# Tagged Questions

For questions about symbolic computation, as opposed to numerical computations.

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### Algebraic expressions on pure functions

I would like to know how to perform algebraic operations with pure functions. Simple version: Here's a silly toy model: I want to transform the algebraic expression Sin*Cos into the function ...
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### Symbolic Integration of Special Functions

Sorry in advance if this formatting comes out strange, this is my first question! I can't find a way to integrate, e.g., a function of the Hermite polynomials for general (still integer) order. For ...
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### Covariant derivative for symbolic tensors

I want to define a "prefix" (D_i) covariant derivative operator CD[] for symbolic tensors in form of a function, i.e. for ...
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### Creating Boolean expressions over a set of indexed variables

I've read lots of examples here on how to set one matrix Equal to another, but how do you nest And and ...
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### Symbolic integration conditional bug?

I just ran across this: Assuming[x > 0, Integrate[1/t^2, {t, 1, x}]] gives the output ...
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### Pulling powers to the outside of expressions (inverting PowerExpand)

Is there something like an inverse of PowerExpand that pulls powers to the outside of expressions: $$x^2 y^2 \leadsto (x y)^2 \\ x^2/y^2 \leadsto (x/y)^2$$ I ...
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### What's the differences between the shift-enter and MakeBoxes running?

I know the example usages of MakeBoxes in the Tutorial like this. but I want to know a subtle distinction between (1) and (3) ...
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Let $p_n\#\equiv\prod_{k=1}^{n}p_k$ (primorial): p[n_] := Times @@ Prime[Range[n]] then the multiplicative partitions of $p_{1,2,3,4}\#$ are $$\{\{2\}\},$$$$\{... 2answers 412 views ### Tweaking Solve for systems of polynomial equations I am trying to solve the following system of 6 quadratic equations in 6 variables: ... 1answer 59 views ### How to assume all variables in my code are reals I won't have any occasion to have any imaginary number in my code. If there are any, that is an error. So allowing the imaginary case simply hinders the equation manipulation and simplification. I ... 1answer 206 views ### Strange behavior of Reduce with a cubic equation This equation: (\frac{-a}{x})^2=\sqrt{\frac{1}{x}} at a > 0 and x > 0 has a clear solution x=a^{4/3}, doesn't it? However, ... 2answers 280 views ### Mixed product identity between tensors in Mathematica 9 How can we simplify tensor expressions in Mathematica 9 using the mixed-product identity (A\otimes B)(C \otimes D) \equiv AC \otimes BD ? Is it possible to implement this kind of evaluations using ... 1answer 415 views ### How can I get Mathematica to recognize equality of symbolic matrix expressions? I have two matrix expressions: X.Transpose[T].Transpose[X] and X.T.Transpose[X] I want Mathematica to recognize that ... 1answer 124 views ### The basic primitive recursive functions How can the basic primitive recursive functions be expressed in the Wolfram Language? Apparently here's an example for primitive recursion: ... 2answers 55 views ### How to avoid 0 OverVector[F] to be evaluated as 0? I am fairly new in Mathematica and I am trying to work with scalars and vectors. I decided to denote vectors using OverVector (as example, ... 3answers 131 views ### How to Integrate trivial products of DiracDelta A long while ago I was able to integrate with Mathematica:$$\int_0^1 \delta(1-x)\delta(x) f(x) \,dx = 0$$using ... 1answer 129 views ### How to get a more compact form of this probability calculation? Inspired by the probability calculation here, I am trying to solve a little general one:$$\mathbb{P} (\sum_{i=1}^{m-1} A_i + \sum_{i=1}^{m} S_i < L < \sum_{i=1}^{m} A_i + \sum_{i=1}^{m+1} S_i)$... 2answers 170 views ### Expectation of a composite Markov-Gamma distribution In a model I have a discrete two-state first order Markov process, defined by a (2x2) transition matrix with two free parameters. If the first state occurs then the process outputs zero for that ... 1answer 421 views ### Problem with limit that requires L'Hôpital's rule to compute Consider the following limit. Limit[(a - Sqrt[a^2 + x])/(a^2 - a*Sqrt[a^2 - x]), x -> 0, Assumptions -> {a > 0}] Mathematica 9.0.1.0 gives ... 1answer 108 views ### Check that a relational expression is true for all complex numbers How can I use Mathematica to check if a statement like $$\left| \frac{\sqrt{1+2z}-2}{2z-3} \right| \le 1$$ is true for all complex numbers$z$? Also, how can I use Mathematica to check such a ... 1answer 351 views ### n-fold symbolic integral in Mathematica I am trying to compute symbolically a n-fold integral (n is a parameter of a function) over, say, the cube [0,a]^n. My code looks like this ... 2answers 86 views ### Problem with Custom Sort/Split/Gather Please help me Sort/Split/Gather/Group(by) a set of symbolic expressions! (extreme TL;DR at bottom) I have a set of symbols (which represent 2-vectors in a plane, ultimately) and I want to sort/... 