The art of manipulating an algebraic expression into the desired form.
6
votes
4answers
2k 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
54 views
Differing behaviour of GeneratingFunction with different numbers of parameters
When given a single variable sequence, GeneratingFunction is automatically expressed in the most "direct form", for example,
...
-1
votes
0answers
59 views
Rearrange this equation so x is the subject [closed]
I have this equation:
y = 0.1x^3-0.2x^2 + 0.4x + 100
Can someone rearrange this equation so x is the subject. Thanks.
9
votes
2answers
258 views
InverseSeries of multiple variables and multiple equations
CONTEXT
Let us consider a bit of the Universe in which we draw spheres
(see a high resolution image here). Astronomers have shown that the density within these spheres
could be predicted quite ...
1
vote
3answers
125 views
How to collect/reduce with respect to multiple variables?
I have this code:
a == b + c + d - e
Is it possible to collect or reduce this expression into this:
c + d == a + e - b
...
3
votes
7answers
215 views
Defining a function that completes the square given a quadratic polynomial expression
How can I write a function that would complete the square in a quadratic polynomial expression such that, for example,
CompleteTheSquare[5 x^2 + 27 x - 5, x]
...
3
votes
3answers
125 views
How to extract phase angle from sinusoid
I'm doing some electric circuit calcualtions and I'm trying to get the phasor representation of some arbitrary function of Sin or Cos. Could be complex like:
...
7
votes
1answer
71 views
ToNumberField won't recognize Root[…] as explicit algebraic number
In Mathematica 9.0.1, it appears that ToNumberField will not always recognize a Root object as an explicit algebraic number.
...
6
votes
0answers
57 views
Apart may use Padé method: what's that?
How does Apart work? The page tutorial/SomeNotesOnInternalImplementation#7441 says, "Apart ...
3
votes
0answers
111 views
Solving recursion relations using Mathematica
I want to solve the recursion relation given in equation 2.7(a/b) on page $6$ of this paper. (..the initial seed is $F_1 = G_1 = 1$ and the functions $\alpha$ and $\beta$ are defined on page $5$ in ...
8
votes
3answers
330 views
How can I convert a complex number a+b I to the exponent form A Exp(I phi)?
When I have an expression such as:
(1/4 + I/4) ((1 - 2 I) x + Sqrt[3] y)
it is hard to get an intuition of the number.
So I want to convert it to the complex ...
7
votes
1answer
255 views
How do I expand a sum?
I have a problem with Mathematica's symbolic manipulations. As an example, consider the following expression:
$$\sum _{i=1}^n -2 x_i \left(-a x_i-b+y_i\right)=0$$
How do I get Mathematica to expand ...
5
votes
1answer
75 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 ...
5
votes
6answers
310 views
How to simplify a complicated Sum in terms of power Sums?
For example, I have:
$a=\sum _{r=1}^n x_r
\left(\left(\sum _{i=1}^n
x_i-x_r\right){}^2-\sum
_{i=1}^n x_i^2\right)$
...
3
votes
1answer
41 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?
16
votes
5answers
486 views
How do I get my equation to have the form $(x-a)^2 + (y-b)^2 + (z-c)^2-d = 0$?
I want Mathematica to express the equation $$-11 - 2 x + x^2 - 4 y + y^2 - 6 z + z^2=0$$ in the form $$(x - 1)^2 + (y - 2)^2 + (z - 3)^2 - 25=0$$ How do I tell Mathematica to do that?
9
votes
1answer
151 views
Why is ReplaceAll behaving like this?
I'm learning to use the ReplaceAll function and I found the behavior of which is quite confusing.
For
Sqrt[f[x, y]] /. f[___] -> u
Mathematica returns
...
2
votes
1answer
92 views
Is there any way to force Mathematica to collect a symbol in a polynomial?
Let's say that I have a polynomial like this:
a + b + c
Is there any way that I can get Mathematica to transform it to:
...
2
votes
2answers
119 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 $L_i$ ($i=1,2,3$), ...
3
votes
2answers
102 views
Unexpected side effect of removing the Orderless attribute from Times
First I make Times orderless:
ClearAttributes[Times, Orderless];
Then I evaluate
...
0
votes
1answer
88 views
Showing steps Mathematica uses for Resolve[ForAll[…]] [duplicate]
I have a quite complicated function of 2 variables:
...
10
votes
2answers
967 views
Why doesn't Mathematica expand Cos[x]^3 Sin[x]^2?
I found some examples of Mathematica's commands usage in an old manual but the program gives me different result than expected
...
8
votes
1answer
193 views
Most efficient way to determine conclusively whether an algebraic number is zero
Let x be an algebraic number of unspecified degree, expressed using arithmetic, rational powers, and algebraic integers (edit: ...
