S-Lang Run-Time Library Reference: Version 1.4.0: Mathematical Functions

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## 6. Mathematical Functions

## 6.1 Conj

Synopsis

  Compute the complex conjugate of a number

Usage

  `z1 = Conj (z)`

Description

  The `Conj` function returns the complex conjugate of a number. If its argument is an array, the `Conj` function will be applied to each element and the result returned as an array.

See Also

  `Real, Imag, abs`

## 6.2 Imag

Synopsis

  Compute the imaginary part of a number

Usage

  `i = Imag (z)`

Description

  The `Imag` function returns the imaginary part of a number. If its argument is an array, the `Imag` function will be applied to each element and the result returned as an array.

See Also

  `Real, Conj, abs`

## 6.3 Real

Synopsis

  Compute the real part of a number

Usage

  `r = Real (z)`

Description

  The `Real` function returns the real part of a number. If its argument is an array, the `Real` function will be applied to each element and the result returned as an array.

See Also

  `Imag, Conj, abs`

## 6.4 abs

Synopsis

  Compute the absolute value of a number

Usage

  `y = abs(x)`

Description

  The `abs` function returns the absolute value of an arithmetic type. If its argument is a complex number (`Complex_Type`), then it returns the modulus. If the argument is an array, a new array will be created whose elements are obtained from the original array by using the `abs` function.

See Also

  `sign, sqr`

## 6.5 acos

Synopsis

  Compute the arc-cosine of an number

Usage

  `y = acos (x)`

Description

  The `acos` function computes the arc-cosine of a number and returns the result as an array. If its argument is an array, the `acos` function will be applied to each element and the result returned as an array.

See Also

  `cos, atan, acosh, cosh`

## 6.6 acosh

Synopsis

  Compute the inverse cosh of an number

Usage

  `y = acosh (x)`

Description

  The `acosh` function computes the inverse cosh of a number and returns the result as an array. If its argument is an array, the `acosh` function will be applied to each element and the result returned as an array.

See Also

  `cos, atan, acosh, cosh`

## 6.7 asin

Synopsis

  Compute the arc-sine of an number

Usage

  `y = asin (x)`

Description

  The `asin` function computes the arc-sine of a number and returns the result as an array. If its argument is an array, the `asin` function will be applied to each element and the result returned as an array.

See Also

  `cos, atan, acosh, cosh`

## 6.8 asinh

Synopsis

  Compute the inverse-sinh of an number

Usage

  `y = asinh (x)`

Description

  The `asinh` function computes the inverse-sinh of a number and returns the result as an array. If its argument is an array, the `asinh` function will be applied to each element and the result returned as an array.

See Also

  `cos, atan, acosh, cosh`

## 6.9 atan

Synopsis

  Compute the arc-tangent of an number

Usage

  `y = atan (x)`

Description

  The `atan` function computes the arc-tangent of a number and returns the result as an array. If its argument is an array, the `atan` function will be applied to each element and the result returned as an array.

See Also

  `cos, atan, acosh, cosh`

## 6.10 atanh

Synopsis

  Compute the inverse-tanh of an number

Usage

  `y = atanh (x)`

Description

  The `atanh` function computes the inverse-tanh of a number and returns the result as an array. If its argument is an array, the `atanh` function will be applied to each element and the result returned as an array.

See Also

  `cos, atan, acosh, cosh`

## 6.11 cos

Synopsis

  Compute the cosine of an number

Usage

  `y = cos (x)`

Description

  The `cos` function computes the cosine of a number and returns the result as an array. If its argument is an array, the `cos` function will be applied to each element and the result returned as an array.

See Also

  `cos, atan, acosh, cosh`

## 6.12 cosh

Synopsis

  Compute the hyperbolic cosine of an number

Usage

  `y = cosh (x)`

Description

  The `cosh` function computes the hyperbolic cosine of a number and returns the result as an array. If its argument is an array, the `cosh` function will be applied to each element and the result returned as an array.

See Also

  `cos, atan, acosh, cosh`

## 6.13 exp

Synopsis

  Compute the exponential of an number

Usage

  `y = exp (x)`

Description

  The `exp` function computes the exponential of a number and returns the result as an array. If its argument is an array, the `exp` function will be applied to each element and the result returned as an array.

See Also

  `cos, atan, acosh, cosh`

## 6.14 log

Synopsis

  Compute the logarithm of an number

Usage

  `y = log (x)`

Description

  The `log` function computes the logarithm of a number and returns the result as an array. If its argument is an array, the `log` function will be applied to each element and the result returned as an array.

