system (in decimals)
˜|10µ|1-3×÷3
116. Number of digitpositions in integers in X X„I
1+(X<0)+˜10µ|x+0=x
117. Number of digit positions in integers in X X„I
1+˜10µ(X=0)+X×1 ¯10[1+X<0]
118. Number of digits in positive integers in X X„I
1+˜10µX+0=X
BRANCH …
119. Case structure according to key vector G X„A0; Y„I1; G„A1
…Y[G¼X]
120. Forming a transitive closure X„B2
…ŒLC—¼Ÿ/,(X„XŸXŸ.^X)¬+X
121. Case structure with integer switch X„I0; Y„I1
…X²Y
122. For-loop ending construct X„I0; Y„I0; G„I0
…Y—¼G‰X„X+1
123. Conditional branch to line Y X„B0; Y„I0; Y>0
…Y—¼X
124. Conditional branch out of program X„B0
…0˜¼X
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
…Y××X
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
…0×¼X
EXECUTE –
132. Test for symmetricity of matrix X X„A2
––'1','†‡'[ŒIO+^/(½X)=²½X],'''0~0¹X=³X'''
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'¹F) F„A1; X„D1
' *'[ŒIO+(²(¯1+˜/A)+¼1+(—/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^.=²A„½X)†'0~0¹X=³X'
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'¹F) F„A1; G„D0; Y„D1; ½Y „… 2
A+.×–F,0½X„Y[1]+(A„--/Y÷G)×0,¼G
143. Test if numeric and conversion to numeric form X„C1
1‡–'0 ',(^/X¹' 0123456789')/X
144. Tests the social security number (Finnish) Y„'01...9ABC...Z'; 10=½X
(¯1†X)=((~Y¹'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*2¬ŒNC 'X')†'X100'
148. Conditional execution X„B0; Y„A1
149. Giving a numeric default value for input X„D0
1½(–,',¼0'),X
150. Assign values of expressions in X to variables named in Y X„C2; Y„C2
A„–,',','(','0','½',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+½½X)½';'),'Y]'
FORMAT •
154. Numeric headers (elements of X) for rows of table Y X„D1; Y„A2
(3²7 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)/¼½A]„'.' ‘ A„•²3†ŒTS
157. Representation of current date (American)
A ‘ A[(' '=A)/¼½A]„'/' ‘ A„•100|1²3†ŒTS
158. Formatting with zero values replaced with blanks X„A
(½A)½B\(B„,('0'¬A)Ÿ' '¬¯1²A)/,A„' ',•X
159. Number of digit positions in scalar X (depends on ŒPP) X„D0
½•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)×½X)½2 1 3³(²G,½X)½(,G,[1.1]Y)•³X
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]+?Y½--/X
165. Removing punctuation characters X„A1
(~X¹' .,:;?''')/X
166. Choosing Y objects out of ¼X with replacement (roll) Y„I; X„I
?Y½X
167. Choosing Y objects out of ¼X without replacement (deal) X„I0; Y„I0
Y?X
GEOMETRICAL FUNCTIONS ±
168. Arctan Y÷X X„D; Y„D
((X¬0)×¯3±Y÷X+X=0)+±((X=0)×.5××Y)+(X<0)×1-2×y<0
169. Conversion from degrees to radians X„D
X×±÷180
170. Conversion from radians to degrees X„D
X×180÷±1
171. Rotation matrix for angle X (in radians) counter-clockwise X„D0
2 2½1 ¯1 1 1×2 1 1 2±X
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+¼½Y
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-¼X+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 ¼
180. Removing elements Y from beginning and end of vector X X„A1; Y„A
((A¼1)-ŒIO)‡(ŒIO-(²A„~X¹Y)¼1)‡X
181. Alphabetical comparison with alphabets G X„A; Y„A
(G¼X)
183. Sum over elements of X determined by elements of Y X„D1; Y„D1
X+.×Y°.=((¼½Y)=Y¼Y)/Y
184. First occurrence of string X in string Y X„A1; Y„A1
(^š(¯1+¼½X)²X°.=Y)¼1
185. Removing duplicate rows X„A2
((A¼A)=¼½A„ŒIO++š^™XŸ.¬³X)šX
186. First occurrence of string X in matrix Y X„A2; Y„A1; ¯1†½Y„…½X
