The art of manipulating an algebraic expression into the desired form.

learn more… | top users | synonyms

2
votes
1answer
27 views

How to gather terms into Elementary Symmetric Polynomials?

I would like to gather the terms of this polynomial (and much higher order ones): $$q = 1-3 c+c^2+p[1]-2 c p[1]+p[2]-2 c p[2]+p[1] p[2]-c p[1] p[2]+p[3]-2 c p[3]+p[1] p[3]-c p[1] p[3]+p[2] p[3]-c ...
1
vote
1answer
48 views

Factor a polynomial Root into Roots of smallest possible degree

Suppose I have a polynomial Root representing an algebraic number. I want to represent it (if possible) as a product of several polynomial ...
0
votes
0answers
41 views

Find the height(h) of a Circular segment based on Radius and Length(c) [on hold]

I have found the formula for calculating the R of a circle, based on a circular segment, which is; R=h/2+c^2/(8h) Where, R is ...
0
votes
1answer
44 views

Simple grouping equations [closed]

I'm new in the Mathematica world. A very basic question. I have been using the command Eliminate on a set of equations as follow: ...
0
votes
1answer
55 views

Eliminate variable on multiple equations [closed]

I'm pretty new with Mathematica. I have to perform a really simple operation, but I'm really struggling with that. I have a set of 4 equations, for example (they can also be more complex): $ AA = 2 ...
4
votes
1answer
86 views

Pertubation series of given equations

I would like to define a function that does the following. If I have an equation, for example: $$f(x)+[1-f^2(x)]+f^{\prime\prime}(x)+f(x)\ f^\prime(x)=0$$ and I am given a value for $f$ to expand ...
0
votes
1answer
35 views

Dividing out any constant factor from expression [closed]

How do I divide out any constants from an expression? Let's say: $2A+4B+2C+6 \rightarrow A+2B+C+3$ What's the right command for this? I have been using ...
4
votes
2answers
161 views

Find condition under which variables fall away

I have a somewhat lengthy expression, looking like expr = 1 + x + b + Pi + 2*a Is there some way of generating a relationship between ...
6
votes
4answers
116 views

Forcing Mathematica to Output $1/\sqrt2$ as $\sqrt2/2$

I am trying to force Mathematica to output $\frac{1}{\sqrt2}$ as $\frac{\sqrt2}{2}$. I tried: {1, Sqrt[2]}*Sqrt[2] Which outputs: ...
5
votes
4answers
102 views

Solving an equation with rational expressions (step by step) [duplicate]

Consider the following equation with rational expressions: $$\frac{5}{x+4}=4+\frac{3}{x-2}$$ We will look at the plot. We will use the Solve command to check our answer. ...
3
votes
4answers
128 views

How can I group constants/parameters using Mathematica?

I am trying to solve a problem which may seem quite simple, although I have been unable to find any solution in the documentation or discussion forums. I am not a mathematician, so please bare with ...
5
votes
1answer
155 views

How to write polynomial expression as commutator form?

I want to write some polynomial expressions as commutator form. For example : $$ \frac{\text{BA}}{2}-\frac{\text{AB}}{2} = -\frac{1}{2}[A,B] $$ or $$ ...
3
votes
2answers
93 views

How to make algebraic substitutions?

I would like to simplify complicated expressions by defining some variable that is a combination of other variables that appear in the expression, but without eliminating the original variables. As a ...
0
votes
3answers
39 views

How to transform a noncommutative product to a different expression?

I have a (long) sum of the following ** (noncommutative) products: gg**qs**rh (each variable always consists of two letters like in the artificial example ...
4
votes
1answer
249 views

Infinite expression encountered when simplifying ArcTan sums although the result is finite

If I attempt to simplify the sum ArcTan[1/x] + ArcTan[x] with ArcTan[ Simplify[ TrigExpand[ Tan[ ArcTan[1/x] + ArcTan[x]]]]] ...
15
votes
2answers
976 views

How to define a non-standard algebra in Mathematica?

I want to define an algebra, where there are three elements: 0, 1 and $\infty$ and two operations, addition and multiplication defined, both commutative: $$\begin{align*} 0+0&=0\\ 0+1&=1\\ ...
1
vote
3answers
103 views

Coefficient and Addition Formula

If I type: Coefficient[Cos[x + b], Cos[x]] I get zero. But I would like Mathematica to apply: $$\cos(x+b)=\cos x\cos b-\sin x\sin b$$ Therefore the ...
0
votes
0answers
64 views

Speed up the Eliminate

I have problem of eliminating some variables from a set of equations, which contain logarithmic function, in order to obtain a differential equation. These are the parameter and functions in ...
0
votes
0answers
35 views

Multivariate remainder of polynomial in respect to a set of polynomials

I would like to have a really fast routine that computes the so called Normal Form of a multivariate polynomial f in respect to a set of other multivariate ...
2
votes
0answers
56 views

Changing variables in a series expansion

I want to compute the Taylor expansion of some pure function f[x_], but then perform a change of variables in the resulting expression. So, for example, the output ...
1
vote
1answer
111 views

Polynomial decomposition algorithm with a hint

If $p,f,g$ are polynomials of degree 2 or higher and $p(x)=f(g(x))$ we have a polynomial decomposition of $p$. When Mathematica (as noted below this was actually on Wolfram Alpha) says ``decomposition ...
5
votes
2answers
116 views

Can one prevent operators like `Factor` or `Apart` from changing full form of some algebraic expressions?

