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 $x$?
polynomials definition
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up 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 $x$?
polynomials definition
Linear combinations of fractional powers can be called fractional polynomials. For negative powers, I don't know.
â Yves Daoust
Sep 10 at 19:06
Laurent polynomials are allowed to have negative powers of the indeterminate.
â Brahadeesh
Sep 10 at 19:10
add a comment |Â
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 $x$?
polynomials definition
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
polynomials definition
edited Sep 10 at 19:32
Bernard
112k636104
112k636104
asked Sep 10 at 19:04
IdleCustard
182
182
Linear combinations of fractional powers can be called fractional polynomials. For negative powers, I don't know.
â Yves Daoust
Sep 10 at 19:06
Laurent polynomials are allowed to have negative powers of the indeterminate.
â Brahadeesh
Sep 10 at 19:10
add a comment |Â
Linear combinations of fractional powers can be called fractional polynomials. For negative powers, I don't know.
â Yves Daoust
Sep 10 at 19:06
Laurent polynomials are allowed to have negative powers of the indeterminate.
â Brahadeesh
Sep 10 at 19:10
Linear combinations of fractional powers can be called fractional polynomials. For negative powers, I don't know.
â Yves Daoust
Sep 10 at 19:06
Linear combinations of fractional powers can be called fractional polynomials. For negative powers, I don't know.
â Yves Daoust
Sep 10 at 19:06
Laurent polynomials are allowed to have negative powers of the indeterminate.
â Brahadeesh
Sep 10 at 19:10
Laurent polynomials are allowed to have negative powers of the indeterminate.
â Brahadeesh
Sep 10 at 19:10
add a comment |Â
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Linear combinations of fractional powers can be called fractional polynomials. For negative powers, I don't know.
â Yves Daoust
Sep 10 at 19:06
Laurent polynomials are allowed to have negative powers of the indeterminate.
â Brahadeesh
Sep 10 at 19:10