(Y^.=X)¼1
187. Indices of ones in logical vector X X„B1
(+\X)¼¼+/X
188. Executing costly monadic function F on repetitive arguments X„A1
(F B/X)[+\B„(X¼X)=¼½X]
189. Index of (first) maximum element of X X„D1
X¼—/X
190. Index of first occurrence of elements of Y X„C1; Y„C1
˜/X¼Y
191. Index of (first) minimum element of X X„D1
X¼˜/X
192. Test if each element of X occurs only once X„A1
^/(X¼X)=¼½X
193. Test if all elements of vector X are equal X„A1
^/ŒIO=X¼X
194. Interpretation of roman numbers X„A
+/A×¯1*A<1²a„0,1000 500 100 50 10 5 1['MDCLXVI'¼X]
195. Removing elements Y from end of vector X X„A1; Y„A
(ŒIO-(~²X¹Y)¼1)‡X
196. Removing trailing blanks X„C1
(1-(²' '¬X)¼1)‡X
198. Index of last occurrence of Y in X (ŒIO-1 if not found) X„A1; Y„A
(¯1 1[2×ŒIO]+½X)-(²X)¼Y
199. Index of last occurrence of Y in X (0 if not found) X„A1; Y„A
(1+½X)-(²X)¼Y
200. Index of last occurrence of Y in X, counted from the rear X„A1; Y„A
(²X)¼Y
201. Index of first occurrence of G in X (circularly) after Y X„A1; Y„I0; G„A
ŒIO+(½X)|Y+(Y²X)¼G
202. Alphabetizing X; equal alphabets in same column of Y Y„C2; X„C
(¯1†½Y)|(,Y)¼X
203. Changing index of an unfound element to zero Y„A1; X„A
(1+½Y)|Y¼X
204. Replacing elements of G in set X with corresponding Y X„A1, Y„A1, G„A
(½G)½A ‘ A[B/¼½B]„Y[(B„Bˆ½Y)/B„X¼A„,G]
205. Removing duplicate elements (nub) X„A1
((X¼X)=¼½X)/X
206. First word in X X„C1
(¯1+X¼' ')†X
207. Removing elements Y from beginning of vector X X„A1; Y„A
(((~X¹Y)¼1)-ŒIO)‡X
(¯1+(X='0')¼0)‡X
209. Index of first one after index Y in X G„I0; X„B1
Y+(Y‡X)¼1
210. Changing index of an unfound element to zero (not effective) X„A; Y„A1
(X¹Y)×Y¼X
211. Indicator of first occurrence of each unique element of X X„A1
(X¼X)=¼½X
212. Inverting a permutation X„I1
X¼¼½X
213. Index of first differing element in vectors X and Y X„A1; Y„A1
(Y¬X)¼1
214. Which elements of X are not in set Y (difference of sets) X„A; Y„A1
(ŒIO+½Y)=Y¼X
215. Changing numeric code X into corresponding name in Y X„D; Y„D1; G„C2
G[Y¼X;]
216. Index of key Y in key vector X X„A1; Y„A
X¼Y
217. Conversion from characters to numeric codes X„A
ŒAV¼X
218. Index of first satisfied condition in X X„B1
X¼1
OUTER PRODUCT °.! °.— °.|
219. Pascal's triangle of order X (binomial coefficients) X„I0
³A°.!A„0,¼X
220. Maximum table X„I0
(¼X)°.—¼X
221. Number of decimals (up to Y) of elements of X X„D; Y„I0
0+.¬(—(10*Y)×10*ŒIO-¼Y+1)°.|—X×10*Y
222. Greatest common divisor of elements of X X„I1
—/(^/0=A°.|X)/A„¼˜/X
223. Divisibility table X„I1
0=(¼—/X)°.|X
224. All primes up to X X„I0
(2=+š0=(¼X)°.|¼X)/¼X
OUTER PRODUCT °.* °.× °.- °.+
225. Compound interest for principals Y at rates G % in times X X„D; Y„D; G„D
Y°.×(1+G÷100)°.*X
226. Product of two polynomials with coefficients X and Y X„D1; Y„D1
+š(ŒIO-¼½X)²X°.×Y,0×1‡X
228. Shur product X„D2; Y„D2
1 2 1 2³X°.×Y
229. Direct matrix product X„D2; Y„D2
1 3 2 4³X°.×Y
230. Multiplication table X„I0
(¼X)°.×¼X
231. Replicating a dimension of rank three array X Y-fold Y„I0; X„A3
X[;,(Y½1)°.×¼(½X)[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 1³X°.-˜/X
234. Test relations of elements of X to range Y; result in ¯2..2 X„D; Y„D; 2=¯1†½Y
+/×X°.-Y
235. Occurrences of string X in string Y X„A1; Y„A1
(Y[A°.+¯1+¼½X]^.=X)/A„(A=1†X)/¼½A„(1-½X)‡Y
