Questions on manipulating complicated expressions and making them look simpler using Simplify, FullSimplify and Reduce.
5
votes
1answer
159 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 ...
0
votes
0answers
108 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 ...
2
votes
3answers
275 views
Why doesn't Mathematica make an obvious simplification?
I am doing some calculation with summation and the Kronecker symbol. Here are my steps :
...
0
votes
0answers
82 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:
...
7
votes
3answers
227 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
55 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 ...
7
votes
1answer
166 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:
...
4
votes
1answer
156 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
2answers
66 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
66 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 ...
20
votes
4answers
553 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:
$$
\frac{\left(h^2 +c^2 h^2 + \sqrt{4 h^2+\left(h^2+c^2 ...
2
votes
2answers
164 views
integral, explicit form
I want to estimate the ratio of integrals:
$$
\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 ...
1
vote
1answer
143 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:
...
2
votes
1answer
98 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 ...
21
votes
2answers
269 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
1answer
139 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]
...
7
votes
1answer
444 views
Assumptions on unknown functions
I'm trying to do analytic calculations in a quantum mechanic harmonic oscillator basis. Specifically I want to be able to evaluate functions of the many particle density.
I define the following ...
4
votes
1answer
365 views
Does the Im function work with symbolic arguments?
Does the Im function work with symbolic arguments?
...
2
votes
2answers
161 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
113 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
325 views
1
vote
1answer
119 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 ...
4
votes
3answers
443 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
...
1
vote
3answers
255 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
205 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
166 views
10
votes
3answers
340 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}
...
6
votes
0answers
91 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 ...
4
votes
1answer
98 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 ...
5
votes
2answers
135 views
1
vote
1answer
74 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 ...
20
votes
1answer
190 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
293 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
254 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:
...
5
votes
2answers
138 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
$$\frac{(1-a) (1+m)^{1-a} ...
6
votes
1answer
492 views
Why does this sum not simplify properly?
I was trying to get Mathematica to simplify some moderately ugly sums and I ran into some pretty weird behaviour, which I tracked down to the following example. I'm working with ...
6
votes
0answers
146 views
Faster simplification of linear combinations of some specific functions
After some profiling I've found that my program spends most of its time in the simplification step. The program uses my simplification function many times (over different data). My calculation is not ...
7
votes
2answers
268 views
How to deduce a generator formula for a polynomial sequence?
Consider a polynomial sequence $\{p_n\}$ generated by some (simple) rule:
$$
\begin{array}{l}
p_1(x)=x \\
p_2(x)=2 x-x^2 \\
p_3(x)= x^3-3 x^2+3 x \\
p_4(x)=-x^4+4 x^3-6 x^2+4 x \\
p_5(x)= x^5-5 ...
11
votes
3answers
650 views
Why doesn't Mathematica simplify a square root of an expression that equals a square of a positive real?
When I try and simplify this expression:
...
3
votes
1answer
224 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 ...
1
vote
0answers
170 views
Can mathematica simplify an expression setting simplified answer equal to zero?
Basically I want to reduce something like:
Subscript[P, 4] - Subscript[P, 5] == Subscript[R, 4, 5]* Subscript[i, 4, 5]
when only one of them is known (...
3
votes
0answers
110 views
Why doesn't Log[Gamma[]] simplify to LogGamma[] where it could?
I have been playing with various equations involving amount of permutations in relatively large sets. Easiest way to look at these is something like Log[10, bignumber!] . Often expressions, even ...
2
votes
1answer
512 views
Replacing term by variable with Mathematica [duplicate]
Possible Duplicate:
Replacing composite variables by a single variable
In order to simplify an given expression with several variables, I want to replace a subterm by a new variable. I ...
3
votes
1answer
256 views
Don't simplify an expression
I have an expression that I want Mathematica to fully expand without any simplification afterwards. I want the output to look like the following example.
...
4
votes
1answer
444 views
Reduce an equation by putting a new variable
I have the following equation given:
$$ (26-x)\cdot\sqrt{5x-1} -(13x+14)\cdot\sqrt{5-2x} + 12\sqrt{(5x-1)\cdot(5-2x) }= 18x+32. $$
In order to solve it, I want to substitute $t = \sqrt{5x - ...
10
votes
1answer
279 views
Is my expression too complicated for FullSimplify or am I doing something wrong?
I have a messily defined function $v(h, w)$ with $h, w \in \mathbb{R}$ and with a removable singularity at $h=1/2$, and I am trying to prove some of its properties using Mathematica. In particular I ...
12
votes
1answer
135 views
Unable to evaluate reasonable max expression
Consider the following statement:
Max[0, Sqrt[1 - Cos[4 \[Theta]]]]
You'll find that Mathematica won't evaluate this, because it doesn't know the range of ...
1
vote
2answers
207 views
Replacing variable in an equation with an Interpolating function polynomial and plotting residual
I was trying to plot the residual for the solution of my PDE. However, I was unsure about a couple of things.
I imported the data and created an Interpolation polynomial with ...
17
votes
3answers
396 views
How can I completely ban usage of some functions in output and mandate use of others?
For example, I hate that Mathematica uses Pochhammer symbol in outputs and prefer all the expressions in Gamma function. How can ...
4
votes
3answers
230 views
How to simplify the following trigonometry expression such that the number of used characters is minimal?
How to simplify the following trigonometry expression such that the number of used characters is minimal?
(13*Cos[t] - 5*Cos[2*t] - 2*Cos[3*t] - Cos[4*t])/4
The ...
