Revision: miles@gnu.org--gnu-2005/emacs--unicode--0--patch-15

Merge from emacs--cvs-trunk--0

Patches applied:

 * miles@gnu.org--gnu-2005/emacs--cvs-trunk--0--patch-95
   Merge from gnus--rel--5.10

 * miles@gnu.org--gnu-2005/emacs--cvs-trunk--0--patch-96
   Move Gnus images into etc/images

 * miles@gnu.org--gnu-2005/emacs--cvs-trunk--0--patch-97
 - miles@gnu.org--gnu-2005/emacs--cvs-trunk--0--patch-105
   Update from CVS

 * miles@gnu.org--gnu-2005/gnus--rel--5.10--patch-14
   Merge from emacs--cvs-trunk--0

 * miles@gnu.org--gnu-2005/gnus--rel--5.10--patch-15
   Update from CVS: lisp/imap.el (imap-log): Doc fix.

 * miles@gnu.org--gnu-2005/gnus--rel--5.10--patch-16
   Merge from emacs--cvs-trunk--0

9 files changed, 666 insertions, 11 deletions

diff --git a/lisp/calc/calc-alg.el b/lisp/calc/calc-alg.el
index 4901883d094..b722261907d 100644
--- a/lisp/calc/calc-alg.el
+++ b/lisp/calc/calc-alg.el
@@ -746,6 +746,55 @@
 		     (list '* (list 'calcFunc-sin (list '* (1- n) a))
 			   (list 'calcFunc-sin a))))))))
 
+(math-defsimplify calcFunc-sec
+  (or (and (math-looks-negp (nth 1 math-simplify-expr))
+	   (list 'calcFunc-sec (math-neg (nth 1 math-simplify-expr))))
+      (and (eq calc-angle-mode 'rad)
+	   (let ((n (math-linear-in (nth 1 math-simplify-expr) '(var pi var-pi))))
+	     (and n
+		  (math-div 1 (math-known-sin (car n) (nth 1 n) 120 300)))))
+      (and (eq calc-angle-mode 'deg)
+	   (let ((n (math-integer-plus (nth 1 math-simplify-expr))))
+	     (and n
+                  (math-div 1 (math-known-sin (car n) (nth 1 n) '(frac 2 3) 300)))))
+      (and (eq (car-safe (nth 1 math-simplify-expr)) 'calcFunc-arcsin)
+           (math-div 
+            1
+            (list 'calcFunc-sqrt 
+                  (math-sub 1 (math-sqr (nth 1 (nth 1 math-simplify-expr)))))))
+      (and (eq (car-safe (nth 1 math-simplify-expr)) 'calcFunc-arccos)
+           (math-div 
+            1
+            (nth 1 (nth 1 math-simplify-expr))))
+      (and (eq (car-safe (nth 1 math-simplify-expr)) 'calcFunc-arctan)
+           (list 'calcFunc-sqrt
+                 (math-add 1 
+                           (math-sqr (nth 1 (nth 1 math-simplify-expr))))))))
+
+(math-defsimplify calcFunc-csc
+  (or (and (math-looks-negp (nth 1 math-simplify-expr))
+	   (math-neg (list 'calcFunc-csc (math-neg (nth 1 math-simplify-expr)))))
+      (and (eq calc-angle-mode 'rad)
+	   (let ((n (math-linear-in (nth 1 math-simplify-expr) '(var pi var-pi))))
+	     (and n
+                  (math-div 1 (math-known-sin (car n) (nth 1 n) 120 0)))))
+      (and (eq calc-angle-mode 'deg)
+	   (let ((n (math-integer-plus (nth 1 math-simplify-expr))))
+	     (and n
+                  (math-div 1 (math-known-sin (car n) (nth 1 n) '(frac 2 3) 0)))))
+      (and (eq (car-safe (nth 1 math-simplify-expr)) 'calcFunc-arcsin)
+	   (math-div 1 (nth 1 (nth 1 math-simplify-expr))))
+      (and (eq (car-safe (nth 1 math-simplify-expr)) 'calcFunc-arccos)
+           (math-div 
+            1
+            (list 'calcFunc-sqrt (math-sub 1 (math-sqr 
+                                              (nth 1 (nth 1 math-simplify-expr)))))))
+      (and (eq (car-safe (nth 1 math-simplify-expr)) 'calcFunc-arctan)
+	   (math-div (list 'calcFunc-sqrt
+			   (math-add 1 (math-sqr 
+                                        (nth 1 (nth 1 math-simplify-expr)))))
+                     (nth 1 (nth 1 math-simplify-expr))))))
+
 (defun math-should-expand-trig (x &optional hyperbolic)
   (let ((m (math-is-multiple x)))
     (and math-living-dangerously
@@ -827,6 +876,28 @@
 	       (math-div (list 'calcFunc-sin (nth 1 math-simplify-expr))
 			 (list 'calcFunc-cos (nth 1 math-simplify-expr))))))))
 
+(math-defsimplify calcFunc-cot
+  (or (and (math-looks-negp (nth 1 math-simplify-expr))
+	   (math-neg (list 'calcFunc-cot (math-neg (nth 1 math-simplify-expr)))))
+      (and (eq calc-angle-mode 'rad)
+	   (let ((n (math-linear-in (nth 1 math-simplify-expr) '(var pi var-pi))))
+	     (and n
+                  (math-div 1 (math-known-tan (car n) (nth 1 n) 120)))))
+      (and (eq calc-angle-mode 'deg)
+	   (let ((n (math-integer-plus (nth 1 math-simplify-expr))))
+	     (and n
+                  (math-div 1 (math-known-tan (car n) (nth 1 n) '(frac 2 3))))))
+      (and (eq (car-safe (nth 1 math-simplify-expr)) 'calcFunc-arcsin)
+	   (math-div (list 'calcFunc-sqrt
+			   (math-sub 1 (math-sqr (nth 1 (nth 1 math-simplify-expr)))))
+                     (nth 1 (nth 1 math-simplify-expr))))
+      (and (eq (car-safe (nth 1 math-simplify-expr)) 'calcFunc-arccos)
+	   (math-div (nth 1 (nth 1 math-simplify-expr))
+                     (list 'calcFunc-sqrt
+			   (math-sub 1 (math-sqr (nth 1 (nth 1 math-simplify-expr)))))))
+      (and (eq (car-safe (nth 1 math-simplify-expr)) 'calcFunc-arctan)
+	   (math-div 1 (nth 1 (nth 1 math-simplify-expr))))))
+
 (defun math-known-tan (plus n mul)
   (setq n (math-mul n mul))
   (and (math-num-integerp n)
@@ -930,6 +1001,58 @@
 	       (math-div (list 'calcFunc-sinh (nth 1 math-simplify-expr))
 			 (list 'calcFunc-cosh (nth 1 math-simplify-expr))))))))
 
