Function - Revision history

Jrheinlaender: /* Built-in other functions */

2024-12-26T11:54:36Z

Built-in other functions

← Older revision		Revision as of 11:54, 26 December 2024
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	=== Built-in other functions ===		=== Built-in other functions ===

			==== <code>denom ( [[expression]] ), numer ( [[expression]] )</code> ====
			Evaluates to the denominator resp. numerator of the expression.

	==== <code>iquo ( [[expression]] ; [[expression]] ), irem ( [[expression]] ; [[expression]] )</code> ====		==== <code>iquo ( [[expression]] ; [[expression]] ), irem ( [[expression]] ; [[expression]] )</code> ====

Jrheinlaender: /* Built-in other functions */

2024-12-26T11:51:45Z

Built-in other functions

← Older revision		Revision as of 11:51, 26 December 2024
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	=== Built-in other functions ===		=== Built-in other functions ===
	~~These functions take exactly two [[number\|numbers]] as arguments.~~
	* <code>max(x; y) min(x; y)</code>

			==== <code>iquo ( [[expression]] ; [[expression]] ), irem ( [[expression]] ; [[expression]] )</code> ====
			Evaluates to the integer quotient and remainder of the given fraction.

			==== <code>interpol ( [[expression]] ; [[expression]] ; [[expression\|expression ; expression ; expression]] )</code> ====
	This function linearly interpolates between two points given as pairs of (x,y)-values in the first four arguments. The fifth argument is the x-value for which the corresponding y-value should be interpolated.		This function linearly interpolates between two points given as pairs of (x,y)-values in the first four arguments. The fifth argument is the x-value for which the corresponding y-value should be interpolated.
	* <code>interpol(x1; y1; x2; y2; x)</code>

			==== <code>max ( [[expression]] ; [[expression]] ), min ( [[expression]] ; [[expression]] )</code> ====
			These functions take exactly two [[number\|numbers]] as arguments. For more general functions, see vmax and vmin.
	=== Built-in functions for vectors and matrices ===		=== Built-in functions for vectors and matrices ===
	====<code>charpoly ( [[expression]] )</code> ====		====<code>charpoly ( [[expression]] )</code> ====
	If the expression contains a matrix, evaluates to the [https://en.wikipedia.org/wiki/Characteristic_polynomial characteristic polynomial] of the matrix.		If the expression contains a matrix, evaluates to the [https://en.wikipedia.org/wiki/Characteristic_polynomial characteristic polynomial] of the matrix.

	~~====<code>concat ( [[expression\|expression ; expression]] )</code> ====~~
	~~If the expressions contain vectors or matrices with matching number of columns, evaluates to the concatenation of the expressions.~~

	====<code>det ( [[expression]] )</code> ====		====<code>det ( [[expression]] )</code> ====

Jrheinlaender: /* Built-in functions for vectors and matrices */

2024-12-26T11:02:28Z

Built-in functions for vectors and matrices

← Older revision		Revision as of 11:02, 26 December 2024
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	====<code>charpoly ( [[expression]] )</code> ====		====<code>charpoly ( [[expression]] )</code> ====
	If the expression contains a matrix, evaluates to the [https://en.wikipedia.org/wiki/Characteristic_polynomial characteristic polynomial] of the matrix.		If the expression contains a matrix, evaluates to the [https://en.wikipedia.org/wiki/Characteristic_polynomial characteristic polynomial] of the matrix.

			====<code>concat ( [[expression\|expression ; expression]] )</code> ====
			If the expressions contain vectors or matrices with matching number of columns, evaluates to the concatenation of the expressions.

	====<code>det ( [[expression]] )</code> ====		====<code>det ( [[expression]] )</code> ====

Jrheinlaender: /* Built-in trigonometric functions */

2024-09-08T18:01:42Z

Built-in trigonometric functions

← Older revision		Revision as of 18:01, 8 September 2024
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	=== Built-in trigonometric functions ===		=== Built-in trigonometric functions ===
	The following trigonometric functions are known to iMath. They all take exactly one argument.		The following trigonometric functions are known to iMath. They all take exactly one argument.
	* <code>cos cosh ~~arcsin~~ arccos</code>		* <code>cos cosh arccos arcosh</code>
	* <code>sin sinh arsinh ~~arcosh~~</code>		* <code>sin sinh arcsin arsinh</code>
	* <code>tan tanh arctan artanh</code>		* <code>tan tanh arctan artanh</code>
	* <code>cot coth arccot arcoth</code>		* <code>cot coth arccot arcoth</code>

