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

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6
votes
3answers
133 views

How to simplify my expression to the style of “a+b*I”?

How to simplify my expression to the style of "a+b*I"? Expand[(E^(I θ) (-1 + E^(I n θ)))/(-1 + E^(I θ))] ...
6
votes
1answer
274 views

Simplifying a trigonometric sum

I want to caculate Cos[θ] + Cos[2 θ]+ ... + Cos[n θ] Sum[Cos[k θ], {k, 1, n}] ...
8
votes
2answers
178 views

How to reduce the number of operations needed to evaluate an expression? [duplicate]

For some numerical calculations in C++ I have, for example, this complicated expression to evaluate. Given as Mathematica input, in its original form it is ...
5
votes
2answers
258 views

How to find monotonically increasing intervals of a function

I tried this code, but not working Clear[f]; f[x_] := x^3 - 3 x + 2; ForAll[{x1, x2}, x1 < x2, f[x1] < f[x2]] Reduce[%, {x1, x2}, Reals] I expected the ...
4
votes
1answer
182 views

Can't simplify Abs[a*Cos[x]]^2

Why doesn't FullSimplify[ Abs[a*Cos[x]]^2, Assumptions -> {{a, x} ∈ Reals}] simplify to (a*Cos[x])^2 but this query ...
1
vote
0answers
137 views

How to prevent simplification of hypergeometric functions resulting from integrations?

Definite integrals from 0 to Infinity over a product of two hypergeometric (including exponential, trigonometric, hyperbolic, ...
5
votes
3answers
436 views

Removing Abs from Abs[a + Exp[I*c]b]^2

Title says it all. Mathematica produces sometimes expressions of the form Abs[a + Exp[I*c]b]^2 where all three quantities a, b and c are positive real numbers. ...
1
vote
0answers
133 views

Is there a way to speed up Simplify and/or PolynomialReduce Modulus-> 2?

I'm trying to simplify a series of equations with at most 64 input terms. As the number of terms involved in the equations increase, the runtime seems to grow exponentially. Does anyone know of ways ...
7
votes
5answers
664 views

How to cancel a common term from numerator and denominator?

What mathematica commands are needed to simplify $\frac{x+n x^m}{x(1+x)}$ to $\frac{1+n x^{m-1}}{(1+x)}$ ? ...
2
votes
0answers
58 views

Simplifying a quadratic [duplicate]

I have a general query about simplifying expressions in Mathematica, which I will illustrate using quadratics. If I tell Mathematica to simplify $a x^2 + b x + c$ then ...
1
vote
1answer
410 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
158 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 ...
2
votes
1answer
214 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
140 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 ...
6
votes
3answers
959 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 ...
4
votes
4answers
757 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 ...
3
votes
2answers
273 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 ...
0
votes
1answer
265 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 ...
11
votes
4answers
2k views

How do I simplify expressions with square roots?

I want $\left\{\frac{1}{1+\sqrt{2}-\sqrt{3}},\sqrt{5-2 \sqrt{6}},\sqrt{4+\sqrt{15}}\right\}$ to be simplified to $\left\{\frac{1}{4} \left(2+\sqrt{2}+\sqrt{6}\right), \sqrt{3}-\sqrt{2}, \frac{1}{2} ...
1
vote
2answers
877 views

Simplifying expressions with square roots

I would like Mathematica to simplify this expression: $4 \left(16 \sqrt{\left(-1+2 c^2\right)^2}-32 c^2 \sqrt{\left(-1+2 c^2\right)^2}+\sqrt{\left(1-8 c^2+8 c^4\right)^2}\right)^2$ ...
3
votes
2answers
674 views

Eliminate doesn't work in Mathematica

Hello Mathematica users, I have problems trying to eliminate variable $Q(x,y)$ froma PDE, but Mathematica output is just True. The problem is that I already found ...
1
vote
1answer
172 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
134 views
3
votes
1answer
546 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. ...
0
votes
1answer
278 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
113 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 ...
0
votes
3answers
199 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 ...
2
votes
2answers
189 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
81 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| ...
1
vote
2answers
188 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 ...
11
votes
1answer
183 views

What are the default TransformationFunctions used in Simplify and FullSimplify?

If I do Simplify[(c^3 - s^3)^2 - (s^3 + c^3)^2, TransformationFunctions -> Automatic] (i.e. a verbose version of default behaviour), what transformation ...
2
votes
1answer
412 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. ...
4
votes
3answers
179 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
121 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 ...
6
votes
2answers
366 views
2
votes
0answers
182 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
271 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
vote
1answer
220 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 ...
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: $$\int ds \;\; s \frac{\partial G(s)}{\partial s}.$$ ...
7
votes
2answers
139 views

How do I invoke the default complexity function?

Documentation on ComplexityFunction says: With the default setting ComplexityFunction->Automatic, forms are ranked ...
5
votes
0answers
86 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 ...
4
votes
1answer
385 views

Checking if an expression is equal to zero

I have 6 points in $\mathbb R^3$ as follows: ...
2
votes
3answers
337 views

Problem with simplifying Sinc function

$Assumptions = x ∈ Reals && y ∈ Reals && a ∈ Reals && b ∈ Reals; These work: ...
8
votes
2answers
199 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
262 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?
5
votes
2answers
359 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, ...
2
votes
2answers
158 views

Substitution to write out powers of expressions

I am looking for a substitution command which will write out powers of expressions like this: $$\frac{a ~b^3~ c}{d~ e^{3/2}~ f^2}\to \frac{a ~b~b~b~ c}{d~ e^{1/2}~ e^{1/2}~ e^{1/2}~ f~f}$$ ...
22
votes
3answers
648 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 ...