+(math-defsimplify calcFunc-sech
+  (or (and (math-looks-negp (nth 1 math-simplify-expr))
+	   (list 'calcFunc-sech (math-neg (nth 1 math-simplify-expr))))
+      (and (eq (car-safe (nth 1 math-simplify-expr)) 'calcFunc-arcsinh)
+	   math-living-dangerously
+           (math-div 
+            1
+            (list 'calcFunc-sqrt 
+                  (math-add (math-sqr (nth 1 (nth 1 math-simplify-expr))) 1))))
+      (and (eq (car-safe (nth 1 math-simplify-expr)) 'calcFunc-arccosh)
+	   math-living-dangerously
+           (math-div 1 (nth 1 (nth 1 math-simplify-expr))) 1)
+      (and (eq (car-safe (nth 1 math-simplify-expr)) 'calcFunc-arctanh)
+	   math-living-dangerously
+           (list 'calcFunc-sqrt
+                 (math-sub 1 (math-sqr (nth 1 (nth 1 math-simplify-expr))))))))
+
+(math-defsimplify calcFunc-csch
+  (or (and (math-looks-negp (nth 1 math-simplify-expr))
+	   (math-neg (list 'calcFunc-csch (math-neg (nth 1 math-simplify-expr)))))
+      (and (eq (car-safe (nth 1 math-simplify-expr)) 'calcFunc-arcsinh)
+	   math-living-dangerously
+           (math-div 1 (nth 1 (nth 1 math-simplify-expr))))
+      (and (eq (car-safe (nth 1 math-simplify-expr)) 'calcFunc-arccosh)
+	   math-living-dangerously
+           (math-div 
+            1
+            (list 'calcFunc-sqrt 
+                  (math-sub (math-sqr (nth 1 (nth 1 math-simplify-expr))) 1))))
+      (and (eq (car-safe (nth 1 math-simplify-expr)) 'calcFunc-arctanh)
+	   math-living-dangerously
+	   (math-div (list 'calcFunc-sqrt
+			   (math-sub 1 (math-sqr (nth 1 (nth 1 math-simplify-expr)))))
+                     (nth 1 (nth 1 math-simplify-expr))))))
+
+(math-defsimplify calcFunc-coth
+  (or (and (math-looks-negp (nth 1 math-simplify-expr))
+	   (math-neg (list 'calcFunc-coth (math-neg (nth 1 math-simplify-expr)))))
+      (and (eq (car-safe (nth 1 math-simplify-expr)) 'calcFunc-arcsinh)
+	   math-living-dangerously
+	   (math-div (list 'calcFunc-sqrt
+			   (math-add (math-sqr (nth 1 (nth 1 math-simplify-expr))) 1))
+                     (nth 1 (nth 1 math-simplify-expr))))
+      (and (eq (car-safe (nth 1 math-simplify-expr)) 'calcFunc-arccosh)
+	   math-living-dangerously
+	   (math-div (nth 1 (nth 1 math-simplify-expr))
+                     (list 'calcFunc-sqrt
+			   (math-sub (math-sqr (nth 1 (nth 1 math-simplify-expr))) 1))))
+      (and (eq (car-safe (nth 1 math-simplify-expr)) 'calcFunc-arctanh)
+	   math-living-dangerously
+	   (math-div 1 (nth 1 (nth 1 math-simplify-expr))))))
+
 (math-defsimplify calcFunc-arcsin
   (or (and (math-looks-negp (nth 1 math-simplify-expr))
 	   (math-neg (list 'calcFunc-arcsin (math-neg (nth 1 math-simplify-expr)))))
@@ -1043,8 +1166,13 @@
 			   (math-equal-int (nth 2 a) 2)
 			   (or (and (eq (car-safe (nth 1 a)) 'calcFunc-sinh)
 				    (list 'calcFunc-cosh (nth 1 (nth 1 a))))
+                               (and (eq (car-safe (nth 1 a)) 'calcFunc-csch)
+				    (list 'calcFunc-coth (nth 1 (nth 1 a))))
 			       (and (eq (car-safe (nth 1 a)) 'calcFunc-tan)
 				    (list '/ 1 (list 'calcFunc-cos
+						     (nth 1 (nth 1 a)))))
+			       (and (eq (car-safe (nth 1 a)) 'calcFunc-cot)
+				    (list '/ 1 (list 'calcFunc-sin
 						     (nth 1 (nth 1 a)))))))))
 	       (and (eq (car-safe (nth 1 math-simplify-expr)) '^)
 		    (list '^
diff --git a/lisp/calc/calc-arith.el b/lisp/calc/calc-arith.el
index 3a436cb1d36..38c10f5cc9f 100644
--- a/lisp/calc/calc-arith.el
+++ b/lisp/calc/calc-arith.el
@@ -70,9 +70,13 @@
 				       calcFunc-max calcFunc-min))
 
