| 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 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 |
| “Xׯ1 1[Y] | ||
| 46. | Sorting Y according to X | X„A1; Y„A1 |
| Y[“X] | ||
| 47. | Sorting X into ascending order | X„D1 |
| X[“X] | ||
| 48. | Inverting a permutation | X„I1 |
| “X | ||
| GRADE DOWN ” | ||
| 49. | Reverse vector X on condition Y | X„A1; Y„B0 |
| X[”Y!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 |
| –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„•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)ׯ3±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 |
| +/Aׯ1*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׌IO]+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*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)+.ײY | ||
| 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 |
| +\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 |
| -/ך0 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 |
| (ך2 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‡Xײ¯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)ׯ1²Y)-(¯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 |
| .05ט.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)ט0.5+Y×10*X | ||
| 537. | Rounding to nearest hundredth | X„D |
| 0.01ט0.5+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׌IO] | ||
| 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 |
| Xׯ1*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