# Questions tagged [simplifying-expressions]

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

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### 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 ...
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 ...
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 ...
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 ...
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 ...
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 ...
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. ...
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 ...
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? ...
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 ...
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: ...
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]] ...
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. ...
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 ...
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: ...
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 ...
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 ...
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. ...
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 ...
129 views

### how to force simplification of power inequalities

These two simple expressions fail to simplify (Mma 11.1): ...
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 ...
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 ...
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 ...
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 ...
361 views

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### 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 ...
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 ...
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 ...
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. ...
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 ...
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[\...
146 views

### Simplifying Redundant Piecewise Cases

I would like to perform a summation from $1$ to $M$ of a simple piecewise function. For example, ...
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 $\sinh$ ...
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: ...
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 ...
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]}],...
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 ...
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, ...
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: ...
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 ...
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))] (* + ...*) ...
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 ...
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: ...
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, ...
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: ...