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3
votes
1answer
81 views

How to efficiently find only the rational roots of a rational complex polynomial?

I need to find all the rational roots of a bunch of high-order polynomials with rational complex coefficients. Is there an efficient way to do this? My best effort on an example polynomial: ...
0
votes
0answers
56 views

Factor Integer function with variable arguments

I'm trying to build a function that gives the highest power of a prime factor of a number. The following works perfectly: ...
0
votes
0answers
84 views

How can we compute a factorization for symmetric indefinite matrices?

I want to compute the factorization of (real) symmetric indefinite matrices in Mathematica. For symmetric positive definite matrices, we can use a permuted version of Cholesky factorization, ...
8
votes
2answers
132 views

Collect/Factor a fraction

Is there a way to tell Mathematica to factor things only containing a specific combination of a fraction, example: $$\tag{1}f = \frac{a+m\cdot a+b+n\cdot b+c+k\cdot c+d+e}{ab}$$ Is there a way to ...
3
votes
1answer
85 views

Can Mathematica factor a polynomial over an algebraic number field?

If I input: Factor[x^2 + x + 1, Extension -> Sqrt[-3]] Mathematica returns: ...
1
vote
1answer
46 views

Formatting the prime factorization of expressions

I have a series expansion in $x$ and $a,b$ are constants which I want to type in $\LaTeX$. But the numbers/integers are pretty large (have a lot of digits) so it becomes a bit messy in $\LaTeX$. ...
1
vote
1answer
52 views

Timing and ListPlot

I am currently trying to examine the Timing function as it relates to generating primes and factorize large integers. What I want to do is to visualize how time ...
-5
votes
1answer
58 views

Finding a seven-digit number with all of its prime factors less than 20? [closed]

How can I find a seven-digit number with all of its prime factors less than 20? I have no clue how to do this.
2
votes
1answer
104 views

One of the factors greater than $x$

Is there an easy way to tell Mathematica to find one of the prime factors of $n$ greater than $x$. For example, if $n=1299709\cdot 7919 \cdot 17$, is there a way to request a factor greater than ...
3
votes
2answers
310 views

Represent a positive integer as a product of its factors

I am trying to illustrate some simple ideas with exponents. I can manually express something like $5^4$ as $5 \cdot 5 \cdot 5 \cdot 5$, but wondered how to get Mathematica to do that for me. I ...
3
votes
2answers
124 views

Factor multiplied matrix with vector

Say I have a matrix multiplication of the form $$B=A\cdot X$$ or $$\left( \begin{array}{c} \text{a11} \text{x1}+\text{a12} \text{x2}+\text{a13} \text{x3} \\ \text{a21} \text{x1}+\text{a22} ...
2
votes
2answers
103 views

Selecting divisors of a large number that meet some criteria using the factors list

I have a list that represents a factorization of a number: its format is identical to the output of FactorInteger. I need to select the divisors that meet some ...
3
votes
1answer
137 views

Factor fraction, where variable occurring in both, numerator and denominator, only appears once

I have an expression like $$\frac{1+a^2+2 a \cos\left(p\right)}{\left(1+b^2\right)z-1-a^2-2 \left(a+b z\right)\cos\left(p\right)}\text{.}\tag{1}$$ Is there a combination of Mathematica functions to ...
0
votes
1answer
128 views

Getting mathematica to factor out constants and apply euler's identity to a table

I'm doing some quantum mechanics homework that I'm going to eventually generalize to higher spin states, so the solutions are going to need to be decently independent of the dimensions of the table ...
1
vote
0answers
36 views

Factoring rationals from equation based on digit complexity?

Consider an equation of the following type: ( poly = (3 x)/35 + (6 y)/7 ) == 0 If we apply the command Factor to this ...
6
votes
6answers
388 views

Rewrite a real polynomial in real (but only linear and quadratic) factors

According to my calculus book: "Every real polynomial can be factored into a product of real (possibly repeated) linear factors and real (also possibly repeated) quadratic factors having no real ...
2
votes
1answer
79 views
1
vote
0answers
53 views

decomposing an expression into absolutely positive terms

I have a big ugly expression which, for unimportant (here) reasons, must be greater than or equal to zero. It is formed from terms which themselves are greater than or equal to zero. As such it ...
2
votes
1answer
252 views

Factoring out a common term

Very simple question, but I can't find a simple answer here or in the documentation. I have an expression: qq = a x + b x^2 + c x^3 and wish to factor out a ...
1
vote
1answer
128 views

Factor terms by kets

I have an expression that contains several kets with numerical factors. I would like to retrieve the individual kets and store each individually as a list element. The expression is as follows: ...
1
vote
1answer
95 views
3
votes
1answer
127 views

Factorize and find the null space of a polynomial in several variables [duplicate]

I've been asked to factor the following polynomial: poly = 6 x^3 + x^2 y - 11 xy^2 - 6 y^3 - 5 x^2 z + 11 xyz + 11 y^2 z - 2 xz^2 - 6 yz^2 + z^3 And to solve for z so that poly = 0 Can anyone help ...
3
votes
0answers
64 views

Explicitly find a guaranteed factorization of large expression?

