Originally Posted by: ioan92 My main concern is not to create nor to criticize SMath but simply to use it.
Can't be more right: Ioan, Martin, Davide as long as the rules are simple algebraic.
Working with "Advanced Algebra" is known as symbolic in scalar maths, that is the great
Maple, Mathematica [two different engines considered ~ equivalent].
Vectors/matrices also go by their own "Advanced Rules". That starts by "baby logic"
I have a matrix, I want it it to be all elements be negative. So the logic comes
what I have I mutltiply. Even if the matrix multiplication is commutative, it's
non sense saying I have (-1) then multiply by something [i.e: matrix].
That's why advanced matrix algebra follow this rule.
In the attached, you can see two applications of advanced vector/matrix algebra.
1. Convolution
2. Cholesky solver.
They go strictly by the rules the "Mathematicians Society" have established to
work universally for all user. To complicate matters, even advanced vector/matrix
algebra are limited in solving. Many decades ago, Souriau [don't recall the decade]
found out a way to transform unusable matrix to usable one : PseudoMatrix by a process
of PseudoInversion [Mathcad "geninv']. What's that doing ? putting wings to stones !
Once in PseudoInverse form, a chemical balance of fractional composition can be
solved generally and in the right proprotion of all "inter actants".
I bet Knovel [essentially Smath] has that implemented... [in visible code ?]
Reverse the order in the "convolution" ... Syntax error or not in correct order.
Cholesky solver is not commutative either.
Think more: think in term of "Eigen stuff" from which "polyroots results".
Follow the rules: don't drive RHS in UK, don't drive LHS in US/Canada.
For an unknown reason to me, in wide routes, horses naturally drove LHS,
English toke it as is. Unfortunately the "church" couldn't burn to stake all
horses to teach them a lesson. But ± imposed human not to be as stupid as the horse.
Working with advanced matrix algebra is like working with Fourier, Laplace...
You convert in the "transform domain", proceed in that domain, reverse from the
"transform domain" back to normal domain and something happened. Isn't great !
Good thing: Smath obeys "advanced Matrix algebra". Just border line in some
applications.
Jean
Convol.sm (100kb) downloaded 21 time(s).