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This module provides several mathematical functions which are likely to be used frequently on the Xenharmonic Wiki. | This module provides several mathematical functions which are likely to be used frequently on the Xenharmonic Wiki. | ||
Namely, the functions in this module can be called from other modules by using <code>require( | Namely, the functions in this module can be called from other modules by using <code>require("Module:Utils")</code> and calling the <code>_</code>-prefixed functions. | ||
== Functions == | == Functions == | ||
* <code>table_contains(tbl, x)</code> Check if table contains x. This function is designed to be used by other modules only; it cannot be called with <code | * <code>table_contains(tbl, x)</code> Check if table contains x. This function is designed to be used by other modules only; it cannot be called with <code>{{((}}#invoke:{{))}}</code>. | ||
* <code>index_of(array, index)</code> Return the first index with the given value (or nil if not found). This function is designed to be used by other modules only; it cannot be called with <code | * <code>index_of(array, index)</code> Return the first index with the given value (or nil if not found). This function is designed to be used by other modules only; it cannot be called with <code>{{((}}#invoke:{{))}}</code>. | ||
* <code>value_provided(s)</code> checks if <code>s</code> is a non-empty string. This function is designed to be used by other modules only; it cannot be called with <code | * <code>value_provided(s)</code> checks if <code>s</code> is a non-empty string. This function is designed to be used by other modules only; it cannot be called with <code>{{((}}#invoke:{{))}}</code>. | ||
* <code>eval_num_arg(input, def_value)</code> checks if <code>input</code> is a number; on error, use <code>def_value</code>. This function is designed to be used by other modules only; it cannot be called with <code | * <code>eval_num_arg(input, def_value)</code> checks if <code>input</code> is a number; on error, use <code>def_value</code>. This function is designed to be used by other modules only; it cannot be called with <code>{{((}}#invoke:{{))}}</code>. | ||
* <code>log(x, b)</code> returns the logarithm base <code>b</code> of <code>x</code>. Parameter <code>b</code> defaults to base 2 (octave) if it is omitted. | * <code>log(x, b)</code> returns the logarithm base <code>b</code> of <code>x</code>. Parameter <code>b</code> defaults to base 2 (octave) if it is omitted. | ||
* <code>gcd(a, b)</code> returns the greatest common divisor of <code>a</code> and <code>b</code>. | * <code>gcd(a, b)</code> returns the greatest common divisor of <code>a</code> and <code>b</code>. | ||
* <code>round_dec(x, places)</code> returns <code>x</code> rounded to a precision of <code>places</code> decimal places. Parameter <code>places</code> defaults to 0 if it is omitted. | * <code>round_dec(x, places)</code> returns <code>x</code> rounded to a precision of <code>places</code> decimal places. Parameter <code>places</code> defaults to 0 if it is omitted. | ||
* <code>round(x, prec)</code> returns <code>x</code> rounded to a precision of <code>prec</code> significant figures. Parameter <code>prec</code> defaults to 6 if it is omitted. | * <code>round(x, prec)</code> returns <code>x</code> rounded to a precision of <code>prec</code> significant figures. Parameter <code>prec</code> defaults to 6 if it is omitted. | ||
* <code>is_prime(n)</code> returns <code>true</code> if the given integer <code>n</code> is a prime number. This function is designed to be used by other modules only; it cannot be called with <code | * <code>is_prime(n)</code> returns <code>true</code> if the given integer <code>n</code> is a prime number. This function is designed to be used by other modules only; it cannot be called with <code>{{((}}#invoke:{{))}}</code>. | ||
* <code>prime_factorization(n)</code> returns the prime factorization of the given integer <code>n</code> using the exponential form (in wikitext). | * <code>prime_factorization(n)</code> returns the prime factorization of the given integer <code>n</code> using the exponential form (in wikitext). | ||
* <code>prime_factorization_raw(n)</code> returns a table encoding the prime factorization of <code>n</code>. This function is designed to be used by other modules only; it cannot be called with <code | * <code>prime_factorization_raw(n)</code> returns a table encoding the prime factorization of <code>n</code>. This function is designed to be used by other modules only; it cannot be called with <code>{{((}}#invoke:{{))}}</code>. | ||
* <code>signum(x)</code> returns 1 for positive numbers, -1 for negative ones, 0 for zero and non-integer inputs. This function is designed to be used by other modules only; it cannot be called with <code | * <code>signum(x)</code> returns 1 for positive numbers, -1 for negative ones, 0 for zero and non-integer inputs. This function is designed to be used by other modules only; it cannot be called with <code>{{((}}#invoke:{{))}}</code>. | ||
* <code>next_young_diagram(d)</code> returns the next Young diagram of the same size; the first one is <code> | * <code>next_young_diagram(d)</code> returns the next Young diagram of the same size; the first one is <code>{{!(}}N{{)!}}</code>, the last one is <code>{{!(}}1, 1, ..., 1{{)!}}</code>. After the last one, <code>nil</code> is returned. The input table is modified. This function is designed to be used by other modules only; it cannot be called with <code>{{((}}#invoke:{{))}}</code>. | ||
Revision as of 19:02, 10 July 2024
This module provides several mathematical functions which are likely to be used frequently on the Xenharmonic Wiki.
Namely, the functions in this module can be called from other modules by using require("Module:Utils") and calling the _-prefixed functions.
Functions
table_contains(tbl, x)Check if table contains x. This function is designed to be used by other modules only; it cannot be called with{{#invoke:}}.index_of(array, index)Return the first index with the given value (or nil if not found). This function is designed to be used by other modules only; it cannot be called with{{#invoke:}}.value_provided(s)checks ifsis a non-empty string. This function is designed to be used by other modules only; it cannot be called with{{#invoke:}}.eval_num_arg(input, def_value)checks ifinputis a number; on error, usedef_value. This function is designed to be used by other modules only; it cannot be called with{{#invoke:}}.log(x, b)returns the logarithm basebofx. Parameterbdefaults to base 2 (octave) if it is omitted.gcd(a, b)returns the greatest common divisor ofaandb.round_dec(x, places)returnsxrounded to a precision ofplacesdecimal places. Parameterplacesdefaults to 0 if it is omitted.round(x, prec)returnsxrounded to a precision ofprecsignificant figures. Parameterprecdefaults to 6 if it is omitted.is_prime(n)returnstrueif the given integernis a prime number. This function is designed to be used by other modules only; it cannot be called with{{#invoke:}}.prime_factorization(n)returns the prime factorization of the given integernusing the exponential form (in wikitext).prime_factorization_raw(n)returns a table encoding the prime factorization ofn. This function is designed to be used by other modules only; it cannot be called with{{#invoke:}}.signum(x)returns 1 for positive numbers, -1 for negative ones, 0 for zero and non-integer inputs. This function is designed to be used by other modules only; it cannot be called with{{#invoke:}}.next_young_diagram(d)returns the next Young diagram of the same size; the first one is[N], the last one is[1, 1, ..., 1]. After the last one,nilis returned. The input table is modified. This function is designed to be used by other modules only; it cannot be called with{{#invoke:}}.