• egg

## Documentation

### Miscellaneous Math Functions

#### Usage

`(import math-utils)`

#### number->sign

[procedure] (number->sign N) -> fixnum

Returns -1, 0, or +1 to represent the sign of the number N.

#### log/base

[procedure] (log-with-base B) -> (real -> real)
[procedure] (log/base B) -> (real -> real)

Returns a function for the base B logarithm.

#### coprime?

[procedure] (coprime? M [N0 ...]) -> boolean

Are the integers M N0 ... coprime?

#### pairwise-coprime?

[procedure] (pairwise-coprime? M [N0 ...]) -> boolean

Are the pairs of integers in M N0 ... coprime?

#### fxcoprime?

[procedure] (fxcoprime? M N) -> boolean

Are the fixnums M N coprime?

```(import (only (srfi 1) filter iota))
(import (only (math-utils) fxcoprime?))

(define (coprimes n)
(filter (cut fxcoprime? n <>) (iota (- n 1) 1)) )```
```(import (only (streams derived) stream-range stream-filter))
(import (only (math-utils) fxcoprime?))

(define (coprime-numbers-stream n)
(stream-filter (cut fxcoprime? n <>) (stream-range 1 n)) )```

#### simple-interest

[procedure] (simple-interest RATE TIME [PRIN]) -> number

The accumulation function, the principle is assumed 1. Returns the simple interest for the RATE over TIME.

RATE ; number ; interest rate
TIME ; number ; time period to cover
PRIN ; number ; principle, default 1

#### compound-interest

[procedure] (compound-interest RATE FREQ TIME [PRIN]) -> number

The accumulation function, the principle is assumed 1. Returns the compound interest for the RATE, applied with FREQ, over TIME.

RATE ; number ; interest rate
FREQ ; number ; compounding frequency
TIME ; number ; time period to cover
PRIN ; number ; principle, default 1
```(compound-interest 0.043 4 6 1500)
;=> 1938.84 ;rounded to 2 places```

#### fibonacci

[procedure] (fibonacci N) -> number

Returns fibonacci of N.

#### fibonacci*

[procedure] (fibonacci* N) -> number

Returns an approximate fibonacci of N.

#### binomial

[procedure] (binomial N1 N2) -> integer

Returns the Binomial in N1 to N2.

N1 ; integer
N2 ; integer

#### cross-ratio

[procedure] (cross-ratio N1 N2 N3 N4) -> number

Returns the Cross-ratio of N1, N2 and N3, N4.

N1 ; number
N2 ; number
N3 ; number
N4 ; number

#### square

[procedure] (square N) -> number

#### cube

[procedure] (cube N) -> number

#### average

[procedure] (average N1 N2 ...) -> number
[procedure] (average NUMS) -> number
N1 ; number
N1 ; number
NUMS ; (list-of number)

#### least-squares

[procedure] (least-squares PNTS) -> number number

Returns b & e such that y ~= b * x + e.

PNTS ; (list-of (pair number number))
list of x,y pairs

#### trapezoid

[procedure] (trapezoid F N1 N2) -> (fixnum -> number)

Returns a function to calculate the area under F between N1 & N2 using the Trapezoid Rule. The function takes the number of estimations as an argument, larger for a "better" result.

F ; (number -> number)
N1 ; number
N2 ; number

#### factorial+

[procedure] (factorial N) -> number
[procedure] (factorial- N1 FALL) -> number
[procedure] (factorial+ N1 RISE) -> number
N ; integer
FALL
number : falling factorial
RISE
number : rising factorial

#### harmonic

[procedure] (harmonic N) -> number

Result of Harmonic series expansion to N terms.

N ; integer

#### big-pi

[syntax] (big-pi F N1 N2) -> number

Product of F in N1 to N2.

F
(number -> number) ;
N1
number ;
N2
number ;

#### big-sigma

[syntax] (big-sigma F N1 N2) -> number

Sum of F in N1 to N2.

F
(number -> number) ;
N1
number ;
N2
number ;

### Miscellaneous Vector Math Functions

#### Usage

`(import (math-utils vector))`

#### absolute-magnitude

[procedure] (absolute-magnitude NUMVEC) -> number
NUMVEC ; (vector-of number)
.

#### cosine-similarity

[procedure] (cosine-similarity NUMVEC1 NUMVEC2) -> number
NUMVEC1 ; (vector-of number)
.
NUMVEC2 ; (vector-of number)
.

Must be same vector-length.

#### vector-compare

[procedure] (vector-compare NUMVEC...) -> number

Result is negative, zero, or positive. Comparison by length when unequal & element-wise when equal.

NUMVEC ; (vector-of number)
.

#### dot-product

[procedure] (dot-product NUMVEC1 NUMVEC2) -> number
NUMVEC1 ; (vector-of number)
.
NUMVEC2 ; (vector-of number)
.

Must be same vector-length.

#### cross-product

[procedure] (cross-product NUMVEC1 NUMVEC2) -> (or number (vector-of number))
NUMVEC1 ; (vector-of number)
.
NUMVEC2 ; (vector-of number)
.

Must be same vector-length.

Only defined for a vector-length of (0 1 2), returning a number, and (3 4 8), returning a (vector-of number). All others generate an error.

#### vector-gcd

[procedure] (vector-mul NUMVEC...) -> (vector-of number)
[procedure] (vector-sum NUMVEC...) -> (vector-of number)
[procedure] (vector-div NUMVEC...) -> (vector-of number)
[procedure] (vector-dif NUMVEC...) -> (vector-of number)
[procedure] (vector-min NUMVEC...) -> (vector-of number)
[procedure] (vector-max NUMVEC...) -> (vector-of number)
[procedure] (vector-lcm NUMVEC...) -> (vector-of number)
[procedure] (vector-gcd NUMVEC...) -> (vector-of number)
NUMVEC ; (vector-of number)
.

Must be same vector-length.

#### vector-apply

[procedure] (vector-apply FUNC VEC1 VEC2 [VEC...]) -> vector
FUNC ; (* * !#rest * -> *)
.
VEC# ; vector
.

Must be same vector-length.

Kon Lovett

## Repository

This egg is hosted on the CHICKEN Subversion repository:

https://anonymous@code.call-cc.org/svn/chicken-eggs/release/5/math-utils

If you want to check out the source code repository of this egg and you are not familiar with Subversion, see this page.

## Version history

1.0.6
Remove mathh dependency since include is unreliable.
1.0.5
Use gcd based algorithm.
1.0.4