Questions tagged [simplifying-expressions]
Questions on manipulating complicated expressions and making them look simpler using Simplify, FullSimplify and Reduce.
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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])
...
49
votes
2
answers
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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 ...
32
votes
3
answers
3k
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 ...
20
votes
4
answers
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Complex number operations: telling Mathematica variables are real
I want to do Conjugate[a + b*I], but when I do that, the solution is
Conjugate[a] - I*Conjugate[b]; when for me, a and b are ...
87
votes
6
answers
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Advice for Mathematica as Mathematician's Aid
I use Mathematica mainly as an aid in symbolic attacks on problems, usually intermediate or harder and often number theoretic. While Reduce, ...
16
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2
answers
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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
2
answers
2k
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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 ...
22
votes
4
answers
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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 ...
18
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2
answers
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Behavior of Reduce with variables as domain
When using Reduce, I accidentally put a set of variables as the domain. To my surprise, it not only seems that Reduce expects ...
17
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1
answer
1k
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How to prevent reduction of a fraction into lowest terms?
I have a question about the concept of simplification. I want to explain it with an example.
When I write the fraction $4/8$ in Mathematica, the output is
1/2.
How ...
10
votes
4
answers
721
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How do I invoke the default complexity function?
Documentation on ComplexityFunction says:
With the default setting ComplexityFunction->Automatic, forms are
ranked ...
29
votes
1
answer
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A one line proof that one is zero using Mathematica 10
a = (Sqrt[2] + 1) (Sqrt[2] - 1) - 1;
{a/a, Simplify[a]/a, b/b == Simplify[b]/b}
{1, 0, True}
This one line "proof" that ...
15
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3
answers
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Combining cosine or sine terms into a single cosine or sine
A function that is the sum of two cosine terms of the same frequency
x[t_] := a1 Cos[w0 t + b1] + a2 Cos[w0 t + b2];
can be simplified to a single ...
12
votes
4
answers
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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 ...
63
votes
2
answers
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What is the difference between a few simplification techniques?
I am trying to understand the difference between Refine, Simplify and FullSimplify, and when ...
31
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4
answers
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FullSimplify wrongly reduces expression to zero
Bug introduced in 9.0 and persisting through 12.2
I get the following output with a fresh Mathematica (ver 10.0.2.0 on Mac) session
...
19
votes
3
answers
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Why does Mathematica simplify $x/x\to1$?
If I enter x/x, I get 1. Such behavior leads to this:
Simplify[D[Sqrt[x^2], x, x]]
0
...
11
votes
2
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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) + g(x)\right)dx}=\int{f(x)...
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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 ...
12
votes
1
answer
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Apart for complex roots?
Let p[x] be a polynomial in x and consider the partial fraction decomposition of 1/p[x].
...
33
votes
1
answer
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A better simplification function
I am creating this question and posting an answer to it as a help for those who have problems with Mathematica simplification oddities that appear in other questions on the site.
First of all, there ...
26
votes
3
answers
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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}
...
15
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2
answers
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Remove annoying Conjugate
Here is an expression
...
13
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3
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Why does Simplify[b-a] give -a+b and not b-a?
Simplify[b - a] results in -a + b. I prefer b - a, which is a bit simpler (3 symbols instead ...
5
votes
1
answer
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Simplifying conditional expressions using assumptions does not work
I have a conditional expression
f[x_] := x /; x ∈ Reals
This works fine for normal numbers and symbols, e.g. ...
4
votes
1
answer
685
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Simplify equations with pattern assumptions
When simplifying an expression using Simplify[expr, assumptions], the assumptions has to be explicit. Is it possible to simplify an expression with pattern ...
20
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3
answers
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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 ...
8
votes
1
answer
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Trace of FullSimplify
I have a symbolic function and I used FullSimplify command to simplify the equation given below. I am calculating it by hand but I couldn't reach the same solution. ...
7
votes
3
answers
5k
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Removing Abs from Abs[a + Exp[I*c]b]^2
Title says it all. Mathematica produces sometimes expressions of the form
Abs[a + Exp[I*c]b]^2
where all three quantities a, b and c are positive real numbers. ...
6
votes
1
answer
662
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 ...
5
votes
2
answers
796
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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
4
answers
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Fullsimplify does not simplify Abs'[1.-a]
I have to simplyfy an expression involving Abs'
This works:
FullSimplify[Abs'[1 - a], a ∈ Reals]
Sign[1 - a]
but this does ...
4
votes
2
answers
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Replacing gamma at half integers by double factorial
It is well-known that for any positive integer $n$ the equality $\Gamma(n+\frac12)=\sqrt\pi\,(2n-1)!!/2^n$ holds, where $!!$ stands for the double factorial. I am using ...
4
votes
1
answer
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What's the correct method to simplify exponentials?
I have a sum of exponentials that I'd like to simplify. The issue is when I use Simplify, Mathematica loves to factor out one exponential factor. See below:
$$e^{-i ...
3
votes
2
answers
695
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How can I simplify $\log(512)$ to $9\log(2)$?
Can you explain me about the result of Integrate.
...
30
votes
4
answers
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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
...
26
votes
1
answer
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Transform Root objects into Trigonometric expressions
Consider the Root objects
roots = Table[Root[-1 + 27 #1^2 - 162 #1^4 + 243 #1^6 &, i],{i,1,6}]
These can be expressed in terms trigonometric functions as ...
21
votes
2
answers
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Expressing a polynomial as a sum of squares
I encountered a degree 4 polynomial in 8 variables f(a1,a2,a3,a4,b1,b2,b3,b4) that I suspect can be written as a sum of squares. While sostools in MATLAB would find ...
17
votes
3
answers
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Extract common factor from vector or matrix
I can't believe this hasn't been asked before but I can't find anything.
Is there a way to convince Simplify or FullSimplify to ...
11
votes
4
answers
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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
1
answer
712
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How to decompose a complex expression containing repeated subexpressions? [duplicate]
Suppose I have an expression like
...
7
votes
1
answer
460
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Arrange equation in normal form
Is there a way, or if not, how could one define a function which takes an equation in any form (for example as given by FullSimplify):
$$(A+X_0) x+By=3x$$
and ...
7
votes
2
answers
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Why doesn't FullSimplify simplify expressions with DiracDelta?
I want to simplify a complicated expression with some Dirac delta distributions, but FullSimplify does not do what I want. Specifically, I want
...
6
votes
1
answer
262
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Simplify oversimplifies. What to do about it?
According to Mathematica 10: $$\mbox{Simplify}\left[\frac{\frac{1}{t^2}-1}{(t+\frac{1}{t})^2}\right]==\frac{1-t^2}{(1+t^2)^2}$$
However, the first equation does not tolerate $t=0$ because of a ...
4
votes
1
answer
548
views
Simplify not evaluating completely with Square roots
Here's a simple question. It's no longer high priority that I know this, but it's something that can come in handy later on.
...
3
votes
1
answer
424
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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
<...
3
votes
1
answer
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Simplifying expressions with head Max
(I saw: Unable to evaluate reasonable max expression but this seems an even easier case an I thought it worth posting)
See the following simplifications of Max operators, which are all very ...
2
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2
answers
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Simplifying expressions with square roots
I would like Mathematica to simplify this expression:
$4 \left(16 \sqrt{\left(-1+2 c^2\right)^2}-32 c^2 \sqrt{\left(-1+2 c^2\right)^2}+\sqrt{\left(1-8 c^2+8 c^4\right)^2}\right)^2$
...
21
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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:
...
18
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1
answer
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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 ...