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Formula editor is case sensitive operates with a lots of types. Result of calculation depends on types of variables.
Let sin(a) be a formula of formula editor. What is its meaning? If a is a real variable then result of formula is a real value. However if a is an array then sin(a) is also an array of componentwise calculation of sin. If a is a real array and b is a real variable then a + b means an array of sums of components of a with b.
Any function of formula editor may be a variable or result of calculation. A function as result is not a value of function but the whole function. This fact seems unusual for people who do not know functional analysis. For example if a is a real variable then f(a) means result of calculation of f. If a is function then f(a) is a composition of functions. It is very convenient. For example the series component
provides three variables:
First variable is an array of abscises of function table. Second one is an array of ordinates. Third one is the function defined by table. Let us consider usage of this function. We have the following situation:
Click here to download this situation.
The Formula 1 component imports and then exports function f from Plot. The Formula 2 imports one function from Formula 1 and another from Plot. In fact it is the same function. Then Formula 2 composes these functions:
Later Formula 3 calculates these functions. In result we have:
The red curve is the function and teal curve is the composition one.
Formula editor supports matrix and vector operations. Examples of usage of vector and matrix operations are presented below :
These examples contains transposition of matrixes, products of matrixes, inversion of matrixes and vector product of 3D vectors.
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