Questions tagged [simplifying-expressions]

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

227 questions with no upvoted or accepted answers
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13
votes
0answers
208 views

Bug? Numerical calculation error with FullSimplify and arbitrary precision

Bug introduced after 5.2, fixed in 8.0, reintroduced in 9.0 and persisting through 11.2 Is this a bug? If I do FullSimplify[n E^(0``10 n)] then it returns <...
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0answers
361 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 ...
10
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552 views

Faster simplification of linear combinations of some specific functions

After some profiling I've found that my program spends most of its time in the simplification step. The program uses my simplification function many times (over different data). My calculation is not ...
7
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212 views

What is a “generic case”?

Introduction With this question I am coming back to a long-standing issue I have with Mma's concept of a "generically correct" result. The basic idea seems to be, vaguely, that if a result is true in ...
7
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105 views

Need explanation on strange behavior of Simplify under given assumption

This is quite surprising to me. Simplify[a == b, {a == {1}, b == {1}}] a == b does not evaluate the equality, while ...
6
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62 views

Unexpected behaviour of Simplify

I'm evaluating an expression and to me the result should be True but Mathematica is giving me a different result. ...
6
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317 views

How to get mathematica to simplify a result

I have the following output $\text{Li}_2\left(3-2 \sqrt{2}\right)-4 \text{Li}_2\left(-1+\sqrt{2}\right)$. This turns out to be equivalent to $\displaystyle\log^2(1+\sqrt{2})-\frac{\pi^2}{4}$. How ...
5
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0answers
121 views

Integrate under assumptions

I am trying to solve the following integral: $$\int_0^\infty u^{\sigma-1} \exp\left[-c u^\sigma\right] \mathrm{d}u$$ under the assumptions $\sigma \in (0,1)$ and $c>0$. I know the result is $$\...
5
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0answers
3k views

How to simplify an expression, using a known term substitution?

I have a complicated algebraic expression that involves a lot of similar terms. In particular, I have a complicated sub-expression involving sums and products that I would like to denote $\alpha$. I ...
5
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0answers
78 views

FullSimplify to minimum number of terms according to assumptions

I have a large expression that I want to simplify according to some conditions, which FullSimplify doesn't seem to take into account. For example, let's say I have: ...
5
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0answers
88 views

External and internal Assumptions on `PiecewiseExpand` and `Mod`

After this question I'm intrigued about the different behaviors depending where and how the assumptions are given. ...
5
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0answers
225 views

Why doesn't Log[Gamma[]] simplify to LogGamma[] where it could?

I have been playing with various equations involving amount of permutations in relatively large sets. Easiest way to look at these is something like Log[10, bignumber!] . Often expressions, even ...
4
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0answers
42 views

On simplification of polynomials in several variables

Let us consider a polynomial expr = Expand[(x - 2*y + 1)^9 - x*(x + y)^8]; Mathematica does her best, simplifying it by ...
4
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118 views

Another example where using FullSimplify gives different result than Simplify

I believe this question is very similar to Result of Series[expression] is different when I simplify the expression, however, due to my lack of Mathematica experience, I am reluctant to call it a bug. ...
4
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0answers
48 views

A simple expression on which `Reduce` fails

The conditions in x ∉ Integers && y ∈ Integers && y == -(1/2) + x/2 are inconsistent but Reduce does not solve ...
4
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0answers
287 views

Simplify hypergeometric function

Theorem: Let $H_n$ be the $nth$ harmonic number. Then $$\sum_{n=1}^\infty \binom{2n}{n} H_n x^n=\frac{2}{\sqrt{1-4x}}\log\bigg(\frac{1+\sqrt{1-4x}}{2\sqrt{1-4x}} \bigg)$$ How can I simplify ...
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107 views

Order of evaluation of FunctionDomain, Reduce, Solve, etc

For the input (mine is much more complicated, this is a toy example): x/x /. x -> 0 the output of 1 (as opposed to ...
4
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0answers
119 views

Why isn't Mathematica listening to my assumptions?

I'm trying to simplify the expression ωplus := 1/2 c (I f V + Sqrt[4 k^2 - f (f + 8 I k) V^2]) so that I can get it in the form $a+i b$. I am using the global ...
4
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726 views

Is it possible to simplify an expression in vector form, which involves crossproduct and dot product?

I often need to simplify expressions involving cross product and dot product, for example: f = Dot[Cross[Cross[p1 - p, e1], Cross[p2 - p, e2]], Cross[p3 - p, e3]] ...
4
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609 views

General suggestions to accelerate Simplify and FullSimplify

To my understanding, the function Simplify[] and FullSimplify[] work by applying a series of built-in transformation rules to ...
4
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0answers
275 views

Better way to compute triple (or higher order) convolution

I have an identity that I want to verify: $$\sum_{i+j+k\ge 2}\binom{n}{i,j,k}{B_{N,i}B_{N,j}B_{N,k}}=\left(\frac{2N^2+n^2-3nN}{2N^2}\right)B_{N,n}+\left(\frac{3n^2-2n-4nN}{2N^2}\right)B_{N,n-1}+\...
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77 views

Derive logistic choice probabilities symbolically

More generally, I am interested in learning what the current limitations of Mathematica are when using it for doing pure mathematics. A recent blog post by Stephen Wolfram (see: http://blog....
4
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118 views

Simplifying expressions involving Divisible

FullSimplify[ Divisible[p^2 - 1, 24] , Element[p, Primes] && p > 3] Should evaluate to True, but I get ...
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34 views

How to speed up xTensor simplification?