236. Sum of common parts of matrices (matrix sum) X„D2; Y„D2
1 2 1 2³X°.+Y
237. Adding X to each column of Y X„D1; Y„D2
1 1 2³X°.+Y
238. Adding X to each column of Y X„D1; Y„D2
1 2 1³Y°.+X
240. Adding X to each row of Y X„D1; Y„D2
2 1 2³X°.+Y
241. Adding X to each row of Y X„D1; Y„D2
1 2 2³Y°.+X
242. Hilbert matrix of order X X„¼0
÷¯1+(¼X)°.+¼X
243. Moving index of width Y for vector X X„A1; Y„I0
(0,¼(½X)-Y)°.+Y
244. Indices of subvectors of length Y starting at X+1 X„I1; Y„I0
X°.+¼Y
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
((½A)½Y÷100)÷A„³1-(1+Y÷100)°.*-X
OUTER PRODUCT °.<°.ˆ °.‰ °.>
247. Matrix with X[i] trailing zeroes on row i X„I1
X°.<²¼—/x
248. Matrix with X[i] leading zeroes on row i X„I1
X°.<¼—/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+(²¼—/A)°.ˆA„+/(¼1+(—/X)-˜/X)°.=X]
251. Barchart of integer values (down the page) X„I1
' Œ'[ŒIO+(²¼—/X)°.ˆX]
252. Test if X is an upper triangular matrix X„D2
^/,(0¬X)ˆA°.ˆA„¼1†½X
253. Number of ?s intersecting ?s (X=starts, Y=stops) X„D1; Y„D1
+/A^³A„X°.ˆY
254. Contour levels Y at points with altitudes X X„D0; Y„D1
Y[+šY°.ˆX]
255. X×X upper triangular matrix X„I0
(¼X)°.ˆ¼X
256. Classification of elements Y into X classes of equal size X„I0; Y„D1
+/(A×X÷—/A„Y-˜/Y)°.‰¯1+¼X
257. Matrix with X[i] trailing ones on row i X„I1
X°.‰²¼—/X
258. Comparison table X„I1
X°.‰¼—/X,0
259. Barchart of X with height Y (across the page) X„D1; Y„D0
' Œ'[ŒIO+X°.‰(—/X)×(¼Y)÷Y]
260. Barchart of integer values (across the page) X„I1
' Œ'[ŒIO+X°.‰¼—/X]
261. Matrix with X[i] leading ones on row i X„I1
X°.‰¼—/X
263. Test if X is a lower triangular matrix X„D2
^/,(0¬X)ˆA°.‰A„¼1†½X
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)/¼½X
266. Which class do elements of X belong to X„D
+/X°.‰0 50 100 1000
267. X×X lower triangular matrix X„I0
(¼X)°.‰¼X
268. Moving all blanks to end of each row X„C
(½X)½(,(+/A)°.>-ŒIO-¼¯1†½X)\(,A„X¬' ')/,X
269. Justifying right fields of X (lengths Y) to length G X„A1; Y„I1; G„I0
(,Y°.>²(¼G)-ŒIO)\X
270. Justifying left fields of X (lengths Y) to length G X„A1; Y„I1; G„I0
(,Y°.>(¼G)-ŒIO)\X
OUTER PRODUCT °.¬ °.=
271. Indices of elements of Y in corr. rows of X (X[i;]¼Y[i;]) X„A2; Y„A2
1++/^\1 2 1 3³Y°.¬X
273. Indicating equal elements of X as a logical matrix X„A1
³X°.=(1 1³<\x°.=x)/x
275. Changing connection matrix X (¯1 … 1) to a node matrix X„I2
(1 ¯1°.=³X)+.×¼1†½Œ„X
276. Sums according to codes G X„A; Y„D; G„A
(G°.=X)+.×Y
277. Removing duplicate elements (nub) X„A1
(1 1³<\x°.=x)/x
278. Changing node matrix X (starts,ends) to a connection matrix X„I2
-/(¼—/,X)°.=³X
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;]¹Y[i;]) X„A2; Y„A2; 1†½X„…1†½Y
Ÿ/1 2 1 3³X°.=Y
281. Test if X is a permutation vector X„I1
^/1=+/X°.=¼½X
282. Occurrences of string X in string Y X„C1; Y„C1
(^š(¯1+¼½X)²(X°.=Y),0)/¼1+½Y
283. Division to Y classes with width H, minimum G X„D; Y„I0; G„D0; H„D0
+/(¼Y)°.=—(X-G)÷H
285. Repeat matrix X„A1; Y„A1
(((¯1²~A)^A„(¯1‡X=1²X),0)/Y)°.=Y
286. X×X identity matrix X„I0
(¼X)°.=¼X
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)—.×¼¯1†½X
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†½X
(2 2½1 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.^ <.< <.ˆ <.‰ ˆ.‰>.>
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†½Y „… 2
X<.
