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1 | ;;; -*-emacs-lisp-*- |
2 | ||
3 | ;;; --- Homebrew functions --- | |
4 | ||
5 | (autoload 'calc-tabular-command "calc-alg-2") | |
6 | ||
7 | (defun calc-path-length (&optional var low high) | |
8 | "Computes the path length of a parametric function. | |
9 | ||
10 | The stack should contain a vector containing the (rectangular only, I'm | |
11 | afraid) components of a vector-valued function. The independent variable is | |
12 | prompted for. If the Hyp flag is set, limits for the parameter are requested | |
13 | and a definite path length is computed; otherwise an indefinite result is | |
14 | computed. | |
15 | ||
16 | The path length of a function `r(t)' between limits `a' and `b' is computed | |
17 | as | |
18 | b | |
19 | / | |
20 | | |r(t)| dt | |
21 | / | |
22 | a | |
23 | ||
24 | If, as is likely, the result is unintegrable, a numeric result can be | |
25 | obtained using `z n' (`calc-integrate-numerically')." | |
26 | (interactive "sPath length variable: ") | |
27 | (if (calc-is-hyperbolic) | |
28 | (calc-tabular-command 'calcFunc-path-length "Path length" "path" | |
29 | nil var low high) | |
30 | (calc-slow-wrapper | |
31 | (if (or (equal var "") (equal var "$")) | |
32 | (calc-enter-result 2 "path" (list 'calcFunc-path-length | |
33 | (calc-top-n 2) | |
34 | (calc-top-n | |
35 | 1))) | |
36 | (let ((var (math-read-expr var))) | |
37 | (if (eq (car-safe var) 'error) | |
38 | (error "Bad format in expression: %s" | |
39 | (nth 1 var))) | |
40 | (calc-enter-result 1 "path" (list | |
41 | 'calcFunc-path-length | |
42 | (calc-top-n 1) | |
43 | var))))))) | |
44 | ||
45 | (defun calcFunc-path-length (f x &optional a b) | |
46 | (let ((d (math-simplify (list 'calcFunc-deriv f x)))) | |
47 | (append (list 'calcFunc-integ | |
48 | (list 'calcFunc-sqrt (list '* d d)) | |
49 | x) | |
50 | (and a b (list a b))))) | |
51 | ||
52 | (defvar var-IntegNumerRules 'calc-IntegNumerRules) | |
53 | (defun calc-IntegNumerRules () | |
54 | (math-read-plain-expr "[ | |
55 | integ(f, x, a, b) := ninteg(f, x, a, b) :: constant(a) :: constant(b) | |
56 | ]")) | |
57 | ||
58 | (defun calc-integrate-numerically () | |
59 | "Computes an approximate result for a symbolic definite integral with | |
60 | constant bounds." | |
61 | (interactive) | |
62 | (calc-slow-wrapper | |
63 | (calc-enter-result 1 "intn" | |
64 | (math-rewrite (calc-top-n 1) var-IntegNumerRules 5)))) | |
65 | ||
66 | ;;; Mode settings stored by Calc on Mon Mar 15 16:25:50 2004 | |
67 | (setq calc-group-char " ") | |
68 | (setq calc-frac-format '("/" nil)) | |
69 | (setq calc-date-format '(Www " " D " " Mmmm " " YYYY (", " h ":" mm ":" ss))) | |
70 | (setq calc-standard-date-formats '("N" "<H:mmCSSpp >Www Mmm D, YYYY" "YYYY-MM-DD< hh:mm:ss>" "Www Mmm BD< hh:mm:ss> YYYY" "Www D Mmmm YYYY<, h:mm:ss>" "D.M.Y< h:mm:SS>" "M-D-Y< H:mm:SSpp>" "D-M-Y< h:mmCSS>" "j<, h:mm:SS>" "YYddd< hh:mm:ss>")) | |
71 | (setq calc-complex-format 'i) | |
72 | (setq calc-previous-modulo '(bigpos 296 967 294 4)) | |
73 | (setq calc-angle-mode 'rad) | |
74 | ;;; End of mode settings | |
75 | ||
76 | ;;; Variable "var-AlgSimpRules" stored by Calc on Thu Jan 6 21:04:23 2000 | |
77 | (setq var-AlgSimpRules '(vec (calcFunc-assign (+ (^ (calcFunc-sin (var x var-x)) 2) (^ (calcFunc-cos (var x var-x)) 2)) 1) (calcFunc-assign (calcFunc-exp (var x var-x)) (^ (var e var-e) (var x var-x))))) | |
78 | ||
