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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2
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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
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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
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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
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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*...
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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] \...
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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 ...
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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
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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
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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
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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
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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?
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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: ...
0
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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
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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
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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
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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
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0answers
99 views

Why does Factor[] not factor -1?

Consider the two expressions -2a-2b and -a-b. The TreeForm[] looks identical However, ...
3
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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
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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
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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?
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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
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1answer
43 views

Not able to multiply the output of the code below

It is the output of the code given below ...
0
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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^...
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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
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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
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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
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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
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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: <...