Difference between revisions of "Factors Command"
From GeoGebra Manual
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;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. | :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}}'' | + | :{{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>}} |
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:{{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. | :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>'', since <math>1024 = 2^{10}</math>. |
| − | + | :* <code><nowiki>Factors[42]</nowiki></code> yields ''{{2, 1}, {3, 1}, {7, 1}}'', since <math>42 = 2^1 * 3^1 * 7^1</math>.</div>}} | |
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| − | :* <code><nowiki>Factors[42]</nowiki></code> yields ''{{2, 1}, {3, 1}, {7, 1}}'' | ||
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{{note|See also [[PrimeFactors Command]] and [[Factor Command]].}} | {{note|See also [[PrimeFactors Command]] and [[Factor Command]].}} | ||
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==CAS Syntax== | ==CAS Syntax== | ||
;Factors[ <Polynomial> ] | ;Factors[ <Polynomial> ] | ||
Revision as of 15:44, 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}}.
- 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}}, since 1024 = 2^{10}.Factors[42]yields {{2, 1}, {3, 1}, {7, 1}}, 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.
