1 | #|
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2 | *--------------------------------------------------------------------------*
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3 | | Copyright (C) 1994, Marek Rychlik (e-mail: rychlik@math.arizona.edu) |
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4 | | Department of Mathematics, University of Arizona, Tucson, AZ 85721 |
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5 | | |
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6 | | Everyone is permitted to copy, distribute and modify the code in this |
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7 | | directory, as long as this copyright note is preserved verbatim. |
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8 | *--------------------------------------------------------------------------*
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9 | |#
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10 |
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11 | (defpackage "MAKELIST"
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12 | (:use "COMMON-LISP")
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13 | (:export makelist-1 makelist list-of set-of union-of select sum summation difference standard-vector))
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14 |
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15 | (in-package "MAKELIST")
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16 |
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17 | #+debug(proclaim '(optimize (speed 0) (debug 3)))
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18 | #-debug(proclaim '(optimize (speed 3) (debug 0)))
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19 |
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20 |
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21 | ;; Macros for making lists with iterators - an exammple of GENSYM
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22 | ;; MAKELIST-1 makes a list with one iterator, while MAKELIST accepts an
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23 | ;; arbitrary number of iterators
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24 |
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25 | ;; Sample usage:
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26 | ;; Without a step:
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27 | ;; >(makelist-1 (* 2 i) i 0 10)
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28 | ;; (0 2 4 6 8 10 12 14 16 18 20)
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29 | ;; With a step of 3:
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30 | ;; >(makelist-1 (* 2 i) i 0 10 3)
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31 | ;; (0 6 12 18)
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32 |
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33 | ;; Generate sums of squares of numbers between 1 and 4:
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34 | ;; >(makelist (+ (* i i) (* j j)) (i 1 4) (j 1 i))
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35 | ;; (2 5 8 10 13 18 17 20 25 32)
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36 | ;; >(makelist (list i j '---> (+ (* i i) (* j j))) (i 1 4) (j 1 i))
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37 | ;; ((1 1 ---> 2) (2 1 ---> 5) (2 2 ---> 8) (3 1 ---> 10) (3 2 ---> 13)
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38 | ;; (3 3 ---> 18) (4 1 ---> 17) (4 2 ---> 20) (4 3 ---> 25) (4 4 ---> 32))
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39 |
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40 | ;; Summation with SUM:
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41 | ;; Sum of squares of integers from 1 to 10:
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42 | ;; >(sum (expt i 2) (i 1 10))
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43 | ;; 385
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44 | ;; Sum of inverses of integers from 1 to 50:
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45 | ;; >(sum (/ n) (n 1 50))
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46 | ;; 13943237577224054960759/3099044504245996706400
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47 | ;; Sum of 1/(m^2+n^2) where m,n vary from 1 to 10:
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48 | ;; >(sum (/ (+ (expt m 2) (expt n 2))) (n 1 10) (m 1 10))
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49 | ;; 125085870045079516933345908893314157/42204464874461454985621846571472000
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50 | ;; Sum of 1/(m^2+n^2) where m,n vary from 1 to 10 and m>n:
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51 | ;; >(sum (/ (+ (expt m 2) (expt n 2))) (n 1 10) (m 1 (1- n)))
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52 | ;; 13092731173226115661182811487147/11962716801151206061684196874000
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53 |
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54 | ;; Evaluate expression expr with variable set to lo, lo+1,... ,hi
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55 | ;; and put the results in a list.
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56 | (defmacro makelist-1 (expr var lo hi &optional (step 1))
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57 | (let ((l (gensym)))
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58 | `(do ((,var ,lo (+ ,var ,step))
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59 | (,l nil (cons ,expr ,l)))
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60 | ((> ,var ,hi) (reverse ,l))
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61 | (declare (fixnum ,var)))))
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62 |
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63 | (defmacro makelist (expr (var lo hi &optional (step 1)) &rest more)
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64 | (if (endp more)
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65 | `(makelist-1 ,expr ,var ,lo ,hi ,step)
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66 | (let* ((l (gensym)))
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67 | `(do ((,var ,lo (+ ,var ,step))
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68 | (,l nil (nconc ,l `,(makelist ,expr ,@more))))
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69 | ((> ,var ,hi) ,l)
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70 | (declare (fixnum ,var))))))
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71 |
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72 | (defmacro sum (&body body)
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73 | `(reduce #'+ (makelist ,@body)))
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74 |
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75 | (defmacro summation (&body body)
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76 | ``(+ ,@(makelist ,@body)))
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77 |
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78 | (defmacro difference (&body body)
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79 | ``(- ,@(makelist ,@body)))
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80 |
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81 | ;; List of all EXPR where VAR varies over the list LST
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82 | (defmacro list-of (expr (var lst) &rest more)
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83 | (if (endp more)
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84 | `(list-of-1 ,expr ,var ,lst)
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85 | (let ((l (gensym)))
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86 | `(let ((,l))
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87 | (dolist (,var ,lst ,l)
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88 | (setf ,l (nconc ,l ,`(list-of ,expr ,@more))))))))
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89 |
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90 | (defmacro list-of-1 (expr var lst)
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91 | (let ((l (gensym)))
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92 | `(let ((,l))
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93 | (dolist (,var ,lst (reverse ,l))
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94 | (setf ,l ,`(cons ,expr ,l))))))
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95 |
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96 | ;; Union of all EXPR where VAR varies over the list LST
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97 | (defmacro union-of (expr (var lst) &rest more)
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98 | (if (endp more)
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99 | `(union-of-1 ,expr ,var ,lst)
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100 | (let ((l (gensym)))
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101 | `(let ((,l))
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102 | (dolist (,var ,lst ,l)
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103 | (setf ,l (union ,l ,`(union-of ,expr ,@more) :test #'equalp)))))))
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104 |
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105 | (defmacro union-of-1 (expr var lst)
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106 | (let ((l (gensym)))
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107 | `(let ((,l))
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108 | (dolist (,var ,lst (reverse ,l))
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109 | (setf ,l ,`(union ,expr ,l :test #'equalp))))))
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110 |
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111 |
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112 | ;; Set of all EXPR where VAR varies over the list LST
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113 | (defmacro set-of (expr (var lst) &rest more)
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114 | (if (endp more)
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115 | `(set-of-1 ,expr ,var ,lst)
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116 | (let ((l (gensym)))
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117 | `(let ((,l))
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118 | (dolist (,var ,lst ,l)
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119 | (setf ,l (union ,l ,`(set-of ,expr ,@more) :test #'equalp)))))))
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120 |
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121 | (defmacro set-of-1 (expr var lst)
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122 | (let ((l (gensym)))
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123 | `(let ((,l))
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124 | (dolist (,var ,lst (reverse ,l))
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125 | (pushnew ,expr ,l :test #'equalp)))))
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126 |
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127 | ;; sublist of LST consisting of elements with indecies in IND
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128 | (defun select (ind lst)
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129 | (cond
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130 | ((endp ind) nil)
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131 | (t (cons (elt lst (car ind)) (select (cdr ind) lst)))))
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132 |
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133 | (defun standard-vector (n k &optional (coeff 1)
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134 | &aux (v (make-list n :initial-element 0)))
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135 | "Returns vector (0 0 ... 1 ... 0 0) of length N, where 1 appears on K-th place."
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136 | (setf (elt v k) coeff)
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137 | v)
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