Questions on manipulating complicated expressions and making them look simpler using Simplify, FullSimplify and Reduce.
4
votes
3answers
86 views
Output to preserve dot product
I am fairly new to Mathematica and I am faced with a problem. I tried to search for the solution but it seems that I don't know how to formulate the short search request.
I need to perform a matrix ...
0
votes
1answer
42 views
Retain required terms in asymptotic expansions
I am using Mathematica 8 to do lengthy asymptotic expansions for use in statistics.
In particular I have
$\lambda=\beta+\epsilon+\delta+\gamma+O(n^{-5/2})$
where the first term is of order ...
-1
votes
0answers
35 views
Simplifying Expressions to minimize multiplications [duplicate]
I have a big matrix, whose coefficients mostly have the following form:
2*(Lz*q*q0+Ly*p*q2-Lx*q*q2+Lz*p*q3-Ly*q0*r-Lx*q3*r)
This was obtained with Simplify, with ...
1
vote
0answers
69 views
Problems with Simultaneous Equation Solving
Let me first explain what I am doing and then I will explain the problem that I can't figure out. I am basically trying to solve 2 equations for 2 unknowns (a1 and ...
1
vote
0answers
72 views
Simplify[] cannot separate multiplied terms like a×b [closed]
How can FullSimplify[] be made smarter? In the example below, the mere combination of q*h prvented ...
4
votes
2answers
130 views
Simplifying the trace of a matrix expression
I have a long expression involving matrices that I derived using the NCAlgebra package. Can I simplify the trace of the expression?
For example, say b is a scalar ...
-1
votes
0answers
65 views
Why is this calculation too slow?
I want to compute the first and second derivatives of a relatively simple function but Mathematica is either taking ages to compute them or aborts printing the following message:
"Simplify::time: ...
3
votes
3answers
105 views
How to prevent Mathematica combining similar terms?
For example, given: x + 2xy - xy + y I need to put it in this form: x(1+2y) - y(x-1).
But Mathematica will simplify ...
4
votes
1answer
77 views
How to decompose a complex expression containing repeated subexpressions? [duplicate]
Suppose I have an expression like
...
2
votes
0answers
43 views
Verifying integration by parts of an arbitrary function [duplicate]
Suppose that I have an arbitrary differentiable function $G$ which depends on $s$: $G(s)$.
Now suppose that I want to do the following integral: $$\int ds \;\; s \frac{\partial G(s)}{\partial s}.$$
...
1
vote
1answer
90 views
Comparative Statics on Mathematica
Let me first explain what I am doing then I will mention my little problem that I could not figure out. I am using Mathematica version 7. I have an equation named "fd" and I took the derivative of ...
7
votes
2answers
79 views
How do I invoke the default complexity function?
Documentation on ComplexityFunction says:
With the default setting ComplexityFunction->Automatic, forms are
ranked ...
2
votes
0answers
78 views
simplify a huge expression containing only Plus and Times
I have some huge expressions which can be written as:
$$\sum _{n=1}^N \left(\prod _{i=1}^{I_n} a_{n,i}\right)$$
$N$ is between 10 and 100, $I_n$ is between 1 and 10 and $a_{i,n}$ represent symbols ...
1
vote
1answer
67 views
Format Preservation of FullSimplify on Indexed System of Autonomous Equations
I currently have a large system of 150 autonomous differential equations. I've indexed a more managable dummy system of identical form, using Part to reference ...
6
votes
3answers
130 views
Counting multiplications (complexity function)
I'm trying to count the number of times multiplication appears in an expression (for the purpose of constructing a ComplexityFunction that would help me simplify a terrible algebraic expression for ...
1
vote
0answers
80 views
How can I say that all quantities need to be positive (and real)?
Can you say at the beginning of a script in mathematica that you want all the quantities to be positive (and real)? So that in all calculations, only the real values of these quantities will be ...
5
votes
0answers
51 views
Faster way to perform SameQ[Reduce[…], Reduce[…]]
I'm have some expressions that I need to confirm the equality of. SameQ[Reduce[...], Reduce[...]] works like a charm for the more simple expressions, however when ...
2
votes
3answers
67 views
Problem with simplifying Sinc function
$Assumptions = x ∈ Reals && y ∈ Reals && a ∈ Reals && b ∈ Reals;
These work:
...
2
votes
2answers
49 views
Expanding Matrix Expressions
I want Mathematica to recognize that
A.(-B.C)+A.B.C = 0
Yet FullSimplify and the like leaves the expression as it is. How do I get around this?
7
votes
2answers
107 views
How to simplify an expression with special functions to zero
The following is a well-known Bessel function identity:
$$J_{-n}(z)=(-1)^n J_n(z),\qquad n\in\mathbb Z$$
To check this, I used the following code and the result is as what I expected.
...
2
votes
2answers
95 views
Substitution to write out powers of expressions
I am looking for a substitution command which will write out powers of expressions like this:
$$\frac{a ~b^3~ c}{d~ e^{3/2}~ f^2}\to \frac{a ~b~b~b~ c}{d~ e^{1/2}~ e^{1/2}~ e^{1/2}~ f~f}$$
...
15
votes
3answers
241 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 ...
4
votes
2answers
259 views
Simplify — is this simplest result Mathematica can provide?
I have a question about Simplify: When I do a simplification the returned result is not as simple as I want. When I ask for the Norm of an complex expression, ...
1
vote
1answer
108 views
Improve performance for finding Fibonacci number which have divisibility property
In this post, the OP requires finding a Fibonacci number having some divisibility property with Mathematica and Maxima. I tired tried that Mathematica code on Mathematica 9.0 and it's still slow ...
