Tagged Questions

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

1answer
283 views

How to find the most compact form of an equation

I would like to know whether there is any general approach to obtain the most compact form of an equation with Mathematica. I used to believe that the ...
2answers
141 views

Simplification with assumptions

I'm trying to make Mathematica do some simplifications for me. I have the expression ((1 + s[1]) (-1 + s[2]) )/(-1 + s[1] s[2]) and want to simplify this with ...
1answer
111 views

Simplifying using assumptions

Is there a way to simplify the following equation (-p(a-x)((a-b)P(b-x)+Q(b+x)(a-b+2x))+q(a+x)(-(a-b)Q(b+x)+P(b-x)(-a +b+2x)))/((b-x)(-a + x)(a+x)(b+x)) assuming ...
1answer
177 views

Why isn't Simplify completely simplifying my expression when it has all the necessary info?

I have a complex variable, and I'm trying to multiply it by its Conjugate[], which should give me a real number. So, I'm currently doing: ...
1answer
214 views

Reduce Cannot Solve Complicated Function

As per the answer to this question: SolveAlways rejects inequality, I tried the following commands: ...
1answer
107 views

How to convert the expression '{a->a0, b->b0}' to the expression 'a=a0; b=b0'? [duplicate]

How to convert the expression '{a->a0, b->b0}' to the expression 'a=a0; b=b0'? I think this is a common question and do not know if someone has asked it before. Any help or suggestion will be ...
1answer
188 views

Decomposing a complex numbers equation into its real and imaginary part

I have an equation such as: a*z^2 + b*(z - c)^2 == d where z is a complex variable and ...
2answers
586 views

Memory leak issues

I am working with noncommuting objects and basically I am using Mathematica to sort large expressions by normal ordering and simplifying them. To this end, I first create an object called ...
2answers
392 views

How can I simplify $\log(512)$ to $9\log(2)$?

Can you explain me about the result of Integrate. ...
0answers
83 views

How to simplify expressions

I read several similar posts but I have not found a solution yet. However, I think that my problem should be quite easy. So here we are. Relations ...
0answers
136 views

Gradient from Vectors type

I'm working with Vectors type in Mathematica 9. For this purpose I use the following command: ...
0answers
202 views

Alternate method of conjugation using replaceall

Mathematica really struggles to simplify complex conjugates of complicated expressions - even given assumptions for every symbol in the expression being real. Often times I've found that I can ...
0answers
256 views

Solving for equilibrium distribution (symbolic) by matrix multiplication

I have a huge transition matrix (81x81). The matrix is too huge to paste here, so I store it in this notebook. (There are constraints on the symbols: $0<p_b<1$ and $0<p_g<1$. If further ...
1answer
303 views

How to simplify to form without imaginary unit

I have an integral that I compute with Mathematica and as a result I get a seemingly complex expression (i.e. the expression contains the imaginary unit, $i$, at some places). However, if I try to ...
1answer
938 views

What is the proper way to verify that two expressions are equivalent?

First of all, it appears to me that $$\left|\frac{1}{x} + x^2\right| \Leftrightarrow \frac{|1 + x^3|}{|x|}$$ is true. I don't know why, but my attempt to verify it in Mathematica failed. ...
2answers
286 views

Cleaning up InverseLaplaceTransforms in Mathematica

I am attempting to use Mathematica to model an electrical circuit in the s domain. The circuit contains capacitances and and inductances. I've written a series of equations using Kirchoff's laws to ...
0answers
279 views

Simplify and Sqrt, inconsistent behavior?

I have encountered some problems when using Simplify with expressions containing a square root and isolated a following test case ...
3answers
117 views

Applying Reduce[] to a table [duplicate]

I have a table for example: t = Table[k,{k,5}] which returns {1,2,3,4,5} and for every element in this table I want to check when it is $\leq 1 + a$. I ...
2answers
334 views

Pulling out common terms when simplifying complicated equations

I have a complicated expression where common terms are apparent but Simplify[] and FullSimplify[] don't appear able, even with plenty of assumptions added, to reduce down to a simpler form with common ...
1answer
301 views

Simplify doesn't simplify HypergeometricPFQ with exact arguments

Consider a series: $$\sum_{t=0}^\infty \frac{8^{-11-2t}(22+4t)!}{t!(11+t)!(11+2t)!(32+t)}$$ ...
2answers
133 views

Can one use Map during Expand?

