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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 many unique count sets can be made from n variables? [migrated]

If I have n letters of the alphabet, how many unique sets of the letters can I make, where each unique set contains 1 to n letters? This is basically factorial arithmetic with the caveat that the set ...
David Wanjiru's user avatar
3 votes
2 answers
137 views

How to divide a known root out of a polynomial?

Consider this simple 5th order polynomial: pol=x^5+x^4+1 Factor[pol] (* (1+x+x^2)(1-x+x^3) *) root=FindInstance[pol==0, x] (* -1/2 -I/2 Sqrt[3] *) ...
Jos Bergervoet's user avatar
5 votes
3 answers
361 views

How to get the analytical form of a solution to an algebraic equation?

The real analytical solution of the algebraic equation $x^5 + 10 x^3 + 20 x == 4$ is $x=-2^{2/5} + 2^{3/5}$, how to get it with Mathematica? I've tried with ...
SHBooKP's user avatar
  • 370
0 votes
0 answers
25 views

How to Factor Out Polynomial Terms which Have Same Coefficient Differing Only by Sign

I'm new to the Mathematica StackExchange. I am trying to simplify a polynomial in Mathematica. In the following, I only show a part of the polynomial Here I want to combine terms with the same ...
Kazuki's user avatar
  • 1
0 votes
1 answer
40 views

How to factorize high-order polynomials that have only complex roots?

I have polynomials like this: ...
homocomputeris's user avatar
3 votes
2 answers
311 views

Better Factorization

It seems Mathematica likes to factor some things in less than optimal ways. For example, for the oscillating exponential function (F) below, is there any way to force it to reduce both the number of ...
ChaSta's user avatar
  • 1,095
2 votes
3 answers
86 views

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 ...
user1620696's user avatar
0 votes
1 answer
41 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 ...
Haiqin Tang's user avatar
1 vote
2 answers
91 views

How to break a term in its individual factors?

I have some algebraic term that looks like this, Conjugate[Subscript[u, 1, 1]] Conjugate[Subscript[u, 2, 1]] \!\(\*SubsuperscriptBox[\(u\), \(1, 1\), \(2\)]\) $$...
Endeavour 's user avatar
5 votes
2 answers
207 views

How to make FactorInteger iterative?

I want to factorize big numbers like 10^100. FactorInteger with no Automatic option can take a lot of time and as I know there ...
Андрей Яндуганов's user avatar
1 vote
1 answer
157 views

How to factor a quartic equation whose coefficient has unknown parameters?

i'm trying to see if a quartic equation I obtained can be factored into simpler forms, such as the product of two quadratics. The problem is that their coefficients are some complex expressions in ...
larry's user avatar
  • 735
6 votes
5 answers
543 views

Prime factors with multiplicity

This is the function I came up with: Flatten[ConstantArray @@@ FactorInteger[#]] & Is there a way to write this cleaner or point-free? Update: I only have ...
qwr's user avatar
  • 413
0 votes
2 answers
176 views

What method is there to retrieve which quantity to replace and complete factorization?

What method is there to retrieve which quantity to replace and complete factorization? The following polynomial equation cannot be directly factorized, and the result obtained by directly factoring is ...
csn899's user avatar
  • 4,315
3 votes
1 answer
114 views

Factor gives non-factorized result

The Factor built-in function is usually idempotent, namely applying it twice gives the same result. However, in the following example it is not. Is that expected? ...
Bruno Le Floch's user avatar
0 votes
0 answers
146 views

Factorization of 5th polynomial with Wolfram-Mathematica

I have a very complicated 5th-degree polynomial form. Using the factor function in Wolfram is impossible to make it because of the high degree. I just want to know that is it possible to factor as I ...
analog_designer's user avatar
1 vote
1 answer
49 views

Factoring without need to guess the extension

To provide a simple example (but I need more complicated ones): I want to factor x^2-6x*y+y^2. After solving x^2-6x*y+y^2==0 I ...
მამუკა ჯიბლაძე's user avatar
0 votes
1 answer
85 views

Stop Apart from automatically simplifying complex rational expressions [duplicate]

I want to conduct partial fraction decomposition to rational function on $\mathbb C$ and tried this ...
Po1ynomial's user avatar
0 votes
0 answers
64 views

How to properly factorize expression with respect to specific combinations of terms?

This is something that I have never been able to properly do in Mathematica so I wish to learn how to do it once and for all. I have the following expression in Mathematica: ...
Meclassic's user avatar
  • 1,015
2 votes
1 answer
74 views

How does Mathematica factor expression with derivatives (i.e. not polynomial)?

I was surprised Mathematica did this automatically. I have an ode and wanted to factor it. I did not think Factor will work and I need to write special code to do ...
Nasser's user avatar
  • 145k
3 votes
2 answers
265 views

Function to write an algebraic expression in terms of another

So I'm working on a physics problem. I have two functions: $\rho = \frac{F}{(\beta F^\alpha+1)^\frac{1}{\alpha}}$, $p = - \frac{F}{(\beta F^\alpha+1)^\frac{1}{\alpha}} + \frac{4}{3}\frac{F}{(\beta F^\...
Vicente Sierra Rosas's user avatar
0 votes
2 answers
58 views

Easiest way to print without breakline

So I have factorized a transfer function and stored the terms in a variable. I want to print the product of terms without Mathematica joining them and without a break line. I have managed the first, ...
Granger Obliviate's user avatar
15 votes
4 answers
2k views

Automating interesting ways to write 2023

Inspired by Interesting ways to write 2023, I was wondering if there are ways to automate the search for results using MMA. I tried ...
Moo's user avatar
  • 3,334
1 vote
0 answers
72 views

Putting everything with the same power together

I'm doing some computations wich involves a lot of big polynomials, for example: ...
User0212's user avatar
0 votes
1 answer
59 views

How to express the given function as a factor $e^{7 i x}$ times a real function?