13
votes
1answer
106 views
How to instruct FullSimplify to assume that PossibleZeroQ returns correct result?
Sometimes I have a really huge expression that cannot be significantly simplified by FullSimplify. I would like to, so to speak, "simplify with faith" using ...
4
votes
1answer
152 views
2
votes
3answers
141 views
Join all square root expressions?
Sometimes I observe Mathematica produce expressions exactly like the following after a simplification step:
$$\frac{a+\sqrt{-(1-b)}\sqrt{\frac{1}{b-1}}}{\sqrt{c}\sqrt{\frac{1}{c}}}$$
Now, any ...
2
votes
0answers
55 views
Simplify yelds an incorrect expression [closed]
I was trying to simplify an expression:
DSolve[d'@t == a + b Sin@d@t, d@t, t]
Simplify[%, Abs@a < -b < 0]
and I got
...
0
votes
2answers
56 views
Conjugate and simplify
I want to get a cosine from taking the real part of a complex exponential: $cos(x) = Re(exp(i x))$. What I do in Mathematica is
...
3
votes
3answers
157 views
Mathematica not able to confirm its own solution to differential equation
I type the following into Mathematica:
DSolve[q''[x] + 2 x/(x^2 - 1) q'[x] - 4*q[x]/(x^2 - 1) == 0, q[x], x]
It gives me the result
...
3
votes
2answers
210 views
Mathematica does not understand (R^3)^(1/3) is the same as R [closed]
In the output from a calculation in mathematica stands a/((R^3*c)^(1/3)), with c and a ...
0
votes
0answers
56 views
Any way to fully expand an expression of two operators?
I am looking for a way to expand a complicate expression like the follow
(A o B + C o (DxE))*(D o (ExF) - ExA + A)
Here o and x are the operator. I want to ...
1
vote
1answer
105 views
Set all instances of Exp[-x_] to zero?
To simplify a huge expression efficiently, which involves a variable in a bunch of exponential functions going to infinity, I have tried to substitute
...
4
votes
2answers
177 views
Is there a way to show the details of a numerical computation?
I have recently started using Mathematica as a calculator while teaching (definitely overkill, but I try to use as few tools as possible). I would like my students to be able to trace simple numerical ...
1
vote
1answer
85 views
Why is a non-convergent series simplified to zero?
Sum[Sin[n*x]*Sin[n] /. x -> 1, {n, 1, Infinity}] ==
Sum[Sin[n*x]*Sin[n], {n, 1, Infinity}] /. x -> 1
Sum::div: Sum does not converge. >>
...
1
vote
1answer
88 views
Trying to show an expression is always zero
I have a symbolic matrix
$$m = \begin{pmatrix}A1 & B1 & C1\\A2 & B2 & C2 \\ A3 & B3 & C3\end{pmatrix}$$
and I believe that Det[m] is ...
0
votes
1answer
72 views
Avoid trigonometric simplifications?
When evaluating the expression
Sinh[x]^2 + Cosh[x]^2 // FullSimplify
I get
Cosh[2 x]
That is indeed a simplification, but ...
1
vote
1answer
57 views
Simplify expression to Abs
FullSimplify[Sqrt[1/(a^2 b^2)], Element[{a, b}, Reals]]
gives
Abs[1/(a b)]
How do I simplify the following expression
...
2
votes
2answers
161 views
How to expand a general expression in cross and dot product in Mathematica
I am looking for a way to simply the general expression in cross product and dot product with general vectors. I got a help in How do I simplify a vector expression? but soon I find that it doesn't ...
5
votes
1answer
78 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
2answers
145 views
on simplifying an expression
After some integration process, I ended up with the following expression:
...
1
vote
0answers
68 views
Problem with using Assumptions in Simplify [closed]
I want to simplify
Log[E^(2 \[Pi] I m/n)]/(2 \[Pi] I)
To obtain m/n.
I have tried
...
0
votes
0answers
119 views
6x6 matrix NullSpace
I'm working with a 6x6 matrix. Whenever I try to find the NullSpace and FullSimplify it, I get the error
No more memory ...
5
votes
2answers
223 views
Simplify expressions with Log
How can I get Mathematica to simplify the following expression
n Log[a] + m Log[b] - m Log[a + b] - n Log[a + b]
into
...
4
votes
1answer
102 views
Simplifying numerical expressions involving special functions
I've encountered the following problem. There is the identity that the special functions EllipticK[x] and EllipticE[x] satisfy:
...
11
votes
4answers
167 views
FullSimplify Over Reals Automatically
Frequently, Mathematica will produce some expression in a complicated form, with a number of unset variables. For me, it is rare that I would be interested in solutions that are generalized to both ...
0
votes
1answer
89 views
Simplifying Complex Numbers that contain physical units
I am trying to evaluate the following:
Simplify[Meter Nano Re[(a + I b)/(Meter Nano)], Assumptions -> Element[{a, b}, Reals]]
However, Mathematica returns:
...
5
votes
2answers
293 views
Log of products to sum of logs
I have a log of products:
$$\log \left(\prod _{i=1}^n \left( g(a(i,i)) \prod _{k=1}^i f(a(i,k))\right)\right)$$
That I turn into a sum of logs (I know everything involved is nice enough):
$$\sum ...
2
votes
2answers
92 views
Puzzling behavior produced by Exists
I need to simplify a set of solutions of a system, say for example:
...
7
votes
1answer
113 views
Why does simplification in Mathematica depend on variable names
Mathematica fails to put the following into an obvious simplest form:
...
