Nerdamer Notation

Function reference

These are the functions recognized inside expressions passed to nerdamer('...'). Open a function to see its syntax, parameters, examples, aliases, and its JavaScript / TypeScript counterpart when one is available.

System solving is documented in depth. The solveeqs reference includes underdetermined systems with free variables, exact nonlinear intersections, irrational and complex solutions, overdetermined systems, and numerical multivariate solving.
Looking for programming features? Conditions, loops, local bindings, blocks, and return flow are documented separately under Nerdamer Scripting.

Algebra

factor(expression)

Factors an expression into a product of simpler factors.

 gcd(arg1, arg2)

Returns the greatest common divisor of two symbolic expressions when their polynomial structure can be resolved.

 groebner(arg1, [arg2])

Computes a Gröbner basis for a polynomial system.

 lcm(arg1, arg2)

Returns the least common multiple of two expressions.

 partfrac(arg1, [arg2])

Decomposes a rational expression into partial fractions with respect to a variable.

 pfactor(value)

Returns the repeated prime factors of a positive integer in ascending order.

 pfactord(value)

Returns prime factors and their occurrence counts.

 polyfactors(arg1)

Returns polynomial factors as a Vector of separate factor expressions.

 simplify(arg1)

Rewrites an expression into a simpler equivalent form using Nerdamer's symbolic simplification rules.

 sqcomp(arg1, [arg2])

Rewrites a quadratic in completed-square form.

Assumptions and sets

assume(arg1)

Adds a real numeric interval assumption for a symbol so assumption-aware operations can use the known range.

 forget(arg1)

Removes stored assumptions for a symbol or clears all assumptions.

 unassign(arg1)

Removes a parser-known value assigned to a variable.

Calculus

C(x)

Computes the normalized Fresnel cosine integral.

 defint(arg1, arg2, arg3, arg4)

Evaluates a definite integral over an interval.

 diff(expression[, variable][, order])

Differentiates an expression symbolically with respect to a variable.

 ilaplace(arg1, arg2, arg3)

Computes a symbolic inverse Laplace transform of an expression.

 integrate(expression[, variable])

Computes a symbolic antiderivative with respect to a variable when Nerdamer has a supported integration path.

 laplace(arg1, arg2, arg3)

Computes the symbolic Laplace transform of an expression.

 limit(expression, variable, value[, direction])

Computes a symbolic limit of an expression as a variable approaches a value.

 product(arg1, arg2, arg3, arg4)

Evaluates a finite symbolic product over an integer index.

 S(x)

Computes the normalized Fresnel sine integral.

 sum(arg1, arg2, arg3, arg4)

Evaluates a finite symbolic sum over an integer index.

Complex

arg(arg1)

Returns the principal argument of a complex expression.

 conjugate(arg1)

Returns the complex conjugate of an expression.

 csgn(arg1)

Returns the complex sign used by Nerdamer's branch-sensitive simplification rules.

 imagpart(arg1)

Returns the imaginary component of a complex expression.

 polarform(arg1)

Converts a complex expression toward polar exponential form.

 realpart(arg1)

Returns the real component of a complex expression.

 rectform(arg1)

Converts supported polar complex forms toward rectangular form.

Linear algebra

augment(left, right)

Horizontally joins two matrices with the same number of rows.

 cross(arg1, arg2)

Computes the cross product of two three-dimensional vectors.

 determinant(arg1)

Computes the determinant of a square matrix.

 dot(arg1, arg2)

Computes the dot product of two vectors.

 imatrix(arg1)

Creates an identity matrix of the requested integer size.

 invert(arg1)

Returns the inverse of a square matrix.

 line(arg1, arg2, [arg3])

Returns the equation expression for the line through two two-dimensional points.

 matrix(row1[, row2, ...])

Constructs a matrix from row vectors.

 nullspace(matrix[, prime])

Returns a basis for the nullspace of a matrix.

 rref(matrix[, prime])

Returns the reduced row-echelon form of a matrix.

 transpose(matrix)

Returns the transpose of a matrix.

Math

abs(arg1)

Computes the absolute value of an expression.

 cbrt(arg1)

Computes the cube root of an expression.

 ceil(arg1)

Rounds a numeric expression up to the nearest integer.

 ceiling(arg1)

Rounds a numeric expression up to the nearest integer.

 contains(arg1, arg2)

Tests membership in a supported finite container.

 continued_fraction(arg1, [arg2])

Returns a continued-fraction decomposition of a value.

 count(arg1)

Returns the number of entries in a supported container.

 degrees(arg1)

Converts an angle in radians to degrees exactly.

 delta(arg1)

Represents the Dirac delta distribution.

 dfact(arg1)

Computes the double factorial of an expression.

 erf(arg1)

Computes the error function.

 erfc(arg1)

Computes the complementary error function 1-erf(x).

 exp(arg1)

Computes the exponential function e raised to an expression.

 expand(arg1)

Expands an expression algebraically.

 fact(arg1)

Computes the factorial of an expression.

 factorial(arg1)

Computes the factorial of an expression.

 floor(arg1)

Rounds a numeric expression down to the nearest integer.

 gamma(arg1)

Computes the gamma function.

 heaviside(arg1)

Computes the Heaviside step function.

 hypot(arg1, arg2)

Computes the Euclidean magnitude sqrt(x^2+y^2).

 log(arg1, [arg2])

Computes the natural logarithm or a logarithm with an explicit base.

 log10(arg1)

Returns the base-10 logarithm of an expression.

 max(arg1, arg2, ...)

