Questions tagged [factorization]
Questions on factoring various types of mathematical expressions, with the use of Factor, FactorInteger, FactorSquareFree and related commands.
148
questions
0
votes
0answers
35 views
Simplify is giving wrong result in Mathematica [closed]
I am trying to do a simple multiplication of variables in Mathematica:
Simplify[n*(n + 1)*(n + 2)] /. {n -> 6*p + 1}
This gives me the output:
...
4
votes
2answers
111 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
84 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
99 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
250 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
79 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
41 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
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0answers
41 views
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 ...
0
votes
0answers
55 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
150 views
How to factor a polynomial expression in MATHEMATICA?
I want to factorize the following polynomial in MATHEMATICA:
$1 - 2 r + r^2 - 2 s + 2 r s + s^2 - 2 t + 2 r t + 2 s t -
4 r s t + t^2$.
...
0
votes
0answers
20 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
vote
1answer
50 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
76 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
104 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
32 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
45 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
169 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
46 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
45 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
48 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
4,4382 gold badges9 silver badges27 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
86 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
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
1
vote
1answer
61 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
96 views
Why does Factor[] not factor -1?
Consider the two expressions -2a-2b and -a-b. The TreeForm[] looks identical
However, ...
3
votes
2answers
123 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
73 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
92 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
60 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
100 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
127 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:
$$(a+1)^2(RC)^2 + 2RC(5/2+a)t+t^...
0
votes
2answers
68 views
Factor not factoring quadratic polynomial [closed]
I'm using version 11.3
Expand[(Sqrt[2] - t)^2]
2 - 2 Sqrt[2] t + t^2,
but
...
0
votes
1answer
40 views
Multiple collection of terms
As the title suggests, I am interested in how to perform multiple collection of terms. This means that for a given expression a*x*b + c*x^2*d+a*x*k, I want to ...
0
votes
1answer
81 views
Can Mathematica factor out constrained functions when it simplifies? [closed]
For example, distributions in the exponential family take a likelihood function of the form $$f(x)g(\theta)e^{\phi(\theta)^{T}u(x)}$$. Given some ugly algebraic expression, can I tell mathematica to ...
7
votes
2answers
369 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
66 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
232 views
2
votes
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 ...
0
votes
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
votes
1answer
98 views
Factoring expression with rational powers
To any great Mathematica-matician. Why Mathematica canāt factor this
Factor[-1+x^(2/3)]
I know that Factor mainly targets ...
0
votes
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 ...
0
votes
0answers
39 views
0
votes
1answer
189 views
0
votes
1answer
154 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
95 views
1
vote
2answers
143 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
314 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:
...