300. Test if X is within range ( Y[1;],Y[2;] ] X„D0; Y„D2; 1†½Y „… 2
X<.ˆy
301. Test if X is within range ( Y[1;],Y[2;] ] X„D; Y„D2; 1†½Y „… 2
X<.ˆy
302. Test if the elements of X are ascending X„D1
X<.‰1²x
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†½Y „… 2
(X,[.1+½½X]X)>.>Y
INNER PRODUCT Ÿ.¬ ^.= +.¬ +.=
306. Removing trailing blank columns X„C2
(²Ÿ\²' '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.¬³X
310. 'X¼Y' for rows of matrices X„A2; Y„A2
ŒIO++š^™XŸ.¬³Y
311. Removing duplicate blank rows X„C2
(AŸ1‡1²1,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†+/^\²X^.=' ')‡X
317. Removing duplicate rows X„A2
(Ÿš<\x^.=³x)šx
318. Removing duplicate rows X„A2
(1 1³<\x^.=³x)šx
319. Test if circular lists are equal (excluding phase) X„A1; Y„A1
Ÿ/Y^.=³(¼½X)²(2½½X)½X
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†½X),½Y)†X)^.=Y)šX
323. Occurrences of string X in string Y X„A1; Y„A1
((-A)‡X^.=(A,1+½Y)½Y)/¼(½Y)+1-A„½X
324. Test if vector Y is a row of array X X„A; Y„A1
1¹X^.=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 Y÷X 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 2½¯1 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+¼½Y)+.×²Y
332. Arithmetic average (mean value) of X weighted by Y X„D1; Y„D1
(Y+.×X)÷½X
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†½X „… 1†½Y
X+.×Y
337. Sum of reciprocal series Y÷X 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=—\X×A„+\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×¼½Y]
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,X÷¼¯1+½Y
343. Alternating series (1 ¯1 2 ¯2 3 ¯3 ...) X„I0
-\¼X
SCAN Š\ <\ ˆ\ ¬\
346. Value of saddle point X„D2
(<\,(x=(½x)½—šx)^x=³(²½x)½˜/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
¬\Y¬X\A¬¯1‡0,A„X/¬\¯1‡0,Y
352. Vector (X[1]½1),(X[2]½0),(X[3]½1),... X„I1; ^/0
¬\(¼+/X)¹+\ŒIO,X
353. Not leading zeroes(Ÿ\) in each subvector of Y indicated by X X„B1; Y„B1
¬\(YŸX)\A¬¯1‡0,A„(YŸX)/Y
354. Leading ones (^\) in each subvector of Y indicated by X X„B1; Y„B1
~¬\(YˆX)\A¬¯1‡0,A„~(YˆX)/Y
355. Locations of texts between and including quotes X„C1
AŸ¯1‡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
((²Ÿ\²A)^Ÿ\A„' '¬X)/X
361. First group of ones X„B
X^^\X=Ÿ\X
362. Removing trailing blank columns X„C2
(²Ÿ\²Ÿš' '¬X)/X
363. Removing trailing blanks X„C1
(²Ÿ\²' '¬X)/X
(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„+/^\²A)++/^\A„' '=²X)²X
367. Decommenting a matrix representation of a function (ŒCR) X„C2
369. Centering character array X with only right edge ragged X„C
(-˜0.5×+/^\' '=²X)²X
370. Justifying right X„C
(-+/^\²' '=X)²X
371. Removing trailing blanks X„C1
(-+/^\²' '=X)‡X
372. Justifying left X„C
(+/^\' '=X)²X
373. Editing X with Y ’-wise X„C1; Y„C1
((~(½A†X)†'/'=Y)/A†X),(1‡A‡Y),(A„+/^\Y¬',')‡X
(+/^\' '=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]½1),(Y[1]½0),(X[2]½1),... Q„I1; Y„I1
(¼+/X,Y)¹+\1+¯1‡0,((¼+/X)¹+\X)\Y
379. Replicate Y[i] X[i] times (for all i) X„I1; Y„A1
((X¬0)/Y)[+\¯1²(¼+/X)¹+\X]
380. Vector (Y[1]+¼X[1]),(Y[2]+¼X[2]),(Y[3]+¼X[3]),... X„I1; Y„I1; ½X„…½Y
ŒIO++\1+((¼+/X)¹+\ŒIO,X)\Y-¯1‡1,X+Y
381. Replicate Y[i] X[i] times (for all i) X„I1; Y„A1; ^/0
Y[+\(¼+/X)¹¯1‡1++\0,X]
382. Replicate Y[i] X[i] times (for all i) X„I1; Y„A1; ^/0
Y[ŒIO++\(¼+/X)¹ŒIO++\X]
383. Cumulative sums (+\) 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
+\+\¼X
387. Insert vector for X[i] zeroes after i:th subvector X„I1; Y„B1
(¼(½Y)++/X)¹+\1+¯1‡0,(1²Y)\X
388. Open a gap of X[i] after Y[G[i]] (for all i) X„I1; Y„A1; G„I1
((¼(½Y)++/X)¹+\1+¯1‡0,((¼½Y)¹G)\X)\Y
389. Open a gap of X[i] before Y[G[i]] (for all i) X„I1; Y„A1; G„I1
((¼(½Y)++/X)¹+\1+((¼½Y)¹G)\X)\Y
390. Changing lengths X of subvectors to starting indicators X„I1
A ‘ A[+\¯1‡ŒIO,X]„1 ‘ A„(+/X)½0
391. Changing lengths X of subvectors to ending indicators X„I1
(¼+/X)¹(+\X)-~ŒIO
392. Changing lengths X of subvectors to starting indicators X„I1
(¼+/X)¹+\ŒIO,X
393. Insert vector for X[i] elements before i:th element X„I1
(¼+/A)¹+\A„1+X
