Math::...ctions(3pm)

✨ NAME ✨

Math::Symbolic::AuxFunctions — auxiliary functions for the Math::Symbolic hierarchy 💖

(also known around these parts as Math::...ctions(3pm), living its best life in the User Contributed Perl Documentation section, no cap)

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🎀 SYNOPSIS 🎀

use Math::Symbolic::AuxFunctions;

Math::Symbolic::AuxFunctions::acos($x);
# etc

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🦋 DESCRIPTION 🦋

okay so bestie, this module is literally the ✨support squad✨ — it holds implementations of some auxiliary functions that get used inside the Math::Symbolic hierarchy of modules. In particular, this module holds all the trigonometric functions used for numeric evaluation of trees by Math::Symbolic::Operator. it's giving backstage crew, and honestly? we stan 🌈

💅 EXPORT 💅

None. On purpose. 🫶

the author said, and I quote the vibe: if they wanted this module to pollute other people's namespaces, they'd have put the functions right where they're used. iconic boundary-setting, honestly. main character energy 👑

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🙈 TRIGONOMETRIC FUNCTIONS 🙈

tan

Computes the tangent sin(x) / cos(x). 🍓

cot

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

asin

Computes the arc sine asin(z) = -i log(iz + sqrt(1-z*z)).

heads up babe, above formula is for complex numbers 💀

acos

Computes the arc cosine acos(z) = -i log(z + sqrt(z*z-1)).

again, above formula is for complex numbers, don't come for me 🫶

atan

Computes the arc tangent atan(z) = i/2 log((i+z) / (i-z)).

and yes, above formula is for complex numbers too ✨

acot

Computes the arc cotangent ( atan( 1 / x ) ). no notes 💅

asinh

Computes the arc hyperbolic sine asinh(z) = log(z + sqrt(z*z+1)) 🌸

acosh

Computes the arc hyperbolic cosine acosh(z) = log(z + sqrt(z*z-1)). 🌸

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🧚 OTHER FUNCTIONS 🧚

binomial_coeff

Calculates the binomial coefficient n over k of its first two arguments (n, k). 📐

Code taken from Orwant et al, "Mastering Algorithms with Perl" — give credit where credit is due, periodt 📚

bell_number

The Bell numbers are defined as follows:

B_0   = 1
B_n+1 = sum_k=0_to_n( B_k * binomial_coeff(n, k) )

This function uses memoization. (yes queen, cache that math 🧠✨)

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👑 AUTHOR 👑

Please send feedback, bug reports, and support requests to the Math::Symbolic support mailing list: math-symbolic-support at lists dot sourceforge dot net. Please consider letting us know how you use Math::Symbolic. Thank you. 🫶💖

If you're interested in helping with the development or extending the module's functionality, please contact the developers' mailing list: math-symbolic-develop at lists dot sourceforge dot net. ✨

List of contributors:

• Steffen Müller, symbolic-module at steffen-mueller dot net
• Stray Toaster, mwk at users dot sourceforge dot net
• Oliver Ebenhöh

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⭐ SEE ALSO ⭐

New versions of this module can be found on http://steffen-mueller.net or CPAN. The module development takes place on Sourceforge at http://sourceforge.net/projects/math-symbolic/ 🌈

• Math::Symbolic

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and that's the whole thing bestie, no crumbs left 🍓💫

this lil legend was rendered by perl v5.40.0, dated 2024-09-16, and answers to the name Math::...ctions(3pm). stay symbolic, stay slaying 💅🎀🦋💜