| ... |
... |
@@ -154,10 +154,11 @@ A number variable is defined by the command `\number` followed by the name of th |
| 154 |
154 |
\function{cut}{f3D[s-2,y]} % indeterminate y is replaced by the value of s-2. This results in a 1-variate function. |
| 155 |
155 |
``` |
| 156 |
156 |
|
| 157 |
|
-The value of a variable of type function is a [function expression](#number-expressions-and-function-expressions) containing (at most) two indeterminates. |
|
157 |
+The value of a variable of type function is a [function expression](#number-expressions-and-function-expressions) containing an arbitrary number of indeterminates. |
| 158 |
158 |
|
| 159 |
|
-If the function contains (at most) one indeterminate, the function is flagged as being displayable in 2D, if it has two indeterminates it can be displayed in 3D-canvases. |
| 160 |
|
-In 3D the indeterminates are ordered alphabetically by default. |
|
159 |
+If the function contains (at most) one indeterminate, the function is flagged as being displayable in 2D, if it has two indeterminates it can be displayed in 3D-canvases. Functions in more than two indeterminates can not be displayed in canvases, but used in the definition of other objects, e.g. by [evaluating one indeterminate](#evaluations-and-subtitutions) of a trivariate function to obtain a bivariate function. |
|
160 |
+ |
|
161 |
+If there are more than one indeterminates, they are ordered alphabetically by default. |
| 161 |
162 |
If you like (e.g. to use a different order or to make sure that a function is recognized for 3D), you can in addition provide the indeterminates for the function, e.g. write `\function{f3D}{sqrt(x^2+y^2), [x,y]}` |
| 162 |
163 |
or `\function{f}{s*sin(x), [x]}` |
| 163 |
164 |
|
| ... |
... |
@@ -814,10 +815,12 @@ In visualizations, a number expression is a mathematical expression that evaluat |
| 814 |
815 |
You can use all of the math functions _abs, acos, acosh, asin, asinh, atan, atanh, cbrt, ceil, clz32, cos, cosh, exp, floor, ln, log, log10, log1p, log2, sign, sin, sinh, sqrt, tan, tanh, trunc_, |
| 815 |
816 |
as well as number values and coordinates of points/vectors defined earlier. |
| 816 |
817 |
|
|
818 |
+## Evaluations and subtitutions |
| 817 |
819 |
You can use evaluations/substitutions of functions in the *value* for other variables by using e.g. `f[1]` or `f[a+1]` for a function variable `f` and a number or function variable `a`. |
| 818 |
820 |
For multivariate functions, you also have to provide the indeterminate that you would like to replace, e.g. write `\function{fsub}{f3D[s-2,y]}` to replace the indeterminate by the value of `s-2`. |
| 819 |
|
-You can even replace both indeterminates of a 2-variate function in one row with e.g. `f[2,x][1,y]`. |
|
821 |
+You can even replace several indeterminates in one call, e.g. `f[2,x][1,y]`. |
| 820 |
822 |
|
|
823 |
+## Derivatives |
| 821 |
824 |
Given a function variable `f` having an indeterminate `x`, you can use its derivative in expressions with the syntax `D[f,x]` that you are used to from expressions in the corrector of problems. |
| 822 |
825 |
|
| 823 |
826 |
**Caution** |
| 824 |
827 |
|