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

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7
votes
3answers
207 views

Is there any way to collect only variables with a specific power?

Suppose I've got this: In[13]:= Expand[(a + b) (b + c) (c + a)] Out[13]= a^2 b + a b^2 + a^2 c + 2 a b c + b^2 c + a c^2 + b c^2 And I want to collect only ...
7
votes
1answer
270 views

Extract common subexpressions from expressions [duplicate]

I am trying to evaluate multiple independent expressions with common parts. I would like Mathematica to somehow give me this common parts. It's probably not so clear, so let me give you an example. ...
6
votes
3answers
673 views

What function can I use to evaluate $(x+y)^2$ to $x^2 + 2xy + y^2$?

What function can I use to evaluate $(x+y)^2$ to $x^2 + 2xy + y^2$? I want to evaluate It and I've tried to use the most obvious way: simply typing and evaluating $(x+y)^2$, But it gives me only $(x+...
6
votes
6answers
405 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 zeros....
6
votes
3answers
169 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 ...
6
votes
3answers
363 views

How to do algebra on unevaluated integrals?

I am working with functions calculated from a set of general basis functions. ...
6
votes
4answers
129 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: ...
6
votes
5answers
2k views

How to group certain symbolic expressions?

For example, I have the following expression : A( 2 x1 + B(y1 + y2) + 2 x2 ) How do I make the output look like this (grouping ...
6
votes
1answer
255 views
6
votes
1answer
210 views

Working with a system of differential equations that cannot be solved explicitly

I have to work a lot with three functions $\;o_1(t), o_2(t), o_3(t)\;$ that are solutions to the certain system of differential equations: ...
6
votes
1answer
194 views

Is there a version of Together that doesn't cancel common factors?

I'm running code that produces a long combination of rational functions with free constants that need to be tuned such that the combination vanishes. My current method is to put the combination over ...
6
votes
1answer
82 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 ...
6
votes
2answers
168 views

Why is ToRadicals[] not able to handle all cases? Is there a workaround?

The documentation for the function ToRadicals says: ♦ There are some cases in which expressions involving radicals can in principle be given, but ...
6
votes
2answers
335 views

How to implement a formal expectation operator over an unknown distribution?

I need to do some simplification of an expression involving averages over a stochastic variable (in order to verify a long analytical calculation). The easiest way to do that, I figured, were if I ...
5
votes
4answers
126 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. ...
5
votes
5answers
349 views

Isolating characters in a string

I'm struggling to find the right function in mathematica to isolate specific characters in a string. I have got a formula as string (I imported it from an excelfile) like this: y = 0.97*x1 + 0.521*...
5
votes
2answers
164 views

Unexpected side effect of removing the Orderless attribute from Times

First I make Times orderless: ClearAttributes[Times, Orderless]; Then I evaluate ...
5
votes
2answers
239 views

How to protect pattern or subexpression when distributing / expanding expression?

I've got an expression like expr = (1-x)(a+b) that I would like to distribute / expand while keeping factors of (1-x) intact, ...
5
votes
1answer
904 views

Reduce an equation by putting a new variable

I have the following equation given: $$ (26-x)\cdot\sqrt{5x-1} -(13x+14)\cdot\sqrt{5-2x} + 12\sqrt{(5x-1)\cdot(5-2x) }= 18x+32. $$ In order to solve it, I want to substitute $t = \sqrt{5x - 1}-\sqrt{...
5
votes
1answer
198 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 $$ \frac{\text{AAB}}{6}-\frac{\text{ABA}}{3}-\frac{\...
5
votes
1answer
264 views

Finding an analytic solution of a cubic equation

I have been trying to solve a cubic equation $$y=zy^3 + z$$ in $y$ – that is, my desired result is a function $y(z)$ satisfying the equation. Now, there are three solutions of this equation and ...
5
votes
1answer
154 views

Working with quantum mechanics spins

I've written the following code for simple quantum mechanics operators on spin states: It seems to work, but the output could be better - how do I let Mathematics know that $0**\ 0==0$, and can I ...
5
votes
1answer
241 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
2answers
4k views

Defining a non-commutative operator algebra in Mathematica

I am trying to develop a function(s) to do some commutator algebra to compute the enveloping algebra and ideals of a Lie algebra. For example if I have $SU(2)$ algebra generated by $L_i$ ($i=1,2,3$), ...
5
votes
1answer
73 views

Ordering in noncommutative multiply

I have an expression like s ** p1 ** p1 ** p2 - s ** p1 ** p2 ** p1 Which should be zero because the commutator between p1 ...
5
votes
1answer
127 views

Rearrange an algebraic expression so that each variable appears only once

Mathematica gave me a solution to an equation in this form: ans1 = (b c)/(a - a c + b c) $\text{ans1} = \frac{b c}{a - a c + b c}$ From solving the same equation ...
5
votes
1answer
1k views