I have the function $f(x,b,t,m)$ for $\{x>0,t,b\}$ all reals and $m=\{1,2,3,4,5,6\}$. For each particular $m\in\{1,2,3,4,5,6\}$, I see that $f(x,b,t,m)$ has a multiplicative factor $e^{7 i x}$ ...
math2021's user avatar
  • 749
0 votes
1 answer
50 views

Getting List of Factors in a monomial. Is FactorList reliable?

Say I'm given a monomial which is a product of factors, $X_{i_1} \times \cdots \times X_{i_n}$. I find that ...
Joe's user avatar
  • 175
4 votes
1 answer
97 views

Simplify polynomials with simple subfactors

I am trying to simplify expressions such as poly = 1 + (-2 + 4 a^2) x^2 + x^4 to the form polySimple = (1-x^2)^2 + 4 a^2 x^2 ...
John Bechhoefer's user avatar
0 votes
0 answers
63 views

Meaning of Extension option in Factor

I would like to ask about the Extension option in Factor function. In the reference, there is the following example. Factor a ...
user153012's user avatar
4 votes
2 answers
392 views

Factorize in a particular way

I was trying to factorise this polynomial expression: TestPolynomial=-p1^2 x1 x2 - p3^2 x1 x3 - p1^2 x2 x3 + 2 p1 p3 x2 x3 - p3^2 x2 x3 into this form, ...
Epsilon's user avatar
  • 1,122
-1 votes
1 answer
80 views

Factorize expression by specific term [closed]

I am new to Mathematica but I would like to know how to force Mathematica to factorize an expression by a specific term. Exemple, imagine I have a term like this: And I have an expression like this: ...
boris gbeasor's user avatar
6 votes
3 answers
211 views

Factoring a quadratic form associated with a $4 \times 4$ matrix into a sum of four squares

The matrix W = $\left( \begin{array}{cccc} 5 & 7 & 6 & 5 \\ 7 & 10 & 8 & 7 \\ 6 & 8 & 10 & 9 \\ 5 & 7 & 9 & 10 \\ \end{array} \right)$ has a ...
1729taxi's user avatar
  • 777
2 votes
0 answers
116 views

A remarkable elimination involving the basic reproduction number R0

I have a polynomial pol of third order, whose coefficients depend on 5 parameters, and whose free coefficient is proportional to R0-1, where R0 is a certain rational function of the parameters (the ...
florin's user avatar
  • 1,798
1 vote
0 answers
76 views

“Largest” symbolic common factor of an integer sequence (not simply GCD)

Suppose, I have a finite fragment of a quickly increasing sequence of integers $\{a_n\}$ that is too complex, unusual, or irregular for FindSequenceFunction to find ...
Vladimir Reshetnikov's user avatar
1 vote
2 answers
122 views

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, ...
akozi's user avatar
  • 873
3 votes
1 answer
155 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]. ...
user13892's user avatar
  • 9,443
0 votes
1 answer
54 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 ...
dtn's user avatar
  • 2,404
3 votes
0 answers
152 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 ...
Math Gaudium's user avatar
0 votes
5 answers
162 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 ...
Display Name's user avatar
  • 2,029
3 votes
1 answer
74 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 ...
tosburn3's user avatar
1 vote
1 answer
146 views

Factorize the multivariate polynomial [closed]

I came across the following problem: Factorize the multivariate polynomial given by: $$w*(A^2-2l*A+1)*f+v*(B^2-2m*B+1)g+u*(C^2-2n*C+1)*h+(w*(x+2A*l+A*s-l*s-A^2-1)+v*(y+2B*m+B*t-m*t-B^2-1)+u*(z+2C*n+C*...
Safwane's user avatar
  • 121
0 votes
2 answers
92 views

Extract subscript of variable in product

My input is a product of the variable x with index: x[1]^2 x[5] x[7] How do I extract the indices of the above product to get ...
Camilo's user avatar
  • 13
0 votes
1 answer
166 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 ...
Chris's user avatar
  • 1,033
0 votes
1 answer
134 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 ...
John Carter's user avatar
1 vote
2 answers
132 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 ...
Jan Eerland's user avatar
  • 2,001
3 votes
1 answer
104 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 ...
Descartes Before the Horse's user avatar
5 votes
1 answer
160 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: <...
Descartes Before the Horse's user avatar
2 votes
0 answers
154 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. ...
Ted Ersek's user avatar
  • 7,134
5 votes
3 answers
304 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,...
spore234's user avatar
  • 601
1 vote
3 answers
180 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 ...
W. Volante's user avatar
3 votes
2 answers
368 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'...
Steven Sagona's user avatar
2 votes
3 answers
280 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 ...
Anti Earth's user avatar
  • 1,211