Consider the large expression LE defined in this file (involving only linearly independent functions), or in this file (linear interdependence present but slightly ...
4
votes
1answer
40 views

Relative factorisation with scalar quantities

I'd like to find a natural way to tell mathematica that a given unknown in a polynomial should be treated as a number, unlike the other variables. Typically I'd like to sum two polynomials in several ...
2
votes
1answer
154 views

can I expand non-integer powers

How can I help Mma to recognize that w can be factored out of (a w)^a (w - a w)^(1 - a). Assumptions: w>0 and 1>a>0.
2
votes
3answers
158 views

Question on alternate forms of polynomial output

EDIT: Would it be possible to do something like let $y=ax+b$ then use Collect[] or Apart[] on the new expression? How would I go about this. I've tried using Collect[%,ax+b], Collect[%,{ax+b}], and ...
3
votes
1answer
185 views

Factoring the imaginary unit

Suppose you have this: Collect[2 u + I + 2 + I,I] It gives the same. Is it possible to factor I in elegant way (not ...
3
votes
1answer
331 views

Tell Mathematica to factor something specific

Is there a way to tell Mathematica to factor $$ \frac{1}{1-x^2} $$ from a large expression? For instance if the expression is A_1+A_2+A_3 and I want to factor ...
1
vote
1answer
179 views

Factoring large integers with the Pollard p-1 method

I am trying to use the Pollard $p-1$ method to find the factors of a large integer. Here is the problem: An RSA-type cipher is based on the integer $n = 140016480344628383$ and exponent ...
-1
votes
1answer
75 views
1
vote
2answers
63 views

Transforming functions

I am not familiar with Mathematica but have the following question: I am trying to write Mathematica code that transforms $x^a+y^a$ to $(x+y)^a$ for any $x$ and $y$ and integer $a$. I also need to ...
0
votes
1answer
90 views

Splitting a polynomial into sum of factors, not necessarily linear

How can I split a given polynomial as sum of factors in Mathematica? For example, let's say I have this polynomial: $2\cdot x^2+7\cdot x+2$. I would like the output to be $(x+1)(x+2)+x(x+4)$. Is ...
0
votes
1answer
80 views

Factoring problem

Keep factoring and concatenating starting with 2 until we get a prime, i.e. 2 = 2 ; 22=2.11 ; 22211=7.19.167 ; 22211719167=..... and so on (the prime factors are arranged from smaller to larger and ...
1
vote
1answer
74 views

Factor bivariate polynomial over the complex numbers

This is very much like Factoring polynomials to factors involving complex coefficients except that I'm concerned about bivariate polynomials, not univariate polynomials. Take for example the ...
3
votes
0answers
638 views

Extract common factor from vector or matrix

I can't believe this hasn't been asked before but I can't find anything. Is there a way to convince Simplify or FullSimplify to ...
4
votes
3answers
441 views

Specific factoring of fourth degree polynomial

I have a pretty unspecific question about a really specific thing -- How would one use Mathematica to find values for an integer, m, such that this polynomial ...
7
votes
3answers
485 views

Better answer to Santa's riddle about sum of a number's divisors?

I was hoping to find an elegant solution to this riddle, using only a line or two of Mathematica: Santa Claus was telling one of his elves: "If I multiply the age of three of my reindeer, I get ...
11
votes
4answers
9k views

Factoring polynomials to factors involving complex coefficients

I've run into some problems using Factor on polynomials with complex coefficient factors. Reading the documentation it looks like it only factors over the ...
1
vote
1answer
136 views

How to factorise a variable out of an indefinite sum?

(I should start by saying I'm a total beginner with Mathematica, so if the answer needs code I'll need it spelled out quite clearly, the learning curve for this is proving steep!) Basically what I am ...
1
vote
2answers
141 views

factorization of integer into two parts with specific prime factors

I would like to write a Mathematica code to decompose an integer into two or more parts with primes in special intervals. For instance, I want to decompose $m=\binom{n}{k}$ into two parts U and V ...
2
votes
1answer
370 views

Why doesn't FullSimplify work properly on this?

I wish to simplify the simple expression fac[n_] := Sum[R^i, {i, 0, n}]; as much as possible for various $n$. FullSimplify or ...
1
vote
4answers
477 views

How do I create a list of 25 random quadratic equations in the form ax^2+bx+c?

My teacher suggests using the RandomInteger command along with the Factor command, but I cannot figure out the syntax. A, b, and c need to be non zero integers between -10 and 10.
5
votes
2answers
186 views

FactorInteger over UFDs

How can I factor 'integers' over other quadratic number fields (not just gaussian integers). For instance, how could I factor $7 = (3 + ω)(2 − ω)$ over Eisenstein integers ($ω = \frac{-1+ I ...
4
votes
1answer
348 views

Factoring a two variable polynomial in a special way

Let $$f=x^9-x^6+4x^5y+2x^3y^2-y^4$$ I would like to factorize $f$ into form: $$(y-F_1(x))\cdots(y-F_k(x))$$ over complex numbers. How can I do it with Mathematica?
1
vote
1answer
304 views

How to represent very long integers with at-most-8-digit(base-10) short integers with * and +

I need an algorithm in Mathematica, which can represent any very long integer, prime or not, into the the product operation "*" and sum "+" forms by short integers (not more than 8 decimal digits). ...
0
votes
1answer
314 views

Partial factorization of multivariate polynomials in terms of given polynomials

I have calculated several homogeneous polynomials in 4,5 or 6 variables $t_1,\dots,t_6$. I would like to rewrite them as a sum of products of specific lower degree polynomials, which have a meaning in ...
1
vote
5answers
150 views

What's wrong with my implementation of SquareFreeQ?

This was a question I had last month: Part A: Looking at the exponent of each of the elements in the list, FactorInteger and using ...
1
vote
0answers
378 views

Polynomial factorization over finite fields with non-prime order

One can easily factor a polynomial over finite fields of prime order, using Factor command: ...