Questions on manipulating complicated expressions and making them look simpler using Simplify, FullSimplify and Reduce.

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4
votes
0answers
89 views

Simplifying expressions involving Divisible

FullSimplify[ Divisible[p^2 - 1, 24] , Element[p, Primes] && p > 3] Should evaluate to True, but I get ...
1
vote
1answer
452 views

How to simplify Sqrt[1/x] Sqrt[x]?

In my expression, there appear terms of the form A^(B Sqrt[1/C] Sqrt[C]). Mathematica doesn't realize that this is just simply ...
7
votes
1answer
171 views

Why does Mathematica not simplify the Gudermannian function?

The Gudermannian function is built into Mathematica, but does not reduce to simpler terms in some simple cases. In particular, the Gudermannian is an odd function of real arguments but Mathematica ...
7
votes
1answer
335 views

Why does Simplify with TimeConstraint return Removed[$$Failure]?

Bug existed in version 7 and is fixed in version 10.0.0 I have a rather ugly Mathematica expression (edit: shown below) that I would like to simplify with a time constraint; simplifying without a ...
10
votes
3answers
1k views

Combining Cos[ ] terms

A function that is the sum of two Cosine terms of the same frequency x[t_] := a1 Cos[w0 t + b1] + a2 Cos[w0 t + b2]; can be simplified to a single ...
2
votes
1answer
244 views

How to select TransformationFunctions based on Assumptions made when using Simplify?

I am re-writing the question using a very simple example so not to confuse matters with the another question being asked where I used the example from there. In general, how to add logic to switch ...
2
votes
1answer
155 views

How to use TransformationFunctions on a compound expression?

I was trying to answer this question but having hard time with the correct way to write the transformation rule. Trying to write a rule to transform ...
3
votes
2answers
347 views

Replacing gamma at half integers by double factorial

It is well-known that for any positive integer $n$ the equality $\Gamma(n+\frac12)=\sqrt\pi\,(2n-1)!!/2^n$ holds, where $!!$ stands for the double factorial. I am using ...
4
votes
4answers
922 views

Simplifying a trigonometric expression

I'm sure this has been addressed before, but I can't find it! I want Mathematica to simplify Sqrt[1 - Sin[π/6 - θ]^2] to ...
0
votes
1answer
323 views

Pull Constants outside of integrals

I would like Mathematica to pull constants outside of an integral: e.g., $\int_0^t f[t] g[s] dt \to g[s] \int_0^t f[t] dt$ This has previously been discussed at replacement rule to pull independent ...
0
votes
1answer
211 views

Simplify function with normalized vector

I made a very simple case: testF[x_, y_, z_] = x^2 + y^2 + z^2 Simplify[testF[x, y, z]] If {x, y, z} is normalized, the simplified result should just be 1. How ...
1
vote
2answers
1k views

Simplifying expressions with square roots

I would like Mathematica to simplify this expression: $4 \left(16 \sqrt{\left(-1+2 c^2\right)^2}-32 c^2 \sqrt{\left(-1+2 c^2\right)^2}+\sqrt{\left(1-8 c^2+8 c^4\right)^2}\right)^2$ ...
1
vote
1answer
177 views

How can I eliminate $x_1$ from my two ODEs?

How can I get Mathematica to eliminate $x_1$ in the equations in the first box to achieve the equation in the second box? My code: ...
1
vote
1answer
135 views

Problem about Solve

See this example : ...
3
votes
1answer
602 views

Simplifying an ArcTan expression

The expression $\tan ^{-1}\left(\frac{\sqrt{L^2 \sin ^2(\theta )}}{\sqrt{L^2 \cos ^2(\theta )}}\right)$ can be simplified to $\theta$. After some attempts I got the following to do the job. ...
1
vote
1answer
290 views

How to tell Mathematica not to simplify an expression

While there is this question with a very similar title, it does not answer my question, which is: I have part of an input, in my case Re[Exp[I*x]] which ...
0
votes
1answer
329 views

Simplify equations using list of rules

I have a set of equations that I want to simplify using a list of rules: ...
0
votes
2answers
116 views

How can I transform a quadratic into an factored equation?

How can I transform a quadratic polynomial in x and y into an equation of the form $(x-a)^2+(y-b)^2=c$? f = -9 x + (3 x^2)/4 + (3 y^2)/4; Completing the Square ...
2
votes
2answers
197 views

Simplifying expression to evaluate limit as $y\rightarrow 0$

I often end up with a function that contains the term $1/(1 + x^2/y^2)$, and I need to evaluate this in the limit $y\rightarrow 0$. By hand, I can rewrite this as $y^2/(y^2 + x^2)$, but how can I tell ...
1
vote
0answers
86 views

How can I get Mathematica to simplify my square root expression? [duplicate]

$$\sqrt{r^2 e^{4 \gamma (r)-4 \psi (r)}}$$ If I set var = r^2*E^(4 \[Gamma][r] - 4 \[Psi][r]) Simplify[Sqrt[var], var > 0] I just get $$\left| r\right| ...
3
votes
1answer
551 views

Trace of FullSimplify

I have a symbolic function and I used FullSimplify command to simplify the equation given below. I am calculating it by hand but I couldn't reach the same solution. ...
6
votes
1answer
1k views

Simplify $\cos(n \pi)$ and $\sin(n \pi)$ when n is an integer

I was trying to calculate this integral in Mathematica 9: 2/π Integrate[ Cosh[a x] Cos[n x], {x, 0, π}, Assumptions -> n ∈ Integers] I got as a result : ...
4
votes
3answers
186 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
124 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 ...
2
votes
0answers
196 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 ...
4
votes
2answers
288 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 ...
5
votes
3answers
618 views

How to prevent Mathematica combining similar terms?

For example, given: x + 2 x y - x y + y I need to put it in this form: x (1 + 2 y) - y (x - 1). But Mathematica will simplify ...
2
votes
0answers
48 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
237 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
154 views

How do I invoke the default complexity function?

Documentation on ComplexityFunction says: With the default setting ComplexityFunction->Automatic, forms are ranked ...
1
vote
1answer
130 views

Format Preservation of FullSimplify on Indexed System of Autonomous Equations

I currently have a large system autonomous differential equations. I've indexed a more managable dummy system of identical form, using Part to reference each ...
7
votes
4answers
400 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
122 views

How can I say that all quantities need to be positive (and real)? [duplicate]

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
89 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
400 views

Problem with simplifying Sinc function

$Assumptions = x ∈ Reals && y ∈ Reals && a ∈ Reals && b ∈ Reals; These work: ...
2
votes
2answers
307 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?
8
votes
2answers
238 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
165 views

Substitution to write out powers of expressions

I am looking for a substitution command which will write out powers of expressions like this: $$\frac{a ~b^3~ c}{d~ e^{3/2}~ f^2}\to \frac{a ~b~b~b~ c}{d~ e^{1/2}~ e^{1/2}~ e^{1/2}~ f~f}$$ ...
24
votes
3answers
735 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 ...
5
votes
2answers
376 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
177 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 ...
15
votes
1answer
180 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
405 views

Checking if an expression is equal to zero

I have 6 points in $\mathbb R^3$ as follows: ...
2
votes
4answers
370 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 ...
0
votes
3answers
225 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
303 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
249 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
147 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
2answers
195 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 ...