GRADE UP “ 
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 Yfold

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 
GRADE DOWN ” 
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°.*²ŒIO¼½X

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. 
Gdegree 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
03†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 

16ƒŒIO'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]ƒŒIOX]„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¬400Y)(0¬100Y)0¬4Y

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¬4Y

82. 
Encoding current date 


100ƒ1003†ŒTS

83. 
Removing trailing blanks 
X„C1 

(1(' '=X)ƒ1)‡X

84. 
Index of first nonblank, counted from the rear

X„C1 

(' '=X)ƒ1 
85. 
Indexing scattered elements 
X„A; Y„I2


(,X)[ŒIO+(½X)ƒYŒIO]

86. 
Conversion of indices Y of array X to indices of raveled X

X„A; Y„I2


ŒIO+(½X)ƒYŒIO

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‚1ŒIO¼X

99. 
Conversion of characters to hexadecimal representation (ŒAV)

X„C1 

,' ',³'0123456789ABCDEF'[ŒIO+16 16‚ŒIOŒAV¼X]

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)



˜10µ13×÷3 
116. 
Number of digitpositions in integers in X

X„I 

1+(X<0)+˜10µx+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. 
Forloop 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 oneelement 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


–X‡'© ...'

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„•1001²3†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. 
Rowbyrow 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. 
Yshaped 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)×12×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) counterclockwise

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 

!X1 
176. 
Binomial distribution of X trials with probability Y

X„I0; Y„D0


(A!X)×(Y*A)×(1Y)*XA„ŒIO¼X+1

177. 
Beta function 
X„D0; Y„D0


÷Y×(X1)!Y+X1 
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 (ŒIO1 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

208. 
Removing leading zeroes 
X„A1 

(¯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*ŒIO¼Y+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(ŒIO¼½X)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 Yfold

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„(1½X)‡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 onecolumn 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)°.>ŒIO¼¯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)°.=—(XG)÷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+(XA„˜/X)—.×Y

288. 
Indices of last nonblanks 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)+1A„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

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„+/^\²A)++/^\A„' '=²X)²X

367. 
Decommenting a matrix representation of a function (ŒCR)

X„C2 

(Ÿ/A)š(½X)½(,A)\(,A„^\('©'¬X)Ÿ¬\X='''')/,X

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

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]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


+\YX\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


((Y1)‡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 tworow determinant

X„D2 

/×/0 1´X 
413. 
Evaluating a tworow 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 oneelement 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 onecolumn 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=2X


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 

(1¼¯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 (nonempty X)

X„A1 

1,1‡X¬¯1²X 
503. 
Test if elements differ from next ones (nonempty 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 nonempty lowerrank 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+1ˆ2X

529. 
Rounding, to nearest even integer for .5 = 1X

X„D 

˜X+.5×.5¬2X 
530. 
Rounding, to nearest even integer for .5 = 1X

X„D 

˜X+.5×.5¬2X 
531. 
Arithmetic progression from X to Y with step G

X„D0; Y„D0; G„D0


X+(G××YX)×(¼1+˜(YX)÷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=400X)Ÿ(0¬100X)^0=4X

541. 
Framing 
X„C2 

'_',[1]('',X,''),[1]'¯'

542. 
Magnitude of fractional part 
X„D 

1X 
543. 
Fractional part with sign 
X„D 

(×X)X 
544. 
Increasing the dimension of X to multiple of Y

X„A1; Y„I0


X,(Y½X)†0/X

545. 
Removing every Y:th element of X

X„A1; Y„I0


(0¬Y¼½X)/X 
546. 
Taking every Y:th element of X

X„A1; Y„I0


(0=Y¼½X)/X 
547. 
Divisors of X 
X„I0 

(0=AX)/A„¼X 
548. 
Removing every second element of X

X„A1 

(2¼½X)/X 
549. 
Elements of X divisible by Y 
X„D1; Y„D0/1


(0=YX)/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 

~2X 
552. 
Last part of numeric code ABBB

X„I 

1000X 
553. 
Fractional part 
X„D 

1X 
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×YˆX 
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 nonempty 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 oneelement 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 nonempty lowerrank 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 (nonempty X)

X„A1 

1,(1‡X)¬¯1‡X

628. 
Ending points of groups of equal elements (nonempty 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


(Y1)‡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


(XŒIO)+¼1+YX

659. 
Empty numeric vector 


¼0 
660. 
Index origin (ŒIO) as a vector



¼1 
LOGICAL FUNCTIONS ~ Ÿ ^ ‹ Š

661. 
Demote nonboolean 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 twocolumn matrix 
X„A1; Y„A1


X,[1.1]Y 
690. 
Forming a tworow 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 twocolumn matrix

X„A1 

((0.5×½X),2)½X 
696. 
Reshaping vector X into a onerow matrix

X„A1 

(1,½X)½X 
697. 
Reshaping vector X into a onecolumn matrix

X„A1 

((½X),1)½X 
698. 
Forming a Yrow 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 fixeddegree 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 (nonempty) 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 

ŒIOX 
731. 
Changing an index origin dependent argument to act as ŒIO=1

X„I 

(ŒIO1)+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 