# 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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### Finding coefficients where part of the coefficient may appear in the terms

A minimal example is given below. My goal is that given a algebraic expression such as: expr = a^2 + a b + a^3 b + 2 a^2 b^2 + a b^3 I'm trying to find a command, ...
546 views

### Factorize trigonometric matrices

Consider two square matrices $A_1$ and $A_2$. Consider the following matrix involving matrix trigonometric functions: \begin{equation} M_1(t)=\begin{bmatrix} \cos(tA_1) & t\mathrm{sinc}(t A_1) \\ ...
103 views

### Is there a way to collect the multiple power into a single power?

I am looking away to factor perfect powers like follows: FactorPerfectPower[16x^2] should produce Inactive[Power][4x,2]. ...
105 views

### Approximate integer factorization

Suppose we would like to compute an approximate prime factorization of a large integer x in the sense that the difference between ...
33 views

### Simple Question: Cut Number in Transfer function

Given transfer function: $W=\frac{10 (s+100)}{2 s^4+219 s^3+1909 s^2+900 s+1000}$ W=(1000 + 10 s)/(1 (1000 + 900 s + 1909 s^2 + 219 s^3 + 2 s^4)) Which command to ...
152 views

### How to convert $a(x-p)^2+q$ to $a(x-\alpha+i\beta)(x-\alpha-i\beta)$ for any real $a$, $p$ and $q$ [duplicate]

I want to factorize any quadratic expressions into two complex-valued linear expressions. My effort below ...
54 views

### Expression should vanish under assumptions. How can I use Mathematica to simplify this type of of expression (and similar)?

This is maybe the worst type of question because it is super specific, but I am hoping that some Mathematica function or rule exists (built-in or custom) that can be helpful for simplifying a somewhat ...
78 views

131 views

### Factoring problem

Keep factoring and concatenating starting with 2 until we get a prime, i.e. 2 = 2 ; 22=2.11 ; 22211=7.19.167 ; 22211719167=..... and so on (the prime factors are arranged from smaller to larger and ...
80 views

### Factor[p(x), a, b] not working in Galois theory package

I have downloaded Galois theory package from http://library.wolfram.com/infocenter/Articles/2872/ and I currently have Mathematica v 12.0. When I loaded the module (I needed to delete the blue stuff ...
54 views

### Removing all prime factors less than n from a number

Is there an efficient way to check a number x and remove all prime factors in the number which are less than some n? For example for n = 200: ...
61 views

### Factorizing non commutative terms

Is it possible to factor a ** b ** c - a ** b ** d as a ** b ** (c - d) ? I am using ...
53 views

### Why is the result of MMA polynomial mod factor different from that of this article? [closed]

Why the polynomial mod factor of MMA is not the same as the result of this SE answer: ...
39 views

### Arrange a polynominal

I have a complex polynomial in more than ten line. I want to rearrange it by the power of another polynomial. For example, I have a powers of (1-A(x)/x^2) as a factor in it, and I want to sort the ...
91 views

### Generating summation formulas for factorized 4th moments

I'm interested in getting summation formulas for the following expression, in Einstein summation notation, with indices ranging from $1$ to $d$ $$c=X_{ik}M_{ijkl}X_{jl}$$ Here $M_{ijkl}$ is ...
107 views

### prime number digits less than n? [closed]

How can I ask mathematica to sieve with only primes with three-digit less than a given number. Thank you for instance I want to find the prime factor of 1337. Thank you
126 views

### Group symbols by a given partition of the occuring symbols

I have following expression $$-3 b_{\sigma _d}-3 b_{\sigma _v}-b-b_2+2 j-2 j_2-2 j_3+2 j_6+12$$ Mathematica input ...
100 views

### Why does Factor[] not factor -1?

Consider the two expressions -2a-2b and -a-b. The TreeForm[] looks identical However, ...
127 views

### Simplify the cubic root of cube assuming real and positive variable

I know this is very simple but I couldn't find a reasonable solution for it in the archive. It seems that my Mathematica does not take into account the assumptions when it wants to simplify the ...
Say I have an expression $$x = L-(L-N)y^2(1+AB)$$ is there a way I can use mathematica to put the expression into the form $$x = M(1+\sigma B)$$ where $M$ and $\sigma$ are lumped terms?
### Mathematica not converting $A A$ to $A^2$ [closed]
I'm trying to factor a large polynomial $p$ in Mathematica. When running $\text{Factor}[p]$, however, one of the factors is $-Aq + A^2 Aq + 2 A q - 2 A Aq^2 q - Aq q^2 + A^2 Aq q^2$. This is clearly ...