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Editorial Team
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Asked: 2026-05-27T05:34:36+00:00

What is the best way to define a numerical constant in Mathematica? For example,

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What is the best way to define a numerical constant in Mathematica?

For example, say I want g to be the approximate acceleration due to gravity on the surface of the Earth. I give it a numerical value (in m/s^2), tell Mathematica it’s numeric, positive and a constant using

Unprotect[g];
ClearAll[g]
N[g] = 9.81;
NumericQ[g] ^= True;
Positive[g] ^= True;
SetAttributes[g, Constant];
Protect[g];

Then I can use it as a symbol in symbolic calculations that will automatically evaluate to 9.81 when numerical results are called for. For example 1.0 g evaluates to 9.81.

This does not seem as well tied into Mathematica as built in numerical constants. For example Pi > 0 will evaluate to True, but g > 0 will not. (I could add g > 0 to the global $Assumptions but even then I need a call to Simplify for it to take effect.)
Also, Positive[g] returns True, but Positive[g^2] does not evaluate – compare this with the equivalent statements using Pi.

So my question is, what else should I do to define a numerical constant? What other attributes/properties can be set? Is there an easier way to go about this? Etc…

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1 Answer

  1. Editorial Team

    I’d recommend using a zero-argument “function”. That way it can be given both the NumericFunction attribute and a numeric evaluation rule. that latter is important for predicates such as Positive.

    SetAttributes[gravUnit, NumericFunction]
N[gravUnit[], prec_: $MachinePrecision] := N[981/100, prec]

In[121]:= NumericQ[gravitUnit[]]
Out[121]= True

In[122]:= Positive[gravUnit[]^2 - 30]
Out[122]= True

    Daniel Lichtblau

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