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

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1
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1answer
232 views

Simplify vector expression - is there something like “Factor” for vectors, dot products etc.?

I am looking for a way to simplify dot products etc. Here is a minimal example: Lets say I have two vectors a and b: Array[a,2] Array[b,2] Now I evaluate their ...
4
votes
2answers
150 views

How to use SuperLog by loading SMLE.m

I am researching a software reliability model that has many parameters that need to be estimated. I want to use a maximum likelihood estimator (MLE) to estimate those parameters. After I searched ...
1
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0answers
60 views

How to take the log of an equation? [duplicate]

I am researching a software reliability model that has many parameters that need to be estimated. I want to use a maximum likelihood estimator (MLE) to estimate those parameters, but my model is too ...
1
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0answers
29 views

How to achieve the real component of my expression? [duplicate]

How to achieve the real component of my expression? Input: expr = Csc[θ/2] Sin[(n θ)/2] (Cos[1/2 (1 + n) θ] + I Sin[1/2 (1 + n) θ]); Re[expr] ...
1
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2answers
131 views

Show Simplified Directives [closed]

Is there a way to force Mathematica to convert an already rendered Graphic to the simplified Directive form of that Graphic. Background: I am currently editing Graphics using Drawing Tools and then ...
6
votes
3answers
129 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
232 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
169 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
220 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
174 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
129 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
361 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
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0answers
118 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
574 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 $\frac{1+n x^{m-1}}{(1+x)}$ ? ...
5
votes
0answers
98 views

Moles/Liters doesn't get simplified to Molar even though Molar*Liters gets simplified to Moles

Why can't Mathematica 9 simplify mol/L to M, when it can simplify M*L to mol? ...
2
votes
0answers
57 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 ...
0
votes
1answer
376 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
151 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
196 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
114 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
866 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
689 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
239 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
222 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 ...
10
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
783 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
620 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
169 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
132 views
3
votes
1answer
469 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
251 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
112 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
174 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
183 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
78 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
179 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
173 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
336 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
178 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
116 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
343 views
2
votes
0answers
176 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
258 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
207 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
132 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
84 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
361 views

Checking if an expression is equal to zero

I have 6 points in $\mathbb R^3$ as follows: ...