Algebra of functions which looks like:
polynomial * exp( -x^2 )
in high dimensions. And lot of other neat stuff.
Example:
x = seq(-2,2,len=300) # some points for the plot
f = Gauss(0.5) # Gaussian bell with standard deviation 0.5
g = lag( Gauss(0.3), 1) # another Gaussian bell moved to origin 1 (mean=1)
matplot(x, cbind(
calc(f ,x), # ploting the values of the function f ...
calc(g ,x), # ... and g
calc(f * g ,x), # their product, ...
calc(f + g ,x), # ... sum ...
calc(f %% g ,x) # ... and convolution
), type="l", lty=1, xlab="x", ylab="y", main="Different operations")
legend("topleft",
c("f","g","fg (multiplicat)",
"f + g", "f * g (convolution)"),
lty=1, col=1:5)
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