How to Make a change of variables

I have the following expresion $$\hat{M}^2=-\left[\frac{1}{\sin\beta}\frac{\partial}{\partial\beta}\sin\beta\frac{\partial}{\partial\beta}+\frac{1}{sin^2\beta}\left(\frac{\partial^2}{\partial\alpha^2}...
5
votes
2answers
177 views

How to check an algebraic number for membership in a list

I need to check an algebraic number for membership in a list of algebraic numbers. The numbers can be expressed in different forms (combinations of radicals, Root ...
5
votes
1answer
236 views

Numbered symbols

I work with an exterior algebra over $R^n$. I have the basis $\{1,\omega_i\}_{i=1}^n$ in this algebra, and my differential operator is defined as $$d\omega_k=\sum_{i>j>0,i+j=k} (i-j)w_i\wedge ...
5
votes
2answers
126 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
1answer
137 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 ...
5
votes
1answer
102 views

Trouble factoring an expression

I've got the term $-1 + 2b^2 + 2b\sqrt {b^2-1}$ appearing several times within several larger expressions. It is easy to see that this expression factors into ${(b+\sqrt{b^2-1})^2}$, but when I use <...
5
votes
1answer
158 views

How to apply tags to expression terms?

I often see on this site and at the mathgroup the repeated questions on how to rearrange expression that Mathematica "likes" to keep in one form, but the user prefers in another. Consider this trivial ...
4
votes
4answers
268 views

How to compute MIN$(A(x), B(x))$

I have two polynomials: $\;A(x) = \sum a_i\;x^i$, $\quad B(x) = \sum b_i\;x^i$. Given $A(x)$, $B(x)$, I want to compute $\;C(x) = $MIN$(A(x), B(x)) = c_i\;x^i$ where $c_i = $MIN$(a_i, b_i)$. How can ...
4
votes
2answers
425 views

How can I simplify $\log(512)$ to $9\log(2)$?

Can you explain me about the result of Integrate. ...
4
votes
5answers
256 views

Extracting Coefficients from a List of Sines

I want to extract the coefficients from the following list: list={16.2219 Sin[16.2219 t], 6.60924 Sin[6.60924 t], 13.927 Sin[ 13.927 t], 2.91309 Sin[2.91309 t]} ...
4
votes
2answers
245 views

What does MinimalPolynomial do?

suppose $x^5-x-1=0$, $y^7-y-1=0$ and $z=x+y$. I want to find a minimal polynomial expression of $z$, such that $p(z)=0$, and the code can be written like this: ...
4
votes
2answers
1k views

expanding a polynomial and collecting coefficients

I'm trying to expand the following polynomial ...
4
votes
1answer
197 views

How do I use “Factor” to get this form

Here is the default answer. However, I want to get the result which looks like this Here is the Mathematica code: ...
4
votes
1answer
199 views

Is Mathematica intended to be used to do lengthy algebraic clculations? [closed]

The last two days I spent improving my Mathematica skills regarding rather simple algebraic calculations: discrete FT splitting sums combining sums changing summation indices replacing a sum with a ...
4
votes
2answers
485 views

Force a negative square root to be interpreted as an I

I have expressions like $$\sqrt{-\sqrt{1+x^2}} $$ how can I force mathematica to systematically rewrite this as $$i(1+x^2)^{1/4} \quad ? $$
4
votes
2answers
185 views

HornerForm of polynomials in terms of E^(i x)

I want to know how to get the HornerForm of the following expression in terms of E^(I x): ...
4
votes
1answer
291 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]]]]] ...
4
votes
1answer
496 views

Plot a cone in spherical co-ordinates

As we all know in spherical coordinates a function phi = π/3 gives us a cone. The cone makes an angle of π/3 with the imagined <...
4
votes
1answer
133 views

Expand power of a polynomial

I'm very new to Mathematica, so excuse my innocence. I have the following expression: $$ \left( \sum_{n=0}^r \frac{(-1)^n}{n!} y^n \right)^f $$ I would like Mathematica to expand out the expression ...
4
votes
2answers
176 views

Exploiting a relation among constants

Say I have two arbitrary real constants $p,q$ that satisfy $p^2+q^2=1$. Is there any way to easily declare this relation in Mathematica? Edit More specifically I have this (among others) expression: ...
4
votes
1answer
1k views

Non commutative multiply- expand expression

I began to use Mathematica a few days. My problem is: How to expand expression like $(a+b)*(a+b)$, where this multiplication is non commutative? Mathematica can do this?
4
votes
1answer
649 views

Showing the terms in a partial sum?

I am trying to get s[n_]:=Sum[1/2^k,{k,1,n}] to show me the actual terms involved in the $n$th partial sum and not just the sum itself. I've tried ...
4
votes
1answer
86 views

Function inversion [closed]

I have an expression of this kind ...
4
votes
1answer
92 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 ...