# math > Native scalar and tensor scientific-math operations. > Generated by `sema doc` from the compiler's authoritative native-signature registry. # math (native) Scientific stdlib namespace — bring it in with `import math` (LANGUAGE §5.32). # unary ## `math.cos(x) -> float | Tensor` Cosine of x. - domain: finite real x (radians) - shape: elementwise - returns: `float | Tensor` - example: `math.cos(0.5)` ## `math.sin(x) -> float | Tensor` Sine of x. - domain: finite real x (radians) - shape: elementwise - returns: `float | Tensor` - example: `math.sin(0.5)` ## `math.tan(x) -> float | Tensor` Tangent of x. - domain: finite real x (radians) - shape: elementwise - returns: `float | Tensor` - example: `math.tan(0.5)` ## `math.acos(x) -> float | Tensor` Arc cosine, in radians. - domain: x in [-1, 1] - shape: elementwise - returns: `float | Tensor` - example: `math.acos(0.5)` ## `math.asin(x) -> float | Tensor` Arc sine, in radians. - domain: x in [-1, 1] - shape: elementwise - returns: `float | Tensor` - example: `math.asin(0.5)` ## `math.atan(x) -> float | Tensor` Arc tangent, in radians. - domain: finite real x - shape: elementwise - returns: `float | Tensor` - example: `math.atan(0.5)` ## `math.cosh(x) -> float | Tensor` Hyperbolic cosine. - domain: finite real x; result must stay finite - shape: elementwise - returns: `float | Tensor` - example: `math.cosh(0.5)` ## `math.sinh(x) -> float | Tensor` Hyperbolic sine. - domain: finite real x; result must stay finite - shape: elementwise - returns: `float | Tensor` - example: `math.sinh(0.5)` ## `math.tanh(x) -> float | Tensor` Hyperbolic tangent. - domain: finite real x - shape: elementwise - returns: `float | Tensor` - example: `math.tanh(0.5)` ## `math.acosh(x) -> float | Tensor` Inverse hyperbolic cosine. - domain: x >= 1 - shape: elementwise - returns: `float | Tensor` - example: `math.acosh(1.5)` ## `math.asinh(x) -> float | Tensor` Inverse hyperbolic sine. - domain: finite real x - shape: elementwise - returns: `float | Tensor` - example: `math.asinh(0.5)` ## `math.atanh(x) -> float | Tensor` Inverse hyperbolic tangent. - domain: x in (-1, 1) - shape: elementwise - returns: `float | Tensor` - example: `math.atanh(0.5)` ## `math.exp(x) -> float | Tensor` e raised to x. - domain: finite real x; result must stay finite - shape: elementwise - returns: `float | Tensor` - example: `math.exp(1.0)` ## `math.exp2(x) -> float | Tensor` 2 raised to x. - domain: finite real x; result must stay finite - shape: elementwise - returns: `float | Tensor` - example: `math.exp2(3.0)` ## `math.expm1(x) -> float | Tensor` exp(x) - 1, accurate near zero. - domain: finite real x; result must stay finite - shape: elementwise - returns: `float | Tensor` - example: `math.expm1(0.5)` ## `math.ln(x) -> float | Tensor` Natural logarithm. - domain: x > 0 - shape: elementwise - returns: `float | Tensor` - example: `math.ln(2.0)` ## `math.log2(x) -> float | Tensor` Base-2 logarithm. - domain: x > 0 - shape: elementwise - returns: `float | Tensor` - example: `math.log2(8.0)` ## `math.log10(x) -> float | Tensor` Base-10 logarithm. - domain: x > 0 - shape: elementwise - returns: `float | Tensor` - example: `math.log10(100.0)` ## `math.log1p(x) -> float | Tensor` ln(1 + x), accurate near zero. - domain: x > -1 - shape: elementwise - returns: `float | Tensor` - example: `math.log1p(0.5)` ## `math.sqrt(x) -> float | Tensor` Square root. - domain: x >= 0 - shape: elementwise - returns: `float | Tensor` - example: `math.sqrt(2.0)` ## `math.cbrt(x) -> float | Tensor` Cube root (defined for negative x). - domain: finite real x - shape: elementwise - returns: `float | Tensor` - example: `math.cbrt(-8.0)` ## `math.abs(x) -> float | Tensor` Absolute value (float kernel). - domain: finite real x - shape: elementwise - returns: `float | Tensor` - example: `math.abs(-2.5)` ## `math.fabs(x) -> float | Tensor` Absolute value (float kernel; alias of abs). - domain: finite real x - shape: elementwise - returns: `float | Tensor` - example: `math.fabs(-2.5)` ## `math.fract(x) -> float | Tensor` Fractional part (x - trunc(x)). - domain: finite real x - shape: elementwise - returns: `float | Tensor` - example: `math.fract(2.75)` ## `math.degrees(x) -> float | Tensor` Radians to degrees. - domain: finite real x (radians) - shape: elementwise - returns: `float | Tensor` - example: `math.degrees(1.0)` ## `math.rad2deg(x) -> float | Tensor` Radians to degrees (alias of degrees). - domain: