# Questions tagged [symbolic]

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

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### 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 ...
6k views

### 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. ...
37k 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,...
6k views

### 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: ...
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 ...
5k views

### Using D to find a symbolic derivative

I need to do the following: Define a function Take the derivative of this function and have a look at the symoblic representation Substitute in some values With the bonus that I want to use the ...
6k views

### 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, ...
9k views

### 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 ...
1k views

### Implement finite Fourier transforms

Recently I came across finite Fourier transforms, which can be used for solving certain type of boundary value problem (BVP) of linear partial differential equation (PDE) with constant coefficient. ...
4k views

### Prevent Part[] from trying to extract parts of symbolic expressions

If you have a list, e.g. {1, 2, 3} then you can extract the $k$th part using Part (...
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., ...
451 views

### Is there an analogue of the Variables command for general expressions? [duplicate]

The command Variables[poly] gives me a list of all variables that appear in the expression poly, which involved sums, ...
5k views

### 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 ...
2k views

### Why Can't DSolve Find a Solution for this ODE?

I wanted to find a basis for the set of solutions of the following ODE. $$y^{''}+\frac{1}{x^2+1}y^{'}(x)+\left[-1-\frac{1}{x^2+1}\right]y(x)=0$$ But when I try to use ...
7k views

### DSolve not finding solution I expected

Try to solve the following ODE via DSolve \left\{\begin{aligned} y'(x)+2 y(x) e^x-y(x)^2 &= e^{2 x}+e^x \\ y'(0) &=1 \end{aligned}\right. The ...
5k views

### 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, ...
653 views

### How do I invoke the default complexity function?

Documentation on ComplexityFunction says: With the default setting ComplexityFunction->Automatic, forms are ranked ...
261 views

### When to use GenerateConditions -> True

Many functions, usuallly those involving integration, take a GenerateConditions option which often defaults to False, or at ...
2k views