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.
- 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).