# Tagged Questions

How to manipulate expressions structurally, not necessarily complying with the rules of algebra.

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### Replacement inside held expression

I wish to make a replacement inside a held expression: f[x_Real] := x^2; Hold[{2., 3.}] /. n_Real :> f[n] The desired output is ...
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I have been working on picking expressions apart using Head and Part and encountered a little mystery. Consider the canonical ...
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### Scan vs. Map vs. Apply

I cannot understand the difference between Apply, Scan, and Map. I have tried to play with ...
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### How do I get my equation to have the form $(x-a)^2 + (y-b)^2 + (z-c)^2-d = 0$?

I want Mathematica to express the equation $$-11 - 2 x + x^2 - 4 y + y^2 - 6 z + z^2=0$$ in the form $$(x - 1)^2 + (y - 2)^2 + (z - 3)^2 - 25=0$$ How do I tell Mathematica to do that?
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### Is it possible to change the color of plot in Show?

For example: p = Plot[Sin[x], {x, 0, 1}] Is it possible to write options in Show to change the curve's color for example into ...
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### List of atomic expressions

I was surprised to see Graph objects are atomic. Is there a way (through documentation or programmatically) to find all atomic heads? The ones I know of are: <...
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### Given an exact formula, how can Mathematica find a probability distribution whose PDF matches it?

So, given some data, Mathematica 10.2 can now attempt to figure out what probability distribution might have produced it. Cool! But suppose that, instead of having data, we have something that is in ...
443 views

### How can I see which transformations Simplify attempts?

The documentation for Simplify[expr] says that it performs a sequence of algebraic and other transformations on expr, and returns the simplest form it finds. How can I see which transformations it ...
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### How can I completely ban usage of some functions in output and mandate use of others?

For example, I hate that Mathematica uses Pochhammer symbol in outputs and prefer all the expressions in Gamma function. How can ...
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### List manipulation to build a functional expression

Since Mathematica deals with Head[a, b] as an expression in this way The first Part of Head[a, b] is ...
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### Why is ReplaceAll behaving like this?

I'm learning to use the ReplaceAll function and I found the behavior of which is quite confusing. For Sqrt[f[x, y]] /. f[___] -> u Mathematica returns <...
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### SeriesData sucks when it can. How do I keep SeriesData from sucking?

When I run Series[f[x]*Sin[x],{x,0,3}, Analytic->False] I get: f[x](x-x^3/3+O[x]^4) as expected. In ...
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### Comparing Mathematica expressions like diff

I am looking for a way to compare (or "diff") two Mathematica expressions, similarly to how to diff utility can compare two text files and report the differences. Has anyone already written such a ...
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### How to do algebra on summations of variable expressions?

Is there any easy, general way to handle algebra on variable Sums? For examples, Gaussian Mixtures or Fourier Series: ...
531 views

### Transform an expression into a graph that can be plotted with TreeGraph (not TreeForm)

I would like to plot an expression (like TreeForm does), but using the new TreeGraph functionality. ...
3k views

### How can I transfer mathematical expressions between Mathematica and Maple?

Is there a simple way to copy mathematical expressions between Mathematica and Maple (or at least in one direction)? I mean only expressions built from numbers and predefined mathematical functions, ...
308 views

### Construct an infix operation from a list

Inspired by this question, if I have a list {a, p, b, q, c} where p and q are binary ...
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### ToExpression processing errors

Is their a way to get a more comprehensive return value when running ToExpression? For example when I run ...
580 views

### How to embed an image into a string?

Note: The bug described in the post is in Mathematica 9, and has been fixed in 10.0. The documentation for String contains the following statements: Strings ...
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### How to completely delete the head of a function expression

Is there any way to completely remove the head of an expression function? For example, how would I remove the head Cos from ...
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### Displaying a series obtained by evaluating a Taylor series

Description of problem I would like to use Mathematica to display the series obtained by substituting a value for $x$ in a Taylor series expansion. The terms of the series will be rational numbers, ...
752 views

### Google Code Jam: Mountain View code review

After participating in Google Code Jam 2012 Round 2, it occurred to me that the Mountain View problem boiled down to solving a set of linear inequalities, which could be done in Mathematica. I've only ...
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### Is there a way to control which special forms Normal converts?

Normal documentation reads: Normal[expr] converts expr to a normal expression, from a variety of special forms. But is there a way to control which special ...
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### How to convert a notebook cell to a string retaining all formatting, colorization of identifiers etc?

I have an opened Mathematica notebook containing several cells. Suppose, I am interested in one of them -- it may contain a complete or incomplete expression (e.g. with syntax errors, highlighted ...
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### What are the default TransformationFunctions used in Simplify and FullSimplify?

If I do Simplify[(c^3 - s^3)^2 - (s^3 + c^3)^2, TransformationFunctions -> Automatic] (i.e. a verbose version of default behaviour), what transformation ...
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### The most external subexpression with given pattern

Suppose there is a deep expression with several instances of some _f. I want to get the most external case of _f from it (I also ...
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### Reading Cells or Boxes expression by expression

Let's say we have a cell: (*newline*) (*newline*) Plot[ x, {x, 0, 1} ] (*newline*) Plot[x, {x, 0, 2}] How to read it expression by expression? ...
153 views

### Thread over uneven (ragged) expressions with full functionality?

There are a number of questions on this site about "threading" including several relating to uneven (ragged) lists. However, none that I could find deal with the full functionality of ...
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### How to automatically get rid of trig functions in an expression?

I have a large expression containing many terms like this: Sin[1/2 ArcTan[(2 Log[5])/(Log[5]^2 - 2)]] where a trig function is invoked on a rational multiple ...