- solve_equationSolve equation
Analytically solve a single equation for a variable. Accepts 'lhs = rhs' or an expression equal to zero.
- solve_systemSolve system
Analytically solve a system of equations for given variables.
- simplifySimplify
Simplify an algebraic expression.
- expandExpand
Expand products and powers in an algebraic expression.
- factorFactor
Factor a polynomial expression.
- substituteSubstitute
Substitute variables in an expression with given values or sub-expressions.
- differentiateDifferentiate
Symbolically differentiate an expression with respect to a variable.
- integrateIntegrate
Symbolically integrate an expression with respect to a variable.
- definite_integralDefinite integral
Evaluate a definite integral ∫_a^b f(x) dx by computing the antiderivative and applying the bounds.
- limitLimit
Compute the limit of an expression as a variable approaches a value (use 'infinity' for ∞).
- sumSummation
Symbolic or numeric summation Σ over an index variable across given bounds.
- productProduct
Product Π of an expression over an index variable across given bounds.
- evaluateNumeric evaluate
Numerically evaluate an expression, optionally substituting variable values first.
- to_latexConvert to LaTeX
Render an expression as a LaTeX string suitable for KaTeX/MathJax.
- partial_fractionsPartial fraction decomposition
Decompose a rational expression into partial fractions in the given variable.
- polynomial_divisionPolynomial division
Divide one polynomial by another and return quotient and remainder.
- polynomial_gcdPolynomial GCD
Greatest common divisor of two polynomials.
- polynomial_lcmPolynomial LCM
Least common multiple of two polynomials.
- coefficientsPolynomial coefficients
Return the coefficients of a polynomial in the given variable, lowest degree first.
- rational_partsNumerator and denominator
Split a rational expression into its numerator and denominator.
- rationalizeRationalize
Combine a sum of rational terms over a common denominator.
- laplace_transformLaplace transform
Compute the Laplace transform of a time-domain expression: ℒ{f(t)}(s).
- inverse_laplace_transformInverse Laplace transform
Compute the inverse Laplace transform ℒ⁻¹{F(s)}(t).
- rectangular_formRectangular form
Convert a complex expression to a + b·i rectangular form.
- polar_formPolar form
Convert a complex expression to r·e^(i·θ) polar form.
- matrix_determinantMatrix determinant
Determinant of a square matrix; entries may be numbers or expressions.
- matrix_inverseMatrix inverse
Inverse of a square matrix; entries may be numbers or expressions.
- matrix_transposeMatrix transpose
Transpose of a matrix.
- matrix_multiplyMatrix multiply
Matrix product A · B; column count of A must equal row count of B.
- dot_productDot product
Scalar dot product of two vectors of equal length.
- cross_productCross product
Vector cross product of two 3-component vectors.