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algebrite

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Computer Algebra System in Coffeescript

github.com/davidedc/Algebrite

davidedc/Algebrite

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### arcsin ===================================================================== Tags ---- scripting, JS, internal, treenode, general concept Parameters ---------- x General description ------------------- Returns the inverse sine of x. ### Eval_arcsin = -> push(cadr(p1)) Eval() arcsin() arcsin = -> n = 0 d = 0 save() p1 = pop() if (car(p1) == symbol(SIN)) push(cadr(p1)) restore() return if (isdouble(p1)) errno = 0 d = Math.asin(p1.d) if (errno) stop("arcsin function argument is not in the interval [-1,1]") push_double(d) restore() return # if p1 == 1/sqrt(2) then return 1/4*pi (45 degrees) # second if catches the other way of saying it, sqrt(2)/2 if (isoneoversqrttwo(p1)) or (car(p1) == symbol(MULTIPLY) && equalq(car(cdr(p1)), 1,2) and car(car(cdr(cdr(p1)))) == symbol(POWER) && equaln(car(cdr(car(cdr(cdr(p1))))),2) && equalq(car(cdr(cdr(car(cdr(cdr(p1)))))), 1, 2)) push_rational(1, 4) push_symbol(PI) multiply() restore() return # if p1 == -1/sqrt(2) then return -1/4*pi (-45 degrees) # second if catches the other way of saying it, -sqrt(2)/2 if (isminusoneoversqrttwo(p1)) or (car(p1) == symbol(MULTIPLY) && equalq(car(cdr(p1)), -1,2) and car(car(cdr(cdr(p1)))) == symbol(POWER) && equaln(car(cdr(car(cdr(cdr(p1))))),2) && equalq(car(cdr(cdr(car(cdr(cdr(p1)))))), 1, 2)) if evaluatingAsFloats push_double(-Math.PI / 4.0) else push_rational(-1, 4) push_symbol(PI) multiply() restore() return if (!isrational(p1)) push_symbol(ARCSIN) push(p1) list(2) restore() return push(p1) push_integer(2) multiply() n = pop_integer() switch (n) when -2 if evaluatingAsFloats push_double(-Math.PI / 2.0) else push_rational(-1, 2) push_symbol(PI) multiply() when -1 if evaluatingAsFloats push_double(-Math.PI / 6.0) else push_rational(-1, 6) push_symbol(PI) multiply() when 0 if evaluatingAsFloats push_double(0.0) else push(zero) when 1 if evaluatingAsFloats push_double(Math.PI / 6.0) else push_rational(1, 6) push_symbol(PI) multiply() when 2 if evaluatingAsFloats push_double(Math.PI / 2.0) else push_rational(1, 2) push_symbol(PI) multiply() else push_symbol(ARCSIN) push(p1) list(2) restore()