Questions tagged [symbolic]

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

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Advice for Mathematica as Mathematician's Aid

I use Mathematica mainly as an aid in symbolic attacks on problems, usually intermediate or harder and often number theoretic. While Reduce, ...
18k views

Can Mathematica do symbolic linear algebra?

For instance, is there some way I can say "let A and B be arbitrary real $m\times n$ and $k\times m$ matrices, Simplify[Transpose[Transpose[A].Transpose[B]]]" and ...
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Analogue for Maple's dchange - change of variables in differential expressions

Maple owns an interesting function called dchange which can change the variables of differential equations, but there seems to be no such function in Mathematica. ...
17k views

How do I work with Root objects?

I want to solve the trigonometric equation : $$(3-\cos 4x )\cdot (\sin x - \cos x ) = 2.$$ I tried Solve[(3 - Cos[4*x])*(Sin[x] - Cos[x]) == 2, x] It returns the ...
35k views

How to calculate scalar curvature, Ricci tensor and Christoffel symbols in Mathematica?

I am seeking a convenient and effective way to calculate such geometric quantities. I've used packages like TensoriaCalc, but they don't work at all time. Sometimes,...
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Symbolic solution(s) to generalized Heat equation

Symbolic solution(s) to Heat equation? or more generally,(eventually) Green functions to known PDEs I am interested in variations of the heat equation: or more generally or even more generally (<...
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Why does Mathematica report that $\int_1^\infty\frac{\sin(\sqrt{x})}{\sqrt{x}}dx$ = $2\cos(1)$?

Bug introduced in 7.0 or earlier and fixed in 11.0 Mathematica 10 gives the following very odd result, Integrate[Sin[Sqrt[x]]/Sqrt[x], {x, 1, ∞}] (* 2 Cos *) ...
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How can I define a new symbolic constant like Pi?

There are a few builtin symbolic constants which behave like numbers, e.g. E, Pi, EulerGamma,...
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Some indefinite integrals evaluate in 11.2 but not in 11.3 - what can be done?

Bug introduced in 11.3 and fixed in 12.0.0 Reported to Wolfram: [CASE:4032137] These integrals evaluate in version 11.2 on windows but when I tried them under version 11.3 they returned unevaluated.,...
960 views

How to augment the realm of functions Mathematica thinks it knows how to integrate symbolically

My question involves extending the functionality of Integrate over specific integrals in the most generic manner. Specifically, is it possible to "hack into" ...
884 views

$\sum_{k=1}^{\infty }\left\lfloor\frac{5}{5^k}\right\rfloor$ giving wrong answer?

Bug introduced in 7.0 or earlier and fixed in 11.0.1 When I try to evaluate the following: $$\sum_{k=1}^{\infty }\Bigg\lfloor\frac{5}{5^k}\Bigg\rfloor$$ using ...
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Extract real part of a complex expression better than Re does

I have a complex expression with real positive variables only. Mathematica Input Style: ...
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What is a type in Wolfram Mathematica programming language?

"Everything is an expression" is a popular citation from many Mathematica guidebooks. So, what is type in Mathematica? How does it relate to common types from Haskell, for example? I did some ...
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Proving the hairy ball theorem using xAct

I would like to formally prove the hairy ball theorem in Mathematica, initially just for $S^2$, and then see about generalizing. An approach I thought about to use the xAct package to define $S^2$ ...
17k views

Replacing composite variables by a single variable

To replace a single variable by another variable, one can simply use the the replace all (/.) operator (e.g., ...
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How to symbolically do matrix "Block Inversion"?

Consider a block (partitioned) matrix matrix = ArrayFlatten[{{a, b}, {c, d}}] where, a, b,...
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How to deal with complicated Gaussian integrals in Mathematica?

As we know, for most Gaussian integrals, we can get the analytical result. Now I have many Gaussian integrals to treat, which have the following general form, ...
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Symbolic integration error

fixed in 10.1 (windows) I'm running Mathematica 10.0.0 and encountered a disturbing error in the symbolic integration of a rather simple function ...
912 views

Transform Root objects into Trigonometric expressions

Consider the Root objects roots = Table[Root[-1 + 27 #1^2 - 162 #1^4 + 243 #1^6 &, i],{i,1,6}] These can be expressed in terms trigonometric functions as ...
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Extracting variables from an expression

I'm looking for a way to extract a list of variables from an expression, for example with an input like: ...
546 views

Backslide of Limit

Backslide introduced in 9.0, and persisting through 12.0. A friend of mine showed me this example: Limit[Sum[Sin[Pi*k/n]/(n + 1/k), {k, 1, n}], n -> Infinity] ...
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Why this real integral yields imaginary results?

This integral yields -1-4Iπ/3 in Mathematica: Integrate[(y - y^2 + x - x^2 + 2*x*y)/(1 - x - y), {x,0,1}, {y, 0, 1}] Since ...
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How to calculate the volume of a convex hull?

