Math Functions and Constants

This is a complete overview of the mathematical functions and constants available for scripting in Algebrakit.

Booleans

Name Description in out
And And[ expr1, expr2, ... ] returns the logical conjunction of all expressions expr1, expr2, .... If its result is indeterminate, it returns And[expri, exprj,…] with indeterminate expressions expri, exprj,... instead. And[True, False] False
Or Or[expr1, expr2, ... ] returns the logical disjunction of expr1, expr2, .... If its result is indeterminate, it returns Or[expri, exprj,…] with indeterminate expressions expri, exprj,... instead. Or[ True, False ] True
Not Not[ expr ] returns the logical negation of expr. If expr is indeterminate, it returns Not expr Not[ True ] False

Constants

Name Description in out rendered reduced
EulerE EulerE represents Euler's constant, "e". Ln[ EulerE^3 ] 3
Infinity Infinity represents the mathematical concept of infinity. Infinity ∞
MinusInfinity MinusInfinity represents the mathematical concept of minus infinity. MinusInfinity -∞
NaN NaN represents the result of an undefined mathematical operation. NaN stands for Not a Number. 2/0 NaN no solution
Pi Pi represents the mathematical constant pi, π. Sin[Pi] 0

Logarithms

Name Description in reduced
Log Log[ n1, n2 ] represents the logarithm of n1 in base n2. Ifn2 is left out, the function returns the logarithm with base 10 by default. log[ 16, 2 ] 4
Ln Ln[ expr ] represents the mathematical absolute value function with argument expr. Reduces to the natural number n if the expression evaluates to Ln[e^n]. If an expression evaluates to a value less than or equal to 0, ln will reduce to False and render as no solution. Otherwise, the expression remains the same as the input. Ln[ EulerE^3 ] 3

Trigonometry

Basic

Name Description in reduced
Sin Sin[ expr ] represents the mathematical sine function as argument an expression expr. For the default radian values, the sine reduces to the corresponding value. Otherwise, it will remain unchanged from the input. Sin[Pi] 0
Cos Cos[ expr ] represents the mathematical cosine function with the expression expr as its argument. For the default radian values, the cosine reduces to the corresponding value. Otherwise, it will remain unchanged from the input. Cos[Pi] -1
Tan Tan[ expr ] represents the mathematical tangent function on an expression expr. For the default radian values, the tangent reduces to the corresponding value. Otherwise, it will remain unchanged from the input. Tan[0] 0

Inverse

Name Description in reduced
ArcSin ArcSin[ expr ] represents the inverse sine function on an expression expr. The Arcsine will reduce to a radian value if the outcome is one of the default radian values. If expr < -1 or expr > 1 the Arcsine will reduce to False and render as no solution. Otherwise, it will remain unchanged from the input. ArcSin[1] 1/2 π
ArcCos ArcCos[ expr ] represents the inverse cosine function with as argument an expression expr. The Arccosine will reduce to a radian value if the outcome is one of the default radian values. If expr < 0 or expr > 1 the Arccosine will reduce to False and render as no solution. Otherwise, it will remain unchanged from the input. ArcCos[0] 1/2 π
ArcTan ArcTan[ expr ] represents the inverse tangent function with as argument an expression expr. The Arctangent will reduce to a radian value if the outcome is one of the default radian values. Otherwise, it will remain unchanged from the input. ArcTan[1] 1/4 π

Inverse Hyperbolic

Name Description in reduced
ArcSinh Arcsinh[ expr ] represents the inverse hyperbolic sine function with as argument an expression expr. Arcsinh[0] 0
ArcCosh Arccosh[ expr ] represents the inverse hyperbolic cosine function with as argument an expression expr. If expr < 1 the Arccosine hyperbolicus will reduce to False and render as no solution. ArcCos[1] 0
ArcTanh Arctanh[ expr ] represents the inverse hyperbolic tangent function with as argument an expression expr. If expr <= -1 or expr >= 1 the Arctangent hyperbolicus will reduce to False and render as no solution. Arctanh[0] 0

Reciprocal

Name Description in reduced
Cot Cot[ expr ] represents the mathematical cotangent function with as argument an expression expr. For the default radian values, the cotangent reduces to the corresponding value. Otherwise, it will remain unchanged from the input. Cot[1/4 pi] 1
Csc Csc[ expr ] represents the mathematical cosecant function with as argument an expression expr. For the default radian values, the cosecant reduces to the corresponding value. Otherwise, it will remain unchanged from the input. Csc[1/2 pi] 1

Miscellaneous

Name Description in out rendered reduced
Abs Abs[ expr ] represents the mathematical absolute value function with argument expr. Abs[ -4 ] 4
Sqrt Sqrt[ expr ] represents the square root of expr, and Sqrt[ expr, n ] the n-th root. In a script, roots are not calculated. Simplify calculates roots with an exact result, such as Sqrt[16] and Sqrt[1/4], and simplifies Sqrt[x^2] to Abs[x]. Other roots are not rewritten: Simplify[Sqrt[8]] stays Sqrt[8]. The square root of a negative number simplifies to NaN. Use Numerical for a decimal approximation. Sqrt[ 16 ] 16\sqrt{16} 4
The cube root of 27. Sqrt[ 27, 3 ] 273\sqrt[3]{27} 3