394. Sums over (+/) subvectors of Y indicated by X X„B1; Y„D1
A-¯1‡0,A„(1²X)/+\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
AŸ¯1‡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„(Y¬1‡Y,0)/+\X
401. Groups of ones in Y pointed to by X X„B1; Y„B1
Y^A¹(X^Y)/A„+\Y>¯1‡0,Y
402. ith starting indicators X X„B1; Y„B1
(+\X)¹Y/¼½Y
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
(¼½Y)¹(+\X)-~ŒIO
408. Changing lengths X of subvectors of Y to starting indicators X„I1
(¼½Y)¹+\ŒIO,X
409. X first triangular numbers X„I0
+\¼X
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 1´X
413. Evaluating a two-row determinant X„D2
-/×š0 1²X
414. Area of triangle with side lengths in X (Heron's formula) X„D1; 3 „… ½X
(×/(+/X÷2)-0,X)*.5
415. Juxtapositioning planes of rank 3 array X X„A3
(×š2 2½1,½X)½2 1 3³X
416. Number of rows in array X (also of a vector) X„A
×/¯1‡½X
417. (Real) solution of quadratic equation with coefficients X X„D1; 3 „… ½X
(-X[2]-¯1 1×((X[2]*2)-×/4,X[1 3])*.5)÷2×X[1]
418. Reshaping planes of rank 3 array to rows of a matrix X„A3
(×/2 2½1,½X)½X
419. Reshaping planes of rank 3 array to a matrix X„A3
(×/2 2½(½X),1)½X
420. Number of elements (also of a scalar) X„A
×/½X
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†((˜-/.5×Y,½X)½' '),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
(¼—/X)¹X
428. Negative infinity; the smallest representable value
—/¼0
429. Vectors as column matrices in catenation beneath each other X„A1/2; Y„A1/2
X,[1+.5×—/(½½X),½½Y]Y
430. Vectors as row matrices in catenation upon each other X„A1/2; Y„A1/2
X,[.5×—/(½½X),½½Y]Y
431. Quick membership (¹) for positive integers X„I1; Y„I1
A[X] ‘ A[Y]„1 ‘ A„(—/X,Y)½0
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
˜/¼0
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 1¹X
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
^/X÷Ÿ/X
440. Removing duplicate rows from ordered matrix X X„A2
(¯1²1‡(Ÿ/X¬¯1´X),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/Y¹X
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 1¹X
446. Parity X„B
¬/X
REDUCTION ^/
447. Number of areas intersecting areas in X X„D3 (n × 2 × dim)
+/A^³A„^/X[;A½1;]ˆ2 1 3³X[;(A„1†½X)½2;]
448. Test if all elements of vector X are equal X„B1
^/X/1²X
449. Comparison of successive rows X„A2
^/X=1´X
450. Test if all elements of vector X are equal X„A1
^/X=1²X
451. Test if X is a valid APL name X„C1
^/((1†X)¹10‡A),X¹A„'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
^/(X¹Y),Y¹X
454. Test if X is a permutation vector X„I1
^/(¼½X)¹X
455. Test if all elements of vector X are equal X„B1
~^/X¹~X
456. Test if X is boolean X„A
^/,X¹0 1
457. Test if Y is a subset of X (Y › X) X„A; Y„A1
^/Y¹X
458. Test if arrays of equal shape are identical X„A; Y„A; ½X „… ½Y
^/,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)÷½X)*2)÷½X)*.5
463. Y:th moment of X X„D1
(+/(X-(+/X)÷½X)*Y)÷½X
464. Variance (dispersion) of X X„D1
(+/(X-(+/X)÷½X)*2)÷½X
465. Arithmetic average (mean value), also for an empty array X„D
(+/,X)÷1—½,X
466. Test if all elements of vector X are equal X„B1
0=(½X)|+/X
467. Average (mean value) of columns of matrix X X„D2
(+šX)÷1†(½X),1
468. Average (mean value) of rows of matrix X X„D2
(+/X)÷¯1†1,½X
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)÷(½X)[Y]
471. Arithmetic average (mean value) X„D1
(+/X)÷½X
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 ² ´
478. Scan from end with function ¸ X„A
²¸\²X
479. The index of positive integers in Y X„I; Y„I1
A[X] ‘ A[²Y]„²¼½Y ‘ A„9999½ŒIO+½Y
480. 'Transpose' of matrix X with column fields of width Y X„A2; G„I0
((²A)×1,Y)½2 1 3³(1²Y,A„(½X)÷1,Y)½X
482. Adding X to each column of Y X„D1; Y„D; (½X)=1†½Y
Y+³(²½Y)½X
483. Matrix with shape of Y and X as its columns X„A1; Y„A2
³(²½Y)½X
484. Derivate of polynomial X X„D1
¯1‡X×²¯1+¼½X
485. Reverse vector X on condition Y X„A1; Y„B0
,²[ŒIO+Y](1,½X)½X
486. Reshaping vector X into a one-column matrix X„A1
(²1,½X)½X
487. Avoiding parentheses with help of reversal
(²1, ...)
