Items tagged with factorization


I have the following Polynomial F. Computing the genus shows that this curve has negative genus and thus is reducible. But using AFactor doesn't produce a factorization. Any ideas?

F := z^9+(-3/2+(3/2*I)*sqrt(3))*y^3*z^6+(-3/2-(3/2*I)*sqrt(3))*x^3*z^6+(-3/2-(3/2*I)*sqrt(3))*y^6*z^3+(-3/2+(3/2*I)*sqrt(3))*x^6*z^3+y^9+(-3/2-(3/2*I)*sqrt(3))*x^3*y^6+(-3/2+(3/2*I)*sqrt(3))*x^6*y^3+x^9-3*(x*y*z)^3:
genus(F, x, y);

hey guys Im new client in maple and today I was about check out the resualt of my mathematic quastion with maple.

I need a step by step solution and exact command to give me true resualts 

for example 

how can I expand a factorization like (x^2-y^2) to (x-y)(x+y)

in a little more  complicated form (cd-1)^2-(c-d)^2/(d^2)(c-1)=5 the value of c=?

for solve this problem I need to expand (cd-1)^2-(c-d)^2 than other expands & in the end value of c

I dont have anymore time for my mathemathic exam so know that how maple works in basic and intermadiate mathematic level is important to me

thank you guys




Would anyone know how to customize the CompleteSquare function. Reason is I am trying to extend it to complex numbers. Examples below. (Unfortunately the text editor is playing up but if you could copy and paste the text below in your Maple you should be able to see it more clearly).


eqn1 := x__1^2+4*x__1*x__2+2*x__2^2;


CompleteSquare(eqn1, [x__1, x__2]);


This gives the answer below which is correct.



However consider the complex function below:



I am trying to factorize this into the following:



The technique I am trying is to first try to come up with a generalized form of the CompleteSquare function and then try to extend it to complex factorization but so far haven't been successful.


Any useful comments appreciated.

Let's say I've got somehow a result of the product:


as series expression and I want to factor out the series of


in order to get


How can I do that with Maple?

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

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