See Also

  `cos, atan, acosh, cosh`

## 6.15 log10

Synopsis

  Compute the base-10 logarithm of an number

Usage

  `y = log10 (x)`

Description

  The `log10` function computes the base-10 logarithm of a number and returns the result as an array. If its argument is an array, the `log10` function will be applied to each element and the result returned as an array.

See Also

  `cos, atan, acosh, cosh`

## 6.16 mul2

Synopsis

  Multiply a number by 2

Usage

  `y = mul2(x)`

Description

  The `mul2` function multiplies an arithmetic type by two and returns the result. If its argument is an array, a new array will be created whose elements are obtained from the original array by using the `mul2` function.

See Also

  `sqr, abs`

## 6.17 polynom

Synopsis

  Evaluate a polynomial

Usage

  `Double_Type polynom(Double_Type a, b, ...c, Integer_Type n, Double_Type x)`

Description

  The `polynom` function returns the value of the polynomial expression:

  > `

  >          ax^n + bx^(n - 1) + ... c

  > `

Notes

  The `polynom` function should be extended to work with complex and array data types. The current implementation is limited to `Double_Type` quantities.

See Also

  `exp`

## 6.18 set_float_format

Synopsis

  Set the format for printing floating point values.

Usage

  `set_float_format (String_Type fmt)`

Description

  The `set_float_format` function is used to set the floating point format to be used when floating point numbers are printed. The routines that use this are the traceback routines and the `string` function. The default value is `"%f"`

Example

  > `

  >          s = string (PI);                %  --> s = "3.14159"
  >          set_float_format ("%16.10f");
  >          s = string (PI);                %  --> s = "3.1415926536"
  >          set_float_format ("%10.6e");
  >          s = string (PI);                %  --> s = "3.141593e+00"

  > `

See Also

  `string, sprintf, double`

## 6.19 sign

Synopsis

  Compute the sign of a number

Usage

  `y = sign(x)`

Description

  The `sign` function returns the sign of an arithmetic type. If its argument is a complex number (`Complex_Type`), it returns the sign of the imaginary part of the number. If the argument is an array, a new array will be created whose elements are obtained from the original array by using the `sign` function.

  When applied to a real number or an integer, the `sign` function returns `-1`, `0`, or `+1` according to whether the number is less than zero, equal to zero, or greater than zero, respectively.

See Also

  `abs`

## 6.20 sin

Synopsis

  Compute the sine of an number

Usage

  `y = sin (x)`

Description

  The `sin` function computes the sine of a number and returns the result as an array. If its argument is an array, the `sin` function will be applied to each element and the result returned as an array.

See Also

  `cos, atan, acosh, cosh`

## 6.21 sinh

Synopsis

  Compute the hyperbolic sine of an number

Usage

  `y = sinh (x)`

Description

  The `sinh` function computes the hyperbolic sine of a number and returns the result as an array. If its argument is an array, the `sinh` function will be applied to each element and the result returned as an array.

See Also

  `cos, atan, acosh, cosh`

## 6.22 sqr

Synopsis

  Compute the square of a number

Usage

  `y = sqr(x)`

Description

  The `sqr` function returns the square of an arithmetic type. If its argument is a complex number (`Complex_Type`), then it returns the square of the modulus. If the argument is an array, a new array will be created whose elements are obtained from the original array by using the `sqr` function.

See Also

  `abs, mul2`

## 6.23 sqrt

Synopsis

  Compute the square root of an number

Usage

  `y = sqrt (x)`

Description

  The `sqrt` function computes the square root of a number and returns the result as an array. If its argument is an array, the `sqrt` function will be applied to each element and the result returned as an array.

See Also

  `sqr, cos, atan, acosh, cosh`

## 6.24 tan

Synopsis

  Compute the tangent of an number

Usage

  `y = tan (x)`

Description

  The `tan` function computes the tangent of a number and returns the result as an array. If its argument is an array, the `tan` function will be applied to each element and the result returned as an array.

See Also

  `cos, atan, acosh, cosh`

## 6.25 tanh

Synopsis

  Compute the hyperbolic tangent of an number

Usage

  `y = tanh (x)`

Description

  The `tanh` function computes the hyperbolic tangent of a number and returns the result as an array. If its argument is an array, the `tanh` function will be applied to each element and the result returned as an array.

See Also

  `cos, atan, acosh, cosh`

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