## AFactor doesn't factor a (supposedly) reducible po...

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?

```with(algcurves):
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:
z:=1:
genus(F, x, y);
evala(AFactors(F));
```

## How to expand and factor this?...

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

Hi,

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;

with(Student[Precalculus]):

CompleteSquare(eqn1, [x__1, x__2]);

This gives the answer below which is correct.

2*(x__2+x__1)^2-x__1^2

However consider the complex function below:

x__1*conjugate(x__1)-conjugate(x__1)*x__2+3*conjugate(x__1)*x__3-conjugate(x__2)*x__1+2*x__2*conjugate(x__2)+3*conjugate(x__3)*x__1+14*x__3*conjugate(x__3)

I am trying to factorize this into the following:

(x__1-x__2+3*x__3)*(conjugate(x__1)-conjugate(x__2)+3*conjugate(x__3))+(x__2+3*x__3)*(conjugate(x__2)+3*conjugate(x__3))-4*x__3*conjugate(x__3)

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.

## How do I factor out it?...

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?

## Square Free Factorization ...

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; g ← f′;
if g ≠ 0 then {
c ← gcd(f, g);
w ← f/c;
while w ≠ 1 do {
y ← gcd(w, c); z ← w/y;
R ← R·zi; i ← i+1; ```
```           w ← y; c ← c/y }
if c ≠ 1 then {
c ← c1/p;```
`           Output(R·SFF(c)p) }`
```     else  Output(R)
else {
f ← f1/p;```
`           Output(SFF(f)p) }`
`  end.The attached file my try to make this, please find and help me to complete this. I am waiting your kind response.Help.mw`

With my best regards and sincerely.

` `

## Complex solution...

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

Digits:=900;

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;;

## Error, (in evala/Factors) input must be polynomial...

Hi,

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 ) {

System.out.println(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.

## Factor symbolic function for martrices...

Hello,

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

then C:= A*B :

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.

vidocq

## Why are polynomials including constants not factor...

Hello,

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

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

to output

`-Pi*(-t+I)*(t+I)`

`Pi*(t^2+1)`

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)

`-pi*(-t+I)*(t+I)`

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

`factor(Pi*(t^2-1));`

results in

`Pi*(t-1)*(t+1)`

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

`factor(Pi*(t^2-1),{});`

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!?

Thanks,

Erik

## how to solve hensel lifting algorithm in maple?...

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]?

## Simplifying a symbolic expression (4th order). Is ...

Hello all,

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

## How can I use factor in equations?...

How can I use factor in equations?

For example:

x^6+y*x^4+z*x^2-g*x^4-3*x^6====>-2*x^6+(y-g)*x^4+z*x^2

or

a*cn+w*dn+e*cn+f*dn=====>(a+e)*cn+(w+f)*dn

These examples are very simple.

Thank you

## How many divisors...

`with(numtheory);divs:=proc(k)local n,q:for n from 1 to infinity doq:=tau(n);if k=q then break;end if;end do;return [q,n];end proc;[seq(divs(i),i=1..20)];`
` `
`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?`
` `
`Eryndis`