ROTATE ² ´
488. Vector (cross) product of vectors X„D; Y„D
((1²X)×¯1²Y)-(¯1²X)×1²Y
489. A magic square, side X X„I0; 1=2|X
A´(A„(¼X)-—X÷2)²(X,X)½¼X×X
490. Removing duplicates from an ordered vector X„A1
(¯1²1‡(X¬¯1²X),1)/X
491. An expression giving itself
1²22½11½'''1²22½11½'''
492. Transpose matrix X on condition Y X„A2; Y„B0
(Y²1 2)³X
493. Any element true (Ÿ/) on each subvector of Y indicated by X X„B1; Y„B1
(X/Y)‰A/1²A„(YŸX)/X
494. All elements true (^/) on each subvector of Y indicated by X X„B1; Y„B1
(X/Y)^A/1²A„(YˆX)/X
495. Removing leading, multiple and trailing Y's X„A1; Y„A0
(1†A)‡(AŠ1²A„Y=X)/X
496. Changing starting indicators X of subvectors to lengths X„B1
A-¯1‡0,A„(1²X)/¼½X
498. (Cyclic) compression of successive blanks X„C1
(AŸ1²A„X¬' ')/X
499. Aligning columns of matrix X to diagonals X„A2
(1-¼¯1†½X)²X
500. Aligning diagonals of matrix X to columns X„A2
(¯1+¼¯1†½X)²X
501. Diagonal matrix with elements of X X„D1
0 ¯1‡(-¼½X)²((2½½X)½0),X
502. Test if elements differ from previous ones (non-empty X) X„A1
1,1‡X¬¯1²X
503. Test if elements differ from next ones (non-empty X) X„A1
(¯1‡X¬1²X),1
504. Replacing first element of X with Y X„A1; Y„A0
¯1²1‡X,Y
505. Replacing last element of X with Y X„A1; Y„A0
1²¯1‡Y,X
506. Ending points for X in indices pointed by Y X„A1; Y„I1
1²(¼½X)¹Y
507. Leftmost neighboring elements cyclically X„A
¯1²X
508. Rightmost neighboring elements cyclically X„A
1²X
TRANSPOSE ³
509. Applying to columns action defined on rows X„A1; Y„I0
³ ... ³X
510. Retrieving scattered elements Y from matrix X X„A2; Y„I2
1 1³X[Y[1;];Y[2;]]
511. Successive transposes of G (X after Y: X³Y³G) X„I1; Y„I1
X[Y]³G
512. Major diagonal of array X X„A
(1*½X)³X
513. Reshaping a 400×12 character matrix to fit into one page X„C2
40 120½2 1 3³10 40 12½X
514. Transpose of planes of a rank three array X„A3
1 3 2³X
515. Major diagonal of matrix X X„A2
1 1³X
516. Selecting specific elements from a 'large' outer product X„A; Y„A; G„I1
G³X°.¸Y
517. Test for antisymmetricity of square matrix X X„D2
~0¹X=-³X
518. Test for symmetricity of square matrix X X„A2
~0¹X=³X
519. Matrix with X columns Y X„I0; Y„D1
³(X,½Y)½Y
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),[¼1](1‡A„(½X)—0,½Y)†Y
522. Widening matrix X to be compatible with Y X„A2; Y„A2
((0 1×½Y)—½X)†X
523. Lengthening matrix X to be compatible with Y X„A2; Y„A2
((1 0×½Y)—½X)†X
524. Reshaping non-empty lower-rank array X into a matrix X„A; 2‰½½X
(1—¯2†½X)½X
525. Take of at most X elements from Y X„I; Y„A
(X˜½Y)†Y
526. Limiting indices and giving a default value G X„A1; Y„I; G„A0
(X,G)[(1+½X)˜Y]
CEILING — FLOOR ˜
527. Reshaping X into a matrix of width Y X„D, Y„I0
((—(½,X)÷Y),Y)½X
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×.5¬2|X
530. Rounding, to nearest even integer for .5 = 1||X X„D
˜X+.5×.5¬2|X
531. Arithmetic progression from X to Y with step G X„D0; Y„D0; G„D0
X+(G××Y-X)×(¼1+|˜(Y-X)÷G)-ŒIO
532. Centering text line X into a field of width Y X„C1; Y„I0
(-˜.5×Y+½X)†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
˜X÷1000
536. Rounding to X decimals X„I; Y„D
(10*-X)×˜0.5+Y×10*X
537. Rounding to nearest hundredth X„D
0.01×˜0.5+100×X
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(0¬100|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|-½X)†0/X
545. Removing every Y:th element of X X„A1; Y„I0
(0¬Y|¼½X)/X
546. Taking every Y:th element of X X„A1; Y„I0
(0=Y|¼½X)/X
547. Divisors of X X„I0
(0=A|X)/A„¼X
548. Removing every second element of X X„A1
(2|¼½X)/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
(A×Y[1]*¯1 1)½(A„(½X)+(Y[1]|-1†½X),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
X×Yˆ|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„~X¹Y)/X
