Difference between revisions of "Factors Command"
From GeoGebra Manual
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;Factors[ <Polynomial> ] | ;Factors[ <Polynomial> ] | ||
: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 | + | :{{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|Not all of the factors are irreducible over the reals.}} | ||
;Factors[ <Number> ] | ;Factors[ <Number> ] | ||
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;Factors[ <Polynomial> ] | ;Factors[ <Polynomial> ] | ||
: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 | + | :{{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 | + | x^4+1&1\\ |
+ | x^2+1&1\\ | ||
x+1&1\\ | x+1&1\\ | ||
− | x | + | x-1&1 |
− | |||
\end{pmatrix}</math>.</div>}} | \end{pmatrix}</math>.</div>}} | ||
:{{note|Not all of the factors are irreducible over the reals.}} | :{{note|Not all of the factors are irreducible over the reals.}} |
Revision as of 13:07, 23 August 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.