Add simplification rules for calcFunc-sec, calcFunc-csc, calcFunc-cot,

calcFunc-sech, calcFunc-csch, calcFunc-coth.

diff --git a/lisp/calc/calc-alg.el b/lisp/calc/calc-alg.el
index 4901883d094b3e93a9dd86a1faaceb2ea20088de..b722261907d4ddea0118d70fd1c9ab099b3303ae 100644 (file)
--- 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 '^