 (defvar math-real-if-arg-functions '(calcFunc-sin calcFunc-cos
-				     calcFunc-tan calcFunc-arctan
+				     calcFunc-tan calcFunc-sec
+                                     calcFunc-csc calcFunc-cot
+                                     calcFunc-arctan
 				     calcFunc-sinh calcFunc-cosh
-				     calcFunc-tanh calcFunc-exp
+				     calcFunc-tanh calcFunc-sech
+                                     calcFunc-csch calcFunc-coth
+                                     calcFunc-exp
 				     calcFunc-gamma calcFunc-fact))
 
 (defvar math-integer-functions '(calcFunc-idiv
diff --git a/lisp/calc/calc-ext.el b/lisp/calc/calc-ext.el
index 374e89ec1f1..d4d50d64658 100644
--- a/lisp/calc/calc-ext.el
+++ b/lisp/calc/calc-ext.el
@@ -801,13 +801,16 @@ math-mul-mat-vec math-mul-mats math-row-matrix)
 
  ("calc-math" calcFunc-alog calcFunc-arccos
 calcFunc-arccosh calcFunc-arcsin calcFunc-arcsincos calcFunc-arcsinh
-calcFunc-arctan calcFunc-arctan2 calcFunc-arctanh calcFunc-cos
-calcFunc-cosh calcFunc-deg calcFunc-exp calcFunc-exp10 calcFunc-expm1
+calcFunc-arctan calcFunc-arctan2 calcFunc-arctanh calcFunc-csc
+calcFunc-csch calcFunc-cos calcFunc-cosh calcFunc-cot calcFunc-coth
+calcFunc-deg calcFunc-exp calcFunc-exp10 calcFunc-expm1
 calcFunc-hypot calcFunc-ilog calcFunc-isqrt calcFunc-ln calcFunc-lnp1
-calcFunc-log calcFunc-log10 calcFunc-nroot calcFunc-rad calcFunc-sin
+calcFunc-log calcFunc-log10 calcFunc-nroot calcFunc-rad calcFunc-sec
+calcFunc-sech calcFunc-sin
 calcFunc-sincos calcFunc-sinh calcFunc-sqr calcFunc-sqrt calcFunc-tan
 calcFunc-tanh math-arccos-raw math-arcsin-raw math-arctan-raw
-math-arctan2-raw math-cos-raw math-exp-minus-1-raw math-exp-raw
+math-arctan2-raw math-cos-raw math-cot-raw math-csc-raw
+math-exp-minus-1-raw math-exp-raw
 math-from-radians math-from-radians-2 math-hypot math-infinite-dir
 math-isqrt-small math-ln-raw math-nearly-equal math-nearly-equal-float
 math-nearly-zerop math-nearly-zerop-float math-nth-root
@@ -1008,9 +1011,11 @@ calc-map-equation calc-map-stack calc-outer-product calc-reduce)
 
  ("calc-math" calc-arccos calc-arccosh calc-arcsin calc-arcsinh
 calc-arctan calc-arctan2 calc-arctanh calc-conj calc-cos calc-cosh
+calc-cot calc-coth calc-csc calc-csch
 calc-degrees-mode calc-exp calc-expm1 calc-hypot calc-ilog
 calc-imaginary calc-isqrt calc-ln calc-lnp1 calc-log calc-log10
-calc-pi calc-radians-mode calc-sin calc-sincos calc-sinh calc-sqrt
+calc-pi calc-radians-mode calc-sec calc-sech 
+calc-sin calc-sincos calc-sinh calc-sqrt
 calc-tan calc-tanh calc-to-degrees calc-to-radians)
 
  ("calc-mode" calc-alg-simplify-mode calc-algebraic-mode
diff --git a/lisp/calc/calc-math.el b/lisp/calc/calc-math.el
index 02c65ac22ea..d2c66c34d49 100644
--- a/lisp/calc/calc-math.el
+++ b/lisp/calc/calc-math.el
@@ -144,6 +144,18 @@
   (calc-hyperbolic-func)
   (calc-sin arg))
 
+(defun calc-sec (arg)
+  (interactive "P")
+  (calc-slow-wrapper
+   (if (calc-is-hyperbolic)
+       (calc-unary-op "sech" 'calcFunc-sech arg)
+     (calc-unary-op "sec" 'calcFunc-sec arg))))
+
+(defun calc-sech (arg)
+  (interactive "P")
+  (calc-hyperbolic-func)
+  (calc-sec arg))
+
 (defun calc-cos (arg)
   (interactive "P")
   (calc-slow-wrapper
@@ -171,6 +183,18 @@
   (calc-hyperbolic-func)
   (calc-cos arg))
 
+(defun calc-csc (arg)
+  (interactive "P")
+  (calc-slow-wrapper
+   (if (calc-is-hyperbolic)
+       (calc-unary-op "csch" 'calcFunc-csch arg)
+     (calc-unary-op "csc" 'calcFunc-csc arg))))
+
+(defun calc-csch (arg)
+  (interactive "P")
+  (calc-hyperbolic-func)
+  (calc-csc arg))
+
 (defun calc-sincos ()
   (interactive)
   (calc-slow-wrapper
@@ -205,6 +229,29 @@
   (calc-hyperbolic-func)
   (calc-tan arg))
 
+(defun calc-cot (arg)
+  (interactive "P")
+  (calc-slow-wrapper
+   (if (calc-is-hyperbolic)
+       (calc-unary-op "coth" 'calcFunc-coth arg)
+     (calc-unary-op "cot" 'calcFunc-cot arg))))
+
+(defun calc-arctan (arg)
+  (interactive "P")
+  (calc-invert-func)
+  (calc-tan arg))
+
+(defun calc-tanh (arg)
+  (interactive "P")
+  (calc-hyperbolic-func)
+  (calc-tan arg))
+
+(defun calc-arctanh (arg)
+  (interactive "P")
+  (calc-invert-func)
+  (calc-hyperbolic-func)
+  (calc-tan arg))
+
 (defun calc-arctan2 ()
   (interactive)
   (calc-slow-wrapper
@@ -220,8 +267,6 @@
   (calc-slow-wrapper
    (calc-pop-push-record 1 "i*" (math-imaginary (calc-top-n 1)))))
 
