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	Calculations
	The Algebra System (G.A.S.)
	provides many predefined operations, functions and constants. Overview geometric functions arithmetic operations arithmetic functions differentiate integrated trigonometric functions more functions logic operators logic functions constants geometric functions Geometric functions require -objects as inputs. Simply specify the name of the object. Objects whith names containing indices have to be written using `_`. E.g. the label of the circle above was input as `k_a`, but is displayed as `k_a`. x-component y-component distance of two points length of a segment radius of a circle Measuring angles in degrees Measuring angles in the radian measure parallel-function orthogonal-funktion x-component Input `X(point)` `point` is a point in . `X` returns the value of the x-coordinate of the point. Example `X(A)` with `A(2.23;1.3)` returns `2.23` y-component Input `Y(point)` `point` is a point in . `Y` returns the value of the y-coordinate of the point. Example `Y(A)` with `A(2.23;1.3)` returns `1.3` Distance of two points Input `Dist(point1,point2)` The distance of two -points `point1` and `point2` is calculated with `Dist`. Example `Dist(A,B)` with `A(1;0)` and `B(0;1)` returns `1.414...` Length of a segment Input `L(segment)` `segment` is a segment in . `L` returns the length of the segment. If `segment` is a line, a ray or a vector then `L` returns the distance of the two defining points. Example `L(a)` with `a` defined by `A(1;0)` and `B(0;1)` returns `1.414...` Radius of a circle Input `R(circle)` `circle` is a circle in . `R` returns the length of the radius. Indices have to be written with `_` (see example). Example `R(k_a)` returns the radius of `k_a` Measuring angles in degrees Input `Deg(punkt1,punkt2,punkt3)` `Deg` returns the angle `point1` (on the first side of the angle) `point2` (vertex) `point3` (on the second side of the angle) measured in degrees. The mathematical orientation of the angle is of relevance. Example `Deg(A,B,C)` with `A(1;0)`, `B(0;1)` and `C(1;1)` returns `45.0` Measuring angles in radian measure Input `Rad(point1,point2,point3)` `Rad` returns the angle `point1` (on the first side of the angle) `point2` (vertex) `point3` (on the second side of the angle) measured in radian measure. Example `Rad(A,B,C)` with `A(1;0)`, `B(0;1)` and `C(1;1)` returns `0.785...` parallel-function Input `Par(line1,line2)` If `line1` and `line2` are parallel, `Par` returns `True`, otherwise `Par` returns `False`. Example `Par(a,b)` with `a` \|\| `b` returns `True` Orthogonal-function Input `Ortho(line1,line2)` If `line1` and `line2` are orthogonal to each other, `Ortho` returns `True`, otherwise `Ortho` returns `False`. Example `Ortho(a,b)` with `a` \|\| `b` returns `False` Top of Page Arithmetic operations Addition Subtraction Multiplication Division Addition Input `argument1 + argument2` Subtraction Input `argument1 - argument2` Multiplication Input `argument1 * argument2` Division Input `argument1 / argument2` Top of Page Arithmetic Functions (natural) exponential function natural logarithm exponentiate square root (natural) exponential function Input `Exp(argument)` Exapmles `Exp(x)` `Exp(X(A))` natural logarithm Input `Log(argument)` Examples `Log(x)` `Log(X(A))` `Log(E^2)` returns `2` exponentiate Inputs `Pow(base, exponent)` `base^exponent` Exapmles `Pow(3, x)` means `3^x` `x^2` `Y(C)^2` square root Input `Sqrt(argument)` Examples `Sqrt(x)` `Sqrt(Y(B))` Top of Page differentiate Input `D(expression, variable)` `D(expression, {variable, n})` `D(expression, variable)/.variable->value` `D(expression, {variable, n})/.variable->value` The function `D` differentiates `expression` with respect to `variable`. `n` specifies that the nth derivative is returned. If `value` is specified the derivative is evaluated