561. Replacing elements of X not in set Y with blanks/zeroes X„A1; Y„A
A\(A„X¹Y)/X
562. Merging X and Y under control of G (mesh) X„A1; Y„A1; G„B1
A ‘ A[(~G)/¼½G]„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
(~(¼(½Y)+1½½X)¹Y+¼½Y)™X
565. Test if numeric X„A1
0¹0\0½X
566. Adding an empty row into X after row Y X„A2; Y„I0
((Y+1)¬¼1+1½½X)™X
567. Underlining words X„C1
X,[ŒIO-.1](' '¬X)\'¯'
568. Using boolean matrix Y in expanding X X„A1; Y„B2
(½Y)½(,Y)\X
569. Spacing out text X„C1
((2×½X)½1 0)\X
COMPRESS / š
570. Lengths of groups of ones in X X„B1
(A>0)/A„(1‡A)-1+¯1‡A„(~A)/¼½A„0,X,0
571. Syllabization of a Finnish word X X„A1
(~A¹1,½X)/A„A/¼½A„(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
(~(¼¯1†½X)¹Y)/X
576. Removing trailing blanks X„C1
(¯1†(' '¬X)/¼½X)½X
577. Lengths of subvectors of X having equal elements X„A1
(1‡A)-¯1‡A„(A,1)/¼1+½A„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)/¼½X
580. Removing multiple and trailing blanks X„C1
((1‡A,0)ŸA„' '¬X)/X
581. Removing leading and multiple blanks X„C1
(AŸ¯1‡0,A„' '¬X)/X
582. Removing multiple blanks X„C1
(AŸ¯1‡1,A„' '¬X)/X
583. Removing duplicate Y's from vector X X„A1; Y„A0
(AŸ¯1‡1,A„X¬Y)/X
584. Indices of all occurrences of elements of Y in X X„A1; Y„A
(X¹Y)/¼½X
585. Union of sets, ž X„A1; Y„A1
Y,(~X¹Y)/X
586. Elements of X not in Y (difference of sets) X„A1; Y„A
(~X¹Y)/X
587. Rows of non-empty matrix X starting with a character in Y X„A2; Y„A1
(X[;1]¹Y)šX
588. Intersection of sets,  X„A1; Y„A
(X¹Y)/X
589. Reduction with function ¸ in dimension Y, rank unchanged Y„I0; X„A
((½X)*Y¬¼½½X)½ ¸/[Y]X
590. Replacing all values X in G with Y X„A0; Y„A0; G„A
(½G)½A ‘ A[(A=X)/¼½A„,G]„Y
591. Indices of all occurrences of Y in X X„A1; Y„A0
(Y=X)/¼½X
592. Replacing elements of G satisfying X with Y Y„A0; X„B1; G„A1
G[X/¼½G]„Y
593. Removing duplicates from positive integers X„I1
A/¼9999 ‘ A[X]„1 ‘ A„9999½0
594. Indices of ones in logical vector X X„B1
X/¼½X
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
(X¬Y)/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[¼G;],[1]((1‡½Y)†X),[1](2†G)‡Y
604. Filling X with last element of X to length Y X„A1; Y„I0
Y†X,Y½¯1†X
605. Input of row Y of text matrix X X„C2; Y„I0
X[Y;]„(1†½X)†
606. First ones in groups of ones X„B
X>((-½½X)†¯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-((-½½X)†¯1)‡0,X
609. Leftmost neighboring elements X„D
((-½½X)†¯1)‡0,X
610. Rightmost neighboring elements X„D
((-½½X)†1)‡X,0
611. Shifting vector X right with Y without rotate X„A1; Y„I0
(-½X)†(-Y)‡X
612. Shifting vector X left with Y without rotate X„A1; Y„I0
(½X)†Y‡X
613. Drop of Y first rows from matrix X X„A2; Y„I0
(2†Y)‡X
614. Test if numeric X„A
0¹1†0½X
615. Reshaping non-empty lower-rank array X into a matrix X„A; 2‰½½X
(¯2†1 1,½X)½X
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+(-½X)†Y
618. Number of rows in matrix X X„A2
1†½X
619. Number of columns in matrix X X„A2
¯1†½X
620. Ending points for X fields of width Y X„I0; Y„I0
(X×Y)½(-Y)†1
621. Starting points for X fields of width Y X„I0; Y„I0
(X×Y)½Y†1
622. Zero or space depending on the type of X (fill element) X„A
1†0½X
623. Forming first row of a matrix to be expanded X„A1
1 80½80†X
624. Vector of length Y with X ones on the left, the rest zeroes X„I0; Y„I0
Y†X½1
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=¼½½X)‡0,[Y]X
632. Ascending series of integers Y..X (for small Y and X) X„I0; Y„I0
(Y-1)‡¼X
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
''½G‡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‡½X
641. Number of columns in matrix X X„A2
1‡½X
642. Conditional drop of Y elements from array X X„A; Y„I1; G„B1
(Y×G)‡X
643. Conditional drop of last element of X X„A1; Y„B0
(-Y)‡X
MEMBER OF ¹
644. Expansion vector with zero after indices Y X„A1; Y„I1