3
votes
2answers
152 views
Eliminate several variables between five Conic_section equations
I want to eliminate x1, x2, y1, y2 between these 5 equations.
I tried
...
3
votes
2answers
95 views
0
votes
0answers
83 views
Need conditions for DSolve
If I have differential equation of fourth order with four solutions $\alpha _1,\alpha _2,-\alpha _1,-\alpha _2 $ where we have appearing the solutions in the form $e^{\text{$i\alpha $}_1 ...
2
votes
1answer
86 views
How to transform equation
Is there any possible way to write this equation of 4th order as a system of two diff equations of second order with two new variables and to do that automatically? statespace command is transforming ...
-1
votes
1answer
172 views
Hyperbolic numbers and their polar form
How can I implement Hyperbolic numbers in Mathematica? How could I express their polar form? How could I calculate their power?
0
votes
1answer
252 views
Decoupling system of differential equations
Here I have one task and it is preparation for small exam. I solved it by hand for first case 1), but I need to check it in $Mathematica$ and to try to implement it for both cases 1) and 2) ...
1
vote
1answer
125 views
Efficient method for factor expressions with square roots
Inspired from this, I tried factor following expressions, Mathematica takes a long time,
I couldn't even wait for it to finish. Maple calculating it takes about 5 sec. Can you recommend an efficient ...
5
votes
4answers
519 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 ...
1
vote
1answer
93 views
How do I expand a sum (again)? [duplicate]
Possible Duplicate:
How do I expand a sum?
How do I expand an equation in the given form:
$\sum _{i=1}^n -2 x_i \left(-a x_i-b+y_i\right)=0$
into this form:
$-\sum _{i=1}^n x_i y_i +a ...
5
votes
1answer
145 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 ...
3
votes
1answer
157 views
How can I express an algebraic expression as a product?
I have a simply expression that I can see that I can express as a product.
...
3
votes
0answers
91 views
Cyclic Noncommutative Multiplication
I work with traces of long matrix products and I want mathematica to employ the cyclicity when simplifying.
I use this redefinition of the non-commutative multiplication:
...
26
votes
6answers
2k views
Finding real roots of negative numbers (for example, $\sqrt[3]{-8}$)
Say I want to quickly calculate $\sqrt[3]{-8}$, to which the most obvious solution is $-2$.
When I input $\sqrt[3]{-8}$ or Power[-8, 3^-1], Mathematica gives the ...
5
votes
3answers
369 views
Square both sides of an equation?
Can I define an equation (for example, x+1 == y^2 + 2), and tell Mathematica to square both sides?
If not, what is an equivalent way to achieve this?
3
votes
5answers
296 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 ...
2
votes
2answers
304 views
Eigensystem, Eigenvalue doesn't output nonreal eigenvalues
Basically I have a matrix and when I used either Eigenvalue or Eigensystem, it doesn't output nonreal eigenvalues, instead it ...
6
votes
3answers
115 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 ...
2
votes
0answers
66 views
How to expand terms within an integral? [duplicate]
Possible Duplicate:
Why aren’t these additions of integrals and summations equal?
I am trying to expand all the terms in a sum in order to apply assignment rules later, but can't figure out ...
2
votes
1answer
173 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 ...
7
votes
4answers
358 views
How to implement dual numbers in Mathematica?
I wonder how can I implement dual numbers in Mathematica, so that all functions work well with them (as with complex numbers).
Particularly, for each function $f$, ...
5
votes
2answers
108 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, ...
8
votes
3answers
475 views
How can I convert x^2 to x*x?
When I try the following code:
a b^2 c /. b c -> e
Mathematica gives me:
a b^2 c
but what I want is:
...
11
votes
4answers
789 views
Is it possible to have Mathematica move all terms to one side of an equation?
I have an inequality expression that I would like to express in terms of the relation of the parameters to zero. More simply, I want to have mathematica move all the terms to one side of the ...
16
votes
4answers
415 views
How do I introduce a new variable in a trigonometric equation?
I have the trigonometric equation
\begin{equation*}
\sin^8 x + 2\cos^8 x -\dfrac{1}{2}\cos^2 2x + 4\sin^2 x= 0.
\end{equation*}
By putting $t = \cos 2x$, I have
\begin{equation*}
\dfrac{3}{16} t^4+ ...
4
votes
1answer
439 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 - ...
4
votes
1answer
225 views
Move variable to one side of the equation
Say if I have a formula like so:
a1*a2*a3^(a4 + 1)*(1 - E^(a5*a6/a3^a4/a2)) == 0
How do I move a3 to the right? I've tried to follow other examples here on stack ...
7
votes
2answers
632 views
How can I rationalize the denominator of an expression?
Mathematica doesn't rationalize the denominator automatically, and I haven't found anything in the documentation about it. But I found an old post on MathGroup, which proposes a solution using ...