for this value. Examples `D(Sin(x),x)` returns `Cos(x)` `D(Sin(x),{x,2})` returns `-Sin(x)` `D(Sin(x),x)/.x->Pi/2` returns `0` `D(Sin(x),{x,2})/.x->Pi/2` returns `-1` Top of Page integrate Input `Int(expression, variable)` `Int(expression, variable)/.variable->value` The function `Int` integrates `expression` with respect to `variable`. If `value` is specified the antiderivative is evaluated for this value. Examples `Int(Sin(x),x)` returns `-Cos(x)` `Int(Sin(x),x)/.x->Pi` returns `1` Top of Page trigonometric functions arc cosine arc sine arc tangent cosine cotangent sine tangent arc cosine Input `ACos(argument)` Exapmles `ACos(x)` `ACos(X(A))` arc sine Input `ASin(argument)` Exapmles `ASin(x)` `ASin(X(A))` arc tangent Input `ATan(argument)` Examples `ATan(x)` `ATan(X(A))` cosine Input `Cos(argument)` Examples `Cos(x)` `Cos(X(A))` cotangent input `Cot(argument)` Examples `Cot(x)` `Cot(X(A))` sine Input `Sin(argument)` Examples `Sin(x)` `Sin(X(A))` tangent Input `Tan(argument)` Examples `Tan(x)` `Tan(X(A))` Top of Page more functions absolute value maximum minimum numerical evaluation round signum truncate absolute value Input `Abs(argument)` Exapmles `Abs(-2)` returns `2` `Abs(x)` returns `-x` if `x<0`, otherwise `x` maximum Input `Max(argument1, ... , argumentN)` Examples `Max(1,2,3)` returns `3` `Max(-3,0.4,-5.1)` returns `0.4` minimum Input `Min(argument1, ... , argumentN)` Exapmles `Min(1,2,3)` returns `1` `Min(-3,0.4,-5.1)` returns `-5.1` numerical evaluation Input `N(argument)` Examples `N(Sqrt(2))` returns `1.414...` `N(E)` returns `2.718...` round Input `Round(argument, n)` `argument` is rounded to `n` decimal places. If the rounded value ends with `0` this `0` is not displayed. If `n` is `0`, the result is displayed with `.0`. Examples `Round(2.234623,2)` returns `2.23` `Round(2.234623,3)` returns `2.235` `Round(2.234623,0)` returns `2.0` `Round(2.2300000,4)` returns `2.23` signum Input `Sign(argument)` Examples `Sign(-2)` returns `-1` `Sign(5.56)` returns `1` `Sign(x)` returns `-1` if `x<0`, `0` if `x=0` and `1` if `x>0` truncate Input `Trunc(number)` The decimal places are `Trunc` cut off. The result is displayed as an integer followed by `.0`. Examples `Trunc(3.523453)` returns `3.0` `Trunc(-3.4564564)` returns `-3.0` Top of Page logical operators equal greater than greater than or equal to lesser than lesser than or equal to unequal "equal"-operator Input `argument1 == argument2` "greater than"-operator Input `argument1 > argument2` "greater than or equal to"-operator Input `argument1 >= argument2` "lesser than"-operator Input `argument1 < argument2` "lesser than or equal to"-operator Input `argument1 <= argument2` "unequal"-Operator Eingabe `argument1 != argument2` Top of Page logical functions logical AND logical OR condition logical AND Input `And(argument1, ... , argumentN)` `argument1 && ... && argumentN` `And` returns `True`, if all arguments are `True`. Otherwise `And` returns `False`. Examples `And(5>0,3<Pi)` returns `True` `a && b` with `a=False` and `b=True` returns `False` logical OR Input `Or(argument1, ... , argumentN)` `argument1 \|\| ... \|\| argumentN` `Or` returns `True`, if at least one of the arguments is `True`. If all arguments are `False`, `Or` returns `False`. Examples `Or(5>0,3>Pi)` returns `True` `a \|\| b` with `a=False` and `b=True` returns `True` condition Input `If(condition, true, false)` If `condition` returns `True`, `true` is executed, otherwise `false` is. Examples `If(5>0,5.3,4.0)` returns `5.3` `If(5<0,5.3,4.0)` returns `4.0` `If(X(A)<0,X(B)=5,X(B)=X(A))` eith `X(A)=-2.5` returns `X(B)=5` Top of Page constants Pi Euler's constant False True Pi Input `Pi` Euler's constant Input `E` False Input `False` True Input `True` Top of Page
	See Also: (x;y)-Punkt Angle (input size) Circle (input radius) Graph of a function parameter curve Text

Calculations