Returns the greatest value when the arguments can be ordered.

 min(arg1, arg2, ...)

Returns the smallest value when the arguments can be ordered.

 mod(arg1, arg2)

Computes the remainder modulo another expression for supported numeric inputs.

 modinv(arg1, arg2)

Computes a modular multiplicative inverse.

 nthroot(arg1, arg2)

Computes the nth root as a principal fractional power.

 numeric(value[, precision])

Evaluates a numeric value to a finite number of significant decimal digits.

 parens(arg1)

Wraps an expression in explicit parentheses for output.

 radians(arg1)

Converts an angle in degrees to radians exactly.

 rect(arg1)

Computes a unit-width rectangular pulse centered at zero.

 round(arg1, [arg2])

Rounds a number to a requested number of decimal places.

 scientific(value[, significantDigits])

Formats numeric values in scientific notation while preserving the expression's mathematical value.

 sign(arg1)

Returns the sign of a real expression when it can be determined.

 size(value)

Returns the dimensions of a structured parser value.

 sqrt(arg1)

Computes the principal square root of an expression.

 step(arg1)

Computes the legacy unit step function.

 subst(arg1, arg2, arg3)

Substitutes one expression for another inside an expression tree.

 tri(arg1)

Computes a triangular pulse centered at zero.

 trunc(arg1)

Truncates a numeric expression toward zero.

Polynomials

coeffs(expression[, variable])

Returns dense polynomial coefficients from constant term upward.

 content(arg1)

Returns the exact numeric content of a polynomial.

 deg(arg1, [arg2])

Returns the degree of a polynomial expression.

 div(arg1, arg2)

Performs polynomial division and returns quotient and remainder.

 divide(arg1, arg2)

Divides expressions using polynomial quotient/remainder reconstruction when possible.

Solving

roots(expression[, variable])

Returns legacy-style polynomial roots as a Vector.

 solve(expressionOrEquation, variable)

Solves an expression or equation for a variable and returns the solutions as a SolutionSet.

 solveeqs(arg1)

Solves linear, nonlinear, symbolic, and supported non-polynomial systems and returns solution assignments.

Special functions

Chi(arg1)

Computes the hyperbolic cosine integral.

 Ci(arg1)

Computes the cosine integral.

 Ei(arg1)

Computes the exponential integral.

 fib(arg1)

Computes a Fibonacci number for an integer index.

 gamma_incomplete(arg1, arg2)

Computes the upper incomplete gamma function.

 gamma_incomplete_lower(arg1, arg2)

Computes the lower incomplete gamma function.

 isprime(arg1)

Tests whether an exact integer is prime.

 Li(arg1)

Computes the logarithmic integral.

 Shi(arg1)

Computes the hyperbolic sine integral.

 Si(arg1)

Computes the sine integral.

 sinc(arg1)

Computes the normalized sinc function, sin(x)/x.

Trigonometry

acos(arg1)

Computes the principal arccosine in radians.

 acosh(arg1)

Computes the principal inverse hyperbolic cosine.

 acot(arg1)

Computes the principal inverse cotangent.

 acoth(arg1)

Computes the principal inverse hyperbolic cotangent.

 acsc(arg1)

Computes the principal inverse cosecant.

 acsch(arg1)

Computes the principal inverse hyperbolic cosecant.

 asec(arg1)

Computes the principal inverse secant.

 asech(arg1)

Computes the principal inverse hyperbolic secant.

 asin(arg1)

Computes the principal arcsine in radians.

 asinh(arg1)

Computes the principal inverse hyperbolic sine.

 atan(arg1)

Computes the principal arctangent in radians.

 atan2(arg1, arg2)

Computes the quadrant-aware two-argument arctangent atan2(y,x).

 atanh(arg1)

Computes the principal inverse hyperbolic tangent.

 cos(arg1)

Computes the cosine of an angle in radians.

 cosh(arg1)

Computes the hyperbolic cosine.

 cot(arg1)

Computes the cotangent cos(x)/sin(x).

 coth(arg1)

Computes the hyperbolic cotangent 1/tanh(x).

 csc(arg1)

Computes the cosecant 1/sin(x).

 csch(arg1)

Computes the hyperbolic cosecant 1/sinh(x).

 sec(arg1)

Computes the secant 1/cos(x).

 sech(arg1)

Computes the hyperbolic secant 1/cosh(x).

 sin(arg1)

Computes the sine of an angle in radians.

 sinh(arg1)

Computes the hyperbolic sine.

 tan(arg1)

Computes the tangent of an angle in radians.

 tanh(arg1)

Computes the hyperbolic tangent.