-
-
 (defun calc-to-degrees (arg)
   (interactive "P")
   (calc-wrapper
@@ -794,6 +839,169 @@
 	(t (calc-record-why 'scalarp x)
 	   (list 'calcFunc-tan x))))
 
+(defun calcFunc-sec (x)
+  (cond ((and (integerp x)
+              (eq calc-angle-mode 'deg)
+              (= (% x 180) 0))
+         (if (= (% x 360) 0)
+             1
+           -1))
+        ((and (integerp x)
+              (eq calc-angle-mode 'rad)
+              (= x 0))
+         1)
+        ((Math-scalarp x)
+         (math-with-extra-prec 2
+           (math-sec-raw (math-to-radians (math-float x)))))
+        ((eq (car x) 'sdev)
+         (if (math-constp x)
+             (math-with-extra-prec 2
+               (let* ((xx (math-to-radians (math-float (nth 1 x))))
+                      (xs (math-to-radians (math-float (nth 2 x))))
+                      (sc (math-sin-cos-raw xx)))
+                 (if (and (math-zerop (cdr sc))
+                          (not calc-infinite-mode))
+                     (progn
+                       (calc-record-why "*Division by zero")
+                       (list 'calcFunc-sec x))
+                   (math-make-sdev (math-div-float '(float 1 0) (cdr sc))
+                                   (math-div-float
+                                    (math-mul xs (car sc))
+                                    (math-sqr (cdr sc)))))))
+           (math-make-sdev (calcFunc-sec (nth 1 x))
+                           (math-div 
+                            (math-mul (nth 2 x)
+                                      (calcFunc-sin (nth 1 x)))
+                            (math-sqr (calcFunc-cos (nth 1 x)))))))
+        ((and (eq (car x) 'intv)
+              (math-intv-constp x))
+         (math-with-extra-prec 2
+           (let* ((xx (math-to-radians (math-float x)))
+                  (na (math-floor (math-div (math-sub (nth 2 xx)
+                                                      (math-pi-over-2))
+                                            (math-pi))))
+                  (nb (math-floor (math-div (math-sub (nth 3 xx)
+                                                      (math-pi-over-2))
+                                            (math-pi))))
+                  (naa (math-floor (math-div (nth 2 xx) (math-pi-over-2))))
+                  (nbb (math-floor (math-div (nth 3 xx) (math-pi-over-2))))
+                  (span (math-sub nbb naa)))
+             (if (not (equal na nb))
+                 '(intv 3 (neg (var inf var-inf)) (var inf var-inf))
+               (let ((int (math-sort-intv (nth 1 x)
+                                          (math-sec-raw (nth 2 xx))
+                                          (math-sec-raw (nth 3 xx)))))
+                 (if (eq span 1)
+                     (if (math-evenp (math-div (math-add naa 1) 2))
+                         (math-make-intv (logior (nth 1 int) 2)
+                                         1
+                                         (nth 3 int))
+                       (math-make-intv (logior (nth 1 int) 1)
+                                       (nth 2 int)
+                                       -1))
+                   int))))))
+        ((equal x '(var nan var-nan))
+         x)
+        (t (calc-record-why 'scalarp x)
+           (list 'calcFunc-sec x))))
+
+(defun calcFunc-csc (x)
+  (cond ((and (integerp x)
+              (eq calc-angle-mode 'deg)
+              (= (% (- x 90) 180) 0))
+         (if (= (% (- x 90) 360) 0)
+             1
+           -1))
+        ((Math-scalarp x)
+         (math-with-extra-prec 2
+           (math-csc-raw (math-to-radians (math-float x)))))
+        ((eq (car x) 'sdev)
+         (if (math-constp x)
+             (math-with-extra-prec 2
+               (let* ((xx (math-to-radians (math-float (nth 1 x))))
+                      (xs (math-to-radians (math-float (nth 2 x))))
+                      (sc (math-sin-cos-raw xx)))
+                 (if (and (math-zerop (car sc))
+                          (not calc-infinite-mode))
+                     (progn
+                       (calc-record-why "*Division by zero")
+                       (list 'calcFunc-csc x))
+                   (math-make-sdev (math-div-float '(float 1 0) (car sc))
+                                   (math-div-float
+                                    (math-mul xs (cdr sc))
+                                    (math-sqr (car sc)))))))
+           (math-make-sdev (calcFunc-csc (nth 1 x))
+                           (math-div 
+                            (math-mul (nth 2 x)
+                                      (calcFunc-cos (nth 1 x)))
+                            (math-sqr (calcFunc-sin (nth 1 x)))))))
+        ((and (eq (car x) 'intv)
+              (math-intv-constp x))
+         (math-with-extra-prec 2
+           (let* ((xx (math-to-radians (math-float x)))
+                  (na (math-floor (math-div (nth 2 xx) (math-pi))))
+                  (nb (math-floor (math-div (nth 3 xx) (math-pi))))
+                  (naa (math-floor (math-div (nth 2 xx) (math-pi-over-2))))
+                  (nbb (math-floor (math-div (nth 3 xx) (math-pi-over-2))))
+                  (span (math-sub nbb naa)))
+             (if (not (equal na nb))
+                 '(intv 3 (neg (var inf var-inf)) (var inf var-inf))
+               (let ((int (math-sort-intv (nth 1 x)
+                                          (math-csc-raw (nth 2 xx))
+                                          (math-csc-raw (nth 3 xx)))))
+                 (if (eq span 1)
+                     (if (math-evenp (math-div naa 2))
+                         (math-make-intv (logior (nth 1 int) 2)
+                                         1
+                                         (nth 3 int))
+                       (math-make-intv (logior (nth 1 int) 1)
+                                       (nth 2 int)
+                                       -1))
+                   int))))))
+        ((equal x '(var nan var-nan))
+         x)
+        (t (calc-record-why 'scalarp x)
+           (list 'calcFunc-csc x))))
+
+(defun calcFunc-cot (x)   ; [N N] [Public]
+  (cond ((and (integerp x)
+	      (if (eq calc-angle-mode 'deg)
+		  (= (% (- x 90) 180) 0)
+		(= x 0)))
+	 0)
+	((Math-scalarp x)
+	 (math-with-extra-prec 2
+	   (math-cot-raw (math-to-radians (math-float x)))))
+	((eq (car x) 'sdev)
+	 (if (math-constp x)
+	     (math-with-extra-prec 2
+	       (let* ((xx (math-to-radians (math-float (nth 1 x))))
+		      (xs (math-to-radians (math-float (nth 2 x))))
+		      (sc (math-sin-cos-raw xx)))
+		 (if (and (math-zerop (car sc)) (not calc-infinite-mode))
+		     (progn
+		       (calc-record-why "*Division by zero")
+		       (list 'calcFunc-cot x))
+		   (math-make-sdev (math-div-float (cdr sc) (car sc))
+				   (math-div-float xs (math-sqr (car sc)))))))
+	   (math-make-sdev (calcFunc-cot (nth 1 x))
+			   (math-div (nth 2 x)
+				     (math-sqr (calcFunc-sin (nth 1 x)))))))
+	((and (eq (car x) 'intv) (math-intv-constp x))
+	 (or (math-with-extra-prec 2
+	       (let* ((xx (math-to-radians (math-float x)))
+		      (na (math-floor (math-div (nth 2 xx) (math-pi))))
+		      (nb (math-floor (math-div (nth 3 xx) (math-pi))))
+		 (and (equal na nb)
+		      (math-sort-intv (nth 1 x)
+				      (math-cot-raw (nth 2 xx))
+				      (math-cot-raw (nth 3 xx)))))))
+	     '(intv 3 (neg (var inf var-inf)) (var inf var-inf))))
+	((equal x '(var nan var-nan))
+	 x)
+	(t (calc-record-why 'scalarp x)
+	   (list 'calcFunc-cot x))))
+
 (defun math-sin-raw (x)   ; [N N]
   (cond ((eq (car x) 'cplx)
 	 (let* ((expx (math-exp-raw (nth 2 x)))
@@ -819,6 +1027,85 @@
       (math-polar (math-cos-raw (math-complex x)))
     (math-sin-raw (math-sub (math-pi-over-2) x))))
 
