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Dear hope you will fine. I am try to make a program of square free factorization over a finite field whose alogrithm is below:

Algorithm: SFF (Square-Free Factorization)
  Input: A monic polynomial f in Fq[x]
Output: Square-free factorization of f

i←1; R ← 1; gf′;
  if g ≠ 0 then {
     cgcd(f, g);
     while w ≠ 1 do {
           ygcd(w, c); zw/y;
           RR·zi; i ← i+1; 
           wy; cc/y }
     if c ≠ 1 then {
           Output(R·SFF(c)p) }
     else  Output(R)
  else {
           Output(SFF(f)p) }

The attached file my try to make this, please find and help me to complete this. I am waiting your kind response.

With my best regards and sincerely.


This may be a trivial question, but does this factor fully with the newer versions of Maple, say at 900 digits?



rho_poly := -2201506283520*rho^32+(-17612050268160+104204630753280*I)*rho^31+(2237195146493952+737798139150336*I)*rho^30+(14065203494780928-29153528496783360*I)*rho^29+(-260893325886750720-161432056834818048*I)*rho^28+(-1240991775275876352+1727517243589263360*I)*rho^27+(8952004373272068096+6696323263091441664*I)*rho^26+(25553042370906292224-37948239682297921536*I)*rho^25+(-135024511500569280512-65293199430849134592*I)*rho^24+(-79740262928225402880+401487130320847241216*I)*rho^23+(956745211126674882560-164797793704574713856*I)*rho^22+(-1213375867282228772864-1655554058430246551552*I)*rho^21+(-1483956336776821211136+3604946201834409820160*I)*rho^20+(6525094787202650144768-1597915397190007586816*I)*rho^19+(-8575469412912592879616-6168391294117580865536*I)*rho^18+(2408139380338842796032+15004449784317106323456*I)*rho^17+(10583091471310114717696-17047513330720373194752*I)*rho^16+(-22619716982813548707840+8898637295768494915584*I)*rho^15+(26538067620972845277184+5129530051326543351808*I)*rho^14+(-21415800164460070789120-17268159356969925234688*I)*rho^13+(11916012071577094946816+22601135173030541677568*I)*rho^12+(-3551246770922037813248-21229478915196610975744*I)*rho^11+(-977434486760953073664+16249214903618313346048*I)*rho^10+(1977414870691507931136-10721551032564274826240*I)*rho^9+(-1197394212949208115968+6172794574205050632192*I)*rho^8+(280273257275327368320-2996290081120136529792*I)*rho^7+(108849195761508531648+1152454823926345101504*I)*rho^6+(-119736267114490955904-327757949185254534784*I)*rho^5+(49149411853848597568+63563541902968683712*I)*rho^4+(-11524495997215059744-7307364351434838944*I)*rho^3+(1585189353379709888+299568910286253408*I)*rho^2+(-116032795768295808+25487628220230528*I)*rho+3299863116538269-2454681763039104*I;;



I'm using Java OpenMaple interface to call Maple functions from Java on Ubuntu Linux. I'm following the examples provided on Maple website. My Java code:


import com.maplesoft.openmaple.*;

import com.maplesoft.externalcall.MapleException;

class test {

    public static void main( String args[] ) throws Exception {

        String[] a = {"java"};

        Engine  t = new Engine( a, new EngineCallBacksDefault(), null, null );

        try {

            t.evaluate( "factor(-8*((16*I)*g**4*(-4*mc**2+u)**(-2)*(4*mb**2-u)**(-2)*u**(-1)*(12*mb**2-u)*(-4*s*mb**2+16*mb**4-4*u*mb**2+t*u-4*t*mb**2)*s*(4*s*mb**2+4*mc**2*s+16*mc**2*mb**2-s**2-4*t*mc**2+t**2-4*t*mb**2)*(12*mc**2-u)+(16*I)*(4*s*mb**2+4*mc**2*s+u**2-4*mc**2*u+16*mc**2*mb**2-4*u*mb**2-s**2)*(12*mc**2-t)*g**4*(t-4*mb**2)**(-2)*(4*mc**2-t)**(-2)*(-t+12*mb**2)*(-4*s*mb**2+16*mb**4-4*u*mb**2+t*u-4*t*mb**2)*s*t**(-1))**2);" );


        catch ( MapleException e ) {






Maple throws exception:

com.maplesoft.externalcall.MapleException: Error, (in evala/Factors) input must be polynomials over the integers

The input polynoial is valid (when coping and pasting `factor(...)` directly into Maple interface, all works). When trying to factor simple polynomials like "x**2 - I*x" all goes fine too. Tried both Maple 17 and 18 (Linux).