In this question I will talk about a toy example, it should be clear what do I actually mean in general. Also, not only Factor but also ...
5
votes
3answers
153 views

Expanding out multiplied terms

Is there any command in Mathematica to expand terms like $x^2\, y^3$ to $x\,x\,y\,y\,y$? I tried PowerExpansion, but it works for expressions like $(x\,y)^2$ which ...
-11
votes
3answers
276 views

A tricky algebraic simplification [closed]

EDIT from the OP: The problem was that I was using a very old version of Mathematica on a friend's computer without realizing it. FullSimplify[] handles it perfectly even on v9. This code produces ...
1
vote
1answer
61 views

Adding algebraic functions to NDSolve

I want to define an integral function which depends on a system of ODE and is also used to NDSolve the ODEs. ...
0
votes
2answers
118 views

Rearranging a simple algebraic equation

Suppose I have a simple algebraic equation like: ChebyshevT[4, p] == 0 1 - 8 p^2 + 8 p^4 == 0 and I want to solve for the ...
3
votes
1answer
126 views

Separate variables in equation

I need to know is there a way to separate the desired variables in the equation at one side of the equality. For instance, the following equation ...
0
votes
1answer
57 views

problem with Collect when using indexed variables [closed]

I'm not getting the expected output when I use Collect with indexed variables. ...
1
vote
1answer
65 views

Using the Norm Function

I am trying to take the norm of a general vector and show that for vectors, v,w, that Norm[v cross w]^2==Norm[v]^2*Norm[w]^2-(v dot w)^2 In Mathematica, here are my steps: ...
6
votes
3answers
346 views

How to do algebra on unevaluated integrals?

I am working with functions calculated from a set of general basis functions. ...
4
votes
1answer
85 views

How to collect terms with z-derivative?

my equations are very long (several pages). Here I will provide simple example: ...
1
vote
0answers
35 views

Changing the order of a factor [duplicate]

I've done: p[x_] := x^2 + x + 1; roots = Solve[p[x] == 0, x] // ComplexExpand; roots = roots /. x -> y; Times @@ (x - y /. roots) Which produces this output: ...
1
vote
2answers
47 views
1
vote
0answers
63 views

“Reduce” works fine for a non-linear system with 9 equations, but cannot solve it if 10 equations. Any ways to improve the code?

I am trying to solve a class of problems, which are basically about a solution to a system of non-linear equations subject to the constraint that some subset of solutions must be non-decreasing. I ...
9
votes
1answer
151 views

Apart may use Padé method: what's that?

How does Apart work? The page tutorial/SomeNotesOnInternalImplementation#7441 says, "Apart ...
1
vote
2answers
77 views

Writing a polynomial quotient with a specific denominator

I have a polynomial quotient $$\frac{1-z+z^4}{(1-z)^2}$$ that I want to write in the form $$\frac{g(z)}{(1 - z) (1 - z^4) (1 - z^5) (1 - z^6) (1 - z^7)}.$$ However, every time I try some combination ...
0
votes
1answer
147 views

Rearranging 5 equations

I am trying to rearrange 5 equations in terms of 5 variables. I have the equations for y1, y2, ...
16
votes
1answer
196 views

Undocumented fourth parameter of Collect; how long has it been there?

While tinkering with How to get a list of monomials of a polynomial without coefficients? on a whim I tried a fourth argument in Collect and found: ...
2
votes
1answer
121 views

How to convert a rational parametric plane curve into implicit form?

This problem is generated from another Green's theorem related question of mine. And here is a forward of the same problem in math.stackexchange. The original equation of the plane curve is not in ...
3
votes
1answer
255 views

Multivariate resultant in Mathematica?

Is there any command in Mathematica 7 which can compute the (McCaulay) resultant of a parametric system of multivariate polynomial equations? In fact, it would be great if there is also a way to ...
11
votes
5answers
2k views

How to get exact roots of this polynomial?

The equation $$ 64x^7 -112x^5 -8x^4 +56x^3 +8x^2 -7x - 1 = 0 $$ has seven solutions $x = 1$, $x = -\dfrac{1}{2}$ and $x = \cos \dfrac{2n\pi}{11}$, where $n$ runs from $1$ to $5$. With ...
8
votes
1answer
235 views

Speed up MinimalPolynomial

My Mathematica code runs slowly MinimalPolynomial[Sqrt[2] + Sqrt[3]+ Sqrt[5]+ Sqrt[7]+ Sqrt[11]+ Sqrt[13], x] runs slowly, but the Maple version ...
5
votes
1answer
134 views

List of unknowns in a differential equation

I often find myself wanting to see what variables/constants are undefined in a large set of differential equations, is there a function that will do this for me? As an example, for the following ODE ...
1
vote
1answer
78 views

How to reduce trigonometric expressions under special conditions

For the following problems I used "FullSimplify" and "TrigReduce" but I manage to reduce more by hand. ...
13
votes
1answer
333 views

ToNumberField won't recognize Root as an explicit algebraic number

Bug fixed in 10.0.0 In Mathematica 9.0.1, it appears that ToNumberField will not always recognize a Root object as an ...
8
votes
2answers
123 views

How to sort arguments of Times in nonstandard order?

Is there an elegant way to sort the arguments of Times in e.g. TraditionalForm so that factors go to the front and state ...
14
votes
4answers
2k views

Is there a way to Collect[] for more than one symbol?

Oftentimes you find yourself looking for polynomials in multiple variables. Consider the following expression: a(x - y)^3 + b(x - y) + c(x - y) + d as you can ...
5
votes
1answer
208 views

Distribute transpose on matrix multiplication

I need to do the following: Transpose[A.(B+C)]=Transpose[B].Transpose[A]+Transpose[C].Transpose[A] How should I do this in mathematica? So far mathematica does ...
5
votes
1answer
71 views

Is there a way to Collect[] for more than one symbol in Mathematica 10.0?

This question has already been asked three years ago (Is there a way to Collect[] for more than one symbol?) but I'm not allowed to comment since I'm new at Mathematica StackExchange. The first ...