+(defun math-sec-raw (x)   ; [N N]
+  (cond ((eq (car x) 'cplx)
+	 (let* ((x (math-mul x '(float 1 0)))
+                (expx (math-exp-raw (nth 2 x)))
+		(expmx (math-div-float '(float 1 0) expx))
+                (sh (math-mul-float (math-sub-float expx expmx) '(float 5 -1)))
+                (ch (math-mul-float (math-add-float expx expmx) '(float 5 -1)))
+		(sc (math-sin-cos-raw (nth 1 x)))
+		(d (math-add-float 
+                    (math-mul-float (math-sqr (car sc))
+                                    (math-sqr sh))
+                    (math-mul-float (math-sqr (cdr sc))
+                                    (math-sqr ch)))))
+	   (and (not (eq (nth 1 d) 0))
+		(list 'cplx
+		      (math-div-float (math-mul-float (cdr sc) ch) d)
+		      (math-div-float (math-mul-float (car sc) sh) d)))))
+	((eq (car x) 'polar)
+	 (math-polar (math-sec-raw (math-complex x))))
+	(t
+	 (let ((cs (math-cos-raw x)))
+           (if (eq cs 0)
+               (math-div 1 0)
+	     (math-div-float '(float 1 0) cs))))))
+
+(defun math-csc-raw (x)   ; [N N]
+  (cond ((eq (car x) 'cplx)
+	 (let* ((x (math-mul x '(float 1 0)))
+                (expx (math-exp-raw (nth 2 x)))
+		(expmx (math-div-float '(float 1 0) expx))
+                (sh (math-mul-float (math-sub-float expx expmx) '(float 5 -1)))
+                (ch (math-mul-float (math-add-float expx expmx) '(float 5 -1)))
+		(sc (math-sin-cos-raw (nth 1 x)))
+		(d (math-add-float 
+                    (math-mul-float (math-sqr (car sc))
+                                    (math-sqr ch))
+                    (math-mul-float (math-sqr (cdr sc))
+                                    (math-sqr sh)))))
+	   (and (not (eq (nth 1 d) 0))
+		(list 'cplx
+		      (math-div-float (math-mul-float (car sc) ch) d)
+		      (math-div-float (math-mul-float (cdr sc) sh) d)))))
+	((eq (car x) 'polar)
+	 (math-polar (math-csc-raw (math-complex x))))
+	(t
+	 (let ((sn (math-sin-raw x)))
+           (if (eq sn 0)
+               (math-div 1 0)
+	     (math-div-float '(float 1 0) sn))))))
+
+(defun math-cot-raw (x)   ; [N N]
+  (cond ((eq (car x) 'cplx)
+	 (let* ((x (math-mul x '(float 1 0)))
+                (expx (math-exp-raw (nth 2 x)))
+		(expmx (math-div-float '(float 1 0) expx))
+                (sh (math-mul-float (math-sub-float expx expmx) '(float 5 -1)))
+                (ch (math-mul-float (math-add-float expx expmx) '(float 5 -1)))
+		(sc (math-sin-cos-raw (nth 1 x)))
+		(d (math-add-float 
+                    (math-sqr (car sc))
+                    (math-sqr sh))))
+	   (and (not (eq (nth 1 d) 0))
+		(list 'cplx
+		      (math-div-float 
+                       (math-mul-float (car sc) (cdr sc))
+                       d)
+                      (math-neg
+                       (math-div-float 
+                        (math-mul-float sh ch) 
+                        d))))))
+	((eq (car x) 'polar)
+	 (math-polar (math-cot-raw (math-complex x))))
+	(t
+	 (let ((sc (math-sin-cos-raw x)))
+	   (if (eq (nth 1 (car sc)) 0)
+	       (math-div (cdr sc) 0)
+	     (math-div-float (cdr sc) (car sc)))))))
+
+
 ;;; This could use a smarter method:  Reduce x as in math-sin-raw, then
 ;;;   compute either sin(x) or cos(x), whichever is smaller, and compute
 ;;;   the other using the identity sin(x)^2 + cos(x)^2 = 1.
@@ -1537,6 +1824,104 @@
 	   (list 'calcFunc-tanh x))))
 (put 'calcFunc-tanh 'math-expandable t)
 
