COLC: factorize a symbolic fraction (returns a symbolic)
FROOTS: input is a fraction, outputs: the list of var (stack
level 3), the list polynomial (2), and the list of root/multiplicity (1)
(each root is followed by its multiplicity). Examples: * 'X^3-6*X^2+11*X-6'
-> 3: { X }, 2:'X^3-6*X^2+11*X-6' , 1: { 2 1 3 1 1 1 }
* '1/X^2' -> 3: { X }, 2: '1/X^2', 1: { 0 -2 }
* 'X^2-Y^2' ->
3: { X Y }, 2: 'X^2+2*X*Y+Y^2', 1: { '-Y' 2 }
For a symbolic, FROOTS factorizes with respect to the variable contained
in VX, or if the symbolic is independant of VX with respect
to the first variable of LVAR applied to the symbolic.
If stack 1 is a real integer, FROOTS computes the roots of a
list polynomial with numeric coefficient using Bairstow method (real
coefficients) or Laguerre method (complex coefficients).
During iterations, you can modify some parameters:
E*10: ( 
)
multiplies the test value by 10, use this when there are multiple roots.
E/10: divides the test value/10, for accurate precision
(use this after you have found all multiple roots)
RAND: reset current iteration (restart with random initial value)
STOP abort iteration (for the next one or two roots)
value).
Before starting the program, you must specify the value and
the number of test-successfully iterations using the following stack input:
{ 1 -21 183 -847 2196 -3024 1728 }
1E-4
3
FROOTS
-> approximatively { 3 3 3 4 4 4 }
The result is bad since 3 and 4 are multiple roots.
FACTO: same stack as FROOT but returns a list of
"prime" factors instead of roots. Example: * 'X^3-6*X^2+11*X-6'
-> 3: { X }, 2: 'X^3-6*X^2+11*X-6', 1: { '(X-2)' 1 '(X-3)' 1 '(X-1)' 1 }
* 21 -> 3: { }, 2: 21, 1: { 3 1 7 1 }
FCOEF: input is a list of roots/multiplicity, output is a
fraction or polynomial with leading coefficient 1 having this roots
(and poles). Example:{ 1 1 2 1 3 1 } -> 'X^3-6*X^2+11*X-6'{ A -1 2 1 } -> '(X-2)/(X-A)'
