Questions tagged [factorization]
Questions on factoring various types of mathematical expressions, with the use of Factor, FactorInteger, FactorSquareFree and related commands.
158
questions
2
votes
0answers
67 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 ...
0
votes
5answers
149 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
...
3
votes
1answer
51 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 ...
1
vote
1answer
69 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*...
0
votes
0answers
52 views
Can mathematica solve this analysis difficult problem ? “Functional” equation
Given two continuous functions $G,H: \mathbb R^+ \rightarrow \mathbb R$ such that $\frac{G}{H}$ is positive and strictly increasing, I am looking for two continuous functions $f_0, f_1 :[0,1] \...
0
votes
2answers
53 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 ...
0
votes
1answer
67 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 ...
0
votes
1answer
115 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
2answers
75 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 ...
3
votes
1answer
61 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 ...
5
votes
1answer
102 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: <...
2
votes
0answers
51 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.
...
5
votes
3answers
235 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
3answers
157 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 ...
3
votes
2answers
133 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'...
1
vote
3answers
103 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
5answers
107 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[] ...
3
votes
2answers
256 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 ...
0
votes
0answers
32 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 ...
4
votes
0answers
109 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
1answer
44 views
A question about FactorList[] [closed]
FactorList[24 + 80 x + 102 x^2 + 62 x^3 + 18 x^4 + 2 x^5]
{{2, 1}, {1 + x, 2}, {2 + x, 2}, {3 + x, 1}}
what does the "1" of "{2,1}" mean?
0
votes
0answers
61 views
Help me factor this equation
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}$$
...
0
votes
2answers
196 views
How to factor a polynomial expression in MATHEMATICA?
I want to factorize the following polynomial in MATHEMATICA:
$1 - 2 r + r^2 - 2 s + 2 r s + s^2 - 2 t + 2 r t + 2 s t -
4 r s t + t^2$.
...
1
vote
1answer
61 views
Force factor extraction from a polynomial [closed]
I have the following polynomial
$$27 m^7 + 117 m^6 s^{\frac{1}{2}} - 114 m^5 s - 273 m^4 s^{\frac{3}{2}} + 15 m^3 s^2 +
91 m^2 s^{\frac{5}{2}} - 7 s^{\frac{7}{2}}$$
and I want to force Mathematica to ...
5
votes
1answer
89 views
Split Expression Into Constant And Non-Constant Summands
I have a partially t-dependent matrix which I want to split into its t-dependent and its t-...
5
votes
2answers
112 views
What exactly does FactorTermsList do?
What exactly does FactorTermsList do? The documentation is not complete in that it only gives examples, not a precise definition:
What exactly is the "overall ...
0
votes
1answer
33 views
Reducing large polynomial expression to product of simplar polynominals
A beginner to Mathematica.
I am trying to express a large symbolic polynomial expression as a product of factors of simpler polynomials:
For example I was able to factor this expression:
...
1
vote
1answer
58 views
Cancel out common factors in algebraic expressions that are equal to zero
I have the following original expression:
(100 c)/(e y) + (100 b x)/(e y) + (100 a x^2)/(e y) == 0
which, after factoring out the common terms looks like this ...
6
votes
1answer
230 views
(Eisenbud) Factorization of a polynomial into factors with matrix coefficients (“matrix factorisation”)
According to the work of David Eisenbud cited below, it is possible to factorize almost any polynomial with matrices (exclusions ~ no linear terms), and this has apparently been of great use to string ...
0
votes
1answer
69 views
Factor polynomial with specific common variables (terms)
I want to factor the following polynomial:
b*p - b*q + c*q - c*r - a*(p - r)
When I use the function FactorTerms. I get the ...
0
votes
2answers
50 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:
...
1
vote
1answer
56 views
Factorizing non commutative terms
Is it possible to factor
a ** b ** c - a ** b ** d
as
a ** b ** (c - d)
?
I am using ...