1answer 84 views ### Need help understanding the output of DSolve I give Mathematica 10 the following command: DSolve[I D[P[x], {x, 2}] f[x] - (P'[x])^2 f[x] + 2 I P'[x] f'[x] == 0, P, x] and I have the following output: ... 1answer 55 views ### How to get Mathematica to make further simplifications to conditional expressions than it has already made? I have the following Mathematica result under the assumption that {ax, bx, px, ay, by, py} \[Element] Reals, and after refinement by ... 1answer 143 views ### Can Mathematica solve this type of recurrence? I have the following recursively defined equation: ... 2answers 145 views ### Eigenvectors of large symbolic matrix I have large symbolic matrix of order 32 x 32 given as ... 1answer 122 views ### Strange integration Bug introduced in 9.0 or earlier and fixed in 10.1 Note: Beginning with V10.1, this integral returns unevaluated but without error messages. I tried to evaluate this line ... 1answer 662 views ### Nested Sums to multiple sum I would like to automatically "move nested sums to the left". I mean, just take out of an expression all the summations and go from a nested Sum to a multiple sum. Something like starting with: ... 1answer 534 views ### Mathematica 9 and later behavior with derivative of a sum Bug introduced in 9.0 or earlier and persisting through 10.3.0 or later ... 1answer 104 views ### Symbolic Output after numerical computation I have a small question about the symbolic output. I started to write a program that generates the coordinates of n-dimensional polytopes by Wythoff construction. For crystallographic groups, all is ... 1answer 306 views ### Sum of positive terms gives negative answer Bug introduced in 7.0 and fixed in 9.0 Mathematica evaluates Sum[((n - y - 1)*(n - y)^2*n^y)/y!, {y, 0, n - 2}] as -2 e^n n. ... 1answer 134 views ### Fundamental question about capabilities of Mathematica to represent abstract mathematics [closed] I have an fundamental question about what Mathematica can and cannot do. I have a book which presents a certain physical theory in an axiomatic manner. The axioms make heavy use of mathematics. Some ... 0answers 75 views ### What is the good source to study advanced custom coding in Mathematica [duplicate] My question is, probably, too general ... I deal a lot with complicated symbolic evaluations, integrations, plotting. I have troubles with optimizing my codes. They come out way too slow. Google and ... 1answer 90 views ### Factor a polynomial Root into Roots of smallest possible degree Suppose I have a polynomial Root representing an algebraic number. I want to represent it (if possible) as a product of several polynomial ... 0answers 65 views ### Simplifying between set theory and logical connectives I'm trying to find out how to switch between set notation and logic, but am having difficulty. For instance, I know that the following two expressions are equivalent ... 0answers 139 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]] ... 0answers 85 views ### Analytical Fourier Transforms with convolution rule [closed] The task is the following, how to extend Mathematica's FourierTransform command in order to be able to analytically deal with non-linear differential equations. To do so it should be able to deal with ... 0answers 88 views ### Symbolically Minimizing a Max function I'm having a tough time with seemingly simple symbolic Minimization/Maximization in Mathematica. I would like to use the Maximize function to work on some unknown random variables and so use min/max ... 0answers 63 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.... 0answers 579 views ### Symbolic matrix calculus: What's new in Version 9 I have seen some of the related posts, which ask about doing matrix calculation on tensors unknown dimensions. One of the posts mentioned that version 9 has some capability, but it was concerned about ... 0answers 156 views ### Fourier transformation of HeavisideTheta functions I want to find 2D-Fourier transformation of the function given below f = HeavisideTheta[y1]*HeavisideTheta[y2 - y1] For the purpose, I use built-in function in ... 0answers 113 views ### What is so special about variable s$?

I found a nice bug in Mathematica 9.0.1.0. Could anyone check to reproduce it? Create a file temp.txt with one line: ...
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### Numerical-Symbolical Integration (Calculus)

I created a simple numeric-symbolic integration. Here you can use symbolical and numerical techniques at the same time. You can also interpolate numerical integrals. The problem with my function is ...
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### Rewriting one expression using a variable representing another expression [duplicate]

I have two expressions: w1 = (a+b)/c^2; w2 = (a^3 + 3 a^2 b + 3 a b^2 + b^3)/c^6; How can I ask Mathematica to try to find an alternative expression for ...
Can Mathematica suggest what a formula means? For example if I input $$\sum_{i=0}^n i$$ can it infer that this is a sum of integer values from $0$ to $n$? Or if I enter $0,1,1,2,3,5,8,13$, can ...