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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Factorization of multivariable polynomial

I have a polynomials of multivariable for instance: $P=yx+2^4xy+3+5^2xz+3^4zx $ Now I would like to do the following: extract those temrs that only has $z$ . extract terms that only has $y$ express ...
3
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2answers
54 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 ...
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1answer
55 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
94 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
39 views

Not able to multiply the output of the code below

It is the output of the code given below ...
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1answer
63 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
50 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
28 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
69 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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0answers
29 views

Simplifying expressions: factorization: reverse distributive property

Is there any Mathematica of the type Factor, FullSimplify, etc. that fully reverses distributive property? I mean, is there a simple way to turn the expression $$ e^{x(t,r)}+e^{x(t,r)+y(t,r)}+e^{x(t,...
7
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2answers
307 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): ...
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1answer
35 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
210 views

Factor polynomial of degree n+3

I'm considering a polynom poly[n,v] in v ...
2
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0answers
51 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 ...
0
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2answers
43 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
94 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 ...
0
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1answer
54 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
36 views

Inconsistent pole/roots decomposition

I have the following function f of ω: ...
0
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1answer
128 views

Pull out the common denominator of fractions

I have this code: ...
0
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1answer
91 views

Factoring the Quadratic Polynomial $a x^2 +b x +c$

I want mathematica to factor the quadratic polynomial $a x^2 +b x +c$ into this standard form $a(x-r_1)(x-r_2)$ with $r_1=-\frac{b}{2a}+\frac{\sqrt{b^2-4ac}}{2a}$ and $r_2=-\frac{b}{2a}-\frac{\sqrt{b^...
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0answers
84 views

Pull out variable and common denominator from fraction

I have this code: ...
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2answers
106 views

Polynomial factorization over number fields that are extensions of the rationals [duplicate]

I want to factor some polynomials into irreducible terms, but not only limited to integers. If I evaluate Factor[x^4+1], it will generate nothing. But in fact I ...
3
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2answers
233 views

Factor out constant terms with square roots

I would like to use FactorTerms to factor out constant numerical terms out of an expression, this works as follows: ...
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0answers
104 views

Prime factorization of numerator and denominator of rationals

I am completely new to Mathematica and I need some help (sorry if it is trivial, but I haven't found the answer). I have this code ...
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2answers
178 views

How to use Replace using some factor from exponent in the replacement rule

Is it possible to directly factor out some exponent to some specific form and replace by some rule? For example I have exp1=x^4 I want to use replacement <...
2
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1answer
74 views

How to factor exponents?

Given Exp[a+b] I want to turn it into Exp[a] Exp[b] How can I achieve this in general? That is I am looking for more or ...
25
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2answers
2k views

Code I get from wolfram isn't working in mathematica

I need to perform the factor as shown here factor(s^5+32s^4+363s^3+2092s^2+5052s+4320) https://www.wolframalpha.com/input/?i=factor(s%5E5%2B32s%5E4%2B363s%5E3%...
4
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1answer
160 views

Checking whether one polynomial is a factor of another

Given two polynomials, $f(x)$ and $g(x)$, I need to determine whether $f(x)$ is a factor of $g(x)$. Seems simple enough, and the way I initially did it was just checking if $f(x)$ is in a FactorList ...
2
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1answer
50 views

Advanced Trivariate Polynomial With Integer Coefficients Manipulation

Suppose $$f(a,b,c)=\left(a+b+c \right)^{2}-2 \left(a^{2}+b^{2}+c^{2}\right)-4abc$$ and $g(a,b,c)$ is some polynomial of total degree 6 with integer coeffients. I want to find a polynomial $h(x)$ with ...
1
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1answer
129 views

How can Mathematica take a prefactor in front of the relation

I have the following term in an expression $$\frac{q_B' \sin2q_B}{P_B Q_B^2}(2 Q_B P_B - \sin^2 q_B \Pi_B) q_1 q_1'$$ the prime denotes differentiation w.r.t a coordinate. Some additional ...
2
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1answer
62 views

wrong LUDecomposition - first row is the last one

I am having a huge problem with my Mathematica notebook. I am trying to evaluate LUDecomposition and it keeps getting wrong - when I multiply ...
4
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2answers
328 views

How to convert an expression a + b*Sqrt[c] to a simpler format?

