Difference between revisions of "Factors Command"
From GeoGebra Manual
| Line 4: | Line 4: | ||
:Returns list of lists ''{factor,exponent}'' such that product of all these factors raised to corresponding exponents equals the given polynomial. | :Returns list of lists ''{factor,exponent}'' such that product of all these factors raised to corresponding exponents equals the given polynomial. | ||
:{{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}}''.</div>}} | ||
| − | :{{note|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> ] | ||
:Returns list of lists ''{prime, exponent}'' such that product of all these primes raised to corresponding exponents equals the given number. Primes are sorted in ascending order. | :Returns list of lists ''{prime, exponent}'' such that product of all these primes raised to corresponding exponents equals the given number. Primes are sorted in ascending order. | ||
:{{example|1=<div> | :{{example|1=<div> | ||
| − | :* <code>Factors[1024]</code> yields ''<nowiki>{{2, 10}}</nowiki>'', because ''1024 = 2<sup>10</sup>''. | + | :* <code><nowiki>Factors[1024]</nowiki></code> yields ''<nowiki>{{2, 10}}</nowiki>'', because ''1024 = 2<sup>10</sup>''. |
| − | :* <code>Factors[42]</code> yields ''{{2, 1}, {3, 1}, {7, 1}}'', because ''42 = 2<sup>1</sup> 3<sup>1</sup> 7<sup>1</sup>''.</div>}} | + | :* <code><nowiki>Factors[42]</nowiki></code> yields ''{{2, 1}, {3, 1}, {7, 1}}'', because ''42 = 2<sup>1</sup> 3<sup>1</sup> 7<sup>1</sup>''.</div>}} |
| − | {{note|See also [[PrimeFactors Command]] and [[Factor Command]].}} | + | {{note| 1=See also [[PrimeFactors Command]] and [[Factor Command]].}} |
==CAS Syntax== | ==CAS Syntax== | ||
;Factors[ <Polynomial> ] | ;Factors[ <Polynomial> ] | ||
| Line 20: | Line 20: | ||
x-1&1 | x-1&1 | ||
\end{pmatrix}</math>.</div>}} | \end{pmatrix}</math>.</div>}} | ||
| − | :{{note|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> ] | ||
:Returns list of lists ''{prime, exponent}'' such that product of all these primes raised to corresponding exponents equals the given number. Primes are sorted in ascending order. | :Returns list of lists ''{prime, exponent}'' such that product of all these primes raised to corresponding exponents equals the given number. Primes are sorted in ascending order. | ||
:{{example|1=<div> | :{{example|1=<div> | ||
| − | :* <code>Factors[1024]</code> yields ''<nowiki>{{2, 10}}</nowiki>'', displayed as <math>\begin{pmatrix} | + | :* <code><nowiki>Factors[1024]</nowiki></code> yields ''<nowiki>{{2, 10}}</nowiki>'', displayed as <math>\begin{pmatrix} |
2&10 | 2&10 | ||
\end{pmatrix}</math>, because ''1024 = 2<sup>10</sup>''. | \end{pmatrix}</math>, because ''1024 = 2<sup>10</sup>''. | ||
| − | :* <code>Factors[42]</code> yields ''{{2, 1}, {3, 1}, {7, 1}}'', displayed as <math>\begin{pmatrix} | + | :* <code><nowiki>Factors[42]</nowiki></code> yields ''{{2, 1}, {3, 1}, {7, 1}}'', displayed as <math>\begin{pmatrix} |
2&1\\ | 2&1\\ | ||
3&1\\ | 3&1\\ | ||
Revision as of 14:08, 9 September 2011
- Factors[ <Polynomial> ]
- Returns list of lists {factor,exponent} such that product of all these factors raised to corresponding exponents equals the given polynomial.
- Example:
Factors[x^8 - 1]yields {{x^4 + 1, 1}, {x^2 + 1, 1}, {x + 1, 1}, {x - 1, 1}}.
- Note: Not all of the factors are irreducible over the reals.
- Factors[ <Number> ]
- Returns list of lists {prime, exponent} such that product of all these primes raised to corresponding exponents equals the given number. Primes are sorted in ascending order.
- Example:
Factors[1024]yields {{2, 10}}, because 1024 = 210.Factors[42]yields {{2, 1}, {3, 1}, {7, 1}}, because 42 = 21 31 71.
Note: See also PrimeFactors Command and Factor Command.
CAS Syntax
- Factors[ <Polynomial> ]
- Returns list of lists {factor, exponent} such that product of all these factors raised to corresponding exponents equals the given polynomial.
- 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> ]
- Returns list of lists {prime, exponent} such that product of all these primes raised to corresponding exponents equals the given number. Primes are sorted in ascending order.
- Example:
Factors[1024]yields {{2, 10}}, displayed as \begin{pmatrix} 2&10 \end{pmatrix}, because 1024 = 210.Factors[42]yields {{2, 1}, {3, 1}, {7, 1}}, displayed as \begin{pmatrix} 2&1\\ 3&1\\ 7&1 \end{pmatrix}, because 42 = 21 31 71.
Note: See also PrimeFactors Command and Factor Command.
