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1
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2answers
57 views

factorization of integer into two parts with specific prime factors

I would like to write a Mathematica code to decompose an integer into two or more parts with primes in special intervals. For instance, I want to decompose $m=\binom{n}{k}$ into two parts U and V ...
2
votes
1answer
135 views

Tell Mathematica to factor something specific

Is there a way to tell mathematica to factor 1/(1-x^2) from a large expression? For instance if the expression is A_1+A_2+A_3 and I want to factor 1/(1-x^2) from A_1+A_2 but leave A_3 alone.
1
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1answer
101 views
1
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4answers
210 views

How do I create a list of 25 random quadratic equations in the form ax^2+bx+c?

My teacher suggests using the RandomInteger command along with the Factor command, but I cannot figure out the syntax. A, b, and c need to be non zero integers between -10 and 10.
2
votes
2answers
127 views

FactorInteger over UFDs

How can I factor 'integers' over other quadratic number fields (not just gaussian integers). For instance, how could I factor $7 = (3 + ω)(2 − ω)$ over Eisenstein integers ($ω = \frac{-1+ I ...
4
votes
1answer
185 views

Factoring a two variable polynomial in a special way

Let $$f=x^9-x^6+4x^5y+2x^3y^2-y^4$$ I would like to factorize $f$ into form: $$(y-F_1(x))\cdots(y-F_k(x))$$ over complex numbers. How can I do it with Mathematica?
1
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1answer
168 views

How to represent very long integers with at-most-8-digit(base-10) short integers with * and +

I need an algorithm in Mathematica, which can represent any very long integer, prime or not, into the the product operation "*" and sum "+" forms by short integers (not more than 8 decimal digits). ...
1
vote
1answer
206 views

Why doesn't FullSimplify work properly on this?

I wish to simplify the simple expression fac[n_] := Sum[R^i, {i, 0, n}]; as much as possible for various $n$. FullSimplify or ...
0
votes
1answer
102 views

Partial factorization of multivariate polynomials in terms of given polynomials

I have calculated several homogeneous polynomials in 4,5 or 6 variables $t_1,\dots,t_6$. I would like to rewrite them as a sum of products of specific lower degree polynomials, which have a meaning in ...
1
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5answers
111 views

What's wrong with my implementation of SquareFreeQ?

This was a question I had last month: Part A: Looking at the exponent of each of the elements in the list, FactorInteger and using ...
1
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0answers
178 views

Polynomial factorization over finite fields with non-prime order

One can easily factor a polynomial over finite fields of prime order, using Factor command: ...
0
votes
1answer
418 views

Factoring a quintic

I am trying to prove that a quintic polynomial, $p(x) = A5 x^5 + A4 x^4 + A3 x^3 + A2 x^2 + A1 x + A0$, which admits at most three real roots. Unfortunately Descartes' rule of signs does not help, ...
1
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1answer
113 views

Forming product of function of prime factors

Given a list of numbers each containing 2 prime factors, I wish to make a list of the products of the logs of each factor. For example, given L = {4,6,9}, I would like to form P = ...
2
votes
1answer
180 views

Expressing large numbers in index form

I have a quick question. Is there anyway of expressing a large number as a power of another number in Mathematica? By this, I mean for example, $1237940039285380274899124224 = 512^{10}$. Is there a ...
3
votes
1answer
171 views

Generating a list of all factorizations

What is the best way to generate a list of all factorizations of some number $n$? I'm quite new to Mathematica so this might be obvious. I have been trying some basic stuff with ...
22
votes
3answers
579 views

Common subexpression from two expressions

I am working with some unpleasantly tedious polynomials, which need to be manipulated in various ways (integrate with respect to some variable, differentiate with respect to another). Since these ...
1
vote
1answer
89 views

Factorize and find the null space of a polynomial in several variables [duplicate]

I've been asked to factor the following polynomial: poly = 6 x^3 + x^2 y - 11 xy^2 - 6 y^3 - 5 x^2 z + 11 xyz + 11 y^2 z - 2 xz^2 - 6 yz^2 + z^3 And to solve for z so that poly = 0 Can anyone help ...
1
vote
1answer
292 views

How can I factor my trigonometric equation?

The equation $$3\sin^2 x - 3\cos x -6\sin x + 2\sin 2x + 3=0$$ has a solution $x = 0$. That means it has a factor of $\cos x - 1$. I tried to write the given equation has the form $$(\cos x - ...
3
votes
2answers
249 views

Find the a factor of an integer which is nearest to another integer

If I know two integers $n$ and $m$ and $m < n$, how can I find two different integers $x$ and $y$ that are nearest to $m$, and satisfy Mod[n,x]==Mod[n,y]==0 ? ...
2
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1answer
142 views

Implementation of Decompose

I'm curious as to how Decompose works so I decided to use Trace with the option ...
5
votes
2answers
245 views

How can I make the output from Solve look nice?

I have a problem with presenting solutions. Roots of 4th order polynomials are big expressions. Is there a way to present the roots, s2 and s3, in normal form with some substitutions? Maybe a way to ...
2
votes
2answers
320 views

Lists of coefficients of derivatives

I want to extract two separate lists of coefficients of derivatives. If I have, for example, ...
2
votes
3answers
425 views

Generating pairs of additive and multiplicative factors for integers

Given an integer $n$, I want to get two lists: a) the set of pairs of the divsors $a,b$ into exactly two factors $n=a\cdot b$, b) the set of pairs $a,b$ of two summands $n=a+b$. The code I ...
5
votes
1answer
355 views

Time approximation of decrypting RSA algorithm

I've written a function that encrypts a text using the RSA algorithm. It then decrypts it using prime factorization, and takes the time it took to decrypt it and puts it in a vector together with the ...
1
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1answer
131 views

Factorize Parametric Polynomials

Is there a possibility to factorize a parametric polynomial expression - meaning that the coefficients are defined as parameters, and not as specific numbers? My example - a polynomial in ...
8
votes
0answers
473 views

Does Mathematica use the Elliptic Curve Method (ECM) in FactorInteger[]?

I'm not a mathematician, and I'm not even going to pretend that I understand anything of the ECM. But I know it can be a fast method for factorization. I benchmarked the factorization of ...
8
votes
4answers
5k views

Factoring polynomials to factors involving complex coefficients

I've run into some problems using Factor on polynomials with complex coefficient factors. Reading the documentation it looks like it only factors over the ...