# Questions tagged [factorization]

Questions on factoring various types of mathematical expressions, with the use of Factor, FactorInteger, FactorSquareFree and related commands.

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### How to factorize $x+y$ in this kind of example?

Consider the following simple polynomial in two variables 5 + 2x + 2y. Suppose I want to simplify it to 5+2(x+y). I have no idea ...
39 views

### How to make MMA distinguish between symbolic coefficients and variables when doing factorization? [closed]

I what to factor a polynomial with complicated symbolic coefficients Factor[p0^2 + k^2 r^2 \[Tau]^2 - 2 k p0 r \[Tau]^2 \[Omega] + p0^2 \[Tau]^2 \[Omega]^2] In ...
1 vote
88 views

88 views

### Extract subscript of variable in product

My input is a product of the variable x with index: x^2 x x How do I extract the indices of the above product to get ...
143 views

### How to prime factorise rational numbers [closed]

I'm aware of the built-in FactorInteger command for finding the prime factorisation of integers. Is there a convenient way of determining the same thing for a rational number, where the prime ...
131 views

### Factorizing large numbers [closed]

I am trying to factorize large prime numbers with the code bellow. The code works properly for values like 1927 and 69527 (results), but gives no result for larger values like 655051. The code goes as ...
1 vote
126 views

### How can I test if the sum of two divisors of a number add up to a perfect square? [closed]

Let's say I have a number $n$ and I want to find the divisors of $n$, I can do that using Divisors[n]. That will generate a list ...
102 views

### Return the factors of a partially-factored polynomial, without factoring

Suppose I have an integer polynomial f that is in a factored form, say f = (1 + x) * (2 + x + x^3) * (2 + x^5). I want a ...
147 views

### Check if polynomial is in factored form, without factoring

I have a large list list of integer polynomials, all of which are the output of Factor. So my list looks something like this: <...
143 views

### About Fermat's Integer Factoring algorithm

An implementation of Fermat's algorithm that is a slight improvement on code in this book is here. ...
296 views

### Speeding up FactorInteger for product of two primes

I have a large integer $N$ of size about 10^150. I know that $N$ is a product of two primes $p$ and $q$. I also know that both $p$ and $q$ are of roughly equal size, so one of them is not, for example,...
1 vote
175 views

### How to factorize $f(x,y)$ into $f_1(x)f_2(y)$? [duplicate]

Suppose we have a real function $f:\mathbb R^2 \rightarrow \mathbb R$ and we would like to know if this function factorizes into $f(x,y)=f_1(x)f_2(y)$ for some real functions $f_1,f_2$. Is there an ...
321 views

### How to factor a polynomial expression with variable coefficients (and imaginary values)

How can I factor terms with variable coefficients? For example for the expression: $x^2 + a$ I know that I can factor this to: $(x+i\sqrt{a})(x -i\sqrt{a})$ How do I do this in mathematica? I would'...
236 views

### Collect with a product of patterns

In the examples below, I notate Subscript[S, n] as Sn for brevity. I'm trying to take expressions like ...
1 vote
121 views

### How to find the 2 smallest integers that is divisible by 40131 and 41405 [closed]

I'm trying to find the two smallest integers that is divisible by 40131 and 41405, i.e 40131|a, 41405|a, 40131|b and 41405|b. There is a hint within the question that says you can use FactorInteger[] ...
340 views

### How to write a positive function as sum of positive terms only

A multivariate polynomial function can be written in a certain form (x^m (1-x)^n y^k + ... ) if the function is Positive in the whole domain and contains a finite ...
41 views

### Can you save each factor of a polynomial?

I have a question I'm factoring a polynomial in Mathematica. After having the polynomial factored, I want to manipulate each factor. So my question is if there is anyway I can save each factor in a ...
204 views

### Prime factorization over the Eisenstein integers $\mathbb{Z}[\zeta]$

I am trying to write a function f[a_,b_] which takes in two integers $a,b$ and returns the unique factorization of $a+be^{2\pi i/3}$ into the primes belonging to \$\...
1 vote
I have the following equation: $$\frac{2\left(a A_3 r + \frac{1}{2} r^2 a'^2 \right)}{a^2 r^2}=\frac{8 G \pi \rho}{3}-\frac{c^2 k}{a^2}$$ ...