1
vote
0answers
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:
...
asked Jan 28 '20 at 2:29
A little mouse on the pampas
5,1702 gold badges9 silver badges28 bronze badges
0
votes
0answers
37 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 ...
1
vote
1answer
89 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}$$
Here $M_{ijkl}$ is ...
2
votes
3answers
107 views
prime number digits less than n? [closed]
How can I ask mathematica to sieve with only primes with three-digit less than a given number. Thank you
for instance I want to find the prime factor of 1337. Thank you
1
vote
1answer
73 views
Factor[p(x), a, b] not working in Galois theory package
I have downloaded Galois theory package from http://library.wolfram.com/infocenter/Articles/2872/ and I currently have Mathematica v 12.0.
When I loaded the module (I needed to delete the blue stuff ...
3
votes
0answers
99 views
Why does Factor[] not factor -1?
Consider the two expressions -2a-2b and -a-b. The TreeForm[] looks identical
However, ...
3
votes
2answers
126 views
Group symbols by a given partition of the occuring symbols
I have following expression
$$-3 b_{\sigma _d}-3 b_{\sigma _v}-b-b_2+2 j-2 j_2-2 j_3+2 j_6+12$$
Mathematica input
...
2
votes
1answer
76 views
Factorization of multivariable polynomial
I have a multivariable polynomial, for instance: $P=yx+2^4xy+3+5^2xz+3^4zx $
I would like to do the following:
extract those terms that only have $z$
extract terms that only have $y$
express my ...
3
votes
2answers
112 views
Simplify the cubic root of cube assuming real and positive variable
I know this is very simple but I couldn't find a reasonable solution for it in the archive. It seems that my Mathematica does not take into account the assumptions when it wants to simplify the ...
0
votes
1answer
62 views
Factoring Algebraic Expressions [closed]
Say I have an expression
$$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)$$
where $M$ and $\sigma$ are lumped terms?
-1
votes
1answer
105 views
Mathematica not converting $A A$ to $A^2$ [closed]
I'm trying to factor a large polynomial $p$ in Mathematica. When running $\text{Factor}[p]$, however, one of the factors is $-Aq + A^2 Aq + 2 A q - 2 A Aq^2 q - Aq q^2 + A^2 Aq q^2$. This is clearly ...
0
votes
1answer
43 views
0
votes
1answer
157 views
Approximate Simplify (or factorization) [closed]
Suppose I have
$$(2+2a+a^2)(RC)^2 + RC(5+2a)t+t^2$$
I can factor $(2+2a+a^2) = 1+(1+a)^2$. When I assume $a \gg 1$ then $1+(1+a)^2\approx (1+a)^2$. Then I can write:
$$(a+1)^2(RC)^2 + 2RC(5/2+a)t+t^...
0
votes
2answers
70 views
Factor not factoring quadratic polynomial [closed]
I'm using version 11.3
Expand[(Sqrt[2] - t)^2]
2 - 2 Sqrt[2] t + t^2,
but
...
0
votes
1answer
55 views
Multiple collection of terms
As the title suggests, I am interested in how to perform multiple collection of terms. This means that for a given expression a*x*b + c*x^2*d+a*x*k, I want to ...
0
votes
1answer
87 views
Can Mathematica factor out constrained functions when it simplifies? [closed]
For example, distributions in the exponential family take a likelihood function of the form $$f(x)g(\theta)e^{\phi(\theta)^{T}u(x)}$$. Given some ugly algebraic expression, can I tell mathematica to ...
7
votes
2answers
396 views
Efficient code for minimum integer with given number of factors
I'm seeking an efficient implementation of the number-theoretic function giving the smallest integer $n$ that has exactly $k$ factors (not necessarily prime):
...
0
votes
1answer
86 views
Factoring out a parameter
I have some function:
f[a_,b_,c_]:=Sqrt[a^2+b^2+c^2]
Is there a way that I can factor out parameter (variable) b like this:
<...