Jrheinlaender: /* reducematrix ( expression; expression; expression) */

2021-08-24T15:43:40Z

reducematrix ( expression; expression; expression)

← Older revision		Revision as of 15:43, 24 August 2021
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	====<code>reducematrix ( [[expression]]; [[expression]]; [[expression]])</code> ====		====<code>reducematrix ( [[expression]]; [[expression]]; [[expression]])</code> ====
	If the first expression is a matrix, and the other expressions evaluate to positive integers, creates a new matrix from the given matrix where the given row and column (second and third expression) are omitted. ~~Note that row and column count starts at zero!~~		If the first expression is a matrix, and the other expressions evaluate to positive integers, creates a new matrix from the given matrix where the given row and column (second and third expression) are omitted.

	====<code>scalprod ( [[expression]] ; [[expression]] )</code>====		====<code>scalprod ( [[expression]] ; [[expression]] )</code>====

Jrheinlaender: /* Built-in functions for vectors and matrices */

2021-08-23T18:13:12Z

Built-in functions for vectors and matrices

← Older revision		Revision as of 18:13, 23 August 2021
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	If the expression contains a matrix, evaluates to the determinant of the matrix.		If the expression contains a matrix, evaluates to the determinant of the matrix.

	====<code>~~diag_matrix~~ ( [[expression]] )</code> ====		====<code>diag ( [[expression]] )</code> ====
	If the expression contains a (row or column) vector, creates a matrix with the elements of the vector in the diagonal.		If the expression contains a (row or column) vector, creates a matrix with the elements of the vector in the diagonal.

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	If both first and second expression are vectors or matrices of equal dimensions, calculates their element-wise product (if the third expression is 0), division (if the third expression is 1) or power (if the third expression is 2). Usually, this function is not used directly. Rather, the [[Operator\|operators]] <code>.*</code>, <code>./</code> and <code>.^</code> should be used. The element-wise product is also called the [https://en.wikipedia.org/wiki/Hadamard_product_(matrices) Hadamard product].		If both first and second expression are vectors or matrices of equal dimensions, calculates their element-wise product (if the third expression is 0), division (if the third expression is 1) or power (if the third expression is 2). Usually, this function is not used directly. Rather, the [[Operator\|operators]] <code>.*</code>, <code>./</code> and <code>.^</code> should be used. The element-wise product is also called the [https://en.wikipedia.org/wiki/Hadamard_product_(matrices) Hadamard product].

	====<code>~~matrix_cols~~ ( [[expression]] )</code> ====		====<code>invertmatrix ( [[expression]] )</code> ====
			If the expression contains a matrix, inverts the matrix.

			====<code>matrixcols ( [[expression]] )</code> ====
	If the expression contains a matrix, counts the number of columns of the matrix.		If the expression contains a matrix, counts the number of columns of the matrix.

	====<code>~~matrix_inverse ( [[expression]] )</code> ====~~		====<code>matrixrows ( [[expression]] )</code> ====
	~~If the expression contains a matrix, inverts the matrix.~~

	~~====<code>matrix_rows~~ ( [[expression]] )</code> ====
	If the expression contains a matrix, counts the number of rows of the matrix.		If the expression contains a matrix, counts the number of rows of the matrix.

	~~====<code>matrix_solve ( [[expression]] ; [[expression]] ; [[expression]] )</code> ====~~
	~~Solves the linear system with the matrix of the first expression, the variables of the second expression and the right-hand side of the third expression.~~

	====<code>mindex ( [[expression]] ; [[expression]] ; [[expression]] )</code>====		====<code>mindex ( [[expression]] ; [[expression]] ; [[expression]] )</code>====
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	See also [[Vector and matrix element access]].		See also [[Vector and matrix element access]].

	====<code>~~ones_matrix~~ ( [[expression]]; [[expression]] )</code> ====		====<code>ones ( [[expression]]; [[expression]] )</code> ====
	If the two first expressions evaluate to positive integers, creates a matrix filled with ones.		If the two first expressions evaluate to positive integers, creates a matrix filled with ones.

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	If the expression contains a matrix, evaluates to the rank of the matrix.		If the expression contains a matrix, evaluates to the rank of the matrix.