finite real x (radians) - shape: elementwise - returns: `float | Tensor` - example: `math.rad2deg(1.0)` ## `math.radians(x) -> float | Tensor` Degrees to radians. - domain: finite real x (degrees) - shape: elementwise - returns: `float | Tensor` - example: `math.radians(180.0)` ## `math.deg2rad(x) -> float | Tensor` Degrees to radians (alias of radians). - domain: finite real x (degrees) - shape: elementwise - returns: `float | Tensor` - example: `math.deg2rad(180.0)` ## `math.recip(x) -> float | Tensor` Reciprocal 1/x. - domain: x != 0 - shape: elementwise - returns: `float | Tensor` - example: `math.recip(4.0)` ## `math.sign(x) -> float | Tensor` Sign of x as -1.0, 0.0 (signed zero), or 1.0. - domain: finite real x - shape: elementwise - returns: `float | Tensor` - example: `math.sign(-3.5)` ## `math.sgn(x) -> float | Tensor` Sign of x (alias of sign). - domain: finite real x - shape: elementwise - returns: `float | Tensor` - example: `math.sgn(-3.5)` ## `math.erf(x) -> float | Tensor` Gauss error function. - domain: finite real x - shape: elementwise - returns: `float | Tensor` - example: `math.erf(0.5)` ## `math.erfc(x) -> float | Tensor` Complementary error function 1 - erf(x). - domain: finite real x - shape: elementwise - returns: `float | Tensor` - example: `math.erfc(0.5)` ## `math.gamma(x) -> float | Tensor` Gamma function Γ(x). - domain: finite real x, not a nonpositive integer; result must stay finite - shape: elementwise - returns: `float | Tensor` - example: `math.gamma(4.5)` ## `math.lgamma(x) -> float | Tensor` Natural log of |Γ(x)|. - domain: finite real x, not a nonpositive integer - shape: elementwise - returns: `float | Tensor` - example: `math.lgamma(4.5)` ## `math.log(x, base?) -> float | Tensor` Natural logarithm, or the base-`base` logarithm with two arguments. - domain: x > 0; base > 0 and base != 1 when given - shape: elementwise - returns: `float | Tensor` - example: `math.log(81.0, 3.0)` # binary ## `math.atan2(y, x) -> float | Tensor` Arc tangent of y/x using both signs to pick the quadrant. - domain: finite reals (signed zeros respected) - shape: elementwise (binary broadcast) - returns: `float | Tensor` - example: `math.atan2(0.75, -0.25)` ## `math.hypot(x, y) -> float | Tensor` Euclidean norm sqrt(x² + y²) without intermediate overflow. - domain: finite reals; result must stay finite - shape: elementwise (binary broadcast) - returns: `float | Tensor` - example: `math.hypot(3.0, 4.0)` ## `math.copysign(magnitude, sign) -> float | Tensor` Magnitude of the first argument with the sign of the second. - domain: finite reals - shape: elementwise (binary broadcast) - returns: `float | Tensor` - example: `math.copysign(3.0, -0.0)` ## `math.pow(base, exponent) -> float | Tensor` base raised to exponent (float power). - domain: finite reals; negative base needs an integral exponent; result must stay finite - shape: elementwise (binary broadcast) - returns: `float | Tensor` - example: `math.pow(2.0, 10.5)` ## `math.fmod(x, y) -> float | Tensor` C-style remainder with the sign of x. - domain: finite reals, y != 0 - shape: elementwise (binary broadcast) - returns: `float | Tensor` - example: `math.fmod(-7.5, 2.0)` ## `math.remainder(x, y) -> float | Tensor` IEEE 754 remainder (nearest-multiple, ties to even). - domain: finite reals, y != 0 - shape: elementwise (binary broadcast) - returns: `float | Tensor` - example: `math.remainder(7.0, 2.0)` ## `math.nextafter(x, toward) -> float | Tensor` Next representable f64 after x toward the second argument. - domain: finite reals - shape: elementwise (binary broadcast) - returns: `float | Tensor` - example: `math.nextafter(1.0, 2.0)` # integer ## `math.factorial(n) -> int` n! with checked i64 overflow. - domain: int 0 <= n <= 20 (i64 result) - shape: scalar - returns: `int` - example: `math.factorial(12)` ## `math.comb(n, k) -> int` Binomial coefficient C(n, k) with checked i64 overflow. - domain: ints n >= 0, k >= 0 (0 when k > n) - shape: scalar - returns: `int` - example: `math.comb(10, 3)` ## `math.perm(n, k?) -> int` Partial permutations P(n, k) with checked i64 overflow. - domain: ints n >= 0, k >= 0 (k defaults to n; 0 when k > n) - shape: scalar - returns: `int` - example: `math.perm(10, 3)` ## `math.gcd(values...) -> int` Greatest common divisor of the arguments. - domain: any i64 ints (absolute values; 0 with no arguments) - shape: scalar - returns: `int` - example: `math.gcd(12, 18, 