Symbolic algebraic expressions🔗ℹ

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🔗ℹ

> (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🔗ℹ

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"