79 | ;;; Custom units stored by Calc on Thu Mar 18 19:02:50 1999 | |
80 | (setq math-additional-units '( | |
f0bf9506 MW |
81 | (EB "1024 * PB" "Exabyte") |
82 | (PB "1024 * TB" "Petabyte") | |
f617db13 MW |
83 | (TB "1024 * GB" "Terabyte") |
84 | (gig "GB" "Gigabyte") | |
85 | (GB "1024 * MB" "Gigabyte") | |
86 | (meg "MB" "Megabyte") | |
40d54672 MW |
87 | (MB "1024 * kB" "Megabyte") |
88 | (KB "kB" "Kilobyte") | |
89 | (kB "1024 * byte" "Kilobyte") | |
f0bf9506 MW |
90 | (Eb "1024 * Pb" "Exabit") |
91 | (Pb "1024 * Tb" "Petabit") | |
f617db13 MW |
92 | (Tb "1024 * Gb" "Teraabit") |
93 | (Gb "1024 * Mb" "Gigabit") | |
40d54672 MW |
94 | (Mb "1024 * kb" "Megabit") |
95 | (Kb "kb" "Kilobit") | |
96 | (kb "1024 * bit" "Kilobit") | |
f617db13 MW |
97 | (byte "octet" "Byte") |
98 | (octet "8 * bit" "Octet") | |
99 | (bit nil "Bit") | |
100 | )) | |
101 | ;;; End of custom units | |
102 | ||
103 | ;;; Variable "var-DeMoivre" stored by Calc on Fri Mar 19 16:06:10 1999 | |
104 | (setq var-DeMoivre '(vec (calcFunc-assign (^ (var e var-e) (var x var-x)) (calcFunc-exp (var x var-x))) (calcFunc-assign (calcFunc-exp (* (var i var-i) (var t var-t))) (calcFunc-evalsimp (+ (calcFunc-cos (var t var-t)) (* (var i var-i) (calcFunc-sin (var t var-t)))))))) | |
105 | ||
106 | ;;; Variable "var-TrigDefRules" stored by Calc on Tue Jan 4 13:47:34 2000 | |
107 | (setq var-TrigDefRules '(vec (calcFunc-phase 1) (calcFunc-assign (calcFunc-sin (var t var-t)) (/ (- (^ (var e var-e) (* (var i var-i) (var t var-t))) (^ (var e var-e) (neg (* (var i var-i) (var t var-t))))) (* 2 (var i var-i)))) (calcFunc-assign (calcFunc-cos (var t var-t)) (/ (+ (^ (var e var-e) (* (var i var-i) (var t var-t))) (^ (var e var-e) (neg (* (var i var-i) (var t var-t))))) 2)) (calcFunc-assign (calcFunc-arcsin (var x var-x)) (* (neg (var i var-i)) (calcFunc-ln (- (* (var i var-i) (var x var-x)) (calcFunc-sqrt (- 1 (^ (var x var-x) 2))))))) (calcFunc-assign (calcFunc-arccos (var x var-x)) (* (neg (var i var-i)) (calcFunc-ln (- (var x var-x) (calcFunc-sqrt (- (^ (var x var-x) 2) 1)))))) (calcFunc-assign (calcFunc-arctan (var x var-x)) (* (frac -1 2) (* (var i var-i) (calcFunc-ln (/ (+ 1 (* (var i var-i) (var x var-x))) (- 1 (* (var i var-i) (var x var-x)))))))) (calcFunc-assign (calcFunc-arctanh (var x var-x)) (* (frac 1 2) (calcFunc-ln (/ (+ 1 (var x var-x)) (- 1 (var x var-x)))))) (calcFunc-phase 2) (calcFunc-assign (calcFunc-tan (var t var-t)) (/ (calcFunc-sin (var t var-t)) (calcFunc-cos (var t var-t)))) (calcFunc-assign (calcFunc-sinh (var t var-t)) (* (neg (var i var-i)) (calcFunc-sin (* (var i var-i) (var t var-t))))) (calcFunc-assign (calcFunc-cosh (var t var-t)) (calcFunc-cos (* (var i var-i) (var t var-t)))) (calcFunc-assign (calcFunc-tanh (var t var-t)) (/ (calcFunc-sinh (var t var-t)) (calcFunc-cosh (var t var-t)))) (calcFunc-assign (calcFunc-arcsinh (var x var-x)) (* (neg (var i var-i)) (calcFunc-arcsin (* (var i var-i) (var x var-x))))) (calcFunc-assign (calcFunc-arccosh (var x var-x)) (* (neg (var i var-i)) (calcFunc-arccos (var x var-x)))))) | |
108 | ||
109 | ;;; Definition stored by Calc on Tue Jan 4 22:44:33 2000 | |
110 | (put 'calc-define 'calc-integrate-numerically '(progn | |
111 | (define-key calc-mode-map "zn" 'calc-integrate-numerically) | |
112 | )) | |
113 | ||
114 | ;;; Definition stored by Calc on Tue Jan 4 22:44:37 2000 | |
115 | (put 'calc-define 'calc-path-length '(progn | |
116 | (define-key calc-mode-map "zp" 'calc-path-length) | |
117 | )) |