30)` ## `math.lcm(values...) -> int` Least common multiple of the arguments with checked i64 overflow. - domain: any i64 ints (0 if any argument is 0); checked overflow - shape: scalar - returns: `int` - example: `math.lcm(4, 6)` ## `math.isqrt(n) -> int` Integer square root: floor of the exact square root. - domain: int n >= 0 - shape: scalar - returns: `int` - example: `math.isqrt(17)` # rounding ## `math.floor(x) -> int | Tensor` Largest integer <= x. - domain: finite scalar (exact for int/rational; i64-checked result) or tensor (stays f64) - shape: elementwise - returns: `int | Tensor` - example: `math.floor(2.75)` ## `math.ceil(x) -> int | Tensor` Smallest integer >= x. - domain: finite scalar (exact for int/rational; i64-checked result) or tensor (stays f64) - shape: elementwise - returns: `int | Tensor` - example: `math.ceil(2.25)` ## `math.trunc(x) -> int | Tensor` Integer part of x (toward zero). - domain: finite scalar (exact for int/rational; i64-checked result) or tensor (stays f64) - shape: elementwise - returns: `int | Tensor` - example: `math.trunc(-2.75)` ## `math.round(x) -> int | Tensor` Nearest integer, ties to even. - domain: finite scalar (exact for int/rational; i64-checked result) or tensor (stays f64) - shape: elementwise - returns: `int | Tensor` - example: `math.round(2.5)` # tensor ## `math.tensor(data) -> Tensor` Build a typed Tensor from rectangular nested data. - domain: uniform nested numeric or bool data with optional matching f64/bool dtype; bounded rank/elements - shape: constructor - returns: `Tensor` - keywords: `dtype` - example: `math.tensor([1.0, 2.0], dtype="f64")` ## `math.matmul(a, b) -> Tensor` Matrix product (or matrix·vector), shape-checked. - domain: 2-D shapes (m,k)·(k,n), or matrix·vector; typed ShapeError otherwise - shape: contraction - returns: `Tensor` - example: `math.matmul(math.eye(2), math.ones([2, 2]))` ## `math.dot(a, b) -> float` Dot product of two vectors. - domain: two equal-length 1-D vectors (bounded reduction work) - shape: reduction - returns: `float` - example: `math.dot(math.tensor([1.0, 2.0]), math.tensor([3.0, 4.0]))` ## `math.zeros(shape) -> Tensor` Tensor of zeros with the given shape. - domain: nonnegative exact int or list/tuple of them (bounded elements) - shape: constructor - returns: `Tensor` - example: `math.zeros([2, 3])` ## `math.ones(shape) -> Tensor` Tensor of ones with the given shape. - domain: nonnegative exact int or list/tuple of them (bounded elements) - shape: constructor - returns: `Tensor` - example: `math.ones(3)` ## `math.eye(n) -> Tensor` n×n identity matrix. - domain: one nonnegative exact int dimension (bounded elements) - shape: constructor - returns: `Tensor` - example: `math.eye(2)` ## `math.arange(stop) -> Tensor` 1-D tensor of 0.0..stop-1. - domain: exact integer stop (negative yields an empty tensor; bounded elements) - shape: constructor - returns: `Tensor` - example: `math.arange(4)` # reduction ## `math.mean(values) -> int | rational | float | Tensor` Mean; exact rational for exact inputs, float once any float enters, or deterministic complex tensor reduction. - domain: non-empty iterable, or finite f64/complex tensor with optional integer axis/keepdims - shape: reduction - returns: `int | rational | float | Tensor` - keywords: `axis`, `keepdims` - example: `math.mean([1.0, 2.0, 4.0])` ## `math.sum(values, start?) -> int | rational | float | Tensor` Sum; exact for exact inputs, float once any float enters, or deterministic complex tensor reduction. - domain: iterable plus optional start, or finite f64/complex tensor with optional integer axis/keepdims - shape: reduction - returns: `int | rational | float | Tensor` - keywords: `start`, `axis`, `keepdims` - example: `math.sum([1, 2, 3], start=4)` # constant ## `math.pi: float` The circle constant π. - domain: attribute read; not callable - shape: scalar - returns: `float` - example: `math.pi` ## `math.e: float` Euler's number e. - domain: attribute read; not callable - shape: scalar - returns: `float` - example: `math.e` ## `math.tau: float` The circle constant τ = 2π. - domain: attribute read; not callable - shape: scalar - returns: `float` - example: `math.tau` ## `math.inf: float` Positive infinity (f64). - domain: attribute read; not callable - shape: scalar - returns: `float` - example: `math.inf` ## `math.nan: float` Quiet NaN (f64). - domain: attribute read; not callable - shape: scalar - returns: `float` - example: `math.nan`