	====<code>~~reduced_matrix~~ ( [[expression]]; [[expression]]; [[expression]])</code> ====		====<code>reducematrix ( [[expression]]; [[expression]]; [[expression]])</code> ====
	If the first expression is a matrix, and the other expressions evaluate to positive integers, creates a new matrix from the given matrix where the given row and column (second and third expression) are omitted. Note that row and column count starts at zero!		If the first expression is a matrix, and the other expressions evaluate to positive integers, creates a new matrix from the given matrix where the given row and column (second and third expression) are omitted. Note that row and column count starts at zero!

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	If both expressions are vectors, evaluates to their [https://en.wikipedia.org/wiki/Dot_product scalar product]. The vector product can only be calculated from a column and a row vector of equal length. Any other dimensions will leave the function unchanged.		If both expressions are vectors, evaluates to their [https://en.wikipedia.org/wiki/Dot_product scalar product]. The vector product can only be calculated from a column and a row vector of equal length. Any other dimensions will leave the function unchanged.

	====<code>~~sub_matrix~~ ( [[expression]]; [[expression]]; [[expression]]; [[expression]]; [[expression]])</code> ====		====<code>solvematrix ( [[expression]] ; [[expression]] ; [[expression]] )</code> ====
			Solves the linear system with the matrix of the first expression, the variables of the second expression and the right-hand side of the third expression.

			====<code>submatrix ( [[expression]]; [[expression]]; [[expression]]; [[expression]]; [[expression]])</code> ====
	If the first expression is a matrix, and the other expressions evaluate to positive integers, creates a new matrix from the given matrix containing the elements beginning at the given offset (second and fourth expression) and having the given number of rows and columns (third and fifth expression). Note that row and column count starts at zero!		If the first expression is a matrix, and the other expressions evaluate to positive integers, creates a new matrix from the given matrix containing the elements beginning at the given offset (second and fourth expression) and having the given number of rows and columns (third and fifth expression). Note that row and column count starts at zero!

	~~====<code>symbolic_matrix ( [[expression]] ; [[expression]] ; [[expression]] )</code> ====~~
	If the two first expressions evaluate to positive integers and the third expression is a string, creates a matrix of the given dimensions filled with symbols of the given base name. For example, <code>symbolic_matrix(2;2;"x")</code> creates the matrix <code>(MATRIX{x_00 # x_01 ## x_10 # x_11})</code>.

	====<code>tr ( [[expression]] )</code> ====		====<code>tr ( [[expression]] )</code> ====
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	If the expression contains a vector or matrix, evaluates to the transposed vector or matrix.		If the expression contains a vector or matrix, evaluates to the transposed vector or matrix.

	====<code>~~unit_matrix~~ ( [[expression]] ; [[expression]] )</code> ====		====<code>ident ( [[expression]] ; [[expression]] )</code> ====
	If the two expressions evaluate to positive integers, creates a [https://en.wikipedia.org/wiki/Identity_matrix unit matrix] of the given dimensions.		If the two expressions evaluate to positive integers, creates a [https://en.wikipedia.org/wiki/Identity_matrix unit matrix] of the given dimensions.

Jrheinlaender: /* Built-in functions for vectors and matrices */

2021-08-22T19:42:43Z

Built-in functions for vectors and matrices

← Older revision		Revision as of 19:42, 22 August 2021
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	====<code>hadamard ( [[expression]] ; [[expression]] ; [[expression]] )</code>====		====<code>hadamard ( [[expression]] ; [[expression]] ; [[expression]] )</code>====
	If both first and second expression are vectors or matrices of equal dimensions, calculates their element-wise product (if the third expression is 0), division (if the third expression is 1) or power (if the third expression is 2). Usually, this function is not used directly. Rather, the [[Operator\|operators]] <code>.*</code>, <code>./</code> and <code>.^</code> should be used. The element-wise product is also called the [https://en.wikipedia.org/wiki/Hadamard_product_(matrices) Hadamard product].		If both first and second expression are vectors or matrices of equal dimensions, calculates their element-wise product (if the third expression is 0), division (if the third expression is 1) or power (if the third expression is 2). Usually, this function is not used directly. Rather, the [[Operator\|operators]] <code>.*</code>, <code>./</code> and <code>.^</code> should be used. The element-wise product is also called the [https://en.wikipedia.org/wiki/Hadamard_product_(matrices) Hadamard product].

