Algebra & calculus in CALCULA
The Algebra & calculus field brings together symbolic (exact) computation and matrix computation. The SymPy engine returns closed forms whenever it can — a fraction, a root, a factorised expression — rather than a decimal approximation.
Solving an equation
You type the equation with the = sign, choose the unknown, and CALCULA returns the whole solution set. For a quadratic:
The term b² − 4ac is the discriminant: positive, two real solutions; zero, one double solution; negative, two complex conjugate solutions.
Example
For x² − 5x + 6 = 0 the discriminant is 25 − 24 = 1, and the solutions are x = 2 and x = 3. CALCULA also shows the factorisation (x − 2)(x − 3).
Differentiating and integrating
The derivative measures the instantaneous slope of a function, the integral the area under its curve. A few basic rules:
CALCULA handles the chain rule, partial derivatives, and definite integrals (with bounds) as well as indefinite ones.
Example
The derivative of f(x) = x³ − 4x is 3x² − 4, which vanishes at x = ±2/√3 — the abscissas of the extrema, drawn on the secondary screen.
Limits, expansions, matrices
You can also take limits (including at infinity and one-sided), Taylor expansions, and linear algebra: determinant, inverse, eigenvalues, solving systems A·x = b. The determinant of a 2×2 matrix:
A matrix is invertible only if its determinant is non-zero.
Typing it into CALCULA
Type the expression in a field, open the “≡” menu and choose the operation (solve, differentiate, integrate, limit, factorise…). Variables carry over from one line to the next. See also the trigonometry & geometry and statistics guides.