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1
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1answer
47 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
53 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.
1
vote
1answer
33 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 $LaTeX$. ...
3
votes
2answers
306 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
113 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
95 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 ...
0
votes
1answer
95 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
33 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
375 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
75 views

How to replace $-x^{}\,y^*-y^{}\,x^*$ by $-(x^{}\,y^*+y^{}\,x^*)$?

Up to now, I have tried some codes like the following: ...
0
votes
1answer
68 views

How to write an expression in the desired form?

I have the following code: ...
1
vote
0answers
50 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
144 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
92 views

Is Factor reliable to find factorization? [closed]

I have two polynomials given by: ...
3
votes
0answers
61 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 ...
3
votes
1answer
126 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 ...
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
145 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
147 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
183 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 ...
1
vote
1answer
125 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
135 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
67 views

Factor out certain terms using Modulus but Mathematica requires that the modulus be an integer [closed]

Mathematica demands that the modulus be an integer. How do I work my way around this?
1
vote
2answers
62 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
87 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
79 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
71 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
500 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
406 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
475 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 ...
2
votes
1answer
103 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 ...
1
vote
1answer
128 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
130 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 ...
3
votes
1answer
284 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
137 views

Collecting terms in an expression [duplicate]

I have an expression: ...
1
vote
4answers
461 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
183 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
338 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
292 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). ...
1
vote
1answer
345 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 ...
0
votes
1answer
292 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
139 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
364 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: ...
0
votes
1answer
658 views

Factoring a quintic

I am trying to prove that a quintic polynomial, $p(x) = A5 x^5 + A4 x^4 + A3 x^3 + A2 x^2 + A1 x + A0$, which admits at most three real roots. Unfortunately Descartes' rule of signs does not help, ...
1
vote
1answer
143 views

Forming product of function of prime factors

Given a list of numbers each containing 2 prime factors, I wish to make a list of the products of the logs of each factor. For example, given L = {4,6,9}, I would like to form P = ...
2
votes
1answer
322 views

Expressing large numbers in index form

I have a quick question. Is there anyway of expressing a large number as a power of another number in Mathematica? By this, I mean for example, $1237940039285380274899124224 = 512^{10}$. Is there a ...
4
votes
1answer
276 views

Generating a list of all factorizations

What is the best way to generate a list of all factorizations of some number $n$? I'm quite new to Mathematica so this might be obvious. I have been trying some basic stuff with ...
27
votes
3answers
1k views

Common subexpression from two expressions

I am working with some unpleasantly tedious polynomials, which need to be manipulated in various ways (integrate with respect to some variable, differentiate with respect to another). Since these ...
3
votes
1answer
124 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 ...
1
vote
1answer
453 views

How can I factor my trigonometric equation?

The equation $$3\sin^2 x - 3\cos x -6\sin x + 2\sin 2x + 3=0$$ has a solution $x = 0$. That means it has a factor of $\cos x - 1$. I tried to write the given equation has the form $$(\cos x - ...