Questions tagged [simplifying-expressions]

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

353 questions with no upvoted or accepted answers
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15
votes
0answers
154 views

Reduce[Sin[x]==0,x] splitting odd and even multiples of Pi

as from Title, I'm wondering why Mathematica does not automatically give a single, simple solution for the problem Reduce[Sin[x] == 0, x] for which I obtain the ...
12
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0answers
366 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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0answers
5k 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 ...
10
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0answers
594 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 ...
8
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0answers
379 views

What is a "generic case"?

Introduction With this question, I am coming back to a long-standing issue I have with Mathematica's concept of a "generically correct" result. The basic idea seems to be, vaguely, that if a ...
7
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0answers
106 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 ...
7
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0answers
65 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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0answers
369 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
96 views

Simplification depends on the names of variables

I am sure this issue has been discussed here, but it has never been asked whether this behavior is a bug. Therefore my direct question to the community: do you think this behavior is a bug? ...
5
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0answers
131 views

Simplify, ComplexityFunction, and expression rearrangement

Context: Mathematica is being used to simplify expressions. These expressions are then exported to be used in a C-family language. Naturally enough, desiderata include execution speed, and avoidance ...
5
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0answers
89 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
1k 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]] ...
5
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0answers
101 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
235 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
35 views

How does Simplify deal with contradictions in the assumptions?

Context Sometimes Simplify does generate a warning when the assumptions are self-contradictory. Take this example: ...
4
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0answers
63 views

Force Solve to respect unit system

I give Solve quantities in FPS and it returns resulting quantities in SI, necessitating that I add an entire section to my workflow where I pick apart the solution ...
4
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0answers
48 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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0answers
129 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
56 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
129 views

how to force simplification of power inequalities

These two simple expressions fail to simplify (Mma 11.1): ...
4
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0answers
443 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 ...
4
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0answers
110 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
136 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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0answers
934 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
361 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}+\...
4
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0answers
85 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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0answers
127 views

Simplifying expressions involving Divisible

FullSimplify[ Divisible[p^2 - 1, 24] , Element[p, Primes] && p > 3] Should evaluate to True, but I get ...
4
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2answers
116 views

Spherical harmonics and Laplace operator

The spherical harmonic function $Y_l^m(\theta,\phi)$ is defined to be an eigenfunction of the angular part of the Laplace operator with eigenvalue $-l(l+1)$. In other words, it solves the PDE: $$\...
4
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1answer
45 views

Is it better to use a single binary operator in each Assumption entry?

I am trying to understand why FullSimplify[x^a < 1, {0 < x^a < 1}] does not simplify but ...
3
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0answers
87 views

FullSimplify gives erroneous answer

FullSimplify gives a wrong expression when simplifying Hypergeometric functions: f = Hypergeometric2F1[1/2 - n, -n, 1 - 2 n, -4 a]; g = FullSimplify[f]; The ...
3
votes
0answers
81 views

Mathematica cannot simplify a rather simple expression with only one term

I run this code on Mathematica 11.2, Simplify[1/x^2,Assumptions->(1/x^2==1)] and hope to get 1, but Mathematica returns me ...
3
votes
1answer
177 views

Does Assumptions not work on Root objects?

Typically, one can restrict symbolic quantities using Assumptions. Suppose, for instance, that I want to solve $a=x^2$ for $x$, with $a>0$, restricting my answer to the positive root. ...
3
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0answers
70 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
votes
0answers
59 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
146 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
809 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
132 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
46 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
votes
0answers
116 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
115 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
131 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
votes
0answers
228 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
votes
1answer
317 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
votes
0answers
304 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
votes
0answers
44 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
votes
0answers
170 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
476 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
41 views

Superfluous un-simplifiable condition returned by Reduce

No real "problem" here, just wondering why this is happening and how one might force Mathematica to simplify this. Consider: ...
2
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0answers
72 views

Analytical Cross-Correlation between two time lagged Sinc functions gives complicated result

I'm trying to calculate the analytical Cross-Correlation between two time-lagged Sinc functions, i.e., \begin{align} R(\tau) = \int_{-\infty}^{\infty} \overline{\textrm{sinc}\left(\pi f \left(t - d_1\...
2
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0answers
37 views

Why doesn't this KroneckerDelta simplify?

When I take D[Sum[a[x[0], x[j]], {j, 1, nsp}], x[0]] I get I would expect that the KroneckerDelta[0, j] would automatically ...

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