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

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7
votes
2answers
203 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
168 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
118 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
243 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 ...
2
votes
1answer
172 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
458 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
125 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 ...
5
votes
2answers
248 views

on simplifying an expression

After some integration process, I ended up with the following expression: ...
8
votes
3answers
2k 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
213 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: ...
12
votes
4answers
451 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
137 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
884 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
105 views

Puzzling behavior produced by Exists

I need to simplify a set of solutions of a system, say for example: ...
7
votes
1answer
202 views

Why does simplification in Mathematica depend on variable names

Mathematica fails to put the following into an obvious simplest form: ...
0
votes
1answer
166 views

Simplify expressions that contain full derivatives

The best way to show what I want is by giving an example: How to go from ...
-1
votes
2answers
464 views

How to simplify expressions containing derivatives

Is there a way to reverse the application of derivative rules in order to simplify expressions including derivatives? e.g. in Mathematica code: Want to go from ...
0
votes
2answers
455 views

Simplifying a trigonometric equation to obtain specific terms

When I try to solve the non-homogeneous differential equation ...
1
vote
1answer
76 views

Declaring a positive variable [duplicate]

Why I have this behaviour? R /: Greater[R, 0] = True R > 0 => True Simplify[Sqrt[R^2]] => Sqrt[R^2] I expect R ...
1
vote
1answer
125 views

Why Solve and Simplify give different results? [closed]

I want to solve the following equation y == (1/(1/4 + y) - 1/(3/4 - y))/((1/4 + y) + 1/(3/4 - y)) I tried ...
7
votes
2answers
2k views

How do I simplify a vector expression?

I am doing vector analysis. I have figured out that the following expression won't be simplified in Mathematica: Simplify[Dot[x, y] - Dot[y, x]] I think the ...
1
vote
2answers
161 views

Construct a sum that evaluates its arguments but doesn't evaluate further

I'm trying to construct a sum like this: Sum[body, range] where body is ...
3
votes
2answers
393 views

Combining and separating sums

How can I combine or separate sums in Mathematica in the way that Together or Expand work for rational expressions? For ...
2
votes
1answer
234 views

Variable substitution in sum's index

How cam I simplify Sum[UnitStep[-1 + n]/Sqrt[n!], {n, 0, ∞}] to $$\sum _{n=1}^{\infty } \frac{1}{\sqrt{n!}}$$ and then to $$\sum _{n=0}^{\infty } ...
1
vote
3answers
120 views

Auto simplifications of power products

Mathematica automatically simplifies Exp[a]Exp[b] to Exp[a+b]. The problem is now that I can't do this ...
0
votes
1answer
111 views

Mathematica not simplifing when using FullSimplify

I am trying to simplify the following $(Z_i - Z_{i+1})^4$ using ...
6
votes
1answer
770 views

Properly Force Mathematica to Simplify Log Expressions/Rules

I want to be able to expand $\log(x^n e^x) = n \log(x) +x$: FullSimplify[Log[x^n Exp[x]], x > 0 && Element[n, Integers] && n > 1] yields ...
5
votes
1answer
224 views

Is there a way to track the Simplify process?

Is there any way to track how Mathematica actually performs Simplify, so that we can see what those "Automatic" transformation functions it applies are and how it ...
21
votes
0answers
2k views

Simplify matrix algebra

I'm trying to simplify some matrix linear algebra, for example, simplify $$\big(a1\times(A1\cdot A2)\big)\cdot\Big(a2\times A3\cdot A4+(a3\times A5)\cdot(a4\times A6)\Big)^{T}$$ where lower case ...
0
votes
1answer
306 views

How Simplify and Assume can be combined on matrix products?

What I am trying to do is to simplify some expressions involving matrices! The problem is that Simplify[] considers the simplifications based on alphabetical order and everything is Commutative. For ...
6
votes
1answer
192 views

Simplify with TransformationFunctions, Bug?

I want to use custom transformation functions in Simplify, but mathematica does not seem to use them properly. Consider the following ...
12
votes
1answer
734 views

Simplify Sin[x]/x to Sinc[x]

I have an expression in the form of $\tt \frac{Sin[x]}{x}$ that I would like to simplify to the form of Sinc[x]. I've tried the ...
4
votes
1answer
133 views

How can I prevent a polynomial from being simplified?

