Questions on manipulating complicated expressions and making them look simpler using Simplify, FullSimplify and Reduce.

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26
votes
1answer
2k 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 ...
4
votes
1answer
43 views

TensorReduce not simplifying transpose for symmetric matrix?

I know Mathematica is not very good with symbolic manipulation of matrix expressions, but I was surprised to find that it can't reduce the following expression: ...
2
votes
1answer
58 views

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. ...
8
votes
1answer
237 views

How to simplify -a*z+a*z to 0 where “a” is an expression

Consider the following: a = 1+(x+y+z+u)^10000 (* Out[57]= 1+(u+x+y+z)^10000 *) e = -a*z+a*z (* Out[59]= z (-1-(u+x+y+z)^10000)+z (1+(u+x+y+z)^10000) *) How can ...
18
votes
1answer
460 views

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 ...
0
votes
3answers
80 views

How can I write a do loop as a table?

I have a do loop that looks like this: Do[a = -1; b = 1; c = n; d = a + b + c; Print[d], {n, 1, 12}] which gives the output: 1 2 3 4 5 ...
4
votes
2answers
356 views

Force a negative square root to be interpreted as an I

I have expressions like $$\sqrt{-\sqrt{1+x^2}} $$ how can I force mathematica to systematically rewrite this as $$i(1+x^2)^{1/4} \quad ? $$
1
vote
2answers
46 views

Simplify power of KroneckerDelta

Why doesn't Mathematica simplify the following expression: FullSimplify[KroneckerDelta[x,y]^3] Since KroneckerDelta only ...
1
vote
2answers
138 views

Show Simplified Directives [closed]

Is there a way to force Mathematica to convert an already rendered Graphic to the simplified Directive form of that Graphic. Background: I am currently editing Graphics using Drawing Tools and then ...
0
votes
0answers
51 views

Computation doesn't Finish

I'm trying to solve some problem by the following code: ...
3
votes
2answers
117 views

Replace expression, but only “outside” of a function [duplicate]

I have a horrid expression, which is basically a sum of exponents with coefficients. Here's a taste: What I want to do is to replace ks with another expression, ...
2
votes
2answers
79 views

Let mathematica combine integral limits

Is there a way to teach mathematica to combine integral limits according to $\int_a^b f dx+\int_b^c f dx=\int_a^cf dx$ to simplify expressions like $\int_0^1 f[t] dt+\int_1^x (1+f[t]) dt$ to $\int_0^t ...
8
votes
0answers
95 views

Why is this evaluation halved when adding units?

Why does this strange behavior occur when dealing with units and quantities? ...
1
vote
2answers
64 views

Simplifying an expression given a known variable relation

I am wondering if there is a way to simplify an algebraic expression given a known variable equation using Mathematica. For instance, I wish to simplify an expression for the heat change in a process: ...
3
votes
1answer
65 views

Merge Roots of Polynomial

How can I make mathematica "merge" solutions of a polynomial by using $\pm$ instead of listing the two solutions fully with only one sign difference? In particular, I am looking to "compactify" the ...
0
votes
0answers
60 views

Symbolic Tensor Algebra

I need to perform basic tensor algebra in order to double check some very complicated simplification. It's nothing fancy, it just has so many factors by the end that it's hard to tell if an error has ...
1
vote
1answer
120 views

Simplify results further

I have an extremely long result in polynomial form following some matrix operations. However, given the symmetry of the problem, I can safely say that the solution will reduce much further than is ...
3
votes
4answers
145 views

Simplify binary expressions

Is it possible for Mathematica to do simplifications for expressions where the variables are binary, such as: a + b = 1 + 2*c => a + b = 1 Here c must be 0 because if it is 1, the RHS is 3 but ...
5
votes
2answers
141 views

How to simplify Boolean expression

I would like to simplify $$((p\oplus q)=True)\wedge(p=True)$$ to $$q=False$$ I was hoping BooleanMinimize[((p ⊻ q) == 1) ∧ (p == True)] would do the trick, but ...
2
votes
0answers
37 views

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 ...
3
votes
0answers
96 views

Why does Mathematica show 4095/4096 terms in TrigExpand?

Clear[x, n]; expr = Cos[x]^(n - 2) (1 - Cos[x]^2 + Sin[x]); r=TrigExpand[expr] Where do those 4095/4096 comes from? It is correct, but it seems very strange ...
4
votes
2answers
124 views

How to simplify only the lowest level of a nested expression

I have a large expression that takes forever to simplify if I apply FullSimplify[...]. The expression has lots and lots of brackets that luckily already groups ...
0
votes
0answers
65 views
5
votes
1answer
183 views
3
votes
1answer
89 views

How to enforce mathematica to analytically evaluate roots?