			====<code>matrix_cols ( [[expression]] )</code> ====
			If the expression contains a matrix, counts the number of columns of the matrix.

			====<code>matrix_inverse ( [[expression]] )</code> ====
			If the expression contains a matrix, inverts the matrix.

			====<code>matrix_rows ( [[expression]] )</code> ====
			If the expression contains a matrix, counts the number of rows of the matrix.

			====<code>matrix_solve ( [[expression]] ; [[expression]] ; [[expression]] )</code> ====
			Solves the linear system with the matrix of the first expression, the variables of the second expression and the right-hand side of the third expression.

	====<code>mindex ( [[expression]] ; [[expression]] ; [[expression]] )</code>====		====<code>mindex ( [[expression]] ; [[expression]] ; [[expression]] )</code>====
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	====<code>ones_matrix ( [[expression]]; [[expression]] )</code> ====		====<code>ones_matrix ( [[expression]]; [[expression]] )</code> ====
	If the two first expressions evaluate to positive integers, creates a matrix filled with ones.		If the two first expressions evaluate to positive integers, creates a matrix filled with ones.

			====<code>rank ( [[expression]] )</code> ====
			If the expression contains a matrix, evaluates to the rank of the matrix.

			====<code>reduced_matrix ( [[expression]]; [[expression]]; [[expression]])</code> ====
			If the first expression is a matrix, and the other expressions evaluate to positive integers, creates a new matrix from the given matrix where the given row and column (second and third expression) are omitted. Note that row and column count starts at zero!

	====<code>scalprod ( [[expression]] ; [[expression]] )</code>====		====<code>scalprod ( [[expression]] ; [[expression]] )</code>====
	If both expressions are vectors, evaluates to their [https://en.wikipedia.org/wiki/Dot_product scalar product]. The vector product can only be calculated from a column and a row vector of equal length. Any other dimensions will leave the function unchanged.		If both expressions are vectors, evaluates to their [https://en.wikipedia.org/wiki/Dot_product scalar product]. The vector product can only be calculated from a column and a row vector of equal length. Any other dimensions will leave the function unchanged.

	====<code>~~ones_matrix~~ ( [[expression]]; [[expression]]; [[expression]]; [[expression]]; [[expression]])</code> ====		====<code>sub_matrix ( [[expression]]; [[expression]]; [[expression]]; [[expression]]; [[expression]])</code> ====
	If the first expression is a matrix, and the other expressions evaluate to positive integers, creates a new matrix from the given matrix containing the elements beginning at the given offset (second and fourth expression) and having the given number of rows and columns (third and fifth expression).		If the first expression is a matrix, and the other expressions evaluate to positive integers, creates a new matrix from the given matrix containing the elements beginning at the given offset (second and fourth expression) and having the given number of rows and columns (third and fifth expression). Note that row and column count starts at zero!

	====<code>symbolic_matrix ( [[expression]] ; [[expression]] ; [[expression]] )</code> ====		====<code>symbolic_matrix ( [[expression]] ; [[expression]] ; [[expression]] )</code> ====
	If the two first expressions evaluate to positive integers and the third expression is a string, creates a matrix of the given dimensions filled with symbols of the given base name. For example, <code>~~ones_matrix~~(2;2;"x")</code> creates the matrix <code>(MATRIX{x_00 # x_01 ## x_10 # x_11})</code>.		If the two first expressions evaluate to positive integers and the third expression is a string, creates a matrix of the given dimensions filled with symbols of the given base name. For example, <code>symbolic_matrix(2;2;"x")</code> creates the matrix <code>(MATRIX{x_00 # x_01 ## x_10 # x_11})</code>.

			====<code>tr ( [[expression]] )</code> ====
			If the expression contains a matrix, evaluates to the trace of the matrix.

	====<code>transpose ( [[expression]] )</code> ====		====<code>transpose ( [[expression]] )</code> ====

Jrheinlaender: /* Built-in functions for vectors and matrices */

2021-08-22T18:40:28Z

Built-in functions for vectors and matrices

← Older revision		Revision as of 18:40, 22 August 2021
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	=== Built-in functions for vectors and matrices ===		=== Built-in functions for vectors and matrices ===
	====<code>~~vmin~~ ( [[expression]] )</code> ====		====<code>charpoly ( [[expression]] )</code> ====
	If the expression contains a ~~vector or~~ matrix ~~of which all elements are [[number\|numbers]]~~, evaluates to the ~~smallest element.~~		If the expression contains a matrix, evaluates to the [https://en.wikipedia.org/wiki/Characteristic_polynomial characteristic polynomial] of the matrix.

