Factoring Polynomials

[TheOAP]

Hi,
If possible could Alan answer this as we're similar in age (84)!

I was first an electronics eng. then a programmer.
Loved both occupations but programming was tops!
Stil writing progs. - math orientated

[1] I'm bothered when reading some Math books etc.
Some say that for a polynomial of degree N there are N roots
but I've some that have no roots.
[2] Written a program - Polynomials - that (tries) to determine factors.
After the standard methods have been used (including Synthetic Division) I run
a procedure DeepScan:
2 equations (both the same) are "fed" with different values of the independent variable 'x'
The "feeds" are stepped by (at first) 1/1000000 and if the 2 equations give a "crossover"
they are stored. When this process is complete 2 at a time of the stored values
are extracted and run with 'x' values of 1/1000000000000 !
My problem is to determine the range that 'x' should be set to.

EG. 185x^7 + x^5 - 3x2 - 29
the scan range would be +/- 185 ...

Help
Pete

 

[nycmathguy]

Hi,
If possible could Alan answer this as we're similar in age (84)!

I was first an electronics eng. then a programmer.
Loved both occupations but programming was tops!
Stil writing progs. - math orientated

[1] I'm bothered when reading some Math books etc.
Some say that for a polynomial of degree N there are N roots
but I've some that have no roots.
[2] Written a program - Polynomials - that (tries) to determine factors.
After the standard methods have been used (including Synthetic Division) I run
a procedure DeepScan:
2 equations (both the same) are "fed" with different values of the independent variable 'x'
The "feeds" are stepped by (at first) 1/1000000 and if the 2 equations give a "crossover"
they are stored. When this process is complete 2 at a time of the stored values
are extracted and run with 'x' values of 1/1000000000000 !
My problem is to determine the range that 'x' should be set to.

EG. 185x^7 + x^5 - 3x2 - 29
the scan range would be +/- 185 ...

Help
Pete

Wow! 84??? I don't feel so bad at 56 answering math questions.

 

[nycmathguy]

Hi,
If possible could Alan answer this as we're similar in age (84)!

I was first an electronics eng. then a programmer.
Loved both occupations but programming was tops!
Stil writing progs. - math orientated

[1] I'm bothered when reading some Math books etc.
Some say that for a polynomial of degree N there are N roots
but I've some that have no roots.
[2] Written a program - Polynomials - that (tries) to determine factors.
After the standard methods have been used (including Synthetic Division) I run
a procedure DeepScan:
2 equations (both the same) are "fed" with different values of the independent variable 'x'
The "feeds" are stepped by (at first) 1/1000000 and if the 2 equations give a "crossover"
they are stored. When this process is complete 2 at a time of the stored values
are extracted and run with 'x' values of 1/1000000000000 !
My problem is to determine the range that 'x' should be set to.

EG. 185x^7 + x^5 - 3x2 - 29
the scan range would be +/- 185 ...

Help
Pete

What do you mean by scan range?

 

[TheOAP]

The 2 (identical) equations :
Delta = 1/1000000 (1E-6)(
Phase 1
---------
x1 = ?
x1---->Equation----> F(x1)
x2 = x1 + Delta
x2---->Equation----> F(x)
F(x1)( & F(x2) are examined for an intercept or a Root - if so they are stored
and x1/x2 are stepped.
X1 --> X2, X2 --> X1+ Delta
Carries on until end of search

Phase 2
----------
set Delta to 1E-12
Examine the results (if any)

Problem
----------

What value should I give to X1 at the start - at the moment it's the
(minus)highest absolute value of the constant or coefficient of the highest exponent!

Pete