I am interested in simplifying expressions involving HeavisideTheta. A simple example could be: HeavisideTheta[1 + x - x^2 + x^3] The best I can achieve is with ...
6
votes
1answer
126 views

How to prevent simplification?

I have a question about the concept of simplification. I want to explain it with an example. When I write $4/8$ in mathematica, output is 1/2. How can i return ...
1
vote
1answer
29 views

hold specific pattern in symbolic calculation

I encounter some questions when I try to simplify a symbolic expression using Mathematica. For example, I got an intermediate expression ...
2
votes
1answer
49 views

Prevent Simplify from using cot

I have the following problem. I got a huge equation to simplify and in there are numerous $\cos(x)$ and $\sin(x)$ terms and now it happens that Simplify changes terms like $(...+\cos(x)*a+...)$ to ...
3
votes
1answer
115 views

Write Integer powers as products

I need to wirte all occasions of (a+b)^3,Ftp^2, Sin[th]^2, ...etc as (a+b)*(a+b)*(a+b), Ftp*Ftp, Sin[th]*Sin[th], ...etc ...
0
votes
0answers
33 views

Using assumptions when calling Simplify from Collect

I am quite new to Mathematica, so please be patient ;) I have a very long equation that I have to sort for powers of a variable called e and that I want to ...
6
votes
4answers
132 views

Minimizing a function with a constant $l > 0$

I'm VERY new to Mathematica and would like some help with minimizing a function. $$f(x) = \frac{1}{2} \sqrt{\frac{\left(l^4+x^4\right)^2}{l^4 x^2}}$$ I want to find which $x-value$ (probably ...
2
votes
1answer
72 views

FullSimplify wont simplify to expression with lower SimplifyCount

I have been trying without success to get FullSimplify to work on some trigonometric expressions. It refuses to convert them to forms that are clearly much ...
3
votes
2answers
200 views

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 ...
4
votes
3answers
370 views

How to transform power of -1 into exponential [duplicate]

After FullSimplify, Mathematica usally gives some coefficients like ((-1)^(1/5)) But I don't want this form, I want ...
1
vote
1answer
46 views

simplification issues

The first are from an old paper, dealing with the evaluation of elastic Green function in a transversely isotropic medium (Hill 1964). ...
1
vote
0answers
57 views

Apart for complex roots?

Let p[x] be a polynomial in x and consider the partial fraction decomposition of 1/p[x]. ...
6
votes
1answer
132 views
6
votes
2answers
255 views

A short notation to fix the assumption that all involved parameters are, say, positive

Often I make simplifications or other operations with assumptions. Sometimes the assumptions simply state that all parameters involved are positive. I wonder, if there is a short notation for such a ...
1
vote
0answers
40 views

Building a ComplexityFunction based on the size of the expression output

I am experimenting with the ComplexityFunction of Simplify and came up with this one: ComplexityFunction->Function[e,Rasterize[HoldForm[e],"BoundingBox"][[1]]] ...
3
votes
1answer
143 views
12
votes
0answers
125 views

Why does this happen with FullSimplify? [duplicate]

It is stated at the Wolfram Documentation Center (FullSimplify/Possible Issues) that: Why and when this could happen? How to avoid it? Any patterns? Edit: As pointed out in the comments, this ...
2
votes
2answers
120 views

A simple expression that Mathematica can't simplify

I'm using Mathematica 9. I encountered an expression that Mathematica couldn't simplify to a simpler form: ...
1
vote
2answers
46 views

Simplifying an exponential expression [duplicate]

I have an expression: (1/a^13)^(1/13) I want Mathematica to simplify it to '1/a'. How do I do it? 'Simplify' and 'FullSimplify' don't work.
2
votes
1answer
67 views

How to show that an expression is 0 if FullSimplify never finishes

I have a huge expression. And I have "checked" numerically that it is 0 for real value variables. However, due to the size and structure of the expression FullSimplify seems to be having a hard time. ...
0
votes
1answer
65 views

Simplifying symbolic expressions involving dot products

I have a function that outputs a large expression containing dot products of vectors. None of the vector components are known, so all dot products are symbolic. For instance, part of the output may ...
4
votes
2answers
100 views

Remove redundant parameters from equation

I have random expressions like (b1 x + b2 x)/(b3 + b4/b5 x) + Sin[b6 x] where $x$ is a variable and {b1, ..., b6} are parameters to be fitted. This expression is ...
1
vote
0answers
76 views

Summing the probability distribution to 1 to convince myself

I have worked out a probability distribution and want to check its sum which is necessarily 1. First we write $$ r \triangleq \frac{(2 \lambda + \mu)^2}{2(\mu + \lambda)^2}, \quad s \triangleq ...