Questions on manipulating complicated expressions and making them look simpler using Simplify, FullSimplify and Reduce.
32
votes
2answers
978 views
What is the difference between a few simplification techniques?
I am trying to understand the difference between Refine, Simplify and FullSimplify, and when ...
31
votes
2answers
566 views
Is it possible to make Mathematica reformulate an expression in a more numerically stable way?
I'm writing a numerical optimization, and I'm having a problem with an expression of the form
$$ e^{-t} (1+\mathrm{erf}(t)) $$
The overall shape of the function looks correct, but when $t$ is small, ...
24
votes
2answers
296 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 ...
20
votes
4answers
564 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 ...
20
votes
1answer
196 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 ...
17
votes
3answers
386 views
Can I simplify an expression into form which uses my own definitions?
This seems like a simple thing to do, but I couldn't find anything relevant from Mathematica documentation.
So suppose I have an expression:
a*b/(a + a*Cos[a/b])
...
17
votes
3answers
403 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 ...
16
votes
2answers
461 views
Why doesn't FullSimplify drop the Re function from an expression known to be real?
For some reason Mathematica does not properly simplify this expression:
...
15
votes
3answers
242 views
Common subexpression from two expressions
I am working with some unpleasantly tedious polynomials, which need to be manipulated in various ways (integrate with respect to some variable, differentiate with respect to another). Since these ...
13
votes
1answer
106 views
How to instruct FullSimplify to assume that PossibleZeroQ returns correct result?
Sometimes I have a really huge expression that cannot be significantly simplified by FullSimplify. I would like to, so to speak, "simplify with faith" using ...
12
votes
1answer
137 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 ...
11
votes
2answers
383 views
Surprises simplifying simple polynomials
I came across some somewhat surprising behavior of Simplify today, on something very simple. Let's take two cubic polynomials that we know have the same value:
...
11
votes
4answers
167 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 ...
11
votes
3answers
684 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:
...
11
votes
2answers
213 views
Simplify assumes Boolean 1 and 0 in logical expressions
Per this chat discussion and this previous question where I encountered the strange behaviour:
...
11
votes
0answers
667 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 ...
10
votes
2answers
1k views
How to specify assumptions before evaluation?
If I request mathematica evaluate an integral for me, I'll often get a more general ConditionalExpression than I want. Example :
...
10
votes
3answers
354 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}
...
10
votes
1answer
289 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 ...
10
votes
3answers
1k views
Strategies for simplifying complicated expressions
I have a very complicated expression involving trigonometric functions, complex numbers etc. You may find it here as it is too long to be pasted here. You may also find a screenshot of it here.
...
10
votes
1answer
345 views
How to get FullSimplify to fully simplify my expression with custom complexity function?
To simplify based on the visual complexity of an expression (i.e. the complexity of the function as displayed in the notebook instead of the internal form, which in some cases may be substantially ...
9
votes
1answer
300 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 ...
8
votes
2answers
270 views
Shaping/simplifying equations in a certain way
A problem I am occasionally facing is to simplify an equation not to it's shortest form but to a form that is simple by other means. Often, this is grouping the term according to certain functions, ...
7
votes
4answers
911 views
Checking if two trigonometric expressions are equal
Say I have two trigonometric expressions which are a bit complicated. Is there a quick way to check if they reduce to the same thing (that they are equal) using Mathematica?
I was solving this: $y'' ...
7
votes
2answers
387 views
Why aren't these additions of integrals and summations equal?
I have the following code:
Simplify[Integrate[f[x] + g[x], x] == Integrate[f[x], x] + Integrate[g[x], x]]
To test:
$$\int{\left(f(x) + ...
7
votes
2answers
107 views
How to simplify an expression with special functions to zero
The following is a well-known Bessel function identity:
$$J_{-n}(z)=(-1)^n J_n(z),\qquad n\in\mathbb Z$$
To check this, I used the following code and the result is as what I expected.
...
7
votes
2answers
370 views
Simplifying the derivative of $|x|$
Context
In[855]:= D[Abs[x], x] /. x -> 1
Out[855]= Derivative[1][Abs][1]
In[856]:= D[x, x] /. x -> 1
Out[856]= 1
Question
Why is ...
7
votes
2answers
272 views
How to deduce a generator formula for a polynomial sequence?
Consider a polynomial sequence $\{p_n\}$ generated by some (simple) rule:
$$
\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 ...
7
votes
4answers
2k views
Factoring polynomials to factors involving complex coefficients
I've run into some problems using Factor on polynomials with complex coefficient factors. Reading the documentation it looks like it only factors over the ...
7
votes
2answers
79 views
How do I invoke the default complexity function?
Documentation on ComplexityFunction says:
With the default setting ComplexityFunction->Automatic, forms are
ranked ...
7
votes
3answers
234 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 ...
7
votes
1answer
339 views
Simplify an expression containing NonCommutativeMultiply
How does mathematica evaluate the following expression to zero:
...
7
votes
1answer
189 views
RootSum result manipulation/simplification
Consider the sum
sum1 = Sum[ k/( k^7 - 2 k + 3), {k, Infinity}]
...
7
votes
1answer
176 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:
...
7
votes
1answer
471 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 ...
7
votes
1answer
113 views
Why does simplification in Mathematica depend on variable names
Mathematica fails to put the following into an obvious simplest form:
...
6
votes
3answers
298 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:
...
6
votes
3answers
132 views
Counting multiplications (complexity function)
I'm trying to count the number of times multiplication appears in an expression (for the purpose of constructing a ComplexityFunction that would help me simplify a terrible algebraic expression for ...
6
votes
2answers
165 views
6
votes
2answers
366 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 ...
6
votes
2answers
149 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
4answers
234 views
Attaching persistent assumptions to symbol definition
Is it possible to attach assumptions to a symbol? This relates to this question. Most of my work involves physical equations, i.e. there are basic assumptions on variables that will always hold true ...
6
votes
1answer
306 views
How to Simplify equations over a Ring with Mathematica?
For example, when we work over a ring, the equation x^3=0 does not imply x^2=0 or x=0, but ...
6
votes
1answer
115 views
How to reduce expressions with complex coefficients in the form of a+0.*I
I'm trying to get an eigenvalue equation in Mathematica, and the result is an expression with coefficients of the form a + 0. I. For example,
Is there any clever ...
6
votes
1answer
93 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
...
6
votes
1answer
502 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
93 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 ...
6
votes
0answers
149 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 ...
5
votes
2answers
181 views
Inequality with assumptions not simplifying
Can someone explain to me why the following does not simplify to True (as all constituents are positive)?
...
5
votes
2answers
224 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
...