+(defun calcFunc-sech (x)   ; [N N] [Public]
+  (cond ((eq x 0) 1)
+	(math-expand-formulas
+	 (math-normalize
+	  (list '/ 2 (list '+ (list 'calcFunc-exp x)
+                           (list 'calcFunc-exp (list 'neg x))))))
+	((Math-numberp x)
+	 (if calc-symbolic-mode (signal 'inexact-result nil))
+	 (math-with-extra-prec 2
+	   (let ((expx (math-exp-raw (math-float x))))
+	     (math-div '(float 2 0) (math-add expx (math-div 1 expx))))))
+	((eq (car-safe x) 'sdev)
+	 (math-make-sdev (calcFunc-sech (nth 1 x))
+			 (math-mul (nth 2 x)
+                                   (math-mul (calcFunc-sech (nth 1 x))
+                                             (calcFunc-tanh (nth 1 x))))))
+	((and (eq (car x) 'intv) (math-intv-constp x))
+	 (setq x (math-abs x))
+	 (math-sort-intv (nth 1 x)
+			 (calcFunc-sech (nth 2 x))
+			 (calcFunc-sech (nth 3 x))))
+	((or (equal x '(var inf var-inf))
+	     (equal x '(neg (var inf var-inf))))
+         0)
+        ((equal x '(var nan var-nan))
+         x)
+	(t (calc-record-why 'numberp x)
+	   (list 'calcFunc-sech x))))
+(put 'calcFunc-sech 'math-expandable t)
+
+(defun calcFunc-csch (x)   ; [N N] [Public]
+  (cond ((eq x 0) (math-div 1 0))
+	(math-expand-formulas
+	 (math-normalize
+	  (list '/ 2 (list '- (list 'calcFunc-exp x)
+                           (list 'calcFunc-exp (list 'neg x))))))
+	((Math-numberp x)
+	 (if calc-symbolic-mode (signal 'inexact-result nil))
+	 (math-with-extra-prec 2
+	   (let ((expx (math-exp-raw (math-float x))))
+	     (math-div '(float 2 0) (math-add expx (math-div -1 expx))))))
+	((eq (car-safe x) 'sdev)
+	 (math-make-sdev (calcFunc-csch (nth 1 x))
+			 (math-mul (nth 2 x) 
+                                   (math-mul (calcFunc-csch (nth 1 x))
+                                             (calcFunc-coth (nth 1 x))))))
+	((eq (car x) 'intv)
+         (if (and (Math-negp (nth 2 x))
+                  (Math-posp (nth 3 x)))
+             '(intv 3 (neg (var inf var-inf)) (var inf var-inf))
+           (math-sort-intv (nth 1 x)
+                           (calcFunc-csch (nth 2 x))
+                           (calcFunc-csch (nth 3 x)))))
+	((or (equal x '(var inf var-inf))
+	     (equal x '(neg (var inf var-inf))))
+         0)
+        ((equal x '(var nan var-nan))
+         x)
+	(t (calc-record-why 'numberp x)
+	   (list 'calcFunc-csch x))))
+(put 'calcFunc-csch 'math-expandable t)
+
+(defun calcFunc-coth (x)   ; [N N] [Public]
+  (cond ((eq x 0) (math-div 1 0))
+	(math-expand-formulas
+	 (math-normalize
+	  (let ((expx (list 'calcFunc-exp x))
+		(expmx (list 'calcFunc-exp (list 'neg x))))
+	    (math-normalize
+	     (list '/ (list '+ expx expmx) (list '- expx expmx))))))
+	((Math-numberp x)
+	 (if calc-symbolic-mode (signal 'inexact-result nil))
+	 (math-with-extra-prec 2
+	   (let* ((expx (calcFunc-exp (math-float x)))
+		  (expmx (math-div 1 expx)))
+	     (math-div (math-add expx expmx)
+		       (math-sub expx expmx)))))
+	((eq (car-safe x) 'sdev)
+	 (math-make-sdev (calcFunc-coth (nth 1 x))
+			 (math-div (nth 2 x)
+				   (math-sqr (calcFunc-sinh (nth 1 x))))))
+	((eq (car x) 'intv)
+         (if (and (Math-negp (nth 2 x))
+                  (Math-posp (nth 3 x)))
+             '(intv 3 (neg (var inf var-inf)) (var inf var-inf))
+           (math-sort-intv (nth 1 x)
+                           (calcFunc-coth (nth 2 x))
+                           (calcFunc-coth (nth 3 x)))))
+	((equal x '(var inf var-inf))
+	 1)
+	((equal x '(neg (var inf var-inf)))
+	 -1)
+	((equal x '(var nan var-nan))
+	 x)
+	(t (calc-record-why 'numberp x)
+	   (list 'calcFunc-coth x))))
+(put 'calcFunc-coth 'math-expandable t)
+
 (defun calcFunc-arcsinh (x)   ; [N N] [Public]
   (cond ((eq x 0) 0)
 	(math-expand-formulas
diff --git a/lisp/calc/calc-rules.el b/lisp/calc/calc-rules.el
index 1ccbf3fffac..7a11cfa5012 100644
--- a/lisp/calc/calc-rules.el
+++ b/lisp/calc/calc-rules.el
@@ -153,10 +153,14 @@ tan(select(2 a))		:=  2 tan(select(a)) / (1 - tan(a)^2),
 tan(select(n a))		:=  (tan((n-1) select(a)) + tan(a)) /
 				    (1 - tan((n-1) a) tan(a))
 				    :: integer(n) :: n > 2,
+cot(select(a + b))		:=  (cot(select(a)) cot(b) - 1) /
+				    (cot(a) + cot(b)),
 sinh(select(a + b))		:=  sinh(select(a)) cosh(b) + cosh(a) sinh(b),
 cosh(select(a + b))		:=  cosh(select(a)) cosh(b) + sinh(a) sinh(b),
 tanh(select(a + b))		:=  (tanh(select(a)) + tanh(b)) /
 				    (1 + tanh(a) tanh(b)),
+coth(select(a + b))		:=  (coth(select(a)) coth(b) + 1) /
+				    (coth(a) + coth(b)),
 x && select(a || b)		:=  (x && select(a)) || (x && b),
 select(a || b) && x		:=  (select(a) && x) || (b && x),
 ! select(a && b)		:=  (!a) || (!b),
@@ -269,12 +273,18 @@ exp(select(x))			:=  1 / exp(select(-x)),
 sin(select(x))			:=  -sin(select(-x)),
 cos(select(x))			:=  cos(select(-x)),
 tan(select(x))			:=  -tan(select(-x)),
+sec(select(x))			:=  sec(select(-x)),
+csc(select(x))			:=  -csc(select(-x)),
+cot(select(x))			:=  -cot(select(-x)),
 arcsin(select(x))		:=  -arcsin(select(-x)),
 arccos(select(x))		:=  4 arctan(1) - arccos(select(-x)),
 arctan(select(x))		:=  -arctan(select(-x)),
 sinh(select(x))			:=  -sinh(select(-x)),
 cosh(select(x))			:=  cosh(select(-x)),
 tanh(select(x))			:=  -tanh(select(-x)),
+sech(select(x))			:=  sech(select(-x)),
+csch(select(x))			:=  -csch(select(-x)),
+coth(select(x))			:=  -coth(select(-x)),
 arcsinh(select(x))		:=  -arcsinh(select(-x)),
 arctanh(select(x))		:=  -arctanh(select(-x)),
 select(x) = a			:=  select(-x) = -a,
diff --git a/lisp/calc/calc-undo.el b/lisp/calc/calc-undo.el
index a49c34010ab..d946a1390d3 100644
--- a/lisp/calc/calc-undo.el
+++ b/lisp/calc/calc-undo.el
@@ -77,7 +77,8 @@
 	   (let ((v (intern (nth 1 action))))
 	     (calc-record-undo (list 'store (nth 1 action)
 				     (and (boundp v) (symbol-value v))))
-	     (if (y-or-n-p (format "Un-store variable %s? " (nth 1 action)))
+	     (if (y-or-n-p (format "Un-store variable %s? " 
+                                   (calc-var-name (nth 1 action))))
 		 (progn
 		   (if (nth 2 action)
 		       (set v (nth 2 action))
diff --git a/lisp/calc/calc-units.el b/lisp/calc/calc-units.el
index e8a3abfe958..4b3c284ddad 100644
--- a/lisp/calc/calc-units.el
+++ b/lisp/calc/calc-units.el
@@ -1241,6 +1241,45 @@ Entries are (SYMBOL EXPR DOC-STRING TEMP-TYPE BASE-UNITS).")
 	      (eq (nth 1 (nth 2 rad)) 'rad)
 	      (list 'calcFunc-tan (nth 1 rad))))))
 
