Built-in Mathematica Symbol

NHoldAll

NHoldAll
is an attribute which specifies that none of the arguments to a function should be affected by N.

NHoldAll, NHoldFirst and NHoldRest are useful in ensuring that arguments to functions are maintained as exact integers, rather than being converted by N to approximate numbers.

Prevent N from affecting the arguments of a function:

System symbols with the NHoldAll attribute:

The arguments of Derivative remain unchanged with N:

N leaves the derivative order while changing the point of evaluation:

Define a pure function:

The function with coefficients converted to numerical values:

The positional parameters remain unchanged with N because Slot has the NHoldAll attribute:

Use an indexed variable:

With this attribute, the variables remain unchanged:

Define a data object that represents a polynomial

in a sparse form ${{c_1,p_1},...}$ :

Make sure that N only affects the coefficients, not the powers:

Default N evaluation of the argument needs to be prevented for the rule above to work:

A representation of the polynomial

:

Get the representation with approximate real coefficients:

Evaluate at

:

HoldAll prevents evaluation while NHoldAll only prevents numerical evaluation:

You can prevent both by setting both attributes: