Q: How alike the polynomial and non polynomial?

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Polynomial vs non polynomial time complexity

In my opinion the question is poorly defined, since "non-polynomial" could be just about anything.

what is non polynomials

No. By the definition of a polynomial, the powers can only be non-negative integers.

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how alike the polynomial and non polynomial

A "non-polynomial" can be just about anything; how alike they are depends what function (or non-function) you specifically have in mind.

A "non-polynomial" can be just about anything; how alike they are depends what function (or non-function) you specifically have in mind.

That depends a lot on what you choose to include in "non-polynomial" - it can be just about anything. If you are referring to functions, what they have in common is anything that defines a function - mainly, the fact that for every value of an independent variable, a unique value is defined for the independent variable.

Polynomial vs non polynomial time complexity

"Non-polynomials" may be just about anything; how alike or different they are will depend on what specific restrictions you put on such functions, or whether you are even talking about functions.

In my opinion the question is poorly defined, since "non-polynomial" could be just about anything.

what is non polynomials

Briefly: A polynomial consists only of powers of the variables - ie the variables multiplied by themselves or one another. A non polynomial can include any other function such as trigonometric, exponential, logarithmic etc.

None, except that they are functions of one or more variables.

An expression is non polynomial if it has : negative exponent fractional exponent variable exponent in the radicand

No. By the definition of a polynomial, the powers can only be non-negative integers.