Symbolic algebraic expressions

This library provides functions to parse and manipulate symbolic algebraic expressions. These expression can be constants, variables, arithmetic operations and exponentiations. Additionally trigonometric functions and logarithms are supported.

1 Example

> (define expr (parse-infix "3*x^2 - 4*x + cos(x)"))

> (define expr-deriv (simplify                        (differentiate expr)))

> expr-deriv

(add  (list   (num -4)   (mul (list (num 6) (sym 'x)))   (mul (list (num -1) (sin_ (sym 'x))))))

> (infix expr-deriv)

"-4 + 6 * x + -1 * sin(x)"

> (sexpr expr-deriv)

'(+ -4 (* 6 x) (* -1 (sin x)))

> (latex expr-deriv)

"-4 + 6 x -\\sin(x)"

> (define f (evaluate expr-deriv))

> (f 3)

13.858879991940134

2 API Reference

expr :		number?
		| symbol?
		| e
		| pi
		| (+ expr ...+)
		| (- expr ...+)
		| (* expr ...+)
		| (/ expr expr)
		| (expt expr expr)
		| (log expr expr)
		| (sin expr)
		| (cos expr)
		| (tan expr)

expr :		number?
		| symbol?
		| e
		| pi
		| (expr)
		| expr + expr
		| expr - expr
		| expr * expr
		| expr / expr
		| expr ^ expr
		| log(expr, expr)
		| sin(expr)
		| cos(expr)
		| tan(expr)

Some examples:

> (infix (simplify (parse-infix "x+x")))

"2 * x"

> (infix (simplify (parse-infix "x^0")))

"1"

> (infix (simplify (parse-infix "2*x^2 + 4*x^2 + 5 - 6")))

"-1 + 6 * (x)^(2)"

> (infix (simplify (parse-infix "2*x^2 / x")))

"2 * x"

> (infix (simplify (parse-infix "2^x^4")))

"(2)^(4 * x)"

Take into account that the resulting expression is not simplified automatically, a further call to simplify is necessary to bring it into a canonical form:

> (define expr (parse-infix "2*x^2 - x"))

> (infix (differentiate expr))

"(x)^(2) * 1 * 2 * (x)^(-1) + 0 * log(x) * 2 + (x)^(2) * 0 + 1 * -1 + x * 0"

> (infix (simplify (differentiate expr)))

"-1 + 4 * x"