Difference between revisions of "Factors Command"
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;Factors[ <Polynomial> ] | ;Factors[ <Polynomial> ] | ||
:Gives 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 ascending order. | :Gives 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 ascending order. | ||
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;Factors[ <Number> ] | ;Factors[ <Number> ] | ||
| − | :Gives 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. | + | :Gives 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>'', since <math>1024 = 2^{10}</math>. | :* <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>}} | :* <code><nowiki>Factors[42]</nowiki></code> yields ''{{2, 1}, {3, 1}, {7, 1}}'', since <math>42 = 2^1・3^1・7^1</math>.</div>}} | ||
{{note|See also [[PrimeFactors Command]] and [[Factor Command]].}} | {{note|See also [[PrimeFactors Command]] and [[Factor Command]].}} | ||
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| − | = | + | In the [[File:Menu view cas.svg|link=|16px]] [[CAS View]] undefined variables can be used as input and the results are returned as proper matrices. |
| − | + | :{{example| 1=<code><nowiki>Factors[a^8 - 1]</nowiki></code> yields <math>\left( \begin{array}{} a - 1 & 1 \\ a +1 & 1 \\a^2 + 1& 1 \\a^4 + 1& 1 \\ \end{array} \right)</math>.}} | |
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| − | :{{example| 1=<code><nowiki>Factors[ | ||
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Revision as of 16:58, 9 October 2015
- Factors[ <Polynomial> ]
- Gives 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 ascending order.
- Example:
Factors[x^8 - 1]yields {{x - 1, 1}, {x + 1, 1}, {x^2 + 1, 1}, {x^4 + 1, 1}}.
- Note: Not all of the factors are irreducible over the reals.
- Factors[ <Number> ]
- Gives 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.
Note: In the 
CAS View undefined variables can be used as input and the results are returned as proper matrices.
CAS View undefined variables can be used as input and the results are returned as proper matrices.
- Example:
Factors[a^8 - 1]yields \left( \begin{array}{} a - 1 & 1 \\ a +1 & 1 \\a^2 + 1& 1 \\a^4 + 1& 1 \\ \end{array} \right).
