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

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4
votes
1answer
259 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: ...
13
votes
4answers
615 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
154 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
1k 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
107 views

Puzzling behavior produced by Exists

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

Why does simplification in Mathematica depend on variable names

Mathematica fails to put the following into an obvious simplest form: ...
0
votes
1answer
204 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
540 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
561 views

Simplifying a trigonometric equation to obtain specific terms

When I try to solve the non-homogeneous differential equation ...
1
vote
1answer
92 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
134 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
3k 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
196 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
480 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
267 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
141 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
114 views

Mathematica not simplifing when using FullSimplify

I am trying to simplify the following $(Z_i - Z_{i+1})^4$ using ...
6
votes
1answer
1k 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
236 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 ...
26
votes
1answer
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
377 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 ...
8
votes
1answer
247 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
959 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
137 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
737 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
168 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
1k views

Why doesn't Mathematica make an obvious simplification?

I am doing some calculation with summation and the Kronecker symbol. Here are my steps : ...
8
votes
3answers
632 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
75 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
663 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
90 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
182 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
318 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 ...
21
votes
4answers
861 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
349 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: $$\sum\limits_{q}^{q\in qV}\sum\limits_{q'}^{q'\in q'V}{f(q)g(q')\delta(q-q')}=\sum_{q}^{q\in qV}{f(q)g(q)}.$$ ...
3
votes
1answer
477 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
257 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
174 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] ...
31
votes
2answers
745 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
301 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
146 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]); ...
4
votes
1answer
2k views

Remove annoying Conjugate

Here is an expression ...
1
vote
1answer
276 views

How do I simplify an embedded sub-expression without affecting other sub-expressions?

I have an expression which is very large and which has several sub-expressions with head Conjugate. What I want to do is simplify the ...
5
votes
3answers
3k views

Mathematica not simplifying square root expressions even with assumptions

I have the following expression: expr=(Sqrt[2]r Sqrt[(4+r^2) (2+r (r+Sqrt[4+r^2]))])/(4+r (r+Sqrt[4+r^2])) Then ...
3
votes
3answers
815 views

Non Commutative sorting in Mathematica

I have been trying to do some oscillator algebra in Mathematica and having troubles with sorting and simplifying expressions. I am using the NCAlgebra package which helps to improve the properties of ...
1
vote
2answers
251 views

Simplify the multiplication such as $a*(b+c)$ to $a*b+a*c$

I am trying to solve this problem here but have to understand basics. Suppose I have a multiplication such as $a*(b+c+d+...+x)$. How can I multiply it to the result $a*b+a*c+...+a*x$? Trials ...
3
votes
2answers
502 views

a problem about simplifing conjugate

the situation is as follows ...
11
votes
1answer
198 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 ...
12
votes
4answers
3k 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
1answer
136 views

Assumptions are not being applied to integral

I am trying to use assumptions to simplify an integral, but I can't seem to get the assumptions to apply themselves. Here is the code I am using: Note the expressions in the assumption can be found ...