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

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183 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 ...
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49 views
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89 views

How to get a rule for, e.g., (x + y) to apply to (-x - y), etc.?

For example, the substitution (x + y) -> s fails here: In[1]:= (-x - y) /. (x + y) -> s Out[1]= -x - y Of course, I ...
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1answer
42 views

PiecewiseExpand doesn't take all kind of assumptions

Running PiecewiseExpand[expr, assum] does not work with all kind of assumptions. For example, the following line will not split the expression with absolute values in the chambers, considering m1=m2. ...
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2answers
90 views

Grouping constants in expressions

Starting from the general expression: i A(a x + b y + c z + ...) + j B(a' x + b' y + c' z + ...) + k C(a'' x +b'' y + c'' z + ...) I'd like to rearrange it to ...
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1answer
222 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 ...
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1answer
155 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 ...
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89 views

How accurate is Collect?

Background: I am trying to compute the Lyapunov exponent for the logistic map given by \begin{equation*} x_{n+1}=F(x_n)=ax_n(1-x_n) \end{equation*} The formula for the Lyapunov exponent for a given ...
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132 views

Problem about Solve

See this example : ...
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77 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, ...
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63 views

Transform Root objects into Trigonometric expressions

Consider the Root objects roots = Table[Root[-1 + 27 #1^2 - 162 #1^4 + 243 #1^6 &, i],{i,1,6}] These can be expressed in terms trigonometric functions as ...
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41 views

How to make noncommutative multiplication agree with commutative multiplication

I need a noncommutative multiplication that is Associative Distributive $A**0=0$, $A**1=A$ Agrees with the commutative multiplication ($A**(k B)=(k A)**B=k (A**B)$) I have found a code ...
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72 views

Define inverse for the custom operator

I want to define simple matrix algebra (inspired by the following posts: Block Matrix Algebra with Mathematica ; How to define custom operators ). I assume the funtion ...
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0answers
103 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 ...
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1answer
183 views

Showing steps Mathematica uses for Resolve[ForAll[…]] [duplicate]

I have a quite complicated function of 2 variables: ...
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1answer
241 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?
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1answer
321 views

How to neglect higher power terms in a polynomial expression

I have a polynomial expression of order n (say n=20). F(x)=1+x+x^2+x^3++...x^20. I want to approximate the polynomial for order 3 only. So I need to make the ...
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1answer
53 views

Using Collect with equations

Is it possible to somehow use the expression that Mathematica has collected once the Collect command has been used? What I mean is, I have an expression like this ...
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1answer
78 views

how to permute bit strings and manipulate their elements

I want to write a function(has 2 paremeter, n=range,k=number of 1 digits) which finds all probable combinatorics of arbitrary bit strings and evaluate sum of tensor ...
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1answer
625 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) ...
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2answers
54 views

Expand expression into quotient of negative power series

I have a function T(z) and want to expand it to the following form: At the end I want to have a list of equations, which can calculate a0, a1, a2, b0, b1 and b2 with different values of h1, h2, ...
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1answer
82 views

Impose an specific Trigonometric expansion with TrigExpand

Is there a way to impose in mathematica an specific trigonometric expansion with TrigExpand? I have various double-angle expressions for cosine and sine in my ...
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1answer
100 views

Replacement rules in combination with pure functions to make a change of variables

I have defined my function in this way w = f[r,Θ] ; After some calculations i obtained my results with respect to the previous function. For instance: ...
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1answer
74 views

Manipulating formal vectors

I want to work with a formal vector space spanned by integer triplets: $$ V=\text{span}\{(a,b,c):a,b,c\in\mathbb N^3\}, $$ such that Mathematica can do additions for me. For example,if I input ...
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1answer
61 views

Force multiplication by a single factor [closed]

I have an expression that Mathematica decides to return in the general form: y = f ( a/f + b/Sqrt[f + 2] + c*f^2/Sqrt[f + 2]) (actually my expression is much ...
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1answer
90 views

How to transform the polynomial in this way?

I have two functions f and g and a polynomial ...
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1answer
109 views

Why do I get a different answer from the use of TrigExpand?

This is an old post but I get two different answers from Mathematica 9.0.1.0 ...
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0answers
52 views

Ordering oscillators with negative powers: Infinite loops

I have been working with ordering of oscillators for example $[a,a^\dagger]=1$ and I have a fairly stable code. I have needed to use inverse oscillators for example expressions like $a^m ...
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49 views

Split absolute value in chambers

I usually expand expression containing absolute values, with the PiecewiseExpand[] function. ...
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0answers
23 views

Jacobian matrix formation from polynomial expressions [duplicate]

I want to find the jacobian matrix for 3 polynomial expression with 3 variables.. the polynomial expressions have the degree of 8.how to form it.?
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67 views

Algebraic condition from a non linear equation

I have got a system of equations which look like this: $\theta_{1}^{2}e^{\phi_{1}\cos(\Omega z)}\tilde{w}\cos^{2}(\theta_{1}\sin\Omega z)\sin^{2}\Omega z+\frac{1-\lambda\cos(2\theta_{1}\sin\Omega ...
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34 views

Solving an algebraic equation with one or more constraints? [duplicate]

Just as a simple example, say I wanted to solve Sin[x] == a for x with the constraints -1<=a<=1 and 0 < x < Pi. Is there any way to do this?
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84 views

Unexpected result from InverseFunction

Given the following two equivalent inverse functions, why does one simplify (using inverse functions that are acceptable to me) and the other doesn't? Is there an assumption or setting I can give ...
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1answer
93 views

Algebra problem [closed]

I have recently run into an algebra problem that goes as follows. Using the numbers 1-9 A + B + C + D = EF E + F + G + H = CJ B + G + J = ?D total = B? where ...
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1answer
296 views

Solving Det[matrix] == 0 with an 8 x 8 matrix [closed]

I want to solve the equation Det[matrix] == 0 which came from the consistency of solutions of a set of 8 equations. This matrix has two constants λ and μ and two variables $P$ and $q$. I want to get ...