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

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calcFunc-sech, calcFunc-csch, calcFunc-coth.
This commit is contained in:
Jay Belanger 2005-02-15 19:23:46 +00:00
parent 43817a7520
commit 6a5412e40d
1 changed files with 128 additions and 0 deletions
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128
lisp/calc/calc-alg.el
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@ -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 '^