what is POLYFORM?

[Han]

(12-01-2014 11:34 PM)Alberto Candel Wrote:  But you may just type {1, 2, 3, 4} STO SUMLIST to see POLYFORM({1,2,3,4}, SUMLIST) on the left and the number 10 on the right. BTW, SUMLIST is \(\Sigma LIST\)

I think you may have found a bug. I reproduced the behavior doing exactly what you suggested. To answer your question, here is what I was able to find:

POLYFORM(expression, var1, var2, …)

The idea is that the command will take an expression and expand it into the form of a polynomial, where the variable priority is given by var1, var2, etc.

In Home view:

POLYFORM((X+Y)^3, X, Y); --> Y^3 + 3*Y^2*X + 3*Y*X^2 + X^3 + 5
POLYFORM((X+Y)^3, Y, X); --> X^3 + 3*X^2*Y + 3*X*Y^2 + Y^3 + 5

You can also do some simple decompositions using POLYFORM(). If you use the syntax

POLYFORM(expression, 'operator')

where the operator is either + or *, then it will decompose the expression into either sums of simple (rational) terms or products of rational terms. For example

POLYFORM(1/(X^2-Y^2,'+'); --> 1/(2*Y)/(X+Y) - 1/(2*Y)/(X-Y)
POLYFORM(1/(X^2-Y^2,'*'); --> 1/((X-Y)*(X+Y))

(Basically, this alternate form somewhat resembles partial fraction decomposition when using '+' and rational factorization when using '*').

The alternate form of POLYFORM() also has a "shortcut":

expression STO STO will simply evaluate the expression and is equivalent to POLYFORM(expression, 'eval')
expression STO + is equivalent to POLYFORM(expression, '+')
expression STO * is equivalent to POLYFORM(expression, '*')

So what's the bug? It appears POLYFORM(expression,var1, var2,…) only behaves properly in Home mode and not in CAS (in CAS mode it does not sort the polynomial correctly according to the variable list). The second form POLYFORM(expression, 'operator') does not seem to be something one can type in whether in Home view or CAS view. However, the shortcut form seems to work in CAS view.

I suspect that it should not have worked for your case: {1,2,3} STO SUMLIST and yet it did anyway.

NOTE: Here, STO is really the arrow character produced by pressing the STO> menu option or using [Shift][EEX].

For those who can read French:

http://www-fourier.ujf-grenoble.fr/~pari...hprime.pdf
http://www-fourier.ujf-grenoble.fr/~pari...prime2.pdf