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Working with MUMIE as author
Working with MUMIE as teacher
Using MUMIE via plugin in local LMS
FAQ
A function may include variables as parameters, independent variables e.g. $x,y,...$ and other functions.
The \field{...}
command determines how the numbers within the function will be interpreted.
\function[<action>]{<variable>}{<expression>}
\function[normalize]{f}{x*x+3+4+0*z} % defines a function f of one variable: f(x)
\function{g}{x^4 - 5*x*y^3 + 4x^2 + 3y + 7} % defines a function g of two variables: g(x,y)
$$f = x^2 + 7$$
$$g = x^4 - 5xy^3 + 4x^2 + 3y + 7$$
12345 \begin{variables}
\number{a}{1}
\number{b}{3}
\function[...]{...}{...}
\end{variables}
Action | Description | Example |
---|---|---|
replace | Replace all variables in the expression (this is the default action and can be omitted) |
\function[replace]{f}{a/b} $f = \frac{1}{3}$ |
normalize | Replaces all variables and normalizes the expression. Normalize applies the following rules. | \function[normalize]{f}{x*x+3+4+0*z} $f = x^2 + 7$ |
expand | Replaces all variables and expands the expression. Expand applies the following rules. | \function[expand, normalize]{f}{(x-1)(x-2)} $f = x^2 - 3x + 2$ |
sort | Replaces all variables and sorts the expression. | \function[sort]{f}{c-b+a*c*b} $f = abc - b + c$ |
calculate | Replaces all variables and calculates the expression. Using this option will always result in a number, in the case where a variable is undefined it takes the value 0. | \function[calculate]{f}{a/b} $f = 0.333333333333333$ amount of digit |
substitute | Creates a new function g by replacing a free variable x in f by an earlier defined variable (possible again a function) g. | \substitute{h}{f}{x}{g} |
Suppose we set the field to real or complex (See \field{...}
). Then the functions evaluated with the calculate option will show the result with 15 digits behind the decimal mark.
Quite often this is undesired when you want to output this value on the screen. In order to reduce the amount of digits behind the decimal mark, you can provide a second (optional) parameter. The calculated result will then be rounded to this precision.
Optional Second parameter
12345678910 % field is real
\number{a}{1}
\number{b}{3}
\function[calculate, 3]{f}{a/b}
% instead of a number one can use the option display
% the result will then be displayed based on \displayprecision
\function[calculate, display]{f}{a/b}
$$f = 0.333$$
More details on precision can be found here
Rounding
The command \substitute is used for the evaluation of a function and for the composition of two functions. Here are two examples for the evaluation of a function:
12345 % field is real
\number{a}{1}
\function{f}{2*x^2 -1} % defines a function f of the variables x
\substitute[normalize]{f(1)}{f}{x}{a} % evaluation at x=1.
The function $$f(x) = 2x^2 - 1$$ evaluated at $$x=2$$ yields $$f(1) = 7$$
1234 % field is real
\function{f}{exp(y)} % defines the exponential function exp(y)
\function{g}{-x^2} % defines the function g(x) = -x^2.
\substitute[normalize]{gauss}{f}{y}{g} % defines the function f(g(x)) = exp{-x^2}
The composition of the functions $$f(y) = \exp(y)$$ and $$g(x) = x^2$$ produces the Gauss-function $$f(g(x)) = \exp(-x^2)$$
Updated by Ruedi Seiler, 1 year, 4 months ago – f0d9fc4