Using canonical definitions, can a polynomial have non-integer degree less than 1? Integer degree less than zero?

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Like all common terms in mathematics, "polynomial" has very slightly different definitions depending upon your reference text; but they differ only in superfluous ways.



Are there any canonical/popular definitions polynomial which allow them to have degree less than 1?



For example, is $frac1x = x^-1$ a polynomial on $x$?



What about non-integer degrees? Is $sqrtx = x^0.5$ a polynomial on $x$?










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  • Linear combinations of fractional powers can be called fractional polynomials. For negative powers, I don't know.
    – Yves Daoust
    Sep 10 at 19:06










  • Laurent polynomials are allowed to have negative powers of the indeterminate.
    – Brahadeesh
    Sep 10 at 19:10














up vote
1
down vote

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Like all common terms in mathematics, "polynomial" has very slightly different definitions depending upon your reference text; but they differ only in superfluous ways.



Are there any canonical/popular definitions polynomial which allow them to have degree less than 1?



For example, is $frac1x = x^-1$ a polynomial on $x$?



What about non-integer degrees? Is $sqrtx = x^0.5$ a polynomial on $x$?










share|cite|improve this question























  • Linear combinations of fractional powers can be called fractional polynomials. For negative powers, I don't know.
    – Yves Daoust
    Sep 10 at 19:06










  • Laurent polynomials are allowed to have negative powers of the indeterminate.
    – Brahadeesh
    Sep 10 at 19:10












up vote
1
down vote

favorite









up vote
1
down vote

favorite











Like all common terms in mathematics, "polynomial" has very slightly different definitions depending upon your reference text; but they differ only in superfluous ways.



Are there any canonical/popular definitions polynomial which allow them to have degree less than 1?



For example, is $frac1x = x^-1$ a polynomial on $x$?



What about non-integer degrees? Is $sqrtx = x^0.5$ a polynomial on $x$?










share|cite|improve this question















Like all common terms in mathematics, "polynomial" has very slightly different definitions depending upon your reference text; but they differ only in superfluous ways.



Are there any canonical/popular definitions polynomial which allow them to have degree less than 1?



For example, is $frac1x = x^-1$ a polynomial on $x$?



What about non-integer degrees? Is $sqrtx = x^0.5$ a polynomial on $x$?







polynomials definition






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edited Sep 10 at 19:32









Bernard

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asked Sep 10 at 19:04









IdleCustard

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  • Linear combinations of fractional powers can be called fractional polynomials. For negative powers, I don't know.
    – Yves Daoust
    Sep 10 at 19:06










  • Laurent polynomials are allowed to have negative powers of the indeterminate.
    – Brahadeesh
    Sep 10 at 19:10
















  • Linear combinations of fractional powers can be called fractional polynomials. For negative powers, I don't know.
    – Yves Daoust
    Sep 10 at 19:06










  • Laurent polynomials are allowed to have negative powers of the indeterminate.
    – Brahadeesh
    Sep 10 at 19:10















Linear combinations of fractional powers can be called fractional polynomials. For negative powers, I don't know.
– Yves Daoust
Sep 10 at 19:06




Linear combinations of fractional powers can be called fractional polynomials. For negative powers, I don't know.
– Yves Daoust
Sep 10 at 19:06












Laurent polynomials are allowed to have negative powers of the indeterminate.
– Brahadeesh
Sep 10 at 19:10




Laurent polynomials are allowed to have negative powers of the indeterminate.
– Brahadeesh
Sep 10 at 19:10















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