Questions on manipulating complicated expressions and making them look simpler using Simplify, FullSimplify and Reduce.
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 :
...
-1
votes
1answer
268 views
simplifying equations [closed]
I have a question that seems easy but I can't solve it.
I have an equation like:
eqgama = -8.33208*10^56 g1 + 8.18264*10^56 g1^2 == -1.42093*10^56
I use the ...
3
votes
1answer
253 views
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:
$$e^{-i ...
7
votes
2answers
382 views
Why aren't these additions of integrals and summations equal?
I have the following code:
Simplify[Integrate[f[x] + g[x], x] == Integrate[f[x], x] + Integrate[g[x], x]]
To test:
$$\int{\left(f(x) + ...
3
votes
2answers
215 views
1
vote
1answer
139 views
Inequality of reciprocal functions
Simplify[1/(1/a + 1/b)]
{ (a b)/(a + b) }
That doesn't look right. The given function has an infinite term for a = 0 and one ...
5
votes
2answers
169 views
Inequality with assumptions not simplifying
Can someone explain to me why the following does not simplify to True (as all constituents are positive)?
...
4
votes
2answers
242 views
How can I get Mathematica to simplify $\Vert\{1,\sin(t),\cos(t)\}\Vert_2$ to $\sqrt{2}$?
Context
Norm[{1, Sin[t], Cos[t]}]
Norm[{1, Sin[t], Cos[t]}] // Simplify
(*
Sqrt[1 + Abs[Cos[t]]^2 + Abs[Sin[t]]^2]
Sqrt[1 + Abs[Cos[t]]^2 + Abs[Sin[t]]^2]
*)
...
10
votes
1answer
332 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 ...
6
votes
4answers
858 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'' ...
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
112 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 ...
28
votes
2answers
904 views
What is the difference between a few simplification techniques?
I am trying to understand the difference between Refine, Simplify and FullSimplify, and when ...
4
votes
1answer
162 views
Checking if an Expression Falls within a Range
Is there a simple way in Mathematica to check under what conditions an expression (involving multiple variables) falls within a given range? For example, say I had a real-valued function f(x,y,z), ...
2
votes
2answers
279 views
How do I make Mathematica understand roots of unity?
Try the following:
z = Exp[2 \[Pi] I / 5]
Z = { { z, 1 }, { 0, 1/z } }
Simplify[MatrixPower[Z, 5]] //MatrixForm
Of course, this should return a 2 x 2 identity ...
4
votes
2answers
149 views
How to expand all portions of an expression?
Consider a toy expression:
expr = Sin[x (a + b)]/(y (z + c))
I would like to expand all parentheses to get something like:
...
31
votes
2answers
549 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, ...
8
votes
2answers
261 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, ...
6
votes
1answer
319 views
Simplify an expression containing NonCommutativeMultiply
How does mathematica evaluate the following expression to zero:
...
5
votes
1answer
212 views
Validating simplifications analytically
I have a rather complex expression which I would like to simplify and check my work along the way (Mathematica does not simplify very basic things and it is frustrating me). In the following example, ...
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 ...
11
votes
2answers
370 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
444 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:
...
17
votes
3answers
370 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])
...
9
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.
...
