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Mathematical Constants Available in MuPAD

Special Real Numbers

MuPAD® provides symbolic representations of the following commonly used special real numbers. You can perform exact computations that include the constants. Also, you can get floating-point approximations with the current precision DIGITS by using the float function.


Euler number (exponential constant, base of natural logarithm)

PIπ ≈ 3.141592653

Euler-Mascheroni constant


Catalan constant


MuPAD provides the symbolic representations for real and complex infinities. Many functions accept infinities as their arguments. For example, you can use infinities when computing sums, limits, integrals, and so on. Also, you can perform arithmetical operations with infinities. MuPAD can return infinities as results of computations:

infinityReal positive infinity

Infinite point of the complex plane


Real positive infinity used in floating-point intervals


Real negative infinity used in floating-point intervals

Boolean Constants

MuPAD uses a three-state logic with the Boolean constants TRUE, FALSE, and UNKNOWN. You can use these constants in computations. MuPAD can return these constants as a result of computations.

Special Values

The following objects in MuPAD represent special values. You can use these special values in computations. MuPAD can return these values as a result of computations:


Imaginary unit .


Null object of the domain DOM_NIL. MuPAD uses this object to indicate missing objects explicitly.


Null (void) object of the domain DOM_NULL. This object does not produce any visible output. MuPAD removes this object from data structures (such as sequences, lists, sets, and so on).

undefinedUndefined value.
RD_NANUndefined value used in floating-point intervals. If you use typeset mode, MuPAD displays this value as in output regions.

Failure object of the domain DOM_FAIL.

Special Sets

MuPAD provides the following predefined sets and lets you use them in computations. For example, you can use these predefined sets to compute intersections, differences, and unions, or to make assumptions. MuPAD can use these sets to return results of computations:


The set of complex numbers


The set of positive integers:


The set of rational numbers


The set of real numbers


The set of integers

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