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
72 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
122 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
152 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
363 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
227 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
114 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
110 views

Mathematica not simplifing when using FullSimplify

I am trying to simplify the following $(Z_i - Z_{i+1})^4$ using ...
6
votes
1answer
656 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
218 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 ...
19
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
284 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
169 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 ...
11
votes
1answer
641 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
129 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
580 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
149 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
867 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
447 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
71 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
417 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
75 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
142 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
266 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
770 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
271 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
321 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
193 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
162 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
502 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
264 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]); ...
3
votes
1answer
1k views

Remove annoying Conjugate

Here is an expression ...
1
vote
1answer
231 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
2k 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
582 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
244 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
321 views

a problem about simplifing conjugate

the situation is as follows ...
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 ...
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
1answer
127 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 ...
4
votes
1answer
145 views

Simplifying expressions using rules that span nonconsecutive terms

Suppose there is some function with the property f[x,y] f[y,x^2] / f[x^3,y] == f[2x,y] How can I simplify an arbitrary expression that contains the lhs of the ...
1
vote
1answer
92 views

Expansion of Expression

I am trying to expand out expressions that have several terms similar to E[-lH] Sinh[l (H - h)] The Expand command just gives ...
6
votes
2answers
323 views

Simplify Binomial Function

The following input ...
20
votes
1answer
301 views

How can I see which transformations Simplify attempts?

The documentation for Simplify[expr] says that it performs a sequence of algebraic and other transformations on expr, and returns the simplest form it finds. How can I see which transformations it ...
6
votes
3answers
445 views

Sum over binary digits of integer

This might seem like a simple enough question but Mathematica seems to simplify inadequately here: How would you sum over the digits of an arbitrary binary number? I already tried this: ...
5
votes
2answers
421 views

Replacements/Substitutions in Mathematica

I am a new user of Mathematica and have some questions about the simplifications of calculated expressions. I am unable to attach an image of the session, but my Mathematica commands are: ...
7
votes
2answers
183 views

Why isn't Simplify doing more simplification of this expression?

When I try this Simplify[(1-a)*(1/(1+x*m))^(1-a)(1+m)^(1-a) + (1-a)*(x*m)^a*((x*m)/(1+x*m))^(1-a)*(1+m)^(1-a)] the output is $$\frac{(1-a) (1+m)^{1-a} ...
7
votes
0answers
235 views

Faster simplification of linear combinations of some specific functions

After some profiling I've found that my program spends most of its time in the simplification step. The program uses my simplification function many times (over different data). My calculation is not ...
3
votes
1answer
330 views

How to implement Condition programmatically?

I am writing my own symbolic functions with custom symbolic properties. So often I wish to introduce some automatic simplifications or evaluations, which return the same head as it's argument. This ...