+(math-defsimplify calcFunc-sec
+  (and math-simplifying-units
+       (math-units-in-expr-p (nth 1 math-simplify-expr) nil)
+       (let ((rad (math-simplify-units
+		   (math-evaluate-expr
+		    (math-to-standard-units (nth 1 math-simplify-expr) nil))))
+	     (calc-angle-mode 'rad))
+	 (and (eq (car-safe rad) '*)
+	      (math-realp (nth 1 rad))
+	      (eq (car-safe (nth 2 rad)) 'var)
+	      (eq (nth 1 (nth 2 rad)) 'rad)
+	      (list 'calcFunc-sec (nth 1 rad))))))
+
+(math-defsimplify calcFunc-csc
+  (and math-simplifying-units
+       (math-units-in-expr-p (nth 1 math-simplify-expr) nil)
+       (let ((rad (math-simplify-units
+		   (math-evaluate-expr
+		    (math-to-standard-units (nth 1 math-simplify-expr) nil))))
+	     (calc-angle-mode 'rad))
+	 (and (eq (car-safe rad) '*)
+	      (math-realp (nth 1 rad))
+	      (eq (car-safe (nth 2 rad)) 'var)
+	      (eq (nth 1 (nth 2 rad)) 'rad)
+	      (list 'calcFunc-csc (nth 1 rad))))))
+
+(math-defsimplify calcFunc-cot
+  (and math-simplifying-units
+       (math-units-in-expr-p (nth 1 math-simplify-expr) nil)
+       (let ((rad (math-simplify-units
+		   (math-evaluate-expr
+		    (math-to-standard-units (nth 1 math-simplify-expr) nil))))
+	     (calc-angle-mode 'rad))
+	 (and (eq (car-safe rad) '*)
+	      (math-realp (nth 1 rad))
+	      (eq (car-safe (nth 2 rad)) 'var)
+	      (eq (nth 1 (nth 2 rad)) 'rad)
+	      (list 'calcFunc-cot (nth 1 rad))))))
+
 
