Questions tagged [factorization]
Questions on factoring various types of mathematical expressions, with the use of Factor, FactorInteger, FactorSquareFree and related commands.
197 questions
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What is the meaning of the output when the modulus is a polynomial?
The documentation of Modulus suggests that the value of this option should be an explicit number (or Automatic). However,
...
- 627
2
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1
answer
149
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Factor out specific term
I want to transform expr by factoring out only the E^(-t γ) term. I could implement it like in my code below, but is there a ...
- 1,484
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Factor polynomial with generalized root extension
Here are two examples with ordinary extensions:
Factor[1 + x^4, Extension -> Sqrt[2]]
Factor[x^2 + 2 Sqrt[3] x + 3, Extension -> Automatic]
But what about &...
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0
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0
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56
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How to factor 8 x^2 - 73 y^2 [duplicate]
Factor[8 x^2 - 73 y^2] returns
8 x^2 - 73 y^2
How do I go about factoring it into
(8^.5 x + 73^.5 y)*(8^.5 x - 73^.5 y)
?
- 2,072
1
vote
0
answers
159
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How to improve polynomial factorization performance [closed]
I was solving a RSA factorization problem with a weak prime. In a given base, the prime was made of a lots of zeroes and can be factorized pretty quickly. See this write-up.
I checked the code for ...
- 382
2
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3
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216
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Factoring Laurent polynomial - how to distribute powers in denominator to get polynomial Laurent factors
Not sure how to do this with Factor/Collect etc. I'm thinking this might not be straightforward at all.
Given a large Laurent polynomial I am trying to factor it into irreducible Laurent polynomials.
...
- 441
3
votes
2
answers
194
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] *)
...
- 381
5
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3
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450
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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 ...
- 433
0
votes
1
answer
133
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How to factorize high-order polynomials that have only complex roots?
I have polynomials like this:
...
- 235
3
votes
2
answers
380
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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 ...
- 1,197
2
votes
3
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150
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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 ...
- 643
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1
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74
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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 ...
0
votes
2
answers
100
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Factorize into only positive terms, when values are known to be probabilities
I have a large term (a small snippet of which is below as an example) that I am aiming to prove is positive. I know that all the involved values are probabilities and in particular, they lie in (0, 1)....
1
vote
2
answers
143
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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[\(u\), \(1, 1\), \(2\)]\)
$$...
- 11
5
votes
2
answers
288
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 ...
1
vote
1
answer
259
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 ...
- 755
8
votes
5
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782
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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 ...
- 433
0
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2
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227
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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 ...
- 1
3
votes
1
answer
146
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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? ...
- 2,049
0
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0
answers
205
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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 ...
1
vote
1
answer
80
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 ...
- 2,459
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1
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137
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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
...
- 181
0
votes
0
answers
90
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:
...
- 1,065
2
votes
1
answer
160
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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 ...
- 156k
3
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396
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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^\...
0
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2
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135
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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, ...
16
votes
5
answers
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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
...
- 3,556
1
vote
0
answers
107
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Putting everything with the same power together
I'm doing some computations wich involves a lot of big polynomials, for example:
...
- 95
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1
answer
109
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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}$ ...
- 749
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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
...
- 175
4
votes
1
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158
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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
...
- 375
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0
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93
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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 ...
- 501
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votes
2
answers
786
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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,
...
- 1,122
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votes
1
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111
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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:
...
6
votes
3
answers
341
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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 ...
- 826
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0
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142
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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 ...
- 2,380
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0
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123
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“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 ...
- 6,611
1
vote
2
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181
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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, ...
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1
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252
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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].
...
- 10.4k
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1
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75
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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 ...
- 2,665
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0
answers
197
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 ...
- 487
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5
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224
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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
...
- 2,069
3
votes
1
answer
116
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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 ...
- 33
1
vote
1
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191
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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*...
- 121
0
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2
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137
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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 ...
- 13
0
votes
1
answer
225
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 ...
- 1,073
0
votes
1
answer
190
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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 ...
- 37
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2
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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 ...
- 2,021
3
votes
1
answer
133
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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 ...
5
votes
1
answer
206
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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: <...