	~~====<code>vmax (~~ [~~[expression]] )<~~/~~code> ====~~
	~~If the expression contains a vector or matrix of which all elements are [[number\|numbers]], evaluates to the greatest element~~.

	~~====<code>transpose ( [[expression~~]~~] )</code> ====~~
	~~If the expression contains a vector or matrix, evaluates to~~ the ~~transposed vector or~~ matrix.

	====<code>det ( [[expression]] )</code> ====		====<code>det ( [[expression]] )</code> ====
	If the expression contains a matrix, evaluates to the determinant of the matrix.		If the expression contains a matrix, evaluates to the determinant of the matrix.

	====<code>~~charpoly~~ ( [[expression]] )</code> ====		====<code>diag_matrix ( [[expression]] )</code> ====
	If the expression contains a matrix, ~~evaluates to~~ the [https://en.wikipedia.org/wiki/~~Characteristic_polynomial characteristic polynomial~~] ~~of the matrix~~.		If the expression contains a (row or column) vector, creates a matrix with the elements of the vector in the diagonal.

			====<code>hadamard ( [[expression]] ; [[expression]] ; [[expression]] )</code>====
			If both first and second expression are vectors or matrices of equal dimensions, calculates their element-wise product (if the third expression is 0), division (if the third expression is 1) or power (if the third expression is 2). Usually, this function is not used directly. Rather, the [[Operator\|operators]] <code>.*</code>, <code>./</code> and <code>.^</code> should be used. The element-wise product is also called the [https://en.wikipedia.org/wiki/Hadamard_product_(matrices) Hadamard product].

	====<code>mindex ( [[expression]] ; [[expression]] ; [[expression]] )</code>====		====<code>mindex ( [[expression]] ; [[expression]] ; [[expression]] )</code>====
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	See also [[Vector and matrix element access]].		See also [[Vector and matrix element access]].

			====<code>ones_matrix ( [[expression]]; [[expression]] )</code> ====
			If the two first expressions evaluate to positive integers, creates a matrix filled with ones.

			====<code>scalprod ( [[expression]] ; [[expression]] )</code>====
			If both expressions are vectors, evaluates to their [https://en.wikipedia.org/wiki/Dot_product scalar product]. The vector product can only be calculated from a column and a row vector of equal length. Any other dimensions will leave the function unchanged.

			====<code>ones_matrix ( [[expression]]; [[expression]]; [[expression]]; [[expression]]; [[expression]])</code> ====
			If the first expression is a matrix, and the other expressions evaluate to positive integers, creates a new matrix from the given matrix containing the elements beginning at the given offset (second and fourth expression) and having the given number of rows and columns (third and fifth expression).

			====<code>symbolic_matrix ( [[expression]] ; [[expression]] ; [[expression]] )</code> ====
			If the two first expressions evaluate to positive integers and the third expression is a string, creates a matrix of the given dimensions filled with symbols of the given base name. For example, <code>ones_matrix(2;2;"x")</code> creates the matrix <code>(MATRIX{x_00 # x_01 ## x_10 # x_11})</code>.

			====<code>transpose ( [[expression]] )</code> ====
			If the expression contains a vector or matrix, evaluates to the transposed vector or matrix.

			====<code>unit_matrix ( [[expression]] ; [[expression]] )</code> ====
			If the two expressions evaluate to positive integers, creates a [https://en.wikipedia.org/wiki/Identity_matrix unit matrix] of the given dimensions.

	====<code>vecprod ( [[expression]] ; [[expression]] )</code>====		====<code>vecprod ( [[expression]] ; [[expression]] )</code>====
	If both expressions are vectors, evaluates to their [https://en.wikipedia.org/wiki/Vector_product vector product]. The vector product can only be calculated with two row or column vectors of three components each. Any other dimensions will produce an error.		If both expressions are vectors, evaluates to their [https://en.wikipedia.org/wiki/Vector_product vector product]. The vector product can only be calculated with two row or column vectors of three components each. Any other dimensions will produce an error.