I'm having a problem with polynomials. Let's say I have a polynomial "2x^2 - 5x + 6 - 3x^2" .. How can I check that this expression is not simplified ? Additionally, I would like to locate the ...
12
votes
2answers
623 views

Simplify assumes Boolean 1 and 0 in logical expressions

Per this chat discussion and this previous question where I encountered the strange behaviour: ...
1
vote
1answer
156 views

Efficient way to give symbolic elements symmetry

I have a symbolic expression that represents a set of operators. These operators have quite a bit of symmetry to simplify expressions: ...
2
votes
3answers
952 views

Why doesn't Mathematica make an obvious simplification?

I am doing some calculation with summation and the Kronecker symbol. Here are my steps : ...
7
votes
3answers
485 views

FullSimplify does not work on this expression with no unknowns

I can't reproduce this simple example from Habrat, 2010 ("Mathematica : a Problem-Centered Approach"). It is supposed to demonstrate the functionality of ...
0
votes
0answers
72 views

Finding real and imaginary parts [duplicate]

Possible Duplicate: Extract real part of a complex expression better than Re does I have an expression and I would like to find its real and imaginary parts. As a simplification, suppose ...
8
votes
1answer
470 views

Why doesn't FullSimplify get rid of the common factor in this expression?

FullSimplify does not get rid of the z factor in the following expression: ...
3
votes
2answers
79 views

Detecting operator Set in Assumptions

Here is a typical issue: Simplify[x + y, x = y] produces 2 True. Is there a way to detect operator ...
1
vote
1answer
147 views

How do you multiply out integer powers in a symbolic expression?

I have the following problem: I want to transform integer powers into a series of multiplications within symbolic expressions. E.g. x^3 should be written as ...
3
votes
2answers
277 views

integral, explicit form

I want to estimate the ratio of integrals: $$ \frac{\int \frac{4 a T^3}{\frac{4 a T^4}{3}+\Lambda_1 \left(\frac{4}{T^3}+1\right)}}{\int \frac{4 a T^3}{\frac{4 a T^4}{3}+\Lambda_0 ...
20
votes
4answers
796 views

An apparently “simple” limit?

Let $c$ and $h$ be real values. I was using Mathematica to compute the limit $(h \rightarrow \infty)$ of the following expression: $$ \frac{\left(h^2 +c^2 h^2 + \sqrt{4 h^2+\left(h^2+c^2 ...
5
votes
1answer
281 views

Simplification of double symbolic sums containing a DiscreteDelta without explicit summation range

I am trying to get Mathematica to automatically do simplifications like the following: $$\sum\limits_{q}^{q\in qV}\sum\limits_{q'}^{q'\in q'V}{f(q)g(q')\delta(q-q')}=\sum_{q}^{q\in qV}{f(q)g(q)}.$$ ...
2
votes
1answer
344 views

Nested Sums to multiple sum

I would like to automatically "move nested sums to the left". I mean, just take out of an expression all the summations and go from a nested Sum to a multiple sum. Something like starting with: ...
3
votes
1answer
208 views

Using Hold correctly with Simplify and ComplexityFunction

It seems like Mathematica immediately evaluates the expression Sqrt@I to (-1)^(1/4). I'm trying to use ...
2
votes
1answer
165 views

How can I get Mathematica to simplify my expression?

4.`*^-12 Sqrt[3.0254210421890627`*^22 - 6.25`*^22 T6^2] The above expression is equal to Sqrt[0.48406736675024997` - T6^2] ...
26
votes
2answers
545 views

Why does Simplify ignore an assumption?

Here is the example: Simplify[x + y, x + y == a] Simplify[x + y, x + y == 5] Mathematica 9 output: x+y 5 I expect the ...
2
votes
2answers
274 views

FullSimplify inconsistency

I'm pulling my hair out with this one. I have two complex functions f and g, ρ is real. ...
4
votes
1answer
139 views

Why are some equal expressions more equal than others?

n1 = 1/3 (2 + (-Sqrt[3] + 2 Sin[(2 π)/9])/(Sqrt[3] Cos[π/9] - Sin[π/9])); n2 = 1/2 + Sin[π/18]/(3 Cos[(2 π)/9] + Sqrt[3] Sin[(2 π)/9]); n3 = 2/3 (1 - Cos[4 π/9]); ...