Calculator Guide

Symbolic algebra

Symbolic expressions use free variables instead of only numbers. When an expression contains a symbol, Hissab keeps the result algebraic, collects like terms, and returns a simplified expression.

12 + 2x^2 - 4x^2 - 2
(x + 2)*(x + 3)
derivative(2x^2, x)
integrate(2x^2 + 3x + 10, x)
limit(sin(x)/x, x, 0)
solve(x^2 - 5x + 6, x)

Symbols

The recognized free variables are x, y, and z. Other identifiers are treated as unknown words and make the expression invalid.

3x - 10y + 13z
x*y + 2x

Implicit multiplication works between a number and a symbol, so 2x means 2*x. Use an explicit operator between symbols: write x*y or x y, not xy.

Simplify and expand

A bare expression with symbols is simplified automatically. simplify(...) is the explicit form.

12 + 2x^2 - 4x^2 - 2
simplify(2x^2 - 4x^2)
(x + 1)*(x + 2)
(x + 1)*(x + 1)

Hissab returns canonical polynomial output ordered by descending degree.

Derivatives

Use derivative(expr, variable). diff is an alias.

derivative(2x^2, x)
diff(sin(x), x)
derivative(x^2*y, x)

With more than one symbol, the variable argument chooses the partial derivative.

Integrals

Use integrate(expr, variable). integral is an alias. Definite integrals add lower and upper bounds.

integrate(2x^2 + 3x + 10, x)
integral(2x^2 + 3x + 10, x)
integrate(2x^2 + 3x + 10, x, 0, 50)

The constant of integration is omitted for indefinite integrals.

Limits

Use limit(expr, variable, point).

limit(4x^2 - 3x + 10, x, 0)
limit(sin(x)/x, x, 0)

When a derivative, integral, or limit has no closed form, Hissab may return a numeric estimate for limits and definite integrals. An indefinite integral with no elementary antiderivative is left in integral form.

sqrt(x) is treated as x^(1/2), so the power rules apply to it.

derivative(sqrt(x), x)
integrate(sqrt(x), x)

Solving equations

solve(expr, x) finds the values of x where expr = 0. Write an equation directly (solve(x^2 = 4, x)) or as two sides (solve(x^2, 4, x)). You can leave out the variable when there is only one.

• Polynomials get every root — exact where they are rational, and complex roots in a + bi form.
• Linear equations with other variables are solved symbolically.
• Anything else in one variable gets a numeric search for real roots. Trig inside solve (and calculus) uses radians.

solve(x^2 - 5x + 6, x)
solve(3x + 4 = 19, x)
solve(x^2, 4, x)
solve(x^3 - 6x^2 + 11x - 6, x)
solve(x^2 + 1, x)
solve(2x + 3y - 8, x)
solve(2^x - 10, x)

The answer (x = 2, x = 3) is a list, so solve(...) must be the whole line.

Common mistakes