Given a spatial curve represented by a parametric equation, is it possible in Mathematica 9 to calculate symbolically (or at least numerically) the volume of its convex hull?
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Derivative of a pure function with SlotSequence

I can live with this but I can't figure out why the following is 0: Derivative[f[##] &][x] 0 From documentation for ...
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Calculating probabilities symbolically

Is there a way to solve for statistical quantities analytically/symbolically in Mathematica? example 1: Lets say that I want to do a calculation that requires Bayes theorem. I know p(a), p(b) and p(...
3k views

Wrong answer from DSolve when solving a differential equation

Bug introduced in 12.0.0, fixed in 12.1.1. I was trying to solve the following differential equation: $$\frac{dy}{dx}=x^2+y^2-1 \quad \text{and} \quad y(0)=1$$ and I used the code below: ...
500 views

Negative probability?

Bug introduced in 9.0.1 and fixed in 10.0.2 I am trying to get the sum of the squares of seven random variables, all uniformly distributed. This is what I tried. ...
561 views

What does f_[whoCalled]^:=f really mean?

I came across the following post by John Doty in this Google Groups discussion: On Friday, January 11, 2013 8:23:16 PM UTC-7, amzoti wrote: It is clear the Mathematica uses Lisp as one ...
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Incorrect results for elementary integrals when using Integrate

There is a rather simple integral ($K_0$ is the 0-th order MacDonald function) $$\int_0^\infty e^{-x \cosh\xi}\, d\xi = K_0(x)$$ which mathematica cannot solve. This even though the documentation ...
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How does Mathematica integrate?

Basically, this question can be considered to be an extenstion to my other question. What I wanted to do was this integral as homework (it is indefinite BTW so no approximations using Simpson's Rule ...
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Incorrect result from Integrate

Bug introduced in 8.0 and fixed in 10.0 I attempted to calculate the following integral: ...
588 views

What does "suitable for symbolic manipulation" in the documentation mean?

This question is related to this other one I posted on Stack Overflow some time ago. There, in a beautiful answer, acl (with some unhumble editing done by me) showed that the derivative of ...
374 views

Mathematica v12 Integration bug?

Bug introduced in 12.0 and fixed in 12.1 After upgrading to mathematica 12, this integral gives the wrong result, also with other types of similar integrals. ...
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How can I evaluate only a single step of a recursive function?

Let's say have a simple recursive function for the Fibonacci sequence f := 1 f := 1 f[n_] := f[n - 1] + f[n - 2] but I want to see how it will expand in a ...
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Is learning to use Mathematica useful for pure theoretical research in Mathematics and Computer Science?

I am looking for opinions from Mathematica users about Mathematica itself. After reading the faq, I thought that in some sense I "wish to solve a problem using Mathematica" ... although I understand ...
6k views

Non-commutative algebra

I'm constantly dealing with non-commutative algebras. ** is inbuilt, non-commutative and associative. That's good :-) But it is not distributive. Rats. ...
400 views

This is probably a very simple question, but I couldn't find a duplicate. As everybody knows, {x, y} + v gives {x + v, y + v}. ...
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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: ...
425 views

Coordinate-free derivative

Given the function \begin{align*} f \colon \mathbb{R}^n &\to \mathbb{R}^n\\ v&\mapsto \dfrac{v}{\|v\|}, \end{align*} I would like to compute the derivative of $f$, that is $df(v)$. It is ...
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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 ...
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Symbolic area calculation for a parametric self-intersecting closed curve

The parametric equation of the curve is: $$\begin{cases} x &= -9 \sin (2 t)-5 \sin (3 t) \\[6pt] y & = 9 \cos (2 t)-5 \cos (3 t) \end{cases}\quad t\in[0,2\pi]$$ which can be easily ...
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Complex number operations: telling Mathematica variables are real

I want to do Conjugate[a + b*I], but when I do that, the solution is Conjugate[a] - I*Conjugate[b]; when for me, a and b are ...
2k views

Why do certain values in ArcSin not fully evaluate?

This is a continuation of: Why do certain fractional values in TriangleWave not evaluate? The analysis by R.M and rasher revealed that problem to reduce to the behavior of: ...
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Does anyone have experience with performing symbolic regression using Mathematica?

I understand that there is at least one Mathematica package, DataModeler commercially available for symbolic regression. I'm seeking any observations with this or any other similar tool. I'm ...
748 views

Mathematica incorrectly giving zero for partial derivative

Bug introduced in 9.0 and fixed in 11.1 Mathematica is incorrectly reporting that the partial derivative of a certain expression is zero. I try to compute the following: ...
855 views

Missing solution - system of equations

Attention! This example already works as expected in Wolfram Mathematica 12.1.1.0 for function Solve. The problem was in version 12.1.0.0. Check out answer of Bob ...