Questions on manipulating complicated expressions and making them look simpler using Simplify, FullSimplify and Reduce.
21
votes
2answers
264 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 ...
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 ...
28
votes
2answers
907 views
What is the difference between a few simplification techniques?
I am trying to understand the difference between Refine, Simplify and FullSimplify, and when ...
17
votes
3answers
371 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])
...
6
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 ...
9
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 :
...
11
votes
2answers
371 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:
...
15
votes
2answers
445 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:
...
7
votes
2answers
383 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:
$$\int{\left(f(x) + ...
4
votes
2answers
167 views
Simplify expressions with Log
How can I get Mathematica to simplify the following expression
n Log[a] + m Log[b] - m Log[a + b] - n Log[a + b]
into
...
4
votes
1answer
365 views
Does the Im function work with symbolic arguments?
Does the Im function work with symbolic arguments?
...
2
votes
1answer
97 views
Using Hold correctly with Simplify and ComplexityFunction
It seems like Mathematica immediately evaluates the expression Sqrt@I to (-1)^(1/4). I'm trying to use ...
20
votes
1answer
190 views
How can I see which transformations Simplify attempts?
The documentation for Simplify[expr] says that it performs a sequence of algebraic and other transformations on expr, and returns the simplest form it finds. How can I see which transformations it ...
4
votes
1answer
440 views
Reduce an equation by putting a new variable
I have the following equation given:
$$ (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 - ...
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 ...
6
votes
2answers
297 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
4answers
224 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 ...
5
votes
2answers
248 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
145 views
How to expand a general expression in cross and dot product in Mathematica
I am looking for a way to simply the general expression in cross product and dot product with general vectors. I got a help in How do I simplify a vector expression? but soon I find that it doesn't ...
10
votes
3answers
339 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}
...
7
votes
2answers
362 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 ...
6
votes
1answer
294 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
113 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 ...
5
votes
2answers
251 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:
...
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 ...
3
votes
2answers
166 views
3
votes
2answers
215 views
0
votes
2answers
50 views
Conjugate and simplify
I want to get a cosine from taking the real part of a complex exponential: $cos(x) = Re(exp(i x))$. What I do in Mathematica is
...
0
votes
2answers
147 views
Simplifying a trigonometric equation to obtain specific terms
When I try to solve the non-homogeneous differential equation
...
-2
votes
2answers
204 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
...
