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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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 ...
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38 views

How to factor the following [duplicate]

I worked on a different example before: Consider the Jacobian: $$ J = \begin{bmatrix} -\frac{\beta I}{N} -\xi & -\frac{\beta S}{N} -\xi \\[1ex] \phantom{-}\frac{\beta I}{N} & \...
5
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1answer
99 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: <...
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0answers
47 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
224 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,...
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3answers
153 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
122 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'...
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3answers
95 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
101 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
255 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 ...
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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
100 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 $\...
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1answer
43 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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Parallelized FactorInteger

FactorInteger has no documented option to be parallelized. Can this be done by some clever hack? Or is there a ready-made substitute that makes use of multiple ...
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0answers
60 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
176 views

How to factor a polynomial expression in MATHEMATICA?

I want to factorize the following polynomial in MATHEMATICA: $1 - 2 r + r^2 - 2 s + 2 r s + s^2 - 2 t + 2 r t + 2 s t - 4 r s t + t^2$. ...
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0answers
23 views

Identifying which polynomials from a list are factors of other polynomials

I have a list of integer polynomials $c_i(x)$ given by s = Table[c[i,x],{i,1,N}] for some large $N$. These polynomials are increasing in degree. I am trying to ...
1
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1answer
56 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
83 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
106 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 ...
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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: ...
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1answer
50 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 ...
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1answer
210 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 ...
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1answer
56 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 ...
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2answers
48 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: ...
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1answer
52 views

Factorizing non commutative terms

Is it possible to factor a ** b ** c - a ** b ** d as a ** b ** (c - d) ? I am using ...
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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: ...
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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 ...
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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
106 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
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1answer
65 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 ...
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0answers
97 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
125 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
75 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
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2answers
100 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
102 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 ...
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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
146 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
69 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
49 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
84 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 ...
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2answers
383 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
73 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: <...
5
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3answers
233 views

Factor polynomial of degree n+3

I'm considering a polynom poly[n,v] in v ...
2
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0answers
72 views

What Transforming Functions does Simplify use? [closed]

Edit: Turns out in my use case I should use ComplexExpand instead of Simplify. My broader question is still worth answering, but ...
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2answers
54 views

Numerical output using Select and FactorInteger

I have concocted a function from other peoples examples to find the powers of two in a prime decompostion, in the example below its $2^2=4$ gives {2,2}. ...
3
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1answer
100 views

Factoring expression with rational powers

To any great Mathematica-matician. Why Mathematica can’t factor this Factor[-1+x^(2/3)] I know that Factor mainly targets ...
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1answer
57 views

Generate terms that can be pre-calculated (optimisation) [closed]

(copyable version) v -> -2 g/j + s/(2 j) + s^2/(4 g j) + t/2 We are working with many equations similar to the one above. We are using CForm to move these ...
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0answers
40 views

Inconsistent pole/roots decomposition

I have the following function f of ω: ...