Can one Map a simplifying function to the summands of an Expand before fully expanding the expression in question first? ...
2answers
158 views

Partial result of aborted evaluation of FullSimplify

When FullSimplify invoked on a large expression, it can run for hours. If I do not have time to wait, and abort the evaluation, I get no result, although, ...
1answer
108 views

Check that a relational expression is true for all complex numbers

How can I use Mathematica to check if a statement like $$\left| \frac{\sqrt{1+2z}-2}{2z-3} \right| \le 1$$ is true for all complex numbers $z$? Also, how can I use Mathematica to check such a ...
4answers
383 views

How to make Mathematica simplify $\cos[(i + j + k)\pi]$ to $(-1)^{i+j+k}$?

We know that: $$\cos\left[(i+j+k)\pi\right] = (-1)^{i+j+k}$$ for $i, j, k$ being positive integers. In Mathematica I've tried: ...
1answer
321 views

Why doesn't FullSimplify work properly on this?

I wish to simplify the simple expression fac[n_] := Sum[R^i, {i, 0, n}]; as much as possible for various $n$. FullSimplify or ...
1answer
169 views

Is there a version of Together that doesn't cancel common factors?

I'm running code that produces a long combination of rational functions with free constants that need to be tuned such that the combination vanishes. My current method is to put the combination over ...
1answer
267 views

Why FullSimplify doesn't work here?

Since the emphasis of this question is on finding a workaround, I decided to post this question with an emphasis on the explanation of the behavior of Mathematica. The Bessel function satisfies the ...
1answer
76 views

How to bail out from a non-applicable transformation function?

I provide a custom function in TransformationFunctions options of FullSimplify that can do a transformation only for some values ...
1answer
283 views

Using FunctionExpand to evaluate symbolic derivatives

Some symbolic derivatives of certain special functions are not expanded automatically, but FunctionExpand often helps to get a derivative-free closed form ...
1answer
736 views

how to simplify large expression with lots of special functions in it (BesselY, Hypergeometric, MeijerG etc…)

I saw this DE in Maple forum. When solving it using Mathematica 9.01, even though the result was correct (both solutions gave the same numerical answer for some random values), Mathematica's answer ...
2answers
290 views

How to simplify an expression with square roots?

The expression $\sqrt{L^2 M+\sqrt{L^2 (-J^2 + L^2 M^2)}}/\sqrt{2}$，can be simplified into $\sqrt{L}(\sqrt{LM + J}+\sqrt{LM - J})/2$, but how can I obtain this result with Mathematica? That is, how ...
2answers
256 views

Calculate information entropy integral in infinite square well problem

In the context of information theory, entropy is a measure of uncertainty of a random variable. In quantum mechanics, the uncertainty principle states that $\Delta x\Delta k \ge 1/2$. The same can be ...
2answers
154 views

FullSimplify used with Assuming giving unexpected results

Can someone shed some light on why Assuming[{x ∈ Reals}, x (Sign[x]^2 - 1)] // FullSimplify returns x (-1 + Sign[x]^2) ...
2answers
113 views

Assumptions within Simplify

I am using the ratio between two error probabilities in various functions. I want Mathematica to display this ratio in the most simple manner. How do I let Mathematica know that, in this case, the ...
2answers
222 views

Simplifying If statements

How can I get Mathematica to simplify the true and false clauses for If[] statements? For example: bar[a_] := a FullSimplify[If[a > b, bar[a], bar[b]]] ...
0answers
79 views

Introducing new variables implicitly [duplicate]

I have a calculation expr111 = cs[giso, xiso, 1, 1, 1] that gives the result -((k x)/(2 (1 + 1/4 k (x^2 + y^2 + z^2)))) ...
0answers
32 views

Find repeated groups in a long algebraic expression [duplicate]

I have an algebraic output (a solution to a de) similar to, but far longer than: {y->(x+3)^2/sin(7*(x+3))+(x+3)^3/7} I'd like to get Mathematica to notice that the group x+3 appears repeatedly, ...
3answers
253 views

Why does Mathematica not seem to know that $i^x$ cannot be equal to $0$?

I am experiencing a curious behaviour of Simplify when handling expressions involving powers of $\mathbf{i}$, such as $\mathbf{i}^x$ where $x$ is unknown. For ...
1answer
279 views

1answer
273 views

Simplify expression after substitution

I tried to substitue variable x of one equation with another variable z (z=nx/(nx+m)). See as follow: ...
1answer
187 views

FullSimplify yielding different results in mathematica 8 and 9

I have been experiencing some problems running a certain mathematica file in version 9. I've tracked the problem to a particular sum that I perform. Running the same code in version 8 and 9 I get two ...
2answers
179 views

HornerForm of polynomials in terms of E^(i x)

I want to know how to get the HornerForm of the following expression in terms of E^(I x): ...
1answer
238 views

Why does Mathematica find a form for this general sum, but not for some special cases?

Today I found a Sum which Mathematica will simplify for a general parameter value $\nu$, but which will not simplify fully for special cases $\nu = 1, 3, ...$ despite the fact that the general answer ...