Abs
The Abs function calculates the absolute value of a number.
Parameters
The Abs function accepts only one numeric parameter.
Return Value
The Abs function returns the absolute value of the input number.
Examples
Abs[-3]; (* => 3 *)
Abs[3.7]; (* => 3.7 *)
Abs[0]; (* => 0 *)
Abs[-4.2]; (* => 4.2 *)
Add
The Add function calculates the sum of a series of numbers,
equivalent to the mathematical calculation of for Add[a, b, c].
Parameters
The Add function requires at least one parameter,
and all parameters must be numeric values.
Return Value
The Add function returns a numeric value.
If the parameter types do not match,
the Add function will throw an error and will not return any value.
Examples
Add[1, 2, 3]; (* => 6 *)
Add[1]; (* => 1 *)
Add["a"]; (* Error! *)
Add[]; (* Error! *)
All
The All function is used to check if all elements in a list satisfy a specific condition.
Parameters
The All function takes two parameters:
the first is the list to be checked,
and the second is the condition to be checked,
which can be either a built-in function, a plugin function, or a Lambda.
Return Value
If all elements in the list satisfy the condition, the function returns #t; otherwise, it returns #f.
Examples
Let[v, {1, 2, 3, 4}];
Let[p1, All[v, Fun[{x}, Less[x, 5]]]];
Print[p1]; (* => #t *)
Let[p2, All[v, Fun[{x}, Greater[x, 2]]]];
Print[p2]; (* => #f *)
And
The And function is used to evaluate the first condition.
Parameters
The And function takes two parameters:
the first parameter must be a boolean value,
and the second parameter can be any value.
Return Value
The And function is short-circuited,
meaning that if the first parameter returns #t,
the And function will return the value of the second parameter.
Otherwise, it will return #f, and the second parameter will not be evaluated.
Examples
And[#t, 2]; (* => 2 *)
And[#f, Div[1, 0]]; (* => #f *)
Any
The Any function is used to check
if at least one element in a list satisfies a specific condition.
Parameters
The Any function takes two parameters:
the first parameter is the list to be checked,
and the second parameter is the condition to be checked.
Return Value
The Any function returns #t
if there exists an element in the list that satisfies the condition,
and #f otherwise.
Examples
Any[{1, 2, 3, 4, 5}, Fun[{x}, Greater[x, 4]]]; (* => #t *)
Any[{1, 2, 3, 4, 5}, Fun[{x}, Less[x, 0]]]; (* => #f *)
Append
The Append function is used to add an element to the end of a list.
Parameters
The Append function takes two parameters:
the first parameter is a list,
and the second parameter is the element to be added.
Return Value
The Append function returns the modified list.
Note that in KSL, all elements are immutable and can only be shadowed, not modified in place.
Examples
Let[v, {1, 2, 3}];
Append[v, 5]; (* => {1, 2, 3, 5} *)
Eq[v, {1, 2, 3}]; (* => #t *)
Apply
The Apply function is used to apply a value that can be applied,
including Lambdas, built-in functions, and plugin functions.
Parameters
The Apply function takes at least one parameter,
where the first parameter is the value to be applied,
and the subsequent parameters are the arguments that the value needs to accept.
Return Value
The Apply function returns the result of applying the value.
Examples
Apply[Fun[{x}, Add[x, 1]], 3]; (* => 4 *)
Apply[Append, {1, 2, 3}, 9]; (* => {1, 2, 3, 9} *)
ArcCos
The ArcCos function calculates the inverse cosine of a number.
Parameters
The ArcCos function accepts only one numeric parameter, which must be between -1 and 1.
Return Value
The ArcCos function returns the arccosine value of the input number in radians.
Examples
ArcCos[0.5]; (* => 1.0471975511965979 *)
ArcCos[-1]; (* => 3.141592653589793 *)
ArcCos[1]; (* => 0 *)
ArcSin
The ArcSin function calculates the inverse sine of a number.
Parameters
The ArcSin function accepts only one numeric parameter, which must be between -1 and 1.
Return Value
The ArcSin function returns the arcsine value of the input number in radians.
Examples
ArcSin[0.5]; (* => 0.5235987755982989 *)
ArcSin[-1]; (* => -1.5707963267948966 *)
ArcSin[1]; (* => 1.5707963267948966 *)
ArcTan
The ArcTan function calculates the inverse tangent of a number.
Parameters
The ArcTan function accepts only one numeric parameter.
Return Value
The ArcTan function returns the arctangent value of the input number in radians.
Examples
ArcTan[1]; (* => 0.7853981633974483 *)
ArcTan[-1]; (* => -0.7853981633974483 *)
ArcTan[0]; (* => 0 *)
ArcTan2
The ArcTan2 function calculates the inverse tangent of two numbers,
considering the signs of both numbers to determine the quadrant.
Parameters
The ArcTan2 function accepts two numeric parameters, x and y.
Return Value
The ArcTan2 function returns the arctangent value of in radians,
taking into account the signs of x and y to determine the quadrant.
Examples
ArcTan2[1, 1]; (* => 0.7853981633974483 *)
ArcTan2[1, -1]; (* => -0.7853981633974483 *)
ArcTan2[-1, 1]; (* => 2.356194490192345 *)
ArcTan2[0, 1]; (* => 1.5707963267948966 *)
ArcTan2[1, 0]; (* => 0 *)