~(¼(½Y)+½X)¹Y+¼½Y
645. Boolean vector of length Y with zeroes in locations X X„I; Y„I0
(~(¼Y)¹X)
646. Starting points for X in indices pointed by Y X„A1; Y„I1
(¼½X)¹Y
647. Boolean vector of length Y with ones in locations X X„I; Y„I0
(¼Y)¹X
648. Check for input in range 1..X X„A
(Y„Œ)¹¼X
649. Test if arrays are identical X„A; Y„A
~0¹X=Y
650. Zeroing elements of Y depending on their values Y„D; X„D
Y×~Y¹X
651. Test if single or scalar X„A
1¹½,X
652. Test if vector X„A
1¹½½X
653. Test if X is an empty array X„A
0¹½X
INDEX GENERATOR ¼
654. Inverting a permutation X„I1
A ‘ A[X]„A ‘ A„¼½X
655. All axes of array X X„A
¼½½X
656. All indices of vector X X„A1
¼½X
657. Arithmetic progression of Y numbers from X with step G X„D0; Y„D0; G„D0
X+G×(¼Y)-ŒIO
658. Consecutive integers from X to Y (arithmetic progression) X„I0; Y„I0
(X-ŒIO)+¼1+Y-X
659. Empty numeric vector
¼0
660. Index origin (ŒIO) as a vector
¼1
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=½Y
(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
(X×G)+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 <ˆ> ¬
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
(0¬X)×Y÷X+0=X
672. Exclusive or X„B; Y„B
X¬Y
673. Replacing zeroes with corresponding elements of Y X„D; Y„D
X+Y×X=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,((½X),Y)½G
676. Catenating Y elements G before every element of X X„A1; Y„I0; G„A0
,(((½X),Y)½G),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
(((½,X),1)×Y*¯1 1)½X
681. Temporary ravel of X for indexing with G X„A; Y„A; G„I
X„A½X ‘ X[G]„Y ‘ X„,X ‘ A„½X
682. Temporary ravel of X for indexing with G X„A; Y„A; G„I
X„(½X)½A ‘ 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
½,X
CATENATE ,
685. Separating variable length lines X„A1; Y„A1
X,ŒTC[2],Y
686. X×X identity matrix X„I0
(X,X)½1,X½0
687. Array and its negative ('plus minus') X„D
X,[.5+½½X]-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
((((½½X)-½½Y)½1),½Y)½Y
693. Identity matrix of shape of matrix X X„D2
(½X)½1,0×X
694. Reshaping vector X into a two-column matrix X„A1
((0.5×½X),2)½X
696. Reshaping vector X into a one-row matrix X„A1
(1,½X)½X
697. Reshaping vector X into a one-column matrix X„A1
((½X),1)½X
698. Forming a Y-row matrix with all rows alike (X) X„A1; Y„I0
(Y,½X)½X
699. Handling array X temporarily as a vector X„A
(½X)½ ... ,X
700. Joining sentences X„A; Y„A1
Y,0½X
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]+X×Y[2]+X×Y[1]
703. Number of columns in array X X„A
(½X)[½½X]
704. Number of rows in matrix X X„A2
(½X)[1]
705. Number of columns in matrix X X„A2
(½X)[2]
706. Conditional elementwise change of sign Y„D; X„B
Y×1 ¯1[1+X]
707. Selection depending on index origin X„A1
X[2×ŒIO]
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 ½
713. Rank of array X X„A
½½X
715. Duplicating vector X Y times X„A1; Y„I0
(Y×½X)½X
716. Adding X to each row of Y X„D1; Y„D; (½X)=¯1†½Y
Y+(½Y)½X
717. Array with shape of Y and X as its rows X„A1; Y„A
(½Y)½X
718. Number of rows in matrix X X„A2
1½½X
RESHAPE ½
720. Forming an initially empty array to be expanded
0 80½0
721. Output of an empty line X„A
0½X„
722. Reshaping first element of X into a scalar X„A
''½X
723. Corner element of a (non-empty) array X„A
1½X
ARITHMETIC + - × ÷
724. Continued fraction
1+÷2+÷3+÷4+÷5+÷6+÷ ...
725. Force 0÷0 into DOMAIN ERROR in division X„D; Y„D
Y×÷X
726. Conditional elementwise change of sign X„D; Y„B; ½X „… ½Y
X×¯1*Y
727. Zero array of shape and size of X X„D
0×X
728. Selecting elements satisfying condition Y, zeroing others X„D; Y„B
Y×X
729. Number and its negative ('plus minus') X„D0
1 ¯1×X
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›|˜-*+±—×÷!²³Ž~½“”,µ?¼0

Last updated 12.7.2002 by Olli Paavola