	====<code>~~scalprod~~ ( ~~[[expression]] ;~~ [[expression]] )</code>====		====<code>vmax ( [[expression]] )</code> ====
	If ~~both expressions~~ are ~~vectors~~, evaluates to ~~their [https://en.wikipedia.org/wiki/Dot_product scalar product]. The vector product can only be calculated from a column and a row vector of equal length. Any other dimensions will leave~~ the ~~function unchanged~~.		If the expression contains a vector or matrix of which all elements are [[number\|numbers]], evaluates to the greatest element.

	====<code>~~hadamard~~ ( ~~[[expression]] ; [[expression]] ;~~ [[expression]] )</code>====		====<code>vmin ( [[expression]] )</code> ====
	If ~~both first and second~~ expression ~~are vectors~~ or ~~matrices~~ of equal dimensions, calculates their element-wise product (if the third expression is 0), division (if the third expression is 1) or power (if the third expression is 2). Usually, this function is not used directly. Rather, the [[~~Operator~~\|~~operators~~]] ~~<code>.*</code>~~, ~~<code>./</code> and <code>.^</code> should be used. The~~ element~~-wise product is also called the [https://en.wikipedia.org/wiki/Hadamard_product_(matrices) Hadamard product]~~.		If the expression contains a vector or matrix of which all elements are [[number\|numbers]], evaluates to the smallest element.

	=== Functions for number display ===		=== Functions for number display ===

Jrheinlaender: /* hadamard ( expression ; expression ; expression ; expression ) */

2018-12-19T19:25:04Z

hadamard ( expression ; expression ; expression ; expression )

← Older revision		Revision as of 19:25, 19 December 2018
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	If both expressions are vectors, evaluates to their [https://en.wikipedia.org/wiki/Dot_product scalar product]. The vector product can only be calculated from a column and a row vector of equal length. Any other dimensions will leave the function unchanged.		If both expressions are vectors, evaluates to their [https://en.wikipedia.org/wiki/Dot_product scalar product]. The vector product can only be calculated from a column and a row vector of equal length. Any other dimensions will leave the function unchanged.

	====<code>hadamard ( ~~[[expression]] ;~~ [[expression]] ; [[expression]] ; [[expression]] )</code>====		====<code>hadamard ( [[expression]] ; [[expression]] ; [[expression]] )</code>====
	If both first and second expression are vectors or matrices of equal dimensions, calculates their element-wise product (if the third expression is 0), division (if the third expression is 1) or power (if the third expression is 2). Usually, this function is not used directly. Rather, the [[Operator\|operators]] <code>.*</code>, <code>./</code> and <code>.^</code> should be used. The element-wise product is also called the [https://en.wikipedia.org/wiki/Hadamard_product_(matrices) Hadamard product].		If both first and second expression are vectors or matrices of equal dimensions, calculates their element-wise product (if the third expression is 0), division (if the third expression is 1) or power (if the third expression is 2). Usually, this function is not used directly. Rather, the [[Operator\|operators]] <code>.*</code>, <code>./</code> and <code>.^</code> should be used. The element-wise product is also called the [https://en.wikipedia.org/wiki/Hadamard_product_(matrices) Hadamard product].

Jrheinlaender: /* hadamard ( expression ; expression ; expression ; expression ) */

2018-06-27T19:35:06Z

hadamard ( expression ; expression ; expression ; expression )

← Older revision		Revision as of 19:35, 27 June 2018
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	====<code>hadamard ( [[expression]] ; [[expression]] ; [[expression]] ; [[expression]] )</code>====		====<code>hadamard ( [[expression]] ; [[expression]] ; [[expression]] ; [[expression]] )</code>====
	If both first and second ~~expressions~~ are vectors or matrices of equal dimensions, calculates their element-wise product (if the third expression is 0), division (if the third expression is 1) or power (if the third expression is 2). Usually, this function is not used directly. Rather, the [[Operator\|operators]] <code>.*</code>, <code>./</code> and <code>.^</code> should be used. The element-wise product is also called the [https://en.wikipedia.org/wiki/Hadamard_product_(matrices) Hadamard product].		If both first and second expression are vectors or matrices of equal dimensions, calculates their element-wise product (if the third expression is 0), division (if the third expression is 1) or power (if the third expression is 2). Usually, this function is not used directly. Rather, the [[Operator\|operators]] <code>.*</code>, <code>./</code> and <code>.^</code> should be used. The element-wise product is also called the [https://en.wikipedia.org/wiki/Hadamard_product_(matrices) Hadamard product].

	=== Functions for number display ===		=== Functions for number display ===