Questions tagged [factorization]
Questions on factoring various types of mathematical expressions, with the use of Factor, FactorInteger, FactorSquareFree and related commands.
126
questions
1
vote
1answer
65 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
94 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
0
votes
0answers
24 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
88 views
Why does Factor[] not factor -1?
Consider the two expressions -2a-2b and -a-b. The TreeForm[] looks identical
However, ...
3
votes
2answers
110 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
...
1
vote
1answer
34 views
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
votes
2answers
59 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
57 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
95 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
42 views
0
votes
1answer
70 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:
$$(a+1)^2(RC)^2 + 2RC(5/2+a)t+t^...
0
votes
2answers
52 views
Factor not factoring quadratic polynomial [closed]
I'm using version 11.3
Expand[(Sqrt[2] - t)^2]
2 - 2 Sqrt[2] t + t^2,
but
...
0
votes
1answer
28 views
Multiple collection of terms
As the title suggests, I am interested in how to perform multiple collection of terms. This means that for a given expression a*x*b + c*x^2*d+a*x*k, I want to ...
0
votes
1answer
71 views
Can Mathematica factor out constrained functions when it simplifies? [closed]
For example, distributions in the exponential family take a likelihood function of the form $$f(x)g(\theta)e^{\phi(\theta)^{T}u(x)}$$. Given some ugly algebraic expression, can I tell mathematica to ...
0
votes
0answers
29 views
Simplifying expressions: factorization: reverse distributive property
Is there any Mathematica of the type Factor, FullSimplify, etc. that fully reverses distributive property?
I mean, is there a simple way to turn the expression
$$ e^{x(t,r)}+e^{x(t,r)+y(t,r)}+e^{x(t,...
7
votes
2answers
320 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
39 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
votes
3answers
216 views
2
votes
0answers
53 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
votes
2answers
46 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
votes
1answer
95 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
votes
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 ...
0
votes
0answers
36 views
0
votes
1answer
134 views
0
votes
1answer
99 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^...
0
votes
0answers
90 views
1
vote
2answers
108 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
votes
2answers
251 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:
...
0
votes
0answers
113 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
...
-1
votes
2answers
184 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
votes
1answer
79 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
votes
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
votes
1answer
166 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
votes
1answer
51 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
vote
1answer
135 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
votes
1answer
64 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
votes
2answers
331 views
How to convert an expression a + b*Sqrt[c] to a simpler format?
Example: we have the following expansions:
...
1
vote
2answers
56 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
vote
1answer
43 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:
$$
l(s)=g(s)...
0
votes
1answer
24 views
Scalar multiplication of an expression containing equality [duplicate]
Suppose:
expr=(a x + a y==0);
expr/a
(*Out:=(a x + a y==0)/a*)
I want a eliminated to obtain ...
14
votes
4answers
691 views
Why Mathematica can not factorize polynomials over algebraic fields?
I noticed that a factorization over algebraic fields is useless in Mathematica. Here is the example over the field containing I*Sqrt[3]:
...
8
votes
2answers
266 views
Factor fails on a simple expression
Bug introduced in 9.0 and fixed in 11.3.0
Consider the following symbolic expression (all the c's are undefined)
...
1
vote
1answer
140 views
Factor Recursively
I'm looking for a way to factor a polynomial recursively. Consider the following example:
expr = Expand[(a + (b + c)^2)^2];
Factor@expr
Simplify@expr
While the ...
5
votes
1answer
292 views
Factor a bivariate polynomial treating one variable as constant
I have a polynomial in two variables, e.g.
16384 k^4 - 20480 k^2 + x^4 - 320 k^2 x^2 - 128 x^2 + 4096
I'd like Mathematica to factor it as
$$(x^2 - f(k))(x^2 - g(...
6
votes
2answers
142 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
votes
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
votes
1answer
344 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
votes
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
votes
0answers
110 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
votes
2answers
121 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 ...