 (defun math-remove-units (expr)
   (if (math-check-unit-name expr)
diff --git a/lisp/calc/calcalg2.el b/lisp/calc/calcalg2.el
index 18b6c1328d7..d5a9009c1ac 100644
--- a/lisp/calc/calcalg2.el
+++ b/lisp/calc/calcalg2.el
@@ -412,6 +412,30 @@
 					 (math-normalize
 					  (list 'calcFunc-cos u))))))))
 
+(put 'calcFunc-sec\' 'math-derivative-1
+     (function (lambda (u) (math-to-radians-2 
+                            (math-mul
+                             (math-normalize
+                              (list 'calcFunc-sec u))
+                             (math-normalize
+                              (list 'calcFunc-tan u)))))))
+
+(put 'calcFunc-csc\' 'math-derivative-1
+     (function (lambda (u) (math-neg 
+                            (math-to-radians-2
+                             (math-mul
+                              (math-normalize
+                               (list 'calcFunc-csc u))
+                              (math-normalize
+                               (list 'calcFunc-cot u))))))))
+
+(put 'calcFunc-cot\' 'math-derivative-1
+     (function (lambda (u) (math-neg
+                            (math-to-radians-2
+                             (math-div 1 (math-sqr
+                                          (math-normalize
+                                           (list 'calcFunc-sin u)))))))))
+
 (put 'calcFunc-arcsin\' 'math-derivative-1
      (function (lambda (u)
 		 (math-from-radians-2
@@ -441,6 +465,24 @@
 					(math-normalize
 					 (list 'calcFunc-cosh u)))))))
 
+(put 'calcFunc-sech\' 'math-derivative-1
+     (function (lambda (u) (math-neg
+                            (math-mul
+                             (math-normalize (list 'calcFunc-sech u))
+                             (math-normalize (list 'calcFunc-tanh u)))))))
+
+(put 'calcFunc-csch\' 'math-derivative-1
+     (function (lambda (u) (math-neg
+                            (math-mul
+                             (math-normalize (list 'calcFunc-csch u))
+                             (math-normalize (list 'calcFunc-coth u)))))))
+
+(put 'calcFunc-tanh\' 'math-derivative-1
+     (function (lambda (u) (math-neg
+                            (math-div 1 (math-sqr
+                                         (math-normalize
+                                          (list 'calcFunc-sinh u))))))))
+
 (put 'calcFunc-arcsinh\' 'math-derivative-1
      (function (lambda (u)
 		 (math-div 1 (math-normalize
@@ -1053,7 +1095,10 @@
 	       (while (and p
 			   (memq (car (car p)) '(calcFunc-sin
 						 calcFunc-cos
-						 calcFunc-tan))
+						 calcFunc-tan
+                                                 calcFunc-sec
+                                                 calcFunc-csc
+                                                 calcFunc-cot))
 			   (equal (nth 1 (car p)) math-integ-var))
 		 (setq p (cdr p)))
 	       (null p))
@@ -1068,6 +1113,9 @@
 			   (memq (car (car p)) '(calcFunc-sinh
 						 calcFunc-cosh
 						 calcFunc-tanh
+                                                 calcFunc-sech
+                                                 calcFunc-csch
+                                                 calcFunc-coth
 						 calcFunc-exp))
 			   (equal (nth 1 (car p)) math-integ-var))
 		 (setq p (cdr p)))
@@ -1619,6 +1667,27 @@
        (math-neg (math-from-radians-2
 		  (list 'calcFunc-ln (list 'calcFunc-cos u))))))
 
+(math-defintegral calcFunc-sec
+  (and (equal u math-integ-var)
+       (math-from-radians-2
+        (list 'calcFunc-ln 
+              (math-add
+               (list 'calcFunc-sec u)
+               (list 'calcFunc-tan u))))))
+
+(math-defintegral calcFunc-csc
+  (and (equal u math-integ-var)
+       (math-from-radians-2
+        (list 'calcFunc-ln 
+              (math-sub
+               (list 'calcFunc-csc u)
+               (list 'calcFunc-cot u))))))
+
+(math-defintegral calcFunc-cot
+  (and (equal u math-integ-var)
+       (math-from-radians-2
+        (list 'calcFunc-ln (list 'calcFunc-sin u)))))
+
 (math-defintegral calcFunc-arcsin
   (and (equal u math-integ-var)
        (math-add (math-mul u (list 'calcFunc-arcsin u))
@@ -1650,6 +1719,18 @@
   (and (equal u math-integ-var)
        (list 'calcFunc-ln (list 'calcFunc-cosh u))))
 
+(math-defintegral calcFunc-sech
+  (and (equal u math-integ-var)
+       (list 'calcFunc-arctan (list 'calcFunc-sinh u))))
+
+(math-defintegral calcFunc-csch
+  (and (equal u math-integ-var)
+       (list 'calcFunc-ln (list 'calcFunc-tanh (math-div u 2)))))
+
+(math-defintegral calcFunc-coth
+  (and (equal u math-integ-var)
+       (list 'calcFunc-ln (list 'calcFunc-sinh u))))
+
 (math-defintegral calcFunc-arcsinh
   (and (equal u math-integ-var)
        (math-sub (math-mul u (list 'calcFunc-arcsinh u))
diff --git a/lisp/calc/calccomp.el b/lisp/calc/calccomp.el
index eff7df2373d..305e155843e 100644
--- a/lisp/calc/calccomp.el
+++ b/lisp/calc/calccomp.el
@@ -35,7 +35,9 @@
   '( calcFunc-log
      calcFunc-ln calcFunc-exp
      calcFunc-sin calcFunc-cos calcFunc-tan
+     calcFunc-sec calcFunc-csc calcFunc-cot
      calcFunc-sinh calcFunc-cosh calcFunc-tanh
+     calcFunc-sech calcFunc-csch calcFunc-coth
      calcFunc-arcsin calcFunc-arccos calcFunc-arctan
      calcFunc-arcsinh calcFunc-arccosh calcFunc-arctanh))