For questions about symbolic computation, as opposed to numerical computations.
10
votes
6answers
908 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., ...
4
votes
2answers
625 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 ...
11
votes
1answer
665 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 ...
16
votes
3answers
1k views
How to symbolically do matrix “Block Inversion”?
Consider a block (partitioned) matrix
matrix = ArrayFlatten[{{a, b}, {c, d}}]
where, a, ...
3
votes
1answer
330 views
Symbolic integration in the complex plane
Context
While answering this question, I defined (symbolic and numerical) path integrations as follows
...
20
votes
3answers
1k 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 ...
8
votes
2answers
660 views
18
votes
3answers
821 views
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 ...
9
votes
2answers
202 views
Find closed form expression for series expansion coefficients [duplicate]
Is there a built-in function that will find a general expression for the coefficient of the series expansion of a function?
Series will only give the explicit ...
10
votes
2answers
555 views
Non-commutative symbolic linear algebra
I am fairly new to Mathematica but I thought I would be a helpful tool to carry out a few simple linear algebra calculations. It seems like an easy task but I cannot figure out how to do it. For ...
7
votes
1answer
2k views
Extract real part of a complex expression better than Re does
I have a complex expression with real positive variables only.
Mathematica Input Style:
...
6
votes
3answers
464 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 ...
5
votes
4answers
525 views
How to get exact roots of this polynomial?
The equation $$ 64x^7 -112x^5 -8x^4 +56x^3 +8x^2 -7x - 1 = 0 $$
has seven solutions $x = 1$, $x = -\dfrac{1}{2}$ and $x = \cos \dfrac{2n\pi}{11}$, where $n$ runs from $1$ to $5$. With ...
5
votes
1answer
488 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 ...
11
votes
2answers
371 views
Surprises simplifying simple polynomials
I came across some somewhat surprising behavior of Simplify today, on something very simple. Let's take two cubic polynomials that we know have the same value:
...
13
votes
5answers
626 views
Does $x>0$ imply that $x\in\mathbb{R}$?
Let’s assume I input
Assuming[x > 0, expression]
Is it assumed by Mathematica that $x$ is a real number? Or that the real part of $x$ is positive? Something ...
7
votes
2answers
383 views
Why aren't these additions of integrals and summations equal?
I have the following code:
Simplify[Integrate[f[x] + g[x], x] == Integrate[f[x], x] + Integrate[g[x], x]]
To test:
$$\int{\left(f(x) + ...
4
votes
1answer
365 views
Does the Im function work with symbolic arguments?
Does the Im function work with symbolic arguments?
...
22
votes
1answer
406 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" ...
11
votes
1answer
168 views
Symbolic computations with already assigned variables
For example I have assigned some variables that could defined in terms of each other. Then I for some reason need to derive some formula using this variables. How to show the result of this ...
16
votes
1answer
275 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 ...
10
votes
1answer
168 views
Why does Assuming[x > 0, TrueQ[x > 0]] return False?
Assuming[x>0,TrueQ[x>0]]
should, as I understand it, test TrueQ[x>0] after assuming ...
7
votes
1answer
235 views
Symbolic Integration along contour: branch cut problem?
Context
Following this question on path integrals in the complex plane, having defined again a numerical and symbolic integrator along a path as
...
7
votes
1answer
270 views
4
votes
4answers
129 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:
...
4
votes
4answers
547 views
Mathematica gives wrong answer for integral
When I execute the following,
Integrate[Exp[-w^2 + I w^3], {w, -\[Infinity], \[Infinity]}]
I get
...
3
votes
1answer
140 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.
...
1
vote
2answers
178 views
Symbolically associate vectors and their norms
I am wondering how to handle the following situation: I do have vectors of known dimension that I would like to handle symbolically. I suppose I can do something like
...
0
votes
1answer
143 views
0
votes
1answer
115 views
Industrial Level Applications. Recipe for mixed notation of equations set
I am working with large (linear) equations set within Mathematica in numerical notation. For example, set from 4056 eq. is solved for a second, no more. There is no doubt, result is great. But even ...
-1
votes
3answers
198 views
Sqrt — how to get negative branch?
One of the many attractions of Mathematica is that integers are generally treated as exact symbolic entities, and not just as numbers. I was just playing with Sqrt, and was puzzled by what appeared to ...
