MathAction ElementaryFunctionStructurePackage example

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In FriCAS expression are represented as rational functions in kernels. exp(2*x) and exp(x) are different kernels, so

fricas

exp(2*x) - exp(x)^2

$\label{eq1}{{e}^{2 \ x}}-{{{e}^{x}}^{2}}$

(1)

Type: Expression(Integer)

gives nonzero result. To recognize that this is really 0 we need to perform extra computation. In this case normalize is enough

fricas

normalize(exp(2*x) - exp(x)^2)

$\label{eq2}0$

(2)

Type: Expression(Integer)

In general, to express function in terms of algebraically independent kernels one can use rischNormalize. It takes two arguments, the first argument is list of expressions to analize, the second is list of variables (rischNormalize treats variables and constants in slightly different way). For example:

fricas

rischNormalize([exp(2*x), exp(x)],[x])

$\label{eq3}\left[{funcs ={\left[{{{e}^{x}}^{2}}, \:{{e}^{x}}\right]}}, \:{kers ={\left[{{e}^{2 \ x}}\right]}}, \:{vals ={\left[{{{e}^{x}}^{2}}\right]}}\right]$

(3)

Type: Record(funcs: List(Expression(Integer)),kers: List(Kernel(Expression(Integer))),vals: List(Expression(Integer)))

The result has three parts. First is list of rewritten expression. Second is list of kernels that were rewritten. The third is list of values assigned to kernels.

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