# Questions tagged [simplifying-expressions]

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

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### 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 12.1 Is this a bug? If I do FullSimplify[n E^(010 n)] then it returns <...
112 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 ...
364 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 ...
578 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 ...
4k 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 ...
254 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 ...
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 ...
64 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. ...
345 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 ...
117 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 ...
135 views

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### 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....
123 views

### Simplifying expressions involving Divisible

FullSimplify[ Divisible[p^2 - 1, 24] , Element[p, Primes] && p > 3] Should evaluate to True, but I get ...
42 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 ...
54 views

### Exploit bilinearity of KroneckerProduct symbolic calculations and inconsistence (apparently)

Mathematica 10 recognizes the bilinearity of the trace and the Kronecker product, as well as Tr$\otimes$Tr$(A\otimes B)=$Tr($A$)Tr($B$). But I have issues trying to implement this in symbolic ...
54 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 ...
43 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[\...
123 views

### Simplifying Redundant Piecewise Cases

I would like to perform a summation from $1$ to $M$ of a simple piecewise function. For example, ...
531 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 $\sinh$ ...
115 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: ...
43 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 ...
113 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]}],...
109 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 ...
98 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, ...
208 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: ...
270 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 ...
265 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 ...
160 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: ...
443 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, ...
45 views

### Simplifying expressions using elementary properties of integrals

I want to be able to use Simplify (or FullSimplify) to simplify expressions involving, for example, sums of integrals, for ...
27 views

### Computations with OptimizedExpressions without completely expanding them

I have to manipulate huge expressions that are rational functions of many (∼30) variables with integer coefficients. Storing them just as a ratio of two polynomials would be impractical. But they can ...
77 views

α = Quantity[-3, ("Radians")/("Seconds")^2]; ω = Quantity[-4, ("Radians")/("Seconds")]; r = Quantity[2, "Feet"]; at = α r an = ω^2 r a = Sqrt[an^2 + at^2] ...
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### Why FullSimplify doesn't work when subscript included?

This is OK. FullSimplify[l[t] + r[t], {m[t] == l[t] + r[t]}] But when I add a subscript to l, FullSimplify can not return the correct result. Is this a bug? I will be grateful if anyone can give me ...
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. ...