I wonder how do people learn Spad at all.

Yes, it's hard. But maybe you look at

http://www.aldor.org/wiki/index.php/User_Guides_for_Compiler_and_Libraries

Aldor developed from SPAD, but it's now a separate language and unfortunately only semi-free and no longer developed. Obviously, Stephen Watt is not interested in really putting it under a GPL compatible license, otherwise he would have invested more energy to make that happen.

Still the Aldor User Guide is a good source to understand how SPAD works. It's not completely one-to-one, but once you understand Aldor, it's easy to map you knowledge to use SPAD.

differences between .input and .spad syntax

That's basically easy. Think of .input files as the same syntax that you use on the command line. The main difference with .spad is that the compiler doesn't implicitly do some coercions. If in SPAD something is of type SparseUnivariatPolynomial and doesn't involve a variable (i.e. is a constant), it is still not of the type of the coefficient domain. Nor would be a constant suddently be a polynomial. So the following wouldn't work in the compiler

(1) -> (1$Integer = 1$Polynomial(Integer))@Boolean

   (1)  true
                                             Type: Boolean

because there is no function

  =: (Integer, Polynomial(Integer) -> Boolean

The interpreter, however, makes you mostly to forget about the types and autocoerces the integer argument to Polynomial(Integer) and only then applies the = function.

It is the first time I have to ask people rather than reading a book
or following a tutorial. I indeed appreciate your help.

No problem. Go on. We all know how steep the learning curve for FriCAS is. And maybe some day we can convince you to help us improving that learning curve. Writing down you experiences in how you got into FriCAS, might probably help others in the future. (So maybe you start taking notes for this already.) ;-)

Best regards

Ralf

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