Difference between revisions of "Factors Command"
From GeoGebra Manual
| Line 2: | Line 2: | ||
{{command|cas=true|function}} | {{command|cas=true|function}} | ||
;Factors[ <Polynomial> ] | ;Factors[ <Polynomial> ] | ||
| − | : | + | :Yields a list of lists of the type ''{factor, exponent}'' such that the product of all these factors raised to the power of the corresponding exponents equals the given polynomial. The factors are sorted by degree in descending order. |
| − | :{{example| 1=<div><code><nowiki>Factors[x^8 - 1]</nowiki></code> yields ''{{x^4 + 1, 1}, {x^2 + 1, 1}, {x + 1, 1}, {x - 1, 1}}''.</div>}} | + | :{{example| 1=<div><code><nowiki>Factors[x^8 - 1]</nowiki></code> yields ''{{x^4 + 1, 1}, {x^2 + 1, 1}, {x + 1, 1}, {x - 1, 1}}'', displayed as <math>\begin{pmatrix} |
| + | x^4+1&1\\ | ||
| + | x^2+1&1\\ | ||
| + | x+1&1\\ | ||
| + | x-1&1 | ||
| + | \end{pmatrix}</math>.</div>}} | ||
:{{note| 1=Not all of the factors are irreducible over the reals.}} | :{{note| 1=Not all of the factors are irreducible over the reals.}} | ||
;Factors[ <Number> ] | ;Factors[ <Number> ] | ||
| − | : | + | :Yields a list of lists of the type ''{prime, exponent}'' such that the product of all these primes raised to the power of the corresponding exponents equals the given number. The primes are sorted in ascending order. |
:{{example|1=<div> | :{{example|1=<div> | ||
| − | :* <code><nowiki>Factors[1024]</nowiki></code> yields ''<nowiki>{{2, 10}}</nowiki>'', | + | :* <code><nowiki>Factors[1024]</nowiki></code> yields ''<nowiki>{{2, 10}}</nowiki>'', displayed as <math>\begin{pmatrix} |
| − | :* <code><nowiki>Factors[42]</nowiki></code> yields ''{{2, 1}, {3, 1}, {7, 1}}'', | + | 2&10 |
| − | {{note| | + | \end{pmatrix}</math>, since <math>1024 = 2^{10}</math>. |
| + | :* <code><nowiki>Factors[42]</nowiki></code> yields ''{{2, 1}, {3, 1}, {7, 1}}'', displayed as <math>\begin{pmatrix} | ||
| + | 2&1\\ | ||
| + | 3&1\\ | ||
| + | 7&1 | ||
| + | \end{pmatrix}</math>, since <math>42 = 2^1 * 3^1 * 7^1</math>.</div>}} | ||
| + | {{note|See also [[PrimeFactors Command]] and [[Factor Command]].}} | ||
| + | |||
==CAS Syntax== | ==CAS Syntax== | ||
;Factors[ <Polynomial> ] | ;Factors[ <Polynomial> ] | ||
Revision as of 15:42, 13 September 2012
- Factors[ <Polynomial> ]
- Yields a list of lists of the type {factor, exponent} such that the product of all these factors raised to the power of the corresponding exponents equals the given polynomial. The factors are sorted by degree in descending order.
- Example:
Factors[x^8 - 1]yields {{x^4 + 1, 1}, {x^2 + 1, 1}, {x + 1, 1}, {x - 1, 1}}, displayed as \begin{pmatrix} x^4+1&1\\ x^2+1&1\\ x+1&1\\ x-1&1 \end{pmatrix}.- Note: Not all of the factors are irreducible over the reals.
- Factors[ <Number> ]
- Yields a list of lists of the type {prime, exponent} such that the product of all these primes raised to the power of the corresponding exponents equals the given number. The primes are sorted in ascending order.
- Example:
Factors[1024]yields {{2, 10}}, displayed as \begin{pmatrix} 2&10 \end{pmatrix}, since 1024 = 2^{10}.Factors[42]yields {{2, 1}, {3, 1}, {7, 1}}, displayed as \begin{pmatrix} 2&1\\ 3&1\\ 7&1 \end{pmatrix}, since 42 = 2^1 * 3^1 * 7^1.
Note: See also PrimeFactors Command and Factor Command.CAS Syntax
- Factors[ <Polynomial> ]
- Yields a list of lists of the type {factor, exponent} such that the product of all these factors raised to the power of the corresponding exponents equals the given polynomial. The factors are sorted by degree in descending order.
- Example:
Factors[x^8 - 1]yields {{x^4 + 1, 1}, {x^2 + 1, 1}, {x + 1, 1}, {x - 1, 1}}, displayed as \begin{pmatrix} x^4+1&1\\ x^2+1&1\\ x+1&1\\ x-1&1 \end{pmatrix}.- Note: Not all of the factors are irreducible over the reals.
- Factors[ <Number> ]
- Yields a list of lists of the type {prime, exponent} such that the product of all these primes raised to the power of the corresponding exponents equals the given number. The primes are sorted in ascending order.
- Example:
Factors[1024]yields {{2, 10}}, displayed as \begin{pmatrix} 2&10 \end{pmatrix}, since 1024 = 2^{10}.Factors[42]yields {{2, 1}, {3, 1}, {7, 1}}, displayed as \begin{pmatrix} 2&1\\ 3&1\\ 7&1 \end{pmatrix}, since 42 = 2^1 * 3^1 * 7^1.
Note: See also PrimeFactors Command and Factor Command.