Example: we have the following expansions: ...
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2answers
55 views

how to extract the elements of the output of FactorInteger function? [closed]

For example, when I evaluate FactorInteger[265^2 - 87463] the output is {{-1, 1}, {2, 1}, {3, 1}, {13, 2}, {17, 1}} I ...
1
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1answer
40 views

Factor by a specific literal (i.e factor by $s^N$ a transfer function)

I've found the closed loop transfer function but I want to know the order of it. So, the idea is to factor the denominator by the highest exponent of s to get an expression like this one: $$ l(s)=g(s)...
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1answer
24 views

Scalar multiplication of an expression containing equality [duplicate]

Suppose: expr=(a x + a y==0); expr/a (*Out:=(a x + a y==0)/a*) I want a eliminated to obtain ...
14
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4answers
684 views

Why Mathematica can not factorize polynomials over algebraic fields?

I noticed that a factorization over algebraic fields is useless in Mathematica. Here is the example over the field containing I*Sqrt[3]: ...
8
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2answers
254 views

Factor fails on a simple expression

Bug introduced in 9.0 and fixed in 11.3.0 Consider the following symbolic expression (all the c's are undefined) ...
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1answer
131 views

Factor Recursively

I'm looking for a way to factor a polynomial recursively. Consider the following example: expr = Expand[(a + (b + c)^2)^2]; Factor@expr Simplify@expr While the ...
5
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1answer
288 views

Factor a bivariate polynomial treating one variable as constant

I have a polynomial in two variables, e.g. 16384 k^4 - 20480 k^2 + x^4 - 320 k^2 x^2 - 128 x^2 + 4096 I'd like Mathematica to factor it as $$(x^2 - f(k))(x^2 - g(...
7
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2answers
141 views

How to factorize polynomials into “shortest possible” pieces

I am using Factor a lot in my work, it is extremely versatile and efficient, except for one aspect. Example: ...
5
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2answers
127 views

Why is Mathematica factoring I out of real expressions, and how can I reverse it?

I am doing some complicated series expansions involving integrals and whatnot, but everything is real the whole time (and I specify that using Assumptions at every ...
13
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1answer
316 views

Factorize trigonometric matrices

Consider two square matrices $A_1$ and $A_2$. Consider the following matrix involving matrix trigonometric functions: \begin{equation} M_1(t)=\begin{bmatrix} \cos(tA_1) & t\mathrm{sinc}(t A_1) \\ ...
5
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1answer
123 views

Factorize expression into matrix/vector operations if possible

I'd like to let MMA factorize an expression (tensor) into matrix operations if that's possible. Example – there's an expression P1 and I want MMA to create another ...
0
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0answers
104 views

Put in evidence and return 1 if already fully factorised

Does anyone have a clever idea how to get the overall factor in front of a polynomial or just return 1 if everything is already put in evidence ? Here is an example with a dummy ...
0
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2answers
119 views

Simplify with Integer Factorization

I have some outputs of Solve applied to algebraic equations with combinatorial coefficients (i.e. integers), and I'd like to see the results from ...
0
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2answers
57 views

Collect function with iterator issue

I've got the following code for the first few terms of an expansion. I want to collect the terms in increasing powers of (s/r) but using an iterator. The code is as ...
2
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2answers
131 views

Simplify to the specific form

I want to simply expression into specific form that I want to have. For example, $e^{-v^2}\frac{ (a*v-b)}{c*v^2-d*v+e}$ (-b + a v)/(e - d v + c v^2) Exp[-v^2] I ...
1
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1answer
216 views

Factor Denominator of Fraction [closed]

How do I get Mathematica to factor the denominator of a fraction? For example, to turn $$\frac{1}{s^2+3s+2}$$ into $$\frac{1}{(s+1)(s+2)}.$$ I tried Factor, but it ...
0
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2answers
162 views

Powers of prime factors of a positive integer $n$ in “Mathematica”?

I would like to find the powers of a prime in the unique prime factorization of an $n$. I want a function $f[n,p]$ such that $n,p$ are given and I need to know what the power of $p$ is. For instance ...
1
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0answers
62 views

What prevents Factor from Working also on Arguments of Sqrt in Expressions?

Consider this example (intersection of a line and a sphere): ...