PS. There is no problem when running this code on OS X (I tried Maple 16, 17, 18),  but I need to be able to run Maple with Java on my Linux cluster.



I would like to ask for help with factorization, collection or decomposition of matricies. If I have the symbolic product of matrices:

A := Matrix(2, 2, {(1, 1) = a[11], (1, 2) = a[12], (2, 1) = a[21], (2, 2) = a[22]})

B := Matrix(2, 2, {(1, 1) = b[11], (1, 2) = b[12], (2, 1) = b[21], (2, 2) = b[22]})

then C:= A*B :

Matrix(2, 2, {(1, 1) = a[11]*b[11]+a[12]*b[21], (1, 2) = a[11]*b[12]+a[12]*b[22], (2, 1) = a[21]*b[11]+a[22]*b[21], (2, 2) = a[21]*b[12]+a[22]*b[22]})

and my question follows:

Can I factor this result C and get the imput matrices A and B ? Is any function for this operation ? I would like to use it for matrices 3 time 3 not only for 2 times 2.

Thank you for your help,




I have trouble in using the function factors. For example, I expect

factor(Pi*(t^2+1), {I});

to output


but instead the result is


This problem does not appear if Pi gets replaced by a general symbol:

factor(pi*(t^2+1), {I});

produces (as I expect it should)


The problem seems to be tied to symbols representing constants, as for example replacing Pi by Catalan also results in no factorization being performed. It further seems to be tied to specifying a splitting field, because


results in


Is this behaviour intended? Probably the reason is that the polynomial does not have algebraic coefficients (as it includes Pi). Indeed,


produces the error message

Error, (in factor) expecting a polynomial over an algebraic number field

But why does this error then not appear for the call factor(Pi*(t^2-1))? If this would assume complex coefficients, it should factor using I. Considering coefficients in an algebraic number field, also the original call factor(Pi*(t^2+1), {I}); should raise an error!?



we use Modern Computer Algebra

let f=x^15-1 belong to Z[x]. take a nontrivial factorization f≡gh mod 2 with g,h belong to Z[x] monic and of degree at least 2. computer g*,h* belong to Z[x] such that   f≡g*h* mod 16 ,deg g*=deg g, g*≡g mod 2.

show your  intermediate. can  you guess some factors of f in Z[x]?


Hello all,

I would like to use Maple to simplify an expresion of this form:

How can I use factor in equations?

For example:




These examples are very simple.

Thank you

I made a prodecure:

local n,q:
for n from 1 to infinity do
if k=q then break;
end if;
end do;
return [q,n];
end proc;
I have make it for i from 1 to 100 too, but it should work in five minutes. I think it should be made somehow with the integer factorization, but i can't realize it. Can someone help me?

I'd like to take the output of ifactor(n::posint), the prime factorization of n, and index the terms of the product to a list. ie: ifactor(256)=2^8 so [2,2,2,2,2,2,2,2]. or 135 -> (3^3)(5)->[3,3,3,5].
Any suggestions? 

if my eqsn is x^4+x^3+x^2 . i can take a common factor x^2 ,then the eqsn will be x^2(x^2+x+1) ...also i can take a common factor of x ...then the eqsn will be x(x^3+x^2+x) can i direct maple about my common factor ...u think this is useless but i have just made my problem simple to ask a qsn so that everyone can understand what i really want to tell

I have a long expression which I want to factor optimally.  If I can cancel terms in the numerator and denominator, great, and if not, I just want to reduce the size as best possible.  Maybe there will be terms such as

(x12 + x32 + y12 +y32)*(x22 + x42 + y22 + y42)

which I see when factoring the denominator by hand.  Here's the worksheet, the final...

I start with a question, but not an how-to question, because I am puzzled by why such a routine is missing.

Why does Maple not have  generalized Schur (real and complex) factorizations with reordering?  The nice solution of many dynamic equations requires this factorization because the lhs is singular. MatLab does have such a routine. At the moment, it seems, one has to have accessible and connect to MatLab or NAG or LAPACK for such routines.

Is this...

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