Questions tagged [factorization]
Questions on factoring various types of mathematical expressions, with the use of Factor, FactorInteger, FactorSquareFree and related commands.
174
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How does Mathematica factor expression with derivatives (i.e. not polynomial)?
I was surprised Mathematica did this automatically. I have an ode and wanted to factor it. I did not think Factor will work and I need to write special code to do ...
- 124k
3
votes
2
answers
144
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Function to write an algebraic expression in terms of another
So I'm working on a physics problem. I have two functions:
$\rho = \frac{F}{(\beta F^\alpha+1)^\frac{1}{\alpha}}$, $p = - \frac{F}{(\beta F^\alpha+1)^\frac{1}{\alpha}} + \frac{4}{3}\frac{F}{(\beta F^\...
0
votes
2
answers
48
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Easiest way to print without breakline
So I have factorized a transfer function and stored the terms in a variable. I want to print the product of terms without Mathematica joining them and without a break line. I have managed the first, ...
15
votes
4
answers
2k
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Automating interesting ways to write 2023
Inspired by Interesting ways to write 2023, I was wondering if there are ways to automate the search for results using MMA.
I tried
...
- 2,570
1
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0
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64
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Putting everything with the same power together
I'm doing some computations wich involves a lot of big polynomials, for example:
...
- 95
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1
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57
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How to express the given function as a factor $e^{7 i x}$ times a real function?
I have the function $f(x,b,t,m)$ for $\{x>0,t,b\}$ all reals and $m=\{1,2,3,4,5,6\}$. For each particular $m\in\{1,2,3,4,5,6\}$, I see that $f(x,b,t,m)$ has a multiplicative factor $e^{7 i x}$ ...
- 659
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1
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Getting List of Factors in a monomial. Is FactorList reliable?
Say I'm given a monomial which is a product of factors,
$X_{i_1} \times \cdots \times X_{i_n}$.
I find that
...
- 165
4
votes
1
answer
70
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Simplify polynomials with simple subfactors
I am trying to simplify expressions such as
poly = 1 + (-2 + 4 a^2) x^2 + x^4
to the form
polySimple = (1-x^2)^2 + 4 a^2 x^2
...
- 193
0
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0
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54
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Meaning of Extension option in Factor
I would like to ask about the Extension option in Factor function.
In the reference, there is the following example. Factor a ...
- 501
4
votes
2
answers
222
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Factorize in a particular way
I was trying to factorise this polynomial expression:
TestPolynomial=-p1^2 x1 x2 - p3^2 x1 x3 - p1^2 x2 x3 + 2 p1 p3 x2 x3 - p3^2 x2 x3
into this form,
...
- 1,092
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votes
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62
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Factorize expression by specific term [closed]
I am new to Mathematica but I would like to know how to force Mathematica to factorize an expression by a specific term.
Exemple, imagine I have a term like this:
And I have an expression like this:
...
5
votes
3
answers
155
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Factoring a quadratic form associated with a $4 \times 4$ matrix into a sum of four squares
The matrix W = $\left(
\begin{array}{cccc}
5 & 7 & 6 & 5 \\
7 & 10 & 8 & 7 \\
6 & 8 & 10 & 9 \\
5 & 7 & 9 & 10 \\
\end{array}
\right)$
has a ...
- 557
2
votes
0
answers
109
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A remarkable elimination involving the basic reproduction number R0
I have a polynomial pol of third order, whose coefficients depend on 5 parameters, and whose free coefficient is proportional to R0-1, where R0 is a certain rational function of the parameters (the ...
- 1,250
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“Largest” symbolic common factor of an integer sequence (not simply GCD)
Suppose, I have a finite fragment of a quickly increasing sequence of integers $\{a_n\}$ that is too complex, unusual, or irregular for FindSequenceFunction to find ...
- 7,048
1
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2
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106
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Finding coefficients where part of the coefficient may appear in the terms
A minimal example is given below. My goal is that given a algebraic expression such as:
expr = a^2 + a b + a^3 b + 2 a^2 b^2 + a b^3
I'm trying to find a command, ...
- 801
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1
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125
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Is there a way to collect the multiple power into a single power?
I am looking away to factor perfect powers like follows:
FactorPerfectPower[16x^2] should produce Inactive[Power][4x,2].
...
- 8,557
0
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1
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45
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Simple Question: Cut Number in Transfer function
Given transfer function:
$W=\frac{10 (s+100)}{2 s^4+219 s^3+1909 s^2+900 s+1000}$
W=(1000 + 10 s)/(1 (1000 + 900 s + 1909 s^2 + 219 s^3 + 2 s^4))
Which command to ...
- 2,262
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0
answers
121
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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 ...
- 449
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5
answers
158
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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
...
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1
answer
59
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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 ...
- 33
1
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1
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115
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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*...
- 121
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2
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75
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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 ...
- 13
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1
answer
120
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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 ...
- 941
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1
answer
125
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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 ...
- 37
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2
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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 ...
- 1,901
3
votes
1
answer
92
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
votes
1
answer
130
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
votes
0
answers
120
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About Fermat's Integer Factoring algorithm
An implementation of Fermat's algorithm that is a slight improvement on code in this book is here.
...
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287
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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,...
- 601
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3
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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 ...
- 125
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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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3
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171
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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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vote
5
answers
118
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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[] ...
4
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2
answers
320
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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 ...
- 1,522
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0
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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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0
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172
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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
1
answer
58
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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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66
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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}$$
...
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2
answers
645
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How to factor a polynomial expression in MATHEMATICA?
I want to factorize the following polynomial in MATHEMATICA:
$1 - 2 r + r^2 - 2 s + 2 r s + s^2 - 2 t + 2 r t + 2 s t -
4 r s t + t^2$.
...
- 177
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vote
1
answer
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Force factor extraction from a polynomial [closed]
I have the following polynomial
$$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 ...
- 133
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1
answer
122
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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-...
- 171
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2
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126
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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 ...
- 150
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1
answer
66
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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
1
answer
188
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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votes
1
answer
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(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 ...
- 2,470
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315
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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 ...
- 219
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2
answers
61
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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:
...
- 471
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votes
1
answer
108
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Factorizing non commutative terms
Is it possible to factor
a ** b ** c - a ** b ** d
as
a ** b ** (c - d)
?
I am using ...
- 13.9k
1
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0
answers
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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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0
answers
42
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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 ...