I need to compute a variation of the 4th rang symmetric tensor. I've written a code that successfully computes it, but when I use the resulting tensor to compute the second variation the ...
3
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0answers
30 views

Kernel crash when simplifying piecewise function

So the kernel appears to just die whenever you try to simplify a piecewise function containing "Nothing". For example: this appears to kill the kernel $$\text{Simplify@}\begin{array}{cc} \Bigl[\...
3
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0answers
36 views

Trouble with simplifying trigonometric / hyper-trigonometric functions

Why (correct) expressions like Assuming[p > 0, 2 ArcTan[Sinh[p]] == Pi - 2 ArcTan[Csch[p]] // FullSimplify] Are not correctly evaluated to: True? What is the ...
3
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0answers
106 views

how to force simplification of power inequalities

These two simple expressions fail to simplify (Mma 11.1): ...
3
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0answers
104 views

Simplifying Redundant Piecewise Cases

I would like to perform a summation from $1$ to $M$ of a simple piecewise function. For example, ...
3
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0answers
367 views

How to simplify exponentials into hyperbolic functions

I have a function of real exponentials and I'd like to simplify it using hyperbolic functions. How can I tell mathematica to use $e^x +e^{-x}=2\cosh(x)$ when simplifying? (and obviusly the $\sinh$ ...
3
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0answers
102 views

PiecewiseExpand fails with min of two piecewise functions

I have two Piecewise functions that are (in this case) just the empirical CDFs of two sets of data: ...
3
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0answers
41 views

Evaluating inequality involving powers

I want to evaluate an inequality of the form $x^a > x$ under the assumptions $x > 1$ and $a > 1$. I expect this inequality to be true, but ...
3
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0answers
112 views

What is are the symbolic simplification rules and when do they apply?

I know that the rules Simplify are obscure but maybe someone has an idea: if I evaluate Simplify[f[g[x]], {Equal[f[g[x]], 3]}],...
3
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0answers
101 views

FunctionExpand does not yield known simplification

Consider: Cosh[a ArcSinh[z]] // FunctionExpand Cosh[a ArcSinh[z]] Which seems to suggest that there is no simplification ...
3
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0answers
80 views

Error when simplifying a series expression

I have the following function which I call FF[q_,y_,u_] and this function is well known to have a reasonable Taylor expansion in all three variables. For example, ...
3
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0answers
179 views

FullSimplify, TransformationFunctions, Assumptions

How can I make Mathematica consider Assumptions in FullSimplify also when applying custom Transformation Functions? It works with the Automatic Transformation Functions: ...
3
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1answer
251 views

Find RSolve solution reflecting special structure of DifferenceRoot[Function[{\[FormalY], \[FormalN]}

RSolve yields a large (multi-page) solution (LeafCount=25891) containing a number of 7F6 (and higher) hypergeometric functions when applied to ...
3
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0answers
240 views

Bringing rational functions to canonical form

I have a complicated expression, which among other things has stuff like functions of rational functions: expr = f[x/(-x^2 + y)] + f[-(x/(x^2 - y))] (* + ...*) ...
3
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0answers
41 views

commutative matching

I've been doing some work that results in the creation of hundreds or thousands of equations with the same answer. To prevent them from collapsing to their simple answers, each has been passed through ...
3
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0answers
158 views

simplify expressions into sum function

Is there a way to have Mathematica simplify long expressions involving sums of variables into expressions using a sum function? Suppose I have something like this: ...
3
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0answers
415 views

How to prevent simplification of hypergeometric functions resulting from integrations?

Definite integrals from 0 to Infinity over a product of two hypergeometric (including exponential, trigonometric, hyperbolic, ...
2
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0answers
50 views

How to remove the Riemann tensor derivatives using Bianchi identity?

For the third-order Lovelock gravity, after varying the Lagrangian versus the metric, I found some derivatives of the Riemann tensor which should not be appeared. How can I remove them? Maybe using ...
2
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0answers
75 views

Expression manipulation

How can one write $\frac{ad+bc}{bd}$ in $\frac{a}{b}+\frac{c}{d}$ form? In other words, is there something opposite of Together[]? Edit My intend was to write <...
2
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0answers
58 views

Computing Definite Sums of Rational Functions

I am attempting to compute a rather complicated sum, $S_n$, that in the end satisfies the relation $(S_n + T_n) = (\frac{(n+1)^2 - 1}{n+1})m^3 + O(m^2)$. I should note that $T_n$ is also unknown. ...
2
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0answers
35 views

How to Simplify/Factorise symbolic non-commutative expressions?

It always strikes me as odd, that Mathematica seems to have a hard time with non-communative multiplications. I can use the horrible TensorExpand (or more performant Distribute) to get ...
2
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0answers
120 views

Substitution of expressions using Groebner basis

I know this topic came up numerous times (most of the results are detailed in the comments of this link Is there a way to to substitute for symbols, simplify, and back-substitute?). However, I have ...
2
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0answers
118 views

Renaming one parameter changes the result of Simplify

Surely the following couple of expressions should both output True: ...
2
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0answers
58 views

Simplifying long expressions leads to memory allocation failure

I am currently trying to manipulate a number of expressions into a particular form that will allow me to determine their poles and zeros: ...
2
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0answers
52 views

How to automatically transform Abs[Cos[x]]Sec[x] to Sign[Cos[x]]?

Out of some simplification, the term Abs[Cos[x]]Sec[x] appears. How can I make the code automatically transform ...
2
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0answers
67 views

Eliminating higher order trigonometric terms

I am interested in eliminating higher-order trigonometric terms from a long symbolic expression. Specifically I want to reproduce this simplification that is done (in a tutorial I am working through)...
2
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0answers
155 views

Speed up Mathematica's Simplify and ComplexExpand functions

I am trying to simplify an expression and taking the real part only. However Mathematica use ages to run the command